Thoughts on Rationality
The aim of this essay is to explain the principles of rational thinking. Like all philosophical essays, this text will not provide a solution for people's problems on Earth. But it will make a proposal of how to approach truth. And truth is at least an important subgoal for many of man's goals, such as justice, wisdom, and progress.

By reading this essay, you acknowledge that I, the author of this essay, do not accept any responsibility for the completeness or correctness of this essay. Loyal to its own principles, this essay is under continuous improvement. If you have comments or suggestions, please send me a mail to fabian@thisDomain .


This essay consists of three parts, each with several chapters, and each with several sections:

Have a look at the highlights of this essay (Highlights).


Particular highlights of this essay are:

If you don't know where to start, start with the definition of rationality (Def), and read the essay top down.



This part covers the definition of rationality (SecDef) and common objections to rationality (SecObj).


This section covers questions concerning the definition and the use of rationality. Metaphorically speaking, rationality tries to build up arguments from statements — much like we build up a tower from bricks.

What is rationality?

Rationality in the sense of this essay is a framework for reasoning. This framework comprises
  1. The concept of clear and matter-of-fact statements
  2. Reasoning techniques on these statements
  3. The concept of goals, and techniques to achieve these goals

Each of these points is addressed by one part of the present essay (PartRat, PartReas, PartGoals).

Seeking the Truth

Rationality can help us pursue certain goals (PartGoals). This essay assumes that one of the central goals is finding the truth. The truth can help us understand the world, help us predict things that will happen, and serve to achieve other goals. This is why the truth takes a central role in this essay (WhatIsTruth). Even if we can probably never know the truth in perfection, every bit we know brings us closer to this goal.

This priority for truth is by no means universal. As Niccolò Machiavelli argued, it can sometimes be rational to be not truthful (Machiavelli).

The effort to understand the universe is one of the very few things which lifts human life a little above the level of farce and gives it some of the grace of tragedy.
Steven Weinberg

What is the Truth?

No-one knows what is the truth. There may even be multiple truths, or no truth at all. This essay dedicates a section to these arguments (SecObj). This essay takes the following stance on truth: We perceive ourselves in a stream of sensory impressions: colors we see, feelings we have, sounds we hear. Our aim is to explain and predict these impressions. We want to know why we had a certain impression, and we want to know what future impressions we will have. For this purpose, we hypothesize what could be the reasons for our past sensations, and what will be likelihoods of future sensations. In other words, we build theories on our stream of sensations. These theories are approximations of truth: The more sensations we gather, the better we are able to understand past sensations, and the better we are able to predict future sensations. Thus, by our very nature, all we do is approximating truth by theories.

This entails, crucially, that we always have to be ready to give up our theories if counter-evidence appears. This is the central insight of rationality: If we want to approach truth, we have to give up convictions that are wrong (Wrong).

This essay will define the notion of truth, and it will outline ways to approach truth. It dedicates an entire section to this concept (SecTruth). However, this essay will not tell us what is true. Rationality gives us a framework for truth, but not truth itself. Finding the truth is left to us as humans.

Rationality is not the truth.
It is a way to seek truth.

What does it mean to speak rationally?

Speaking rationally means speaking with the goal of finding the truth (SeekTruth). This means in particular
  1. Making clear, matter-of-fact statements
  2. Basing statements on reasons
  3. Being open to the discussion and revision of these statements
This essay dedicates a chapter to each of these goals. There is one chapter about the art of making clear statements (ChapStat), there is a chapter about reasoning (ChapDed), and there are chapters about discussion (ChapDisc) and openness (ChapAdv). Rational speaking is not just a way to phrase statements. It also has a social component, and it comes with a certain attitude.

This does not mean that speaking rationally would be the only good way to speak. There are many domains of life where it is not necessary or appropriate to speak rationally (NoUse).

What is a rational argument?

A rational argument is a proof. The proof shows that if certain obvious statements are true, then a certain hypothesis must also be true. This way, an argument helps us illuminate a bit more of truth and reality (SeekTruth). This essay dedicates a section to proof techniques (SecProofs), a section to what an "obvious statement" is (SecFounding), and a chapter about making an argument together with other people (ChapDisc).

What does it mean to be rational?

Being rational means using rationality (Def) to do the things that are most useful to achieve your goals. This essay dedicates a section to the formal definition of goals and the types of goals (SecGoals) and a part to how these goals can be achieved (PartGoals).

Such a focus on goals may sound like an egoistic killjoy ideology. However, whether rationality is egoistic or not depends on how you choose your goals. For example, it can be your goal to help a friend, to be an honorable member of society, or to achieve world peace, but it can also be your goal to make the best of your vacation, to learn dancing or to allocate enough time everyday for doing nothing. It is your own choice how to set your goals — egoistic or altruistic, fun or serious. Rationality will then help you achieve these goals efficiently.

A goal without a plan is just a wish.
Antoine de Saint-Exupéry

Why is rationality useful?

Rationality (Def, Speak, Arg, Rational) comes with a number of advantages: This is not to say that rationality would bring only advantages. It can also bring plenty of disadvantes if applied wrongly (SecLess, NoUse). However, if applied in the right places, rationality proves a useful tool.
What you believe = what you say = what you do
(basic recipe for inner harmony)

Where is rationality not useful?

It is not always necessary and also not always useful to express thoughts in a rational way. The arts, for example, including poetry, music and painting, would be crippled if reduced to rationality. Their goal is not to produce rational statements (Speak) or to make rational arguments (Arg), but to express certain feelings or thoughts, to create beauty, or to convey a certain impression on the audience.

In general, tasks that require creativity can often not be accomplished by purely rational means. Rationality can prove statements and help achieve goals, but it cannot (by itself) discover new paths to solutions. In fact, rationality often needs creativity to discover such paths (ChapGoals).

Emotions, too, are often best left without rational arguments. Even though it is possible talk rationally about emotions (Feelings), that may not always be necessary or useful. Religion is another topic where rationality may be inadequate. Unfortunately, also the foundations of ethics go beyond rationality. It is hard to arrive at common ethic standards through purely rational means (see, e.g, [Thoughts on Ethics / General Thoughts on Ethics] for a discussion). Thus, moral standards will be nothing more than personal preferences in rational arguments (Moral).

One problem rationality does not solve either is the divergence of personal preferences. Different people find different things important. Rationality cannot change that. For example, rationality cannot be used to "prove" that one sort of ice cream is better than another (Preferences). Therefore, rational conversations are rarely about personal preferences. This makes them often abstract and impersonal.

If you talk rationally with a friend of yours about a problem of his, you might be signed off as un-empathic. This is a little unfair, because a rational analysis of his problems is a much greater proof of friendship than blind support, because it shows that you value his well-being more than your relationship. However, it is not always appreciated.

Sometimes, too much of rationality may also cause problems. One pitfall is trying to give evidence for every single statement. Every evidence is again a statement and requires new evidence. In general, it is impossible to give cycle-free, finite evidence for every statement [Wikipedia / Infinite Regress]. Thus, one has to stop at some moment and accept certain statements as assumptions (Basic).

A similar problem appears when one seeks to define common words. Each definition consists again of words and these words have to be defined. As before, it is in general impossible to define all words of a language in a cycle-free, language-inherent and finite way (see [Thoughts on Atheism / Ultimate reason] for mathematical details). As a proof, look into a Chinese dictionary. It defines all words, but you will still not learn a single new word unless you already speak Chinese. Furthermore, an exact and correct definition of a word (as opposed to a description) can be arbitrarily complex. Ludwig Wittgenstein famously showed how difficult it is to define what a "game" is. Therefore, it is necessary to stop drilling deeper at some point and resort to the intuitive meaning of the words (Language, TalkToArgueWords). This essay will point out a way to do that (Mean).

Rationality is often misused for the sole purpose of cantankerousness. Once a discussion dives into the details of a question with no practical relevance, rationality becomes a tool of quarrel. When people argue, the goal should not be to be proven right. Rather, the goal should be to discover new insights and to get closer to truth (SeekTruth). In a similar bad spirit, rationality is often used to make destructive arguments, i.e. statements that serve the sole purpose of invalidating somebody else's view, without offering an alternative. This can poison human relations. This essay dedicates a section to this phenomenon (SecLess).

Thus, it turns out that rationality is just a tool. If applied in the wrong place, it can be inconvenient or even provoke harm. If applied in the right place, it can be useful.

Newton's flaming laser sword:
   "What cannot be settled by experiment is not worth debating."
While this sword undoubtedly cuts out the crap, it also seems to cut out almost everything else as well, as it prevents taking position on several topics such as politics or religion.
Mike Alder

What is the cost of using rationality?

Using rationality (Def, SeekTruth) requires a lot of effort. It is difficult to arrive at new statements, it is cumbersome to find reasons and it is strenuous to verify an argument (Arg). Furthermore, rationality often shows that we know far less than we thought we would know. Many of our convictions may turn out to be nothing more than assumptions. Rationality might also destroy the statements on which we wanted to build further arguments. Thus, rationality might lead us to much weaker conclusions than we were aiming at. Thus, we might be forced to give up quite a number of convictions (GiveUp).

The conclusion of a rational argument may be something different from what we expected when we started building the argument. It may be something we can hardly believe, something we don't like or something we just don't want to be true. This is highly inconvenient. Moreover, rational arguments are often perceived by others as cold and merciless. For example, if you talk rationally with a friend of yours about a problem of his, you might be signed off as un-empathic (NoUse).

Furthermore, rationality does not allow us to do the things that we often enjoy so much. First, rationality does not allow us to be self-rightous. If we follow the rational principle, we are forced to consider every statement objectively, no matter who advocates it. Second, rationality does not allow us to lump together unrelated problems. Instead, we have to consider each problem separately (DontMix). This way, the success or failure of one problem is not allowed to spread to another one. Third, rationality does not allow fleeing the problems (Think). Rationality forces us to face a problem and to decompose it. Last, rationality does not allow blind support of somebody's view. When asked, we might be forced to contradict a friend. This is strenuous (NoWish).

In general, however, the upsides of rationality outweight the effort we have to invest in it (WhyUse).

Watch your thoughts, for they become words.
Watch your words, for they become actions.
Watch your actions, for they become habits.
Watch your habits, for they become character.
Watch your character, for it becomes your destiny.
an unknown source


Rationality may not always be useful (NoUse). Worse, it is sometimes perceived as inappropriate, cold, or insulting. This section covers some common concerns about rationality. This essay dedicates another section on how to be "less rational" (SecLess).

If rationality is not always useful, why use it at all?

As we have seen (NoUse), rationality is not always helpful. Consequently, the question arises whether it should be used at all.

This question transfers to several domains:

The answer to all these questions is the Pragmatic Principle:

A partial benefit is better than no benefit at all.
Or, metaphorically speaking: Half a bar of chocolate is better than no chocolate at all. The same principle applies to tools, such as hammers, screw drivers or, indeed, rationality: If the tool is useful in some cases, it should be used in these cases. It may bring benefit even if it is not universally applicable.
It is better to light one candle than to curse the dark
a Chinese proverb

Sometimes it can be reasonable to be not truthful

Rationality is a tool to achieve goals (Rational). This essay assumes that truth is one of these goals (SeekTruth). However, there are cases where it can be reasonable for one's goals to deviate from the truth. These cases are, e.g.:

This argument has been supported most strongly by the Renaissance philosopher Niccolò Machiavelli [Wikipedia / Machiavelli]. Indeed, falsehood can be rational, in the sense that it can serve our goals (Goals). Yet, the present essay is based on the assumption (Assumptions) that truth is among our goals (SeekTruth). This is because, in the vast majority of cases, truth serves all of our goals well. Not last, speaking falsehood can be immoral, and thus counteract the goal of morality (Moral). Therefore, this essay views rationality as a means to find truth. This view corresponds to the scientific, humanist, enlightement-inspired view of the world. Yet, it is not the only possible view.

Occasionally words must serve to veil the facts. But let this happen in such a way that no one become aware of it; or, if it should be noticed, excuses must be at hand to be produced immediately.
Niccolò Machiavelli

What is wrong with non-rationality?

This essay advocates the use of rational statements (Speak). However, as we have seen, also non-rational statements have their purpose (NoUse). Non-rational statements serve, e.g., in poetry, music, religion, and art. So the question arises why we are not just fine with the non-rational statements.

The problem with non-rational statements is that some of them are as "true" (and therefore as "false") as their opposites. Have a look at the following non-rational statements:

These statements are unfalsifiable (Unfalsifiable), general valuations (GenVal) or abstract universal hypotheses (AUH). This makes them non-rational. Such statements may not be used in rational arguments (Arg). This section dedicates a section to these kinds of statements (SecNonRat).

This does not mean that non-rational statements would be useless. They can still serve their purpose. However, they cannot serve the purpose of convincing someone or yourself of something. Whenever we want the opposite of our statement to be false, rational statements are our best bet.

It is impossible to give reasons for all statements on principle!

A rational argument aims at giving evidence for a statement (Arg). Unfortunately, every evidence is again a statement and requires new evidence. In general, it is impossible to give cycle-free, finite evidence for every statement [Wikipedia /Infinite Regress, Regress argument]. See [Thoughts on Atheism / Ultimate reason] for a proof.

To avoid this, we have to rely on founding statements. These are, for example, statements about our immediate perception. A statement such as "I have the impression of seeing something blue" cannot be wrong. This essay dedicates a section to these founding statements (SecFounding).

You cannot believe only what you can prove!

Rational thinking produces theories about this world (Theories), and uses them to make predictions (Truth). There are statements that cannot be proven this way. These include, among other things, personal preferences (Preferences) and ethical convictions (Moral). They also include statements about God.

If a statement cannot be proven this way, then it might be that statement is not objectively valid. It is subjective. That means that different people can have different views about that statement. This holds for example for many ethic convictions. Even supposedly "basic" principles (such as "You shall not kill"), are in fact disputable (e.g., in countries that allow the death penalty). This also holds for religious beliefs. For most religious beliefs, there are people who believe something different. Therefore, subjective statements should not be regarded as absolute truth (NoSubjective).

This does not mean that we should not believe in subjective statements. Everybody is free to believe as he wishes. In fact, most people do believe in non-provable statements, simply because the realm of provable statements is so limited. Furthermore, non-provable statements do have their role in rational arguments. They are assumptions (Assumptions). For example, most people believe that it is morally wrong to kill someone without a reason (Moral). Even if that statement cannot be proven, it may still form the basis of a valid rational argument. Likewise, one can have a rational discussion about God once one assumes his existence. Thus, the fact that some statements cannot be proven does not render the rational principle useless.

Suppose someone had a basket full of apples and wanted to take out the rotten ones. Wouldn't he tip the whole lot out of the basket, and then pick up and put back in the basket only those he saw to be sound?
René Descartes

Some assumptions may be wrong!

Rational arguments must assume that some initial statements are true (Arg). If it turns out that an assumption was wrong, the whole argument collapses.

Wrong assumptions are indeed a major problem in all domains of reasoning. This applies in science, and in human thinking in general. Rationality offers means to mitigate this problem: It sees all of our thinking in general as nothing more than an approximation of truth (WhatIsTruth). Thus, it is clear from the beginning that all our arguments and thoughts are nothing more than attempts to approach reality. This entails that we have to be ready to give up our convictions if they do not serve this purpuse.

Therefore, rationality emphasizes that every statement shall be open to verification and questioning (Speak). The more people are allowed to check a rational argument, the less likely it is that there are wrong assumptions in it (QPerson). Furthermore, rationality emphasizes the art of determining, abandoning, and improving false assumptions. This continuous strive for the truth, even at the expense of past beliefs, is one of the cornerstones of rationality (SeekTruth). Thus, while rationality cannot always exclude wrong assumptions, it offers at least mechanisms to detect and eliminate them. This cannot be said about every school of thought.

Life can only be understood backwards
but it must be lived forwards
Soren Kierkegaard

Logic is undecidable.

Classical first-order logic is undecidable. That means that there exist statements for which we will never be able to find out whether they are true or false. Thus, if rationality uses first order logic, it faces statements within its own domain that it cannot handle.

Indeed, rationality faces statements that it cannot prove or disprove. One such statement is for example:

This sentence is false
If we prove this sentence to be true, it will be false. If we prove it to be false, it will be true. This is related to quite a number of paradoxes, see [Wikipedia / Paradoxes] for an entertaining list. In reality, the effect of unprovable and undisprovable statements is limited, for two reasons: First, the unprovable statements that appear in reality mostly involve self-reference and thus can be detected. Second, first-order logic is at least correct, which means that every statement that one proves is indeed true and every statement that one disproves is indeed false. Thus, even if there exist statements for which we cannot say whether they are true or false, all those statements where we succeed are indeed true or false as predicted. Therefore, by the pragmatic principle, rationality still remains useful. The section on proofs offers a more technical discussion of these problems (SecProofs).

Even rational theories change over time!

Newton's theory of gravitation, for example, was for sure a rational one. Yet it has been replaced by Einstein's theory of relativity. Other scientific theories are changed as well. Does this not show the limits of the rational principle?

In the framework of rationality, our view of the world is just an approximation of reality (WhatIsTruth). We try to find theories that explain this world, and that predict what will happen. If we find out that a theory does not work, we change it. This way, we approximate truth better and better over time. The clear disadvantage of this technique is that our theories change from time to time. However, this technique is still better at predicting and explaining than most alternatives. For example, rationality is clearly better than the alternative of not making any theories at all. Rational theories help us understand at least some things of this world. This property makes them useful by the pragmatic principle.

Also, changing a theory is clearly better than sticking to a wrong theory, if we want to predict things. This is why rationality puts particular emphasis on the ability to change convictions. It turns out that those people who do not change their convictions in the face of counter-evidence are less good at predicting things. Indeed, scientific theories are constantly being evaluated and challenged, in order to always get them closer to truth.

It is considered one of the beauties of science (and of the rational principle in general) that it evaluates itself over time. If a predicted statement turns out to be false, we may challenge the argument that lead to it. We may correct it, possibly by admitting that some assumptions were wrong or that some conclusions were invalid. Thereby, we learn new things. This is a call that appears repeatedly in this essay (WhatIsTruth, Wrong, Contingency).

If someone says he has understood quantum theory, then he has not.
Richard Feynman

Science has brought us many ills!

Science has brought us progress on many accounts, but also many ills: Wars have become more sophisticated, weapons have become more dangerous, environmental damage has become more profound, and many of our philosophical and spiritual foundations have been shattered. Thus, we may ask whether rational thinking (and science as one of its applications) is good for humanity.

Science and thinking by itself is neither good nor bad (Good). It is a tool that helps us understand and use our physical environment in a more effective way. Whether this is good or bad depends on what this tool is being used for: It is "good" if it is used to develop a new medicine, and "bad" if it is used for developing a more lethal weapon. Thus, the question of good and bad is not a question of science, but of ethics (Moral). Rational thinking cannot replace ethics, but help us understand and formalize it.

Rationality can only work if we admit the principle of identity. This principle, however, is not self-evident.

This objection relates to the classical paradox of Theseus' ship. It goes as follows: Suppose we built a large ship. Over the years, all parts of a ship will eventually be replaced by newer parts. When all parts have been replaced, is the ship still the same ship? If not, when did it stop being the same ship? If yes, what if we took all the old parts and assembled another ship. Would that be the same ship?

This paradox shows that the question of when two things are the same is not trivial to answer. (See [Wikipedia / Ship of Theseus] for a discussion). For most rational arguments, we need indeed the concept of identity. However, we usually only require the concept of real, unaltered identity. This concept is usually undisputed. For example, if we do not replace the parts of Theseus's ship, then everbody will agree it is still the same ship.

If we replace the parts of the ship, the relation of identity becomes disputable. Fortunately, nobody forces us to define the notion of "identity" for these cases. We can just say that we do not know whether the ships are identical or not (Unknown). The theory of rationality put forward in this essay says that words are nothing more than human artifacts (Mean, TruthEtc). They have no foundation in nature. "identity" is not something that is there in this world, and that we have to define. Rather, it is a term that we humans apply in certain cases. Thus, it is up to us to decide whether we want to apply the word "identity" to Theseus' ship or not (Definitions).

In general, we can avoid the problem by making our statements more precise (BePrecise, TalkToArgueWords). For example, we can say that the structure of the ship is still the same, while the parts are not. This does away with the conundrum.

Rationality assumes that the concept of truth exists. This assumption may be wrong.

Assume that truth does not exist. Then, the statement "Truth does not exist" would be true. Hence truth exists in any case. [Wikipedia / List of Paradoxes]

In other words: The very attempt to argue that truth does not exist presumes that it exists, because making a claim and arguing for a claim is only possible if truth exists. If truth did not exist, then the claim "truth exists" would not be any different from the claim "truth does not exist". This essay dedicates a section to these conundrums (SecTruth).

Even if we ask "What is 'Being'?", we keep with an understanding of the "is",
though we are unable to fix conceptually what that "is" signifies.
(i.e., it does not make sense to ask what existence is
because by asking for it, we already presume it.)
Martin Heidegger

Rationality assumes that there exists a reality. This assumption may be wrong.

It has been argued that we cannot be sure whether the physical system in which we perceive ourselves really exists. There could be no such system at all. There could be also multiple such systems. Then, our sensations would be just impressions. We would live in a reality similar to the one outlined in the movie "The Matrix" [Matrix]: Everything is just impressions and nothing really exists.

The hypothesis that reality would not exist is unfalsifiable (Unfalsifiable). Therefore, there is no use arguing about this statement. As all unfalsifiable statements, the truth or falsehood of this hypothesis has absolutely no influence on our life. As we have no way of escaping our reality, no way of perceiving other realities and no way of determining whether there exist other realities, the existence of other realities is completely irrelevant in everyday life. It just does not matter whether everything around us is simulated or real — because these two notions become equivalent if we cannot prove them different. Therefore, rationality explicitly excludes such notions (Unfalsifiable).

This essay offer the following solution to these conundra: We perceive ourselves in a stream of sensations (WhatIsTruth). Whether these sensations are "real" or "unreal" in some unfalsifiable sense is irrelevant. The goal of rationality is, given some sensations, predicting others. For this purpose, we build up theories that help us make predictions (Theories). The theory that reality exists is a very successful theory. Therefore, most people accept and use it. The concepts of reality and truth are discussed in detail later on (Reality, SecTruth).

Anyone who believes that the laws of physics are mere social conventions is invited to try transgressing those conventions from the windows of my apartment. I live on the 22nd floor.
Alan Sokal

Rationality assumes that people around us exist. This assumption may be wrong.

It has been argued that our fellow humans might be just machines that act as if they had a conscience — but that do not. Such machines are called "zombies" in philosophy. In this scenario, the social part of our perceived reality would be just simulated by things that seem human but that are not.

By definition, it is impossible to distinguish between a machine that mimics a conscious human in a perfect way and a real human. Therefore, such a hypothesis is unfalsifiable (Unfalsifiable). An unfalsifiable hypothesis is irrelevant, because it will make no difference if this hypothesis is true or false.

As a matter of fact, I assume that the reader of this essay is a human with consciousness. Whether he is or not, he is kindly invited to discuss the concept of rationality, with or without consciousness [Thoughts on Atheism / Matrix]. In particular, he is invited to read this essay for a definition of the concept of reality (Reality).

There is no objective truth

It is surprising to learn how few things we really know for sure. As an example, take a seemingly obvious statement, such as the observation "This apple is green". If taken with philosophical rigor, a number of questions arise from just this simple statement. First of all, how can we be sure that there is an apple in the first place? It could be just an illusion. After all, people fall prey to all kinds of optical illusions. For example, people see oases in the desert even though there are none. So there is no reason to assume that this apple is real. The only way we have to verify that there is an apple are our sensory organs — and these are untrustworthy. Furthermore, even if we agree that there is an structure of atoms in the shape of an apple, how can we be sure that this structure of atoms is an apple to both of us? After all, it is just an arbitrary structure in the sea of atoms around us. Last, how can we make sure that your concept of an apple is the same as mine? We never discussed the concept of an apple, and I cannot be sure whether your idea of an apple is not, by chance, that of a long, bended yellow fruit, which I would call "banana".

Now assume that we managed to agree that there is an apple. Then we might still disagree about the notion of "green". Your sensory impression might be completely different from mine and we have absolutely no way of exchanging them. Furthermore, different cultures might have different notions and granularities of "green". Your "green" might be different from mine. Last, the apple might not actually be "green", but have red spots. Then, can we still call the apple "green"?

These arguments can easily be contined to infinity, and that is what many philosophers do. It has been argued that objective truth cannot exist and that, for this reason, we can never agree on reality. Surprisingly, proponents of this theory want us to agree on that. However, how can we be sure that we understood what they were saying, given that there is no objective truth? Why do they even talk if, strictly speaking, no one can understand them? This shows that the very discussing of the hypothesis that we do not agree on reality proves it wrong. It seems that, even though there might be no objective truth, people do agree on most things of the physical world, on words and on their meanings.

We might be tempted to point out that people argue all the time about things they disagree on. This, however, is just because there is no point discussing the things that one agrees on. Indeed, the fact that people do discuss the things they disagree on proves that they do agree on the vast majority of things and meanings, because otherwise they would be unable to discuss the ones they do not agree on.

This essay argues that we perceive ourselves in a stream of sensations (WhatIsTruth). We make hypotheses about this stream of sensations, and we build up theories about them. Some of these theories are particularly successful — in the sense that they help us predict following sensations with astonishing accuracy. For example, we come up with the theory that most people agree on the basic things of reality (such as green apples). This theory allows us to predict that most people will say "there is a green apple" when asked what they see when we show them a green apple. These theories are not always right, but they are usually so good that no one questions them. Still, this essay dedicates a topic and a section to those who wish to go into detail (Truth, SecTruth).

The paralysis of thought that comes to philosophers: One saying to the other: "you don't know what you are talking about!". The second one says: "what do you mean by talking? What do you mean by you? What do you mean by know?"
Richard Feynman

Rationality assumes that free will exists. But does it?

Rationality is all about goals and ways to achieve these goals (Rational). This setting assumes that people are capable of deciding for a certain solution and then implementing that solution. However, it is not clear whether people really have the power to decide what they do. First, people's decisions are much more influenced by their background, their upbringing, their culture, their emotions, and social constraints than we commonly like to admit. Is someone who hits somebody in anger really in control of his actions? Can someone with a conservative upbringing really decide to have a liberal life style? Can a drug-addict really decide to stop taking drugs?

The answer is probably: partially. While we cannot control all of our actions, we do control a great deal of them. It would be a waste of opportunity of we gave up the control that we do have (Pragmatic Principle). Worse, it would be irresponsible to blame external factors for something that lies in our own hands. This essay will repeatedly advocate responsibility for one's own actions (BeResponsible, Moral).

The second argument against free will is more of a philosophical nature. It says that our so-called free will is in fact the outcome of a chemical process in the brain. Our decisions are determined not by ourselves, but by the state of our neurons. If we knew the state of all neurons, we could predict what a person will decide. Indeed, a some of our decisions are caused by known neuro-chemical processes: Drugs can influence our mood, and diseases of the nervous system can bring hallucinations, depression, anxiety, and paranoia. This makes it conceivable all our mental life, including our decisions and reasoning, would be driven by physical processes. If that is the case, then no-one can really be responsible for his actions — because no one is free to choose or change the state of his neurons. In this scenario, we could not even blame a person for a crime, because his actions are just the result of his brain activity, which he cannot change.

From a pragmatic perspective, however, it makes no difference whether a person's actions are determined by his brain activity or by what we call "free will". The concept of "free will" allows us to describe and predict people's behavior. If someone says that "He wants ice cream" (Desires), then we know that giving that person ice cream will make him happy — no matter whether this desire for ice cream is the outcome of a chemical process or not. If we tell someone that if he commits a crime, he will be punished, then that person is less likely to commit a crime — no matter whether this consequence is the outcome of a purely materialistic computation or the active decision of a conscious self. For this reason, the concept of free will is a useful assumption, in the sense that it allows us to predict reality. This essay will give a limited definition of this concept further down (FreeWillEx). For this essay, the notion of free will is an auxiliary notion that serves a purpose (Aux, Truth, Reality).

The self is like a sword that cuts, but cannot cut itself;
like an eye that sees, but cannot see itself
a Zen poem
Technical remarks
In his book "A New Kind of Science", Stephen Wolfram puts forward the idea that simple phenomena can combine to very complicated processes. These processes can be so complicated that it would be impossible to predict the process by any types of natural laws, mathematical models, or regularities (Rules). The only way to "predict" where such a process goes is to simulate it in its entirety. Applied to the notion of free will, this theory says that human decisions could indeed be predicted — but only if we reconstruct the entire brain, down to the level of neurons, cells, and atoms. This means basically that if we could reconstruct the human being, then we could predict his thoughts. In this sense, free will may be predictable, but it is a very weak predictability. It means that free will would emerge in an irreducible way from the behavior of the individual cells. Emergence is a phenomenon that is responsible also for a number of other phenomena, such as the shape of snowflakes, plants, etc. [Wikipedia / Emergence].

Rationality, including this essay, relies on natural language. Natural language, however, is inherently fuzzy.

It is well-known that natural language is ambiguous and fuzzy. Thus, it can be asked whether natural language is the right vehicle to express rational thoughts.

Indeed, people have run into this problem when they tried to formalize proofs. This is why formal langages (such as the languages of math and logic) have been developed. They provide an unambiguous way to express statements.

In most cases, however, natural language is still the vehicle of choice (and be it only to teach the formal languages). Fortunately, natural language has a built-in mechanisms to deal with unclear statements: In order to determine whether a message has been received, we can ask the receiver to paraphrase the message. If there is doubt about a statement, the statement can be discussed and clarified. And indeed, in most cases, natural language succeeds quite well in transmitting its message — as the reader experiences while reading this text. Therefore, it is justified to assume a basic understanding of words (WordMeaning). This essay will argue that such an implicit understanding of words is all we need (Mean). As Augustine of Hippo remarked once concerning the definition of the word time:

If no one asks me, I know what it means
Augustine of Hippo

Who guarantees that the outcome of a logical conclusion holds in reality?

If we start from premises that correspond to reality, and if we use a valid logical argument, then we will arrive at conclusions that correspond again to reality. This is the basic mechanism of rational arguments (Arg). For example, if we know that
Alice either comes by bike or by car
and if we know that
Alice did not come by bike
then we can deduce that
Alice came by car
If the first two statements are true, then the last one will also be true. On a philosophical level, it is astonishing that we can transform reality into statements, reason on them and then produce statements that correspond again to reality. This is the "Miracle of Logic".

This essay cannot explain why this is in this way. On the contrary, it has to assume that the Miracle of Logic works. This essay will make extensive use of this principle to explain the mechanisms of reasoning (ChapDed).

You simply cannot see the world in this way!

It may seem strange to describe the world by statements that build on each other. It appears that this approach is too simplistic for a world that is so complex.

Yet the statements of rationality are very powerful. They can express the uncertain, the unclear, the unknown and that it is unknown whether something is unknown. They can even say that they cannot say something. This essay later presents a list of things that we can express rationally (SecStat).

You do not know everything!

Rationality builds its arguments on statements. These statements can only be made if one has certain knowledge about the world. Therefore, the question arises whether the principle of rationality does not overestimate the knowledge that we have.

We are certainly far away from knowing everything that there is to know. Fortunately, rationality by itself does not require that much about the world be known. On the contrary, rationality will probably reveal many things that we thought we know, but do not know (Cost). Rationality allows us to express what we do not know (Unknown).

The sky is not the limit. The ground is.

People just don't act rationally!

Rationality may be a great theory, but reality shows that people just do not always act rationally. Therefore, we can ask what is the benefit of rationality, if people mostly behave irrationally.

It is true that people often do not act rationally (Rational). This, however, does not deprive rationality of its raison d'être. Just like a law is a good thing, even if people break it, rationality is a good thing, even if people don't follow it. Just like the law, rationality serves as a yard-stick rather than as a description of reality. Rationality can serve to assess the usefulness, the reasonableness or the morality of a behavior, even if that behavior is useless, unreasonable or immoral.

Besides, if we do act rational, we can count on certain benefits (Use). Therefore, even if not everybody behaves rationally, rationality still serves a purpose to those who do (WhyUse).

If we can rationalize all questions, then do we need humans at all? Can't all the reasoning be done by a machine?

It is a very interesting question whether reasoning can be outsourced completely to computers. The renaissance philosopher Leibniz dreamed of a machine that, given all the political preferences and military facts, would compute whether the country should go to war.

The central problem is that rationality provides the framework for such reasoning, but is disconnected from reality. The framework does not "know" whether a certain assumption is true or not. For example, the framework does not know whether the statement "The target country has rich oil resources" is true or not. For now, the connection between rationality and reality has to be established by humans. This is also the reason why we cannot outsource, e.g., legal court decisions to reasoning machines: Whether or not a certain term (such as "malevolent intention") applies in reality or not has to be decided by humans.

Furthermore, rationality is not always the right way to go (NoUse). If we outsourced all reasoning to a machine, then we would deprive ourselves of the non-rational options.

However, there are some cases where both conditions are fulfilled: rational thinking is the preferred way to go and the truth of statements is computer-accessible. In these cases, computers can indeed help with making decisions. This holds in particular when the rational argument is huge, with millions of assumptions and consequences. And indeed, computers do the reasoning for us in these cases. They do computations for train schedules, bridge achitectures and aircraft steering. In these cases, the reasoning can be out-sourced.

If rationality works, then all people should always arrive at the same conclusions. However, they usually don't.

Rationality emphasizes the objectivity of an argument (Arg). In principle, people sharing the same assumptions should arrive at the same conclusions. However, in reality, we witness a vast diversity of opinions and behaviors, disputes and sometimes wars — even if everybody claims to act rationally. Why is this the case?

Several factors might play a role here:

Everybody is a prisoner of his own convictions.

Sounds all great and you are surely right, but sometimes I just cannot be rational.

Rationality has some benefits that other approaches do not have (Use). However, rationality demands a lot of effort and energy (Cost). Therefore, nobody can always be rational — even if he wanted to.

This seems to be a very normal phenomenon. After all, we cannot always succeed with everything. Still, by the Pragmatic Principle, rationality remains a useful thing to have. Even if we do not apply it in all cases where it would be useful, it can still be of benefit in those cases where we do apply it (WhyUse).

Don't believe everything you think.


Statements are the building blocks of rationality (Def). This part of the essay will talk about different types of statements:
  1. rational statements (SecStat)
  2. nearly rational statements (SecNearly)
  3. irrational statements (SecNonRat)
  4. founding statements (SecFounding)

Rational Statements

The world is so complex and diverse that it may seem impossible to approach it with rationalism. But rationality can deal with many different types of things, including supposedly "irrational" ones. Far from having to neglect irrational things, rationality can express them and deal with them. This section will explain how different phenomena of this world, irrational as they might seem, can be "wrapped" into rational statements. For this purpose, the section introduces different types of statements. Metaphorically speaking, we will introduce the types of bricks with which we can build our towers. This section will also propose wordings for the statements. These wordings are by no means compulsory. Clearly, people can phrase their statements any way they want. The wordings proposed here just serve as examples.

Simple Statements

Rationality builds on statements. Statements in the sense of rationality are only declarative sentences, i.e. sentences that can be true or false. For example, the following sentence is a statement:
The Earth is flat.
Obviously, this is a false statement. However, it is still a statement. Statements, both true ones and false ones, are the building blocks of rationality. The following utterances are not statements in the sense of rationality: Statements do not need to follow the strict form of declarative sentences. In reality, plenty of non-declarative sentences can have the character of statements in the sense of rationality. For example, if someone says "yes", then this is not a declarative sentence. Still, it can be understood as a statement in the sense of rationality, because it is an affirmation of another statement. Ultimately, the meaning of utterances relies exclusively on social conventions. This essay will not deal with their respective forms and pitfalls, but simply assume the existence of statements as an auxiliary notion (Aux). See [Thoughts on Ethics/ Declaration] for a treatise.


Statements can be negated. For example, we can negate the statement "The Earth is flat" and say
It is not the case that the Earth is flat.
If a statement is false, then its negation is true and vice versa. Given a statement X, we will denote its negation by

Some care has to be taken with negations. For example, the negation of "The Earth is flat" is not

The Earth is round.
The reason is that "not flat" does not mean "round". "Not flat" could mean anything from "round" to "elliptic" or "box-shaped". Therefore, we have to negate the statement more precisely by saying
It is not the case that the Earth is flat
This sentence says that something is not the case. This can be because the Earth is ball-shaped, cube-shaped, or because it does not exist at all. To illustrate this point, consider another example:
Bob stopped beating his wife.
The negation of this sentence is not:
Bob did not stop beating his wife.
The reason is that if we negate the sentence this way, it presumes that Bob did indeed beat his wife (Loaded). That need not be the case. Hence, the correct negation is:
It is not the case that Bob stopped beating his wife.
... and this can be because he still continues beating her or because he never beated her. Consider another example:
Paul believes that unicorns exist
The negation of this sentence is not
Paul believes that unicorns do not exist.
The reason is that the opposite of "believing" is not necessarily "believing that not". For example, assume that Paul does not know what a unicorn is. In this case, he neither believes in their existence nor in their inexistence. He simply does not have any belief. Hence, the correct negation of the sentence is
It is not the case that Paul believes that unicorns exist.
This just states that the idea that Paul believes in unicorns is false — without asserting anything else about Paul's believes (or Paul). See [Thoughts on Atheism / Strong] for a dicussion.

Statements about the Unknown

For many statements (in fact, for the vast majority of statements), we do not know whether they are true or false. For example, we do not know whether there is intelligent life on the Planet Mars. Rationality allows us to express this, e.g., by statements of the form "As of now, I do not know whether ...". For example, the following statement is a rational statement:
As of now, I do not know whether there is intelligent life on Mars.
The semantics of such a statement is: The statement is true unless we learn of a rational argument that proves or disproves the wrapped hypothesis. For example, as long as no rational argument proves or disproves that there is intelligent life on Mars, the above statement is true. As soon as we hear of a rational argument that proves the wrapped hypothesis, the statement becomes false. This way, we have transformed a statement that may be true or not into a statement that is true.

This transformation might sound trivial. It might seem as if the new statement did not carry any value. However, even a statement of the form "I do not know..." carries value. For example, assume that you are driving a truck that weights 8 tons. Assume you come to a bridge and you ask the bridge guard whether the bridge can withstand the weight of your truck. If the bridge guard replies "We do not know whether the bridge can withstand the weight of 8 tons", then this is a strong argument for you not to try it out. The argument goes like this: Whenever you do not know whether your action will cause harm and whenever the expected harm is huge, you will refrain from that action (RuleInvention). This way, the unknownness of a statement becomes part of your rational argument (Arg).

In fact, many unnecessary problems arise because people think that they always have to know the answer. It is much more rational to say "I do not know" than to give a false account. It is OK to not know something (AvoidIKnow, NoOp).

Directional statements

Sometimes, an argument is not sufficient to support a hypothesis. For example, if a journalist is murdered in some country, we would like to deduce that the press freedom in that country is under threat. However, such a conclusion may be too strong and the evidence too week. In such cases, we can make a directional statement. Such a statement can take the form "This seems to indicate that..." or "This seems to support the hypothesis that...". In the example, we can say:
A journalist has been murdered in Timbuti.
This seems to support the hypothesis that the press freedom in Timbuti is under threat.
The semantics of such a statement is that the first statement can be used as support for the second statement, but that it is not enough by itself to prove the second statement.

Directional statements are useful to structure rational arguments. They are also useful to indicate the purpose or broader aim of an argument. At the same time, they avoid premature conclusions, because they do not actually entail a statement.

Existential statements

Sometimes, it is not possible to make an absolute, general statement. For example, not all Germans are blond. Therefore, we may not say "Germans are blond" (Generalizations). The statement might apply only to certain instances, only in certain cases, or only at certain points of time. To make this explicit, we should use an existential statement. An existential statement can, e.g., take one of the following forms in a rational argument: In the example, we can say "Many Germans are blond". Existential statements are weaker than absolute statements. Still, they are very useful. For example, if you suffer from an illness and you consult a doctor, it will be very useful for the doctor to know where you feel pain — even if you do not "always" feel pain, but only "sometimes". If a building is evacuated because of a fire, it will be very useful for the fire fighters to know that "some" people are still in the building, even if their number is not certain.

Unfortunately, existential statements are not always used when they would be appropriate. Rather, people tend to make generalizations (Generalizations, AvoidIKnow).

Statements about possibility

In many cases, we want to point out that something is possible — without actually implying that it will happen. For example, if you are driving a car and if you are having an accident, it is possible that you are catapulted through the windshield, even though this does not necessarily have to happen. In the simplest case, we can express such possibilities by statements of the form "It is possible that...". In the example, we could say:
It is possible that a car accident throws you through the windshield.
Variants use the auxiliary verbs "can" or "might" or the modifiers "maybe" or "potentially". Such a statement is much weaker than the actual assertion ("A car accident will throw you through the windshield"). Therefore, the statement could be seen as a toothless device. However, statements about possibilities are useful in rational arguments, because they illustrate a scenario even if we cannot prove that this scenario will materialize. For example, we can state that, if you are wearing a safety belt, you cannot be catapulted through the windshield. Then, a rational argument could deduce that if a relatively minor effort (the safety belt) eliminates the possibility of a rather major damage (the encounter with the windshield), then this effort should be made (RuleInvention). Thereby, a statement about a purely hypothetical possibility has lead to very concrete actions through a rational argument (Arg).

Belief Statements

Many things we talk about are not proven facts, but beliefs. For example, people believe that a certain soccer tem will win, that genetically modified food is dangerous, that the theory of the Bing Bang is true or that a certain religious faith is right. Beliefs are a phenomenon that seems to escape rational thinking. Yet, also beliefs can be "wrapped" into rational statements. Such statements start with "I believe..." and are called belief statements. For example, the following sentence is a rational belief statement:
I believe that genetically modified food is dangerous.
The truth of this sentence is independent of the truth of the actual wrapped sentence. For example, even if it is proven one day that genetically modified food is not dangerous, that person can still believe it is. This way, we have projected an "irrational" belief into a rational statement.

It might seem as if this statement did not carry any value, because it ultimately wraps an unproven statement. Still, the statement can be a useful part of rational arguments (Arg). For example, if you believe that GM food is dangerous, then you will avoid GM food. This is a very rational conclusion. This argument is independent of whether GM food is actually dangerous or not. Similarly, opponents of GM food can found lobby groups based on their belief that GM food is dangerous, even if we do not yet know whether it is dangerous or not. This way, beliefs can become part of rational arguments.

It seems that a number of problems could be avoided if people made a better distinction between what they know and what they believe. It is much better to say that we believe something than to say that we know something if we don't (NoSubjective). Another problem seems to be that as soon as someone states his belief, other people who have a different belief start arguing against it. Such an effort is futile — unless the speaker's belief has an effect on other people or if the speaker is interested in discussing the belief (TalkToArgue).

It may also happen that the speaker does not have an opinion at all about something. For example, the speaker may simply have no clue about whether GM food is good or bad. Then he should say so:

I don't know yet what to think of genetically modified food.
Technically, this statement says that the speaker does not have a belief concerning the danger of GM food. It is often forgotten that it is OK not to have an opinion about something. It is much better to listen and learn than to decide for an arbitrary opinion and argue for it (NoOp).

Statements about Uncertainty

Uncertainty is closely related to the phenomena of beliefs (Beliefs) and of unknownness (Unknown). Rationality can deal with uncertainty by sentences of the form "It is uncertain whether...". For example, if it is uncertain whether a certain number wins the lottery, then we can say:
It is uncertain whether the number 42 wins in the lottery.
This statement is rational and certain. This way, uncertain statements can be wrapped into certain statements. Their semantics is that the wrapped statement is practically unprovable until it validates itself. Different from statements about unknownness (Unknown), statements about uncertainty are independent of the knowledge of the speaker. Statements about uncertainty can be very useful. For example, if it is uncertain whether 42 wins the lottery, then we should not bet our house on it. This argument is a perfectly rational conclusion — from an uncertain statement (Arg).

Mathematicians have developed a theory that can be used to describe the phenomenon of uncertainty and randomness. This is the Probability Theory [Wikipedia / Probability theory]. It can make rational statements about uncertain phenomena. For example, even though it cannot predict the outcome of a single dice roll, it can predict with high accuracy what amount of money you will win if you always bet on the same number and roll the dice a large number of times.

Private Reasons

Rationality emphasizes the public verifiability of arguments (Speak). However, we may not always wish to relinquish our private reasons for something. Rationality allows wrapping private reasons for a certain conclusion into a generic statement of the form "These are private reasons". For example, we can say
For private reasons, I have to find another job.
The semantics of this statement is that the speaker has to find another job, and that this desire is justified by statements that the speaker would not like to disclose. By such a black box statement, the speaker assumes the sole responsibility for the conclusion ("I have to find another job"). To the outside world, only the conclusion is visible. Hence, any following public argument should take this conclusion as a fact and not investigate its reasons.

This technique bears certain problems. For example, people might start guessing the reasons for the conclusion and that is seldom desired. Furthermore, the fact that a person has private reasons can already raise suspicions. If that could become a problem, the speaker will have to refrain from discussing the argument with others — or he will have to discuss it with a friend in private. A rational argument without public scrutiny is more likely to contain mistakes, but can still be useful. See [Thoughts on Ethics / Privacy violarion] for a moral discussion of privacy violations.

Statements about Feelings

Emotions and rationality are traditionally seen as two opposing phenomena. Yet, this dichotomy is unjustified. Rationality allows wrapping a feeling into a rational sentence. For example, we can say:
I am feeling happy.
Statements about feelings can be used in rational arguments (Arg). For example, if we know someone is feeling happy, we may conclude that he is not feeling sad. If someone says he is feeling happy, but tells somebody else that he is actually unhappy, we may conclude that he is lying to at least one interlocutor.

It is very hard to find a rational argument that has as its conclusion a statement about the emotional state of a person. In other words, there will be no rules that allow us to predict an emotion in a provably correct way. However, in many cases, we will be able to derive dispositions for feelings (Dispositions).

Likewise, it is often impossible to give reasons for feelings or to predict feelings from rational arguments. This, however, makes statements about feelings no less rational than statements about other unpredictable phenomena. A person's emotional state is a fact in its own right and does not require reasons (EmotionalState).

Statements about Desires

A desire is a feeling (Feelings) of hoping for a certain state of the world. A desire can be expressed rationally by a statement of the form "I want...". For example, we can say:
I want to eat chocolate.
The semantics of such a statement is that the speaker will feel happy if that state of the world is attained without violating other desires. It is futile to ask for reasons for desires. Some desires will have reasons, but these reasons are likely to be desires again (EmotionalState). For example, it is simply unprovable why a certain person wishes to eat chocolate at a certain point of time. Desires are simply facts in their own right without need for justification. Still, that desire can become part of a rational argument (Arg). For example, if a person wants to eat chocolate, then the most rational way to achieve this goal is to go and buy chocolate (Rational).

Many desires are not "rational" in the sense that they contradict other goals. For example, the desire to eat chocolate is "irrational" in the sense that it is in conflict with the goals of healthy teeth and healthy body weight. Still, desires can rationally lead to advice (Advice) or other logical conclusions. In fact, we would have a number of problems less in this world if people were not afraid to state what they really want — for fear of being "irrational" (SayWant).

Happiness means to continue desiring what you have.
Saint Augustin

Disposition Statements

A disposition is a state of the world that is considered likely. For example, if you take away somebody's bicyle, that person is likely to get angry. However, we cannot prove a priori that he will get angry. In fact, he might not get angry at all. To reason with these likely, but unproven states of the world, rationality allows disposition statements of the form "It is likely that...". For example, we can state
If you take away his bicycle, it is likely that he gets angry.
The semantics of such a disposition is: In the past, similar circumstances have often lead to this state of the world. Nothing allows us to prove that this state of the world will occur also in the present case. It is close to impossible to provably predict a person's behavior. All we can prove are dispositions — which may or may not become true.

Still, dispositions can be used in rational arguments (Arg). For example, assume that we have the following statements:

If you take away his bicycle, it is likely that he gets angry.
You do not want him to get angry.
If an action is likely to lead to a state that you do not want, you should not perform that action.
This is one conditional statement about a feeling (Feelings), one statement about a desire (Desires) and one conditional statement about an advice (Advice). All of these statements are commonly perceived as "non-rational". Still, it follows logically from these statements that you should not take away that guy's bicycle.
Technical issues
The above reasoning is based on the following rule (Rules):
(A => B) => To avoid B, you should not do A
This implication can serve as a rule (SecRules) in a rational argument.

Inclusion Statements

Often, we would like to rely on facts or assumptions that have been made beforehand. Rationality allows us to take over an existing body of statements by an inclusion statement. An inclusion statement for a source X takes the form "We assume all statements in X". For example, we can use an inclusion statement to take over all definitions of the national civil law:
We assume all statements in the national civil law.
Technically, an inclusion is an assumption for all the statements in the given set. For example, the national civil law likely contains a statement like the following:
A thief is someone who takes away a thing that he does not own.
Assume that we make the following statements:
We assume all statements in the national civil law.
Bob takes away Alice's bicycle.
Then, these statements are equivalent to the following statements:
A thief is someone who takes away a thing that he does not own.
(... many more statements from the national civil law...)
Bob takes away Alice's bicycle.
This allows us to conclude that Bob is a thief. We can draw this conclusion without actually discussing each statement from the civil law. Thus, inclusion statements are merely a syntactic tool for simplifying the arguments. It is common to use inclusion with bodies of knowledge such as the current theory of physics, the laws of some country or the content of a science book (Authority).


Statements can come from several sources. People, newspapers, books and TV shows all produce statements. These statements are not necessarily true. For example, a book might say "The Hogwarts School of Witchcraft and Wizardry is a Boarding School of magic.". This statement is false. However, rationality can wrap it into a citation statement. A citation statement takes, e.g., the form "X says that ...". In the example, the citation statement is:
The Harry Potter books say that the Hogwarts School of Witchcraft and Wizardry is a Boarding School of magic.
This statement is true. Through citation, wrong or fictional statements can be transformed into true statements. This allows us to discuss the assertions made in a book or in a TV show in a rational way, even if they are false.

We may also choose to assume the statements of the given source (Inclusion). For example, the following is a valid rational argument (Arg):

The Economist states that Europe's gross domestic product sank in 2009.
We assume the statements that the Economist makes.
Europe's gross domestic product sank in 2009.
Technical issues
The above reasoning is based on the following rule (Rules):
We include X & X says A => A
This rule can be used in a rational argument (ChapDed).

Personalized Statements

Some statements are not universally valid, but depend on the speaker. For example, Bob may find Alice beautiful, but everybody else may find her ugly. Then, the statement "Alice is beautiful" is debatable. Still, rationality allows personal statements to be wrapped into rational statements by sentences of the form "I find...". In the example, Bob may say:
I find Alice beautiful.
This sentence is true, no matter whether Alice is actually beautiful or not. A personalized statement gives much less reason for dispute than a universal one. At the same time, it is also weaker, because it allows fewer conclusions. Still, personalized statements may become part of a rational argument (Arg). For example, with appropriate assumptions, we may conclude that Bob will make Alice happy if he tells her his opinion about her appearance — even if she is actually ugly. In fact, a number of disputes could be avoided if people used personalized statements instead of generalizing statements (NoSubjective).

There exist personal statements on which a large majority of people agree. For example, most people will say that a colorful sunset is beautiful. In this case, we may (with a certain degree of sloppiness) say that the sunset is beautiful. However, this is just a simplification. We may actually meet someone who does not find the sunset beautiful.

Beauty is no quality in things themselves: It exists merely in the mind which contemplates them; and each mind perceives a different beauty.
David Hume
Technical Issues
Technically, a personalized statement translates to a binary predicate. For example, instead of making the assertion "beautiful(Alice)", we should make the assertion "beautifulFor(Alice, Bob)". Then, we may generalize that "beautiful(Alice)" holds, if, for all or most people X, it holds that "beautifulFor(Alice, X)".

Meta Statements

Meta statements are statements about other statements. For example, the following statement is a meta statement:
The statement "Alice is beautiful" is not true. (*)
This statement talks about another statement, namely about the sentence "Alice is beautiful". Meta statements can introduce all kinds of problems, notably undecideability (Undecidable). Still, they may be useful. One example for the usefulness of meta-statements is this very essay: It consists of meta statements about rational statements.

People often talk about "the meta level". In fact, there is not only one meta level, but infinitely many. This is because each statement on a meta level can be again the object of a new meta statement, such as the following:

The statement marked with (*) appears in the present essay.
Every meta statement is a statement. Meta statements can be again the subject of other, "higher" meta statements. This shows that there is no dichotomy between "statements" and "meta statements". Everything is just statements.


A definition is a statement that defines one notion to mean another notion. For example, we can define that the word "bachelor" shall mean "unmarried man":
We define a bachelor to be an unmarried man.
Now, instead of using the words "unmarried man", we can simply say "bachelor". Thus, a definition serves as an abbreviation. Technically, a definition is an assumption (Assumptions) about the meaning of a word. Definitions being assumptions, they can be contradictory. For example, if we later define a bachelor as a university diploma, we contradict the above definition. Definitions can also contradict the standard meaning of words. For example, we can also define a bachelor to be a married man, if we wish so. (TalkToArgueWords).

If a word already exists with some standard meaning, a re-definition of that word can be namespaced by attaching a qualifier:

We define a bachelor (in the sense of the education system) as a university diploma.
Even though the word "bachelor" has a predefined common meaning, the word "bachelor (in the sense of the education system)" can be defined freely.

Definitions can be useful to shorten complicated explanations. Such definitions can be implicitly namespaced to the current argument. For example, people can agree to call a country "peaceful" if it was not involved in a war in the last 50 years:

For the sake of simplicity, let's call a country "peaceful" if it has not been involved in a war in the last 50 years.
This definition might not coincide with the standard definition of the word "peaceful", because for a country to be really peaceful, we might also want it to be politically stable in the interior. However, if the definition is namespaced to the current argument, it does not really matter what the word means outside the argument. Once the word has been defined in this way, we can talk about "peaceful countries" in a precise sense, without explaining each time what we mean with it.

Limit Statements

There are cases where we have only a very vague idea of a certain quantity. For example, assume that we do not know how long the next meeting with the boss will take. Assume, however, that we definitively know that meetings with the boss always take longer than 2 hours. Rationality allows us to describe this state by a limit statement. A limit statement is a statement that does not specify a quantity, but an upper or lower bound of that quantity:
The meeting with the boss will take longer than 2 hours.
Even if the speaker does not know the exact quantity (the duration of the meeting), he can still make a rational statement about that quantity with the limited knowledge he has. Such a statement, albeit limited, can be useful. Assume for example that your colleague would like to have an extended lunch break while the boss is in the meeting. Then the above limit statement will definitively be of value to your colleague — even if you cannot tell him the duration of the meeting.

Unfortunately, limit statements are used far too seldom. It often happens that people inquire about a quantity ("Do you know how long the meeting will take?") and the other person, having only a vague idea of the quantity, says that he does not know the answer ("I do not know how long the meeting will take."). But in many cases, just the vague knowledge would already be of use to the first person. Therefore, rather than saying that we do not know the answer, we should provide whatever little information we have ("I do not know how long the meeting will take. All I know is that it will definitively take longer than 2 hours.") (SayIt). In order to trigger such an answer from our interlocutor, we can use a trick and ask for a very absurd bound for the quantity. If we are lucky, our interlocutor will reply with the bounds he knows ("Do you think the meeting will take rather 15 minutes or rather the whole afternoon?" — "Oh, certainly not 15 minutes! Meetings with the boss always take longer than 2 hours."). (See also AvoidIKnow)


A pattern is a description of a certain generic behavior — whether this behavior appears in the real world or not. For example, the following collection of statements is a pattern:
The person believes that he is being attacked and starts fighting back. In reality, however, the person is not being attacked. The enemies are imaginary.
Patterns usually have a name. The above pattern is the Don Quixote pattern, or the Tilting-at-Windmills pattern [Wikipedia / Tilting at Windmills]. Patterns can be expressed as statements with variables or generic names (Rules). They can also be expressed metaphorically (Metaphors). The Windmill-pattern, for example, can be expressed more poetically as follows:
Just then they came in sight of thirty or forty windmills that rise from that plain. And no sooner did Don Quixote see them that he said to his squire, "Do you see over yonder, friend Sancho, thirty or forty hulking giants? I intend to do battle with them and slay them." [Don Quixote, by Miguel de Cervantes]
Seen this way, literature is a collection of patterns.

In the framework of rationality, a pattern definition is the assignment of a certain name ("The Don Quixote pattern") to a certain pattern ("The person believes that he is being attacked and starts fighting back"). A pattern definition does not make any claim about reality. For example, when we define the Don Quixote pattern, we do not claim that people would imagine their enemies. We do not even claim that there exist people who imagine their enemies. We just say that, if someone imagines his enemies, then he can be called a Don Quixote.

Pattern definitions are definitions in the sense of rationality (Definitions). Just like other definitions, pattern definitions serve to abbreviate. It is easier to say "He is a Don Quixote" than to explain that he is someone who imagines his enemies and fights them in vain. As soon as we apply a defined pattern, we do make a statement about reality. Beyond that, patterns serve mainly illustrational purposes.

Personal Preferences

A personal preference is a statement about what the speaker likes or dislikes. For example, if you like the movie "The Life of Brian", you will say
I like "The Life of Brian".
Just like desires (Desires) and other emotional statements, personal preferences mostly do not have non-personal reasons. We may ask for the reason why somebody likes something, but the answer is likely again a personal preference. For example, if we ask why you like "The Life of Brian", you might answer that you like funny movies.

It may seem as if personal preferences are irrational. But, on the contrary, they can be used very effectively in rational arguments (Arg). A statement such as "I like 'The Life of Brian'", for example, may lead you prefer this movie over another one, when it comes to decide what DVD to rent. This is a perfectly rational argument, based upon a supposedly irrational statement.


A generalization is a statement that makes an all-embracing claim about a large class of people, objects or events. One example is
There is no even prime number, except the number 2
Generalizations are statements with a truth value and hence they form valid building blocks of rational arguments. They are true in the following cases:

Other generalizations can be problematic. Examples for such generalizations are "Italians are unpunctual", "The postal service is slow" or "Germans are blond". Such statements are problematic, because, technically speaking, they are proven wrong as soon as we find a single counter-example (SecRuleTruth). Furthermore, if the statement is pejorative, we may actually insult people with it (depending on your moral framework (MoralFrame), see e.g. [Thoughts on Ethics / Insult]). Therefore, generalizations should be watered down, if they are not meant with mathematical rigorosity (NoGen, Personal, Existential, Guarded). We may not automatically assume that a generalization is intended in the watered-down meaning, because some generalizations (such as scientific statements) are indeed meant in their all-embracing meaning.

Guarded Generalizations

A guarded generalization is a statement that talks about the majority of cases without making a claim about all cases. Such statements can, e.g., take one of the following forms: Such statements are weaker than true generalizations (Generalizations). This means in particular that they cannot be used to deduce facts about a particular instance. For example, the following guarded generalization is correct:
In general, people have two legs
However, we may still meet a person that has only one leg.

Guarded generalizations serve to make observations that cannot be formulated as true generalizations (Generalizations) because they do not apply in all cases. Guarded generalizations cannot yield statements about a particular instance, but they can yield disposition statements (Dispositions) and existential statements (Existential) and insight in general.


Rationality emphasizes objectivity and shuns generalizations (NoGen). However, we cannot always just make dry statements about facts of the world. We want to attach a value to them. Rationality allows this in the following cases:
  1. We can say that a certain behavior advances or obstructs a certain goal (SecGoals, Good). We say that the behavior is "good" or "bad" for this goal. We have to mention this goal in order for the judgement to be valid.
  2. We can say that a certain behavior is immoral with respect to a certain moral framework (Moral). If the behavior is immoral with respect to all common moral frameworks, we do not have to specify the framework explicitly. We can say that the behavior is immoral.
  3. We can say that we like or dislike a certain thing, fact or person (Preferences, Personal).
  4. After having gone through a decision process (SecDec), we can judge a certain behavior with respect to certain goals. A decision process can evaluate different behaviors with respect to different goals. This may lead to advice (Advice).

These are the only cases in which rational language allows attaching a value to a fact.


A Schranken-Schluss is a statement that says that, even though a certain property is vague or fuzzy (Fuzzy), the property holds to such a strong degree that it is justified to say so. For example, we can say
Even though the exact definition of "unfriendly" is unclear, a person who calls us a bitch clearly behaves in an unfriendly way.
The property itself can be difficult to assess. In the example, unfriendliness is a trait that is very hard to define. It may appear with a stronger or weaker degree (Fuzzy) and different people will have different opinions about it (Personal). However, if a person behaves in such a clearly unfriendly way that we believe most people agree with us, we may frame this conviction into a Schranken-Schluss statement. This way, we can make rational statements about fuzzy properties, even if the exact definition of the property is unclear or debatable.


A comparison is a statement that says that one thing has a property to a higher degree than another thing. For example, we can say:
An airplane is faster than a car.
The property itself can be difficult to assess. For example, it is difficult to assess whether an airplane is fast (given that rockets, meteorites and light move much faster). Such properties are called "fuzzy properties" and these are inadmissible in rational arguments (Fuzzy). However, the fuzzy property becomes assessible if it is used in a comparison. Even if it is unclear what "fast" means by itself, we can verify that an airplane moves faster than a car.

Nearly Rational

Some statements are not rational in the strict sense. Instead, they implicitly stand for a rational statement (SecStat). Such abstract statements are called nearly rational. Nearly rational statements are useful because they are less clumsy than the purely rational statements they represent. If we want to use a nearly rational statement in an argument (Arg), though, we have to be ready to replace them by their rational counterpart.

Context-dependent Statements

Some statements are only true in a certain context. Take, for example, the following statement:
Barack Obama is the president of the United States
This statement is only valid in the context of a certain time and a certain country (the United States). Therefore, to be rational, such statements have to be accompanied by an explicit form, in which the context is mentioned expressis verbis:
In 2009, Barack Obama was the president of the United States.
This statement will always be true.

Colloquial time references ("today", "now") and colloquial space references ("here") can be handled in a similar way: Whenever someone makes a statement that employs such a colloquial reference, we should think of it as if the reference had been replaced by the actual date or location. For example, if an American citizen says on the 1st of May 2009 that Barack Obama is his president, then we shall read this statement as

On the 1st of May 2009, Barack Obama was the president of the United States
This statement will always be true.

In most cases, the context of a statement is obvious to the reader. If it is not, however, it should be made explicit in order to be a valid rational statement.

Stressed sentences

A stressed sentence is a sentence in which one component (such as the verb or a noun) is stressed. Such a sentence commonly implies that the negation of the sentence holds if this component is replaced by something else.

Take for example the sentence

I know what happened: Bob ate the cake yesterday.
From this sentence, we understand that Bob ate a cake. This sentence by itself does not say anything about what Bob did today, or what Alice did yesterday. However, if stress is added, the sentence starts implying more information:

The implied sense of stressed sentences may not always be clear, because it depends on the audience, the circumstances and the intention of the speaker. Furthermore, the implied meaning of a stressed sentence gets lost when the sentence is passed on to other people or when it is written down. Therefore, stressed sentences should always be accompanied by the implied statement in order to be a valid rational statement.


A reproach is a statement that implies that the listener did something wrong. A reproach often implicitly implies the request to stop, justify, and compensate that behavior. For example, a reproach can be:
You are stepping on my feet!
A reproach always goes together with a moral rule that is supposedly violated (Moral). In the example, the moral rule is
The moral codex of our society calls it morally wrong to hurt another person.
The reproach states that the listener is violating this moral rule. The moral rule, together with the reproach and the moral framework (MoralFrame), will ultimately allow the conclusion (Rules)
You are behaving morally wrong according to the moral codex of our society.

A reproach is only a valid rational statement if it comes with the moral rule. In case the moral rule is not given, one may ask for it. If the moral rule does not exist, then the reproach is a false reproach (FalseReproaches).


A metaphor is a statement that draws an analogy between the state of the world and an object or idea. One famous example is a monologue from Shakespeare's "As you like it", which compares the world to a theater stage:
All the world's a stage,
And all the men and women merely players;
They have their exits and their entrances
The object about which the metaphor talks literally is called the vehicle (in this case: the stage). The object about which the metaphor talks implictly by analogy is called the tenor (in this case: human life) [Wikipedia / Metaphor]. A metaphor is not to be taken literally (the world is not a stage). Rather, a metaphor claims that there are certain aspects that the vehicle and the tenor have in common (people are born and die much like players enter and exit the stage). Metaphors can be expressed rationally by sentences of the form "Metaphorically speaking, ...". In our case, we can say:
Metaphorically speaking, the world is a stage.
To be a rational statement, a metaphor has to come with a supporting statement, outlining the analogy between the vehicle and the tenor:
Humans enter and exit the world much like players enter and exit the stage.
The metaphor statement and its supporting statement embed metaphors into the world of rational arguments.

One of the most frequent pitfalls of rational discussions is to draw conclusions from metaphors. For example, people might start arguing that, since the world is a stage, there should be someone who has written the play. This, in turn, entails all kinds of unsupported conclusions (predestination of our behavior, existence of an audience etc.). Worse, this pitfall can be used to put words in somebody's mouth ("Shakespeare has said that the world is a stage. Hence he believed that our actions are predetermined by some kind of script."). A metaphor makes a statement only about one single analogy between the vehicle and the tenor. It does not allow us to conlude that there would be other analogies.

Metaphors may seem like very weak rational statements. And indeed, metaphors by themselves cannot be used to deduce other statements. Rather, metaphors serve to illustrate a point. Metaphors are more catchy and easier to remember than pure descriptive statements. For example, we can say

At Macrosoft, the customer is the king.
This is a metaphor. The supporting statement is:
At Macrosoft, the customer is a person that is very important — as important as the king is in a kingdom.
In this way, a metaphor can abbreviate more complex statements.

Abstract statements

An abstract statement is a statement whose literal reading does not yield concrete truth conditions. For example, the following statement is an abstract statement:
Germany is a peaceful country.
It is not clear what exactly is meant by "peaceful". Therefore, in order to be rational, an abstract statement has to be accompanied by explanation statements, i.e., by non-abstract statements that are true if and only if the abstract statement shall be considered true. In the example, the explanation statements could be:
Germany has not been involved in a war of aggression in the last 50 years.
Germany has had no civil war in the last 50 years.
An abstract statement serves to abbreviate the explanation statements. More often than not, the explanation statements are obvious for the reader or listener. In this case, they are implictly assumed. If they are not obvious, we may ask the speaker for the explanation statements ("What do you mean by that?").


A policy is a goal (Goals) whose literal meaning does not directly yield truth conditions for the desired state. For example, the following statement is a policy:
Our country shall be a multi-cultural country.
It is not directly clear what this goal implies. Therefore, a policy has to be accompanied by concrete goals that push the state of the world closer to the goal of the policy. Finding these goals is called operationalizing the policy. In the example, such an analysis could yield: If the operationalization is obvious, it can be omitted. If it does not exist, the statement is not rational.

Fuzzy statements

A fuzzy property is a characteristics that can be fulfilled to a certain degree. For example, properties such as "easy", "expensive" or "important" are fuzzy in nature. If a thing has a fuzzy property to a certain degree, then the thing also has the opposite property to a certain degree. For example, writing your name is "easy". However, it is still so complicated that a baby cannot do it.

Therefore, fuzzy properties are admissible in rational arguments only if they appear in comparisons (Comparisons) or schranken-schlusses (Schrankenschluss). Alternatively, fuzzy statements can be wrapped into a simple statement (Simple) that says that the fuzzy statement holds to a certain degree:

98% of people in the US find writing their name easy.

Loaded statements

A loaded statement is a statement that requires implicitly that another statement is true. Consider for example the question
Have you stopped beating your wife?
Whether you answer with "yes" or with "no", it will always imply that you did beat your wife. In other words, the statement "You have stopped beating your wife" is only a valid statement if a certain pre-condition is fulfilled. This pre-condition is called the presupposition. The statement itself is the loaded statement. Loaded statements are only rational statements if the presupposition is fulfilled. Otherwise, they are not admissable in rational arguments.

We cannot always avoid loaded statements. For example, the statement "The Earth is round" presupposes the existence of the Earth. Presuppositions can be factored out by assuming them (Assumptions), by proving them or by using them as a condition (Implications). This way, loaded statements can become rational statements.


There are types of statements that look rational, but that are poisonous to a rational argument. These are non-rational statements. This section lists a few of them.

Implicit statements

An implicit statement is a statement that is intended by the speaker, often also heard by the listener, but not made explicit in what is said. Examples are:

Implicit statements convey information without making it the subject of discourse. Thereby, implicit statements violate the call for clarity and explicitness of rationality (Speak). Therefore, implicit statements are not rational. They have no place in a rational argument (Arg). They should be uncovered wherever possible (Uncover). Indeed, implicit statements are the root of a considerable number of communication problems (NoReproach, NoContradiction, Uncover, Simplicity).

Principle of Simplicity

Sentences can have multiple meanings and readings, and also implicit meanings (Implicit). These lead to misunderstandings. The Principle of Simplicity assumes that the intended meaning of a sentence is the meaning that cannot be expressed easily more explicitly [TOE / Declaration]. For example, assume that someone says "I will be at the party tonight". There are different possible readings of this phrase: It is easy to express the second meaning more explicitly — simply by saying "I plan to be at the party tonight". By contrast, it is not trivial to express the first meaning in a simpler way than by the above statement. Therefore, the meaning of the sentence is that the person will be at the party tonight.

Cultural statements

Not all statements that people make are rational statements in the sense of this essay — even if they may seem so. For example, in many cultures, it is common to say "yes", even if one does not agree. In these cases, politeness is valued more than the literal meaning of the words. Another example is the US, where it is common to ask "How are you?", even though people rarely care. It is common to answer "great!" even though this is rarely true. In a similar spirit, some cultures may shun explicit statements about sensitive topics, preferring an implicit understanding between speaker and listener instead. This attitude may also vary from speaker to speaker.

Rationality is based on the principles of explicitness and exactness (Speak). Therefore, in order to incorporate such culturally colored statements into a rational argument, the statements have to be "translated" first into explicit statements. This may potentially come at the cost of lost politeness or unwelcome explicitness. At the same time, it yields all the benefits of rationality (Use) and cross-cultural interoperability.

False Reproaches

A reproach is a statement that implies that the listener is doing something wrong (Reproaches). A reproach always goes hand in hand with a moral rule that is being violated. A false reproach is a statement that is intended to be a reproach, but does not have this moral rule. In other words, a false reproach claims that some behavior is wrong, even though there is no reason why it is wrong.

An example for a false reproach is:

You did not come to the party yesterday!
If uttered with an angry intonation, this sentence sounds like a reproach. Yet, the listener probably did not violate any moral rule by not coming to the party yesterday. Therefore, the reproach is a false reproach. One appropriate answer to a false reproach is
So what?
The phenomenon of false reproches is illustrated in the following Hägar quote:
Helga: You simply sit here, guzzle, and drink all day! (walks off in protest)
Hägar: She says this as if it were something bad...
Chris Browne in "Hägar the Horrible"

Colored language

Colored language is wording that attempts to influence the listener or reader by appealing to emotion [Wikipedia / Loaded language]. Colored language as understood in this essay involves in particular Colored language always conveys implicit statements. Therefore, colored language should be avoided for rational arguments (Speak). Colored words should be replaced by their neutral counterparts or made explicit in a new sentence. As an example, consider the colored statement
The pope claims that contraception does not help against AIDS.
This statement cites the pope. In addition, it implies that the pope's statement would be wrong. A rational way to express this is
The pope said that contraception does not help against AIDS.
I believe that contraception does help against AIDS.
These statements have decomposed the colored language into a citation (Citations) and a belief (Beliefs). Colored language also serves for sideswipes (Sideswipes).
Technical issues
It is no coincidence that many of the examples come from Wikipedia's manual of style [Wikipedia / Wikipedia:Words to watch]. Wikipedia, as well as this essay, strive for making clear statements.


A sideswipe is a statement that values or devalues something or someone or a statement, while this assessment is not the main content of the statement. This includes for example Sideswipes can hide a disputable statement in an objective statement. Thereby, sideswipes do not fulfill the requirement of clarity and explicitness in rationality (Speak). Therefore, sideswipes should be avoided in rational arguments. They should be decomposed and made explicit, for example as follows:
I saw my brother in the train.
I think he is idiotic.
These statements are still not very polite, but at least rational: They express a fact and a personal opinion (Personal).

Empty phrases

Empty phrases are phrases that carry no significant meaning. These include for example

These phrases do not carry meaning. Therefore, they have no use in rational language (Speak). While they are not harmful, and while it may not always be possible to avoid them, avoiding them is good rational practice (StdGoals, Flooding).

Noisy phrases

Noisy phrases are phrases that emphasize something emotionally without adding new information. While these phrases do not say anything wrong, they usually heat up the discussion needlessly. Therefore, it is good rational practice to see where they can be avoided (Speak, StdGoals, Flooding). Examples are:

Unfalsifiable Statements

A statement is falsifiable if we could theoretically find out if it was wrong. In other words, a statement is falsifiable if we can imagine a situation that proves that the statement is false. For example, the following statements are falsifiable:

This seems to be a very natural property of statements. Yet, it is not. The following statements are not falsifiable:

Falsifiability is about the possibility that, in theory, a counter-argument could be found. Thereby, falsifiability is a purely theoretical property of a statement — it does not actually require proving or disproving something.

This theoretical property has a very concrete consequence: For every falsifiable statement, there is some hypothetical situation that proves it wrong. This means that, if the statement is true, this hypothetical situation will not appear. For example, if it is true that "the Earth has only one moon", then the situation where we find a second moon will not appear. This means that a falsifiable statement always makes a claim about the real world. By taking a position concerning the world, falsifiable statements become vulnerable — and thereby useful.

Non-falsifiable statements have no such benefit. They not exclude any state of the world or any event that may happen. (Because, if they excluded a state or event, they would become falsifiable) This means that such a statement carries no predictive meaning about the world (Conclusions). If you assume such a statement, you will not be able to predict that some things will happen or will not happen. Therefore, you are as wise as before.

Nothing about the real world can be deduced from a non-falsifiable argument. Nothing can prove or disprove a non-falsifiable statement. Therefore, it simply does not make sense to assume that a non-falsifiable statement is true (or false) in order to learn something about the world. Such statements may only be used as assumptions, and only in purely theoretial rational arguments. Once they served as assumptions, the conclusions of the argument will also be unfalsifiable. We should never hope to prove or disprove an unfalsifiable hypothesis from real world facts (Popper).

Unfortunately, non-falsifiable statements abound and create never-ending disputes (see, e.g., [Thoughts on Atheism / Supported]). Such statements should simply not be argued about, because their truth or falsity has no effect on the world.

For every statement, ask yourself what you would accept as a proof for its falsehood.
If there is no such thing, the statement is unfalsifiable. Abandon it.

General Valuations

People seem to love statements that value or devalue a thing, country, event or person. We will call these statements general valuations. Examples for such statements are "Life in Italy is great" or "The party was crap". Such statements are very likely to cause debate. This is because their truth conditions are not clear. What feels great for one person may feel awkward for another. Every argument that says that something is great will find a matching argument that says it is bad. For example, if we say that life in Italy is great, because it is always sunny, we may also argue that life is not so great because of corruption.

Since general valuations have no clear truth conditions, they are not rational statements (Speak, Arg). If we want to speak rationally, we can instead

If a general valuation occurs in a discussion, we should not start finding arguments against it in order to prove it wrong. This is because a general valuation cannot, by its very character, be part of a rational argument (Arg). Rather, a general valuation should be seen as an invitation to find positive and negative aspects of the subject. In the example, the statement "Life in Italy is great" should be seen as an invitation to find positive and negative aspects of life in Italy. We should not hope to prove or refute the statement that "Life in Italy is great", because it is not a rational statement (NoArgGenVal).

Abstract universal hypotheses

An abstract universal hypothesis is a general statement about the world that does not have clear truth conditions. This means that the statement cannot be instantiated, that it is not true in all instantiations (Instantiations), or that it is not possible to falsify it (Unfalsifiable), to make it concrete (Abstract) or to operationalize it (Policies). Such statements often play on metaphors without tenor (Metaphors), fuzzy properties without comparison (Fuzzy) or abstract statements without explanations (Abstract).

Examples are:

Since abstract universal hypotheses lack clear truth conditions, they are not rational statements (Speak). They should be replaced by metaphors (Metaphors), patterns (Patterns), theories (Theories) or more concrete statements (Basic, SecNearly).

In so far as a scientific statement speaks about reality, it must be falsifiable.
And in so far as it is not falsifiable, it does not speak about reality.
Karl Popper

Founding Statements

If we always wanted to give reasons for our statements, we would end up in an infinite cycle — always giving a reason for the previous reason (Basic). This is why we have to rely on founding statements that require no further reasons. In the brick metaphor (SecDef), these statements are those that need no other bricks below them. Whether or not a statement can be a founding statement depends on its credibility. Different types of statements (as introduced in the previous section, SecStat) can serve as founding statements, depending on whether we trust them or not. In the brick metaphor, this means that we can use bricks of different colors as the foundations of our towers.

Founding statements

Rationality always questions statements. Even seemingly obvious statements can be questioned, because they can be plain wrong. This includes, for example, the things we see: A spoon put in a glass of water looks bent — even though it is not. Thus, strictly speaking, we have no way of making statements about reality that do not deserve being questioned (Objective). However, if we always question our statements, we would never be able to make any statement. This is because every statement we make requires other statements as justification. These statements require again other statements as justification and so forth (Basic). Therefore, if we want to make statements, we have to assume some statements.

The statements that we assume in an argument are called the founding statements. A founding statement is a statement that we will not question not for the current argument [Wikipedia / Basic belief]. This section will list some of the types of statements that make good founding statements. They are "good" in the sense that they allow for true predictions (Truth).

Founding statements are not immune to questioning. They can be (and should be) put in doubt whenever they appear suspicious (Wrong). They can even be wrong. The question of truth is treated further down in this essay (Truth). The current section just lists statements that make good working hypotheses for our arguments (Arg).

Statements about the speaker's emotional state

People know in general how they are feeling. Therefore, the following types of statements are valid founding statements, if they are about the speaker himself: These statements do not require justification.

Statements about perceptual evidence

Perceptual evidence is something that can be seen or touched or otherwise perceived. A perceptual statement says that the speaker has a certain perception, e.g.
I have the impression of seeing something green.
A statement about one's own perceptual evidence is a valid founding statement.

Statements about reality

If we see or otherwise perceive something, then the fact that we perceive that something is trivially true (Perceptual). However, this does not mean that what we perceive is actually the case in reality.

However, in the vast majority of cases, our perceptual evidence does correspond to reality (in the sense of Reality). Therefore, the assumption that perceptual evidence corresponds to reality is a good founding statement (Founding). It is such a good founding statement that we will omit the distinction between what someone perceives and the state of reality. Instead of saying "I perceive a green apple", we will just say "there is a green apple".

There are cases where perceptual statements are justly put in doubt. People may hallucinate or succumb to optical illusions. However, in the vast majority of cases, perceptual evidence is a reasonable working hypothesis.

Standard Goals

People have different goals in life (Goals). We may not assume that they share their goals. However, here are some of the more common goals, where it is reasonable to assume that most people share them:

For people whose goal is to be rational (Rational), we may also assume the following sub-goals:

Note that a goal does not mean that a person actually thrives for it (or for its sub-goals). This is because there can be conflicting goals. It can also be because the person does not know consciously about the goal or does know how to achieve it — or for a wide variety of other reasons.

Inclusion statements from authoritative sources

Strictly speaking, there is no such thing as an ultimate authority in rational thinking. Statements by scientists can be questioned just like statements by the police, by the president, by the king, by Jesus or by the Dalai Lama (Decompose). However, it is common to rely on authorities in domains in which we are not knowledgeable. For example, it is common to assume statements made in scientific consensus literature. These are usually good founding statements (Inclusion).

Statements about the meaning of words

For this essay, words are artifacts that humans create to express and share theories. The meaning of a word is nothing that is fixed in nature. Rather, it is the set of logical rules that the word appears in (Mean). Then the question arises how we can ensure that people mean the same thing when they use a word. Theoretically, people could be understanding completely different things when they talk to each other (and this is indeed sometimes the case). Yet, it is reasonable (in the sense of Truth) to assume that the people with whom we talk have the same understanding of basic words. Otherwise, we would probably not have been able to talk with them in the first place. Indeed, in most cases, natural language succeeds quite well in transmitting its message — as the reader experiences while reading this text. Therefore, it is justified to assume a basic shared understanding of common words (Language, Mean).

For the other, non-basic words, there is the dictionary. The dictionary explains the meaning of a more complex word through more basic words (Mean). We can include the dictionary into our argument by inclusion (Inclusion). Thereby, words mean what the dictionary says. It is a reasonable assumption to assume the inclusion of the dictionary.

It is also possible to claim that a word is often used with a different meaning than the one in the dictionary. Such a claim is not a founding statement and would require reasons. It is also possible to decide to use a word in a different meaning (Definitions).

Previous results

If previous arguments have already established a statement, it is valid to take that statement over as a founding statement. This is because, if the statement is questioned, one already has a way to prove it. In practice, this technique is very common. It is simply inefficient to re-build every argument from scratch.

Common knowledge

There are some statements of common knowledge that are so obvious that they are commonly taken for true. These include knowledge about basic processes of nature, basic properties of things or basic facts of this world. The following statements are examples of common knowledge: In most cases, these are statements on which all interlocutors agree on without further decomposition. There is always the danger to assume a statement as common knowledge that is actually wrong (Wrong). However, in most cases, common knowledge yields very reasonable founding statements.


An assumption is a statement that we take for true for the sake of the argument (Arg). Thus, assumptions are those statements that we are pretty sure of, that we do not want to discuss, and where we assume that our interlocutor shares this opinion. This does not make these statements true, to be sure. Assumptions can be false.

An assumption typically takes the form

I/We assume that...
Assumptions serve to build up an argument (Arg). They can also to make a point in a hypothetical world (see Scenarios). They can also be used to postpone the discussion of a statement about the real world.

Common Assumptions

It is common to make the assumption (Assumptions) that things happen the way they usually happen. Examples for these assumptions are: These assumptions do not need to be true, to be sure. But if we wanted to enumerate or even prove these assumptions each time we make a rational argument, we would never get to any interesting conclusion. Therefore, it is common to make these assumptions implicitly. They form very common founding statements.

Once we are done with our argument, we can revisit the common assumptions and elaborate cases where the common assumptions do not hold. For example, when planning a trip, it can be useful to have "a plan B" in case the public transport to the airport is blocked (PlanB). It is reasonable to revisit first the assumptions that are least likely to hold.

Technical issues
The common assumptions can also be made explicit by stating "Under the common assumptions" (or, in Latin "Praesumens praesumendum") before an argument.

Logical Axiom Schemata

Axiom schemata are statements that contain variables for other statements (Axioms). Some axiom schemata are necessarily universally valid. For example, the following axiom schema is universally valid:
If X is true and Y is true, then Y is true and X is true.
(If it rains and we have fog, then we have fog and it rains.) Such axiom schemata make good founding statements. We will see such axiom schemata in further down (SecRules).



This part introduces rules (SecRules) and their truth conditions (SecRuleTruth). Rules allow deducing new statements from known statements. The part goes on to discuss the concepts of truth and proofs (SecTruth). After these rather technical sections, we discuss other, informal, techniques of rational thinking (SecTec).


Rules are one particular type of rational statements. A rule says that certain things entail other things. Rules are an essential notion of rationality. This section will start with the notion of implications, and then generalize it to the notion of rules.


An implication is a statement that says that if a set of statements are true, then another statement must be true as well. For example, the following statement is an implication:
If the lamp is plugged in and switched on, then it will light up
The statement in the "if" part of the statement is called the premise. The premise can be a simple statement (Simple) or a conjunction or multiple statements (".. and...") or any other complex statement. The statement following "then" is called the conclusion of the implication. Likewise, it can be arbitrarily complex. We will denote an implication with the premise P and the conclusion C as follows:
P => C

An implication, as any other statement, can be true or false. In the example, the implication may be false (if the lamp is broken). Yet, the statement is still an implication nevertheless.

In everyday language, implications can be formulated more loosely. Here are some examples of statements that are sloppily formulated, but still acceptable implications:

Note that these statements are implications, no matter whether we agree with them or not (Simple). An implication only works in one direction: The premise implies the conclusion. If the conclusion holds, this does not tell us much about the conditions in general. It is a logical fallacy to use the fact that the conclusion holds to deduce that the conditions hold (SecNonRatArg).

Unfortunately, people sometimes read implications the other way round. A journal recently reported that scientists discovered that "If the wind blows from a certain direction with a certain strength, then the water of the Red Sea is blown away, leaving a land passage between the two shores.". From this implication, the journal deduced that "If the water of the Red Sea yields a land passage, then the wind blows from a certain direction". (That is: The journal read the implication the other way round.) Therefore, the journal concluded, God did not part the waters as described in the Bible. This line of reasoning is false. Even if the wind can part the waters, it need not be the only force that can do so. Furthermore, God might also have used the wind to part the waters. Note that the argument used in the journal is false no matter whether God actually parted the waters or not. Even if we believe that it was indeed the wind that parted the waters, the way the journal argues is wrong.


A rule is an implication (Implication) that talks about all people or all things that fulfill a certain condition. Usually, a rule starts with "If someone..." or "If something". For example, the following statement is a rule:
If someone steals something, he is a thief
This statement is an implication that makes an assertion about all people who fulfill a certain condition. Hence it is a rule. Note that the statement does not say that every person is a thief. It just says that, if someone steals, then he is a thief — and this observation applies to every person. To be more formal, we will express a quantified statement with variables in place of the pronouns. This allows us to express more complex constellations:
If X steals something from Y, then X is a thief and Y is a victim of theft.

Note that a rule does not have to be true. The following rule, e.g., is wrong:

If X steals something from Y, then X will later give it back to Y.
We will deal with the truth of rules further down (SecRuleTruth).


Instantiation means replacing the variables in a rule (Rules) by concrete people or things. For example, if we have the rule
If X steals something, then X is a thief.
then we may use instantiation to produce
If Bob steals something, then Bob is a thief.
If Alice steals something, then Alice is a thief.
Thus, instantiation makes implications out of rules (Implications). This is one of the fundamental techniques of rationality.
Technical issues
Technically, the instantiation corresponds to the unification process in resolution or to a substitution process in general. Note that the instantiation is usually defined itself by rules with variables ("If we have a rule R..."). Thus, instantiation requires itself for its own definition. Hence, it is ill-defined. I have not found a way to define the principle of substitution without actually using substitution. Neither has he found any text book that explains substitution without already relying on it on the meta level. Thus, substitution seems to be an atomic concept that has to be defined outside the system.

Axiom Schemata

An axiom schema is a rule (Rules) that has variables for other statements. For example, the following statement is an axiom schema:
If Bob says X, then X.
Much like rules (Rules), axiom schemata can be instantiated (Instantiations), i.e., one can replace the variables by statements. In the example, we can produce:
If Bob says he's drunk, then he's drunk.
In this case, X has been replaced by the sentence "He's drunk". In many respects, rules and axiom schemata behave the same. Both have variables that can be instantiated. Therefore, this essay will not distinguish between rules and axiom schemata.
Technical issues
Traditionally, rules and axiom schemata often take different roles. In the present essay, they don't (URS).

Claim rules

Any simple statement (SecStat) can be transformed into a rule. This works by using the statement as a conclusion, and using as premise a statement that is trivially true, such as "1=1". For example, the statement "The Earth is not flat" can be transformed into the following rule:
If 1=1, then the Earth is not flat

Circular rules

A rule (Rules) is circular, if its consequence is one of the premises. The following rule, e.g., is circular:
If X receives his diploma and X weeps for joy, then X receives his diploma.
One particular instance of a circular rule is a rule where the premise is the conclusion:
If X receives his diploma, then X receives his diploma.

Time rule

A time rule says that whenever something happens, something else happens, too. The following statement, e.g., is a time rule:
Whenever Bob sings, it rains.
Such a statement stand implicitly for a rule with a variable for the time point. In the example, the rule is:
If Bob sings at time point X, then it rains at time point X.
We will instantiate time rules (Instantiations) in a more casual form. For example, we will instantiate the above rule as
If Bob sings at time point 2012-06-08 15:45, then it rains at time point 2012-06-08 15:45.
If Bob sings today, then it rains today.
If Bob sings now, then it rains now.

Class rules

A class rule is a statement about all instances of a certain concept. For example, the following statement is a class rule about dogs:
Dogs are mammals.
Such a statement stands implicitly for the following rule (Rules):
If X is a dog, then X is a mammal.
By instantiation (Instantiations), this statement can yield
If Bello is a dog, then Bello is a mammal.
This can help us deduce, e.g.,
Bello is a mammal.

These kind of deductions work only if the statement about classes is phrased as a rule. Therefore, class statements have to be implicitly understood as rules when used in a rational argument.

Other Rules

Rules and axiom schemata can formalize many real world laws. Examples for such rules are

Such rules are used to formalize a domain of discourse. The rules are usually employed as assumptions (Assumptions) in a rational argument. Note that the rules can be, but do not have to be prescriptive. For example, rules can formalize legal or moral rules. Yet, in our context, rules are mainly descriptive: They say that certain things imply other things. If we use such a rule as an assumption, we assume that the rule describes reality.

The Truth of Rules

In this section, we will discuss when a rule is true and when it is wrong. Crucially, we will discuss the truth of a rule not with respect to universal truth, but with respect to our knowledge.


Knowledge is a set of simple statements (Simple) or negated simple statements (Negations). For example, the following is such a set of statements:
Bob loves Alice.
It is not the case that the Earth is flat.
Now let us consider another simple statement, S. This statement S can fall into three classes:
  1. If S appears in the set of statements, then we will call S true with respect to our knowledge,
  2. If S appears negated in the set of statements, or if S is negated, and appears positive in the set of statements, then we will call S false with respect to our knowledge,
  3. In all other cases, we will call S unknown with respect to our knowledge.
Here are examples of such evaluations:

Note that the truth of a statement is, up to now, only defined with respect to a given knowledge. If a statement is true with respect to our knowledge, this does not mean that the statement corresponds to reality. It does not even mean that the "knowledge" corresponds to reality. We will discuss the more general notion of reality later (Truth).

In all of the following, we assume a given set of statements as knowledge. We assume that this set contains roughly all common sense knowledge (the Earth is not flat, etc.). Thus, the notions of "true" and "false" will be defined with respect to this set of statements for now.

Truth of an implication

An implication (Implications) expresses an if-then-situation. The if-part is the premise of the implication, and the then-part is the consequence of the implication. An implication is wrong with respect to our knowledge (Knowledge), if the premise is true, but the consequence is false. Consider the following example:
If the moon orbits around the Earth, then the Earth must be flat.
In this implication, the premise is true, but the consequence is false. In this case, we the implication does not hold.

In all other cases, the implication is said to be true. The following implication, e.g., is true:

If the moon orbits around the Earth, then the Earth is ball-shaped.
In this case, the implication is true, because both premise and consequence are true. Note that there need not be a causal relationship between premise and consequence to make the implication true. The implication is simply true if both components are true.

The implication is also said to be true if the premise is false. With a false premise, we can make an arbitrary number of true implications:

If the Earth is flat, then Bill Gates is poor.
If the Earth is flat, then Alice loves Bob.
In these cases, the implication is said to be "vacuously true".
So mancher Hahn denkt, die Sonne würde wegen ihm aufgehen.
(Some cocks think the sun rises because of them)
Theodor Fontane

Existential Variables

A variable that appears in the conclusion of a rule (Rules), but not in the premise is called an existential variable. Such variables mean that there is something unspecified that will take the role of the variable. Consider the following example:
If X keeps sending secret SMS all day long, then probably X is in love with Y.
Here, the Y is an existential variable. The rule says that there must be some person Y with whom X is in love, but it does not give the name of that person. Y is best understood as "someone". That someone may be a different person for each X.

Existential variables may not be instantiated (Instantiations). Thus, the instantiations of the rule are:

If Bob keeps sending secret SMS all day long, then Bob is in love with Y.
If Alice keeps sending secret SMS all day long, then Alice is in love with Y.
The existential variable Y remains alive in the instantiations.

If the conclusion of an instantiated rule contains an existential variable, then the conclusion is true with respect to our knowledge (Knowledge), if we can find a value for the variable such that the conclusion is true. Suppose, for example, the following knowledge:

Bob keeps sending secret SMS all day long.
Carla is in love with Bob.
Alice keeps sending secret SMS all day long.
Alice is in love with Bob.
Alice is in love with Frank.
With this knowledge, the conclusion "Bob is in love with Y" is false: There is no value for Y such that the statement is true with respect to our knowledge. The conclusion "Alice is in love with Y", in contrast, is true: There is a value for Y such that the conclusion is true with respect to our knowledge. In fact, there are even two values: Bob and Frank.

Confidence of a rule

A rule (Rules) generalizes an implication (Implications). Consider, e.g., the rule "Alice likes everything that is sweet". Formally, this rule is:
If X is sweet, then Alice likes X.
Through instantiation (Instantiations), this rule can be applied to every single object:
If chocolate is sweet, then Alice likes chocolate.
If honey is sweet, then Alice likes honey.
If cake is sweet, then Alice likes cake.
If soup is sweet, then Alice likes soup.
Now let us assume the following knowledge (Knowledge):
Chocolate is sweet.
Alice likes chocolate.
Honey is sweet.
Alice likes honey.
Cake is sweet.
Let us see whether the instantiations of our rule are true or false with respect to our knowledge . We have already seen (ImpTruth) that the last instantiation (the one with soup) is vacuously true, since soup is not sweet. We say that the rule does not apply in this case.

Now let us look at the cases where the rule applies. These are the first 3 instantiations of the rule. The consequence of the rule is true in the first instantiation (with chocolate), in the second (with honey), but not in the third (with cake). Thus, the rule is correct in 2 out of 3 cases where is applies. Thus, its confidence is 2/3 = 66%. This means that the rule is correct 66% of the cases.

Formally, the confidence of a rule with respect to our knowledge (Knowledge) is the number of instantiations where both the premise and the consequence are true, divided by the number of instantiations where the premise is true.

If the confidence is 100%, we say that the rule holds in our knowledge. If the confidence is not 100%, we call the rule incorrect.

Support of a rule

The confidence of a rule indicates the proportion of cases where the rule is correct (Rules, Confidence). There is a second important measure, the support of a rule. The support of a rule with respect to our knowledge (Knowledge) is the number of instantiations where both the premise and the conclusion are true (Instantiations). The support of a rule is important to deal with rules such as the following:
If X is called Fabian and if X writes this essay, then X loves logic.
This rule is true for all instantiations. Hence, it has a confidence of 100% (Confidence). However, it has only one single instantiation where the premise is true. Hence, it is not of great use. It has a low support.
Technical issues
Confidence and support correspond to the notions of confidence and support in the context of association rule mining in database research.

Applicable rules

A rule is applicable to our knowledge (Knowledge), if there is an instantiation where the premise is true (Instantiations). Consider, e.g., the following rule:
If X is below 18 years of age, and if X is accompanied by his grandchildren, then X may use the train for free.
This rule may stem from the travel regulations of the train operator (OtherRules). This rule will most likely have no instantiation where the premise is true. Hence, it is not applicable. This means also that it is not supported (Support).

Now let us look at the following rule:

If X behaves nice to his fellow humans, then X will go to heaven.
There may be people who are always nice to their fellow humans. Hence, the rule is applicable. However, the consequence of the rule is always unknown. Therefore, the rule is not supported (Support). It is predictive (Predictiveness).

Explicative Rules

A rule (Rules) is explicative with respect to our knowledge (Knowledge), if it has high support (Support) and high confidence (Confidence). This means that the rule correctly predicts many statements in our knowledge, and it does not predict many wrong ones. We say that the rule "explains" our knowledge.

As an example, assume that we have knowledge about countries in the Americas. We discover the rule "Whenever I cross a border, there is a border control". This rule is explicative, because it has high confidence and high support. Indeed, whenever we go from one country to another country in the Americas, there is a border control. The rule ceases to be explicative once we gain knowledge about European countries. Large parts of Europe have no border controls.

Coverage of a rule

Confidence and support are the main properties of rules (Confidence, Rules, Support). There is a third property, which plays a lesser role: the coverage. Consider, e.g., the following example:
If someone always eats fatty food, he has an unhealthy life.
This rule has a high confidence with respect to our knowledge (Knowledge), because whenever someone always eats fatty food, he has an unhealthy life (Confidence). Yet, there are many more ways to lead an unhealthy life. Thus, the rule explains some cases of unhealthiness, but not all of them. This is formalized by the concept of coverage. The coverage of a rule with respect to our knowledge (Knowledge) is the number of instantiations (Instantiations) where both premise and consequence are true, divided by the number of instantiations where the consequence is true. In the example, the coverage of the rule is the number of people who eat fatty food and have an unhealthy life, divided by the total number of people with an unhealthy life.

The coverage of a rule is the confidence of the inverse of the rule, where premise and consequence are interchanged.

Technical issues
Confidence can be seen as the precision of a rule in the sense of information retrieval sciences. The coverage is the recall of the rule, in the sense that it measures the cases where the consequence is true but the rule did not predict it. This explains the dualism between coverage and confidence, where coverage is the confidence of the inverse of the rule.

In some sense, confidence corresponds to the correctness, and coverage corresponds to the completeness of the rule.

Negating Rules

A rule has a premise and a consequence (Rules). Each of these components can be negated(Negations). Assume for example the following rule:
If X smokes excessively, X will attract cancer
We can now negate the parts of the rule:

Precise rules

A rule is more precise than another rule in our knowledge, if both have the same premise, and if the consequence of the first rule implies the consequence of the second rule with high confidence (Rules, Knowledge, Confidence). For example, consider the two following rules:
Whenever X eats toothpaste, X gets diarrhea.
Whenever X eats toothpaste, X does not feel well.
The first rule is more precise than the second rule, because the consequence of the first implies the consequence of the second. In other words, the following rule has high confidence in our knowledge (Knowledge, Confidence):
If X gets diarrhea, X does not feel well.
A more precise rule usually has higher coverage (Coverage). If that is the case, we call the rule factually more precise. The goal is usually to make the rule as factually precise as possible (GoodRules). If there is another rule that is factually more precise, then our rule is not factually precise.

Too Precise Rules

We want rules to be as precise as possible (PreciseRules). However, rules can also be too precise. As an example, assume that we visit a coal mine. We see that every miner has his personal pickaxe. So we want the general rule
If M is a miner, then M has a pickaxe.
However, this rule is not precise, because we could make it more precise by saying:
If M is a miner, then M has one of the pickaxes of this coal mine.
This rule has the same support and confidence on our knowledge (Support, Confidence, Knowledge). It is also precise (PreciseRules). However, it is too precise, because if we ever meet a coal miner from another mine, the rule will turn out false.

Thus, preciseness and confidence are a trade-off: We can make the rule more precise, but then we risk making false predictions on new evidence.

Predictive Rules

A rule is predictive with respect to our knowledge (Rules, Knowledge), if some of its instantiations have a true premise and an unknown conclusion. For example, the following rule is predictive:
Whenever the sky is cloudy, it will rain the next day
Assume that we know the weather of today and that we do not know tomorrow's weather (Knowledge). Assume also that the sky is cloudy today. Then the rule is predictive. It makes a prediction about tomorrow's weather.

Our goal will be to find rules that are predictive, because they tell us something that we do not yet know (GoodRules). At the same time, we do not want only conclusions about the future. We also want the rule to make some conclusions about the past or present, so that we can verify them with today's knowledge. In the example, the rule makes also conclusions about the weather in the past. Thus, we can check the confidence of the rule (Confidence). Only if this confidence is high, we will trust the predictions of the rule for the future. Thus, we want the rule to be both supported (having non-zero support (Support) and coverage (Coverage)), and predictive. At the same time, the rule may not be too predictive (TooPredictive).

Prediction is very difficult, especially about the future.
Niels Bohr

Too Predictive Rules

In general, we want rules to be predictive (Rules, Predictiveness). However, rules can also be too predictive. Consider for example the following rule:
If X is a fire, then X has been lit an intelligent being.
This rule is true in our knowledge (Knowledge) for a large number of fires, namely those lit by humans. For a large number of non-human fires, the rule postulates that they have been lit by an intelligent being (such as for example a demon or ghost). This rule has a high support (Support), it has a high confidence (Confidence), and it is also predictive (Predictiveness). It is also general but not too general (GeneralRules). It is also precise, because we cannot make it more precise (PreciseRules). However, it is too predictive, in the sense that it predicts a generality for which we have no support. With the same argument, we could produce the following rule:
If X is a fire, then X has been lit by a being with two eyes.
Both rules are nonsense. More formally, the rules are too predictive, because if we add the conclusion to the premise, then the rule is not precise. In our example, we would produce the rule:
If X is a fire and X has been lit by a being with two eyes, then X has been lit by a being with two eyes.
This rule is circular (CircularRules) and thus trivially true. Apart from that, it is also not precise (PreciseRules). This is because the following rule is more precise:
If X is a fire and X has been lit by a being with two eyes, then X has been lit by a human.
Whenever we can construct such a more precise rule, then the original rule is too predictive. With this thought experiment, we can discredit rules that are draw conclusions for which there is no evidence.

General rules

A rule is more general than another rule in our knowledge, if both have the same conclusion, and if the premise of the second implies the premise of the first rule with high confidence (Rules, Knowledge, Confidence). For example, consider the two following rules:
If X eats too much sweets, then X attracts caries.
If X eats too much chocolate, then X attracts caries
The premise of the second rule implies the premises of the first rule. In other words, the following rule has high confidence in our knowledge (Knowledge):
If X eats too much chocolate, then X eats too much sweets.
Therefore, the first rule is more general than the second rule. The goal is usually to make rules as general as possible.

Note that we can always make the rule more general, simply by adding true premises to the premise. For example, the following rule is even more general:

If X eats too much sweets and 1 equals 1, then X attracts caries.
This is because the premise "1 equals 1" is always true. However, we are only interested in cases where the generalization makes the rule applicable in more cases. For example, "X eats something sweet" is applicable in more cases than "X eats chocolate". Thus, the rule with "X eats something sweet" has a higher support (Support). If the rule has a higher support, we call the rule factually more general. The goal is usually to make the rule as factually general as possible without losing confidence (GoodRules, TooGeneralRules).

Too General Rules

If a rule is more general than another rule (GeneralRules) without having higher support (Support), then the rule is too general in our knowledge (Knowledge). Consider, e.g., the following two rules:
If X eats too much sweets, then X attracts caries.
If X eats too much sweets or climbs Mount Everest, then X attracts caries.
Assume that we know no one who climbed Mount Everest. Then both rules have the same confidence (Confidence). The second rule is more general than the first rule (GeneralRules), because if the first rule applies to a person X, then the second rule also applies to that person X. However, its support did not increase. Thus, it is not factually more general. Rather, it adds an additional premise that fell from the sky. We say that the rule is too general, given our knowledge (Knowledge).

Strictly speaking, even the rule "If X eats too much sweets" is too general. To be less general, we should restrict it to the cases where we have concrete evidence. If, e.g., we have observed caries in a scientific study in the year 2012, then the less general rule would be:

If X was one of the participants of the scientific study in the year 2012, and if X ate too much sweets, then X attracted caries.
This rule is not too general, because it applies only to the cases we have seen. At the same time, it will not be predictive (Predictiveness). It will not allow us to deduce anything about other people who eat too much sweets — even though we would like it to apply also to those people. So we find ourselves in a trade-off: Either we make the rule more general, but then we risk being too general and making false predictions. Or we make the rule less general, but then we risk being unable to make predictions. This trade-off is one of the fundamental trade-offs in rule deduction.
Science may be described as the art of systematic over-simplification — the art of discerning what we may with advantage omit.
Karl Popper

Typed Generalizations

The typed generalization of a rule is a rule that has the same conclusion, and whose premise just binds all variables to their semantic classes (Rules). For example, consider the following rule:
If X has blue eyes, then X has blond hair.
This rule applies only if X is a person. Therefore, its typed generalization is
If X is a person, then X has blond hair.
Obviously, the typed generalization will not have the same confidence (Confidence). In the example, the original rule might have a reasonable confidence. The typed generalization, however, has a very low confidence, because few people have blond hair. In fact, if the typed generalization has the same confidence, then something is fishy (Independence, Trivial).

Trivial Rules

A rule (Rules) is called trivial, if its typed generalization (TypedGen) has a high confidence (Confidence). For example, the following rule is trivial:
If X has blue eyes, then X has two legs.
This rule is trivial, because the typed generalization has high confidence:
If X is a person, then X has two legs.
Trivial rules are not general (GeneralRules). They can be generalized to their typed generalization.

Independence of events

The premise and the consequence of a rule are called independent in our knowledge (Knowledge), if the typed generalization of the rule has the same confidence as the original rule (TypedGen, Confidence, Rules). Consider for example the following rule:
If X has brown eyes, then X is a female.
Let us look at people that have brown eyes. We will find that 50% of them are female. Thus, the confidence of the rule is 50%. Now let us replace the premise of the rule by its typed generalization:
If X is a person, then X is female.
Since half of all persons are female, the new rule also has a confidence of 50%. This means that the premise of the rule (brown eyes) does not help us understand the consequence (gender). Hence, the two phenomena are called independent.

If premise and conclusion are independent, then we can generalize the rule, gaining support, and not losing confidence (Support, Confidence, GeneralRules).

Good rules

A rule in the sense of this essay is an observation about a regularity in life (Rules). For example, a rule is "When the moon has a halo, it will rain". Rules can be measured on various dimensions. We will call a rule "good" if it has a number of properties. The first two properties can be verified without looking at whether the rule is applicable or not:

The two most important properties of a good rule are as follows:

In addition, we want the rule to be the "right" rule in comparison to other similar rules:

The following picture illustrates the properties of a rule with respect to our knowledge (Knowledge): This figure assumes that all conclusions of the rule are positive statements.


A correlation is a rule with high confidence (Confidence) and high coverage (Coverage). This means that whenever the premise is true, the consequence is true — and vice versa. This can be indicated by saying "if and only if". For example, the following rule is a correlation:
The tide rises if and only if the moon is close to the Earth.
This correlation stands for two rules with high confidence and coverage:
Whenever the tide rises, the moon is close to the Earth.
Whenever the moon is close to the Earth, the tide rises.
Thus, the rule works in both directions. Correlation is often confused with causation (Causation).


One thing causes another thing if, whenever we do the first, the second happens. For example, excessive smoking causes cancer, because if we smoke excessively, we will (likely) get cancer. In the framework of rationality, a causation takes the form of a rule (Rules):
If X smokes excessively, X will attract cancer.
A rule that describes a causality has to be of high confidence (Confidence), and it has to have a non-zero support (Support). Yet, not all supported rules with high confidence describe causalities. For example, the following rule also as a high confidence, and high coverage (Coverage), but it does not describe a causality:
Whenever the flags flap in the wind, the windmills run fast.
This rule describes two phenomena caused by the same extrinsic reason, namely the wind. Thus, it does not express a causation, but a correlation (Correlations). It actually

We define causation as follows: A rule expresses a causation, if

  1. there are instantiations (Instantiations) where the premise is false in our knowledge (Knowledge).
  2. for some of these instantiations, we can change the world so that the premise becomes true in our knowledge.
  3. in all of the instantiations where we make the premise true, the conclusion becomes true in our knowledge (Knowledge).
  4. the rule has high confidence (Confidence)
If items 1 and 2 are fulfilled, we call the rule testable. If items 1-4 are fulfilled, we call the rule a causation. A causation is a rule that says that making the premise true makes the conclusion true. Thus, in order to test for a causal relationship, we have to be able to actually make physical change in the world.

Truth of a rule

A rule is the phenomenon that the truth of a certain statement often entails the truth of another statement (Rules). Properties of the rule, such as its (Confidence), (Coverage), and support (Support) are defined only with respect to our knowledge (Knowledge). As our knowledge grows, the confidence of our rule may decrease. Assume for example that we believe that "All sheep are white". As long as we only see white sheep, that rule has a confidence of 100%. If, one day, we see a black sheep, the confidence of the rule decreases.

Thus, we can never be sure whether a rule will not one day produce an incorrect prediction. Thus, we cannot prove that a predictive rule is true (Predictiveness). However, we may be able to prove that a rule is wrong, in the sense that it has not 100% confidence. If we keep increasing our knowledge, and one day we find that a prediction of the rule turns out false, then the rule is not 100% correct. This is the central insight of Karl Popper's theory of scientific falsification (Unfalsifiable). However, there are a few cases in which we can establish the truth of a rule (Generalizations), or at least with a certain probability (EstablishRule).

No matter how many instances of white swans we may have observed, this does not justify the conclusion that all swans are white
Karl Popper

Establishing a rule

We may never hope to prove a predictive rule true (Predictiveness, Popper). The confidence of a rule is based only on the knowledge we have (Confidence, Knowledge). Still, we would like to know the confidence of our rule on the "total set of knowledge", i.e., on the set of all statements that are true in reality. We call this confidence the true confidence. If the rule has a true confidence of 100%, we say that the rule holds in reality.

Even if we do not know that total set of knowledge, we can still make statements about the true confidence of a rule under certain conditions. As an example, assume a tourist guide in Rome, who has the impression that the Swedes in his groups are always very polite. Let us assume that he never sees an impolite Swede. So he comes up with the following rule (Class):

If X is a Swede, then X is polite.
He can make the following statements about the true confidence of this rule.
  1. If the guide has seen no case where the rule applies (no Swede), then he can make no statement about the confidence of the rule.
  2. If he has seen a few instances, he can make an existential statement (Existential). For example, he can say "I have had some Swedes in my groups who were very polite". He cannot say anything about the true confidence of the rule.
  3. If all or of the instantiations of the rule that he has seen are true, he can make an existential statement, a guarded generalization, or a generalization about the people he saw (Existential, Guarded, Generalizations). For example, he can say "All Swedes who I saw in my groups were very polite".
    He can also say that the rule holds with respect to his knowledge (Knowledge). But he cannot say anything about the true confidence of the rule.
  4. If he has seen a statistically significant number of instances of the rule (which were all true), then he can say that the rule holds in reality with a certain probability — for the Swedes who participate in his tourist groups. For example, he can say "With a probability of 95%, the rule 'The Swedes in my groups are polite' holds in reality.". Statistical science tells us how many instances of the rule we have to see to make such a statement (typically at least 100). The rule can still turn out to be wrong on the total set of knowledge. If, for example, from that day on, the Swedes in his groups are always thugs, then we have hit the 5% probability where the rule does not hold in reality. In any case, the statement applies only to Swedes who participate in the tourist groups. The guide cannot say anything about Swedes in general, because those who participate in his groups may already be a selection of Swedes (those that are interested in Italian culture).
  5. If the sample of Swedes is unbiased, and if the guide has seen a significant number of instances, then he may say that the rule about all Swedes holds in reality with a certain probability. Statistical theory tells us what number is significant and how an unbiased sample can be collected.
  6. If the guide has seen all possible instances (all Swedes), then he can establish the true confidence of the rule with certainty.
The coverage of a rule can be estimated analogously, as the confidence of the inverse of the rule (Coverage).
The plural of "anecdote" is not "data"
multiple sources

Fuzzy implications

Statements do not always hold with 100% certainty (Fuzzy). For example, the statement "Ethiopia is a poor country" may hold only to some degree, because not all people in Etiopia are poor. It may hold only to a certain percentage, say 60%, because 60% of people in Ethiopia live on less than 2 USD a day. Let us assume we have another statement that holds to a certain degree, say "Ethiopia is illiterate", which holds at 20%. Then we may ask what is the degree of truth of the following implication (ImpTruth):
If Ethiopia is illiterate, then it is poor.

There are a number of ways to define the degree of truth of this implication. These use the notion of T-norms of Fuzzy Logic [Wikipedia / T-norm]. If a and b are truth values between 0 and 1, then the T-norm indicates to what degree the conjunction of them is true. There are a number of standard ways to determine that degree:

An implication is true if it is not the case that the premise is true and the consequence is false (ImpTruth). Thus, the degree of truth of an implication is 1-norm(p, 1-c), where p is the degree of truth of the premise, c is the degree of truth of the consequence, and norm is a T-norm of our choice. For example, if we use the Tmin Norm, then the truth value of the example implication is 1-min(20%, 1-60%)=80%.

Fuzzy rules

We have seen that statements and implications can hold to some degree (Fuzzy, FuzzyImp). Then the question arises whether rules, too, can hold to a certain degree. It turns out that yes, they can. Our knowledge in this case is a set of fuzzy statements, each with a degree of truth. Let us look at all instantiations of the rule, and let us denote the degree of truth of the i-th premise as pi, and the degree of truth of the i-th conclusion as ci. Then the notions of Confidence, Coverage, and Support transfer as follows: where norm is a T-norm of our choice (FuzzyImp).

This topic is dealt with in detail in [SocialTags / Chapter 2.2.2].


This section will introduce the notion of proofs. A proof is a formal procedure that establishes that something must be true. Metaphorically speaking (Metaphors), a proof is like a tower of bricks. Every brick is a statement, and it serves as the reason for deducing new statements.


A theory is a set of statements. The theory is called rational if its statements are rational. This means that they take the form discussed in SecStat or SecNearly, and no statement takes a form discussed in SecNonRat.

The statements of the theory do not have to be true, they can be any statements. Theories can also contain rules (Rules). A theory can be introduced by saying something like "Let me share some unproven thoughts on this" or "I have a theory on this". For example, we can say:

I have a theory on bananas: The yellow color of bananas makes people happy. Therefore, people who eat more bananas than the average are happier than the average.
This theory contains a class rule (Class) with comparisons (Comparisons), saying that those people who eat more bananas than the average are happier than the average. Theories consist of rational statements, but no statements about reality can be deduced from a theory (unless one assumes the theory to be true). Still, theories play an important role for illustrational purposes and also for the concept of truth, as we shall see (Conclusions, Truth).


Inference is a process that takes a theory (Theories) and that adds a new statement to the theory. We will concentrate here on one particular type of inference, called rule application. Rule application picks one of the rules from the theory (Rules). It instantiates the rule (Instantiations) in such a way that the premise of the rule appears in the theory. Then, it adds the conclusion of the instantiated rule to the theory.

Let us look at an example. Assume that our theory is

Bello is a dog.
If X is a dog, then X is a mammal
Then, rule application will instantiate the rule in line 2 to
If Bello is a dog, then Bello is a mammal
The premise of this rule appears in the theory. Therefore, we can now add the conclusion of the rule to our theory:
Bello is a mammal(Rule Application from 1 and 2)
This statement is called the conclusion. The process itself is called inference or deduction. The process can be repeated, always adding new statements to the theory.

Technical: Deduction Systems

In this essay, we use only Rule Application to do inference (Inference). There are many other ways to perform inference. These methods differ in several aspects:

A system defined by these three components is called a deduction system. Deduction systems come with a number of interesting properties and challenges. I have summarized these concepts in [Algorithms].

Technical: The Universal Replacement System

In this essay, we use only Rule Application as a rule of inference (Inference). Rule Application subsumes the rules of inference that are commonly known as Modus Ponens and Instantiation. Thereby, Rule Application is powerful enough to be a deductive system on its own right (Deduction). To illustrate this, I have invented the Universal Replacement System, URS for short. URS is a minimalistic formal system that uses Rule Application as its only built-in mechanism. As a minor formal deviation from the present essay, URS uses the snake arrow "~>" in place of the "if... then" to represent rules (Rules). URS also has a mechanism to include external axioms (Axioms, Inclusion). Thereby, it can simulate propositional logic, set theory, lambda calculus, and other systems. A detailed description of URS and a demo can be found in [URS].

Technical: Formal Languages

The Universal Replacement System (URS) can work with different types of formal languages: with infix notation, with prefix notation, with latin characters as well as with binary symbols or other symbols. In the present essay, we use natural language. Natural language has well-known shortcomings when it comes to the logical representation of facts. However, if only rational statements are used as defined in this essay (SecStat), natural language is sufficiently precise to do the limited types of inference that we do in this essay (Inference). In order to really work with a formal deduction system, the natural language sentences might have to be structured with parentheses, so that that matching substrings is avoided.

Technical: Complexity of Deduction Systems

In general, the complexity of a deduction system (Deduction) can be either in its logical axioms (Axioms) or in its inference rules (Inference): Systems that have few rules of inference usually need many axioms. Conversely, systems that have few axioms or no axiom need many rules of inference. In URS (URS), almost the entire complexity is in the logical axioms. URS has only one single rule of inference (Rule Application). This sets the hard-wired, built-in part of the formalism to a minimum, and allows applications to choose and add an arbitrary number of application-dependent axioms. This can be done by assuming axioms (Axioms) as proof assumptions (Pasm).

We cannot reduce the number of inference rules to zero. We need to treat at least the Modus Ponens as a built-in rule. To see this, consider the problem of the tortoise and Achilles. This is a fictitious dialog between a tortoise and person named Achilles, which was written by Lewis Carroll. In the dialog, the tortoise accepts a statement X and it also accepts the statement X=>Y. However, the tortoise does not accept Y. Achilles will argue that, if we have a statement X and if we have the statement X=>Y, then these statements together imply Y. This is by itself an implication:

X and (X=>Y) => Y
The tortoise will accept this implication, but will still not want to see why Y should hold. Achilles gets tangled in an ever-growing list of implications, but he does not succeed in proving that "X" and "X=>Y" force us to deduce Y. This shows that the Modus Ponens principle, which will allow to deduce Y, has to be accepted as a principle [Wikipedia / What the Tortoise Said to Achilles].

Technical: Semantics

In deduction systems (Deduction), one commonly distinguishes between the syntax of the system and its semantics. The syntax defines the form of the input, i.e., the formal language of the system (FormalLan). The semantics defines what the syntax "means".

As an example, take the statement "All men are mortal". In the formal language of First Order Logic, this statement looks as follows:

∀ x: man(x) => mortal(x)
The semantics of this statement is that every x that has the property of being a man also has the property of being mortal. More formally, one defines a universe, i.e., a set of objects of discourse. This universe could contain, e.g., all people and animals in a city. One also defines a mapping of the terms in the statement ("man" and "mortal") to sets in the universe ("man" to be the set of all men in our universe, and "mortal" to be the set of all mortal beings in our universe). Then, the above statement is called true if and ony if the set of men is a sub-set of the set of mortal beings. This way, the question of whether the sentence is true has been reduced to the question of whether one set includes the other.

It becomes clear that this formalization does not solve any problem. Once the statement has been reduced to the question of set inclusion, we can start asking for the semantics of set inclusion. Paradoxically, the semantics of sets is usually defined in terms of First Order Logic. Thus, what is called semantics is just the syntactic transformation of one formal language into another — back and forth. Sometimes, the semantics is defined in terms of natural language. We would say that the above First Order Language statement is true, if and only if every man is mortal. Yet, even natural language is nothing more than a formal language — with a set of allowed words and a grammar that tells us how to assemble the words to syntactically correct sentences. Thus, what is usually known as semantics is nothing more than a mapping of one formal language into another.


A hypothesis is a statement (SecStat) of which we do not know whether it is true. The statement might be a belief, a conviction or a subjective opinion, but possibly not a fact (Unprovable).

Technically speaking, a hypothesis is a statement of which we will show whether it follows from a theory (Theories). This is the purpose of a proof, as we will see (Proofs).

Whatever is not deduced from the phenomena is to be called a hypothesis.
Isaac Newton

Proof Assumptions

A proof assumption is a statement that we assume to be true for the sake of a proof (Proofs). Technically, all proof assumptions together form a theory (Theories). The theory can contain simple statements (SecStat) and rules (Rules).

Usually, one uses as proof assumptions statements that are certain to be true: One uses founding statements such as common knowledge, known facts, or statements about perceptual evidence (SecFounding). Proof assumptions can also be the rules of a domain (OtherRules). These rules formalize the domain knowledge of a certain scientific, legal, or common sense domain. Usually, one assumes only rules with 100% confidence or near perfect confidence (Confidence). Proof assumptions can also be logical axiom schemata (LogicalAxioms). These schemata formalize reasoning principles, such as e.g., First Order Logic axioms, rules of equality, or rules of computation.


Informally speaking, a proof is a process that establishes that a hypothesis (Hypotheses) is true. Technically, a proof is a process that starts from proof assumptions (Pasm). It repeatedly applies inference (Inference), until the hypothesis is derived. Thereby, the proof establishes that, if the proof assumptions are true, then the hypothesis has to be true as well.

Let us look at an example. Assume that we are standing in front of the office door and it is locked. We are wondering whether we left the keys inside. Technically, we want to prove the hypothesis

I have the keys of my office.
We use the following proof assumptions (Pasm):
The office door is locked
Whenever the office door is locked, I locked it
Whenever I locked the office door, I have the keys of my office
This constitutes our initial theory (Theories). Now, a proof would proceed as follows: We use Rule Application (Inference) to Line 1 and Line 2. We derive:
I locked the office door(from 1 and 2)
This statement is added to the theory, which now contains 4 statements. We apply rule application again, and we conclude that since I locked the door, I must have the key:
I have the keys of my office(from 3 and 4)
This proves that the hypothesis follows from the proof assumptions.

In general, a proof can have three outcomes:

  1. The proof can find that the hypothesis follows from the proof assumptions (i.e., that the hypothesis is true)
  2. The proof can find that the negation of the hypothesis (Negations) follows from the proof assumptions (i.e., that the hypothesis is false)
  3. The proof can find that neither the hypothesis nor its negation follow from the proof assumptions. That is, if the assumptions are true, the hypothesis can be either true or false.
One may not always succeed to reach one of these 3 outcomes (CompDed).

Technical: Computability

The purpose of a proof (Proofs) is to prove whether a certain hypothesis (Hypotheses) follows from the proof assumptions (Pasm). The logical axioms and the inference rules are given by a deduction system (Deduction). There are some hypotheses that a deduction system can never prove or disprove — no matter how good the system is or how long we keep proving.

To see this, consider the following hypothesis:

This sentence is false.
If the deduction system says that this sentence is true, then it is false. If the deduction system says that the sentence is false, then it is true. This phenomenon is called undecideability. This problem is related to quite a number of paradoxes, see [Wikipedia / Paradoxes] for an entertaining list.

This problem appears because the sentence refers to itself. It may, however, also appear with other sentences (e.g., the sentence "This algorithm terminates"). If we restrict the set of sentences that we want to consider, then we can ensure that deductive systems can prove or disprove our hypotheses. See [Wikipedia / Decideable fragments of FOL] for some sets of decideable statements. See [Wikipedia / Ackermann class] for one of the more powerful sets.

If we do not restrict the set of sentences, then we can use arbitrary logical statements as assumptions and as hypotheses. Unfortunately, it may happen that we hit or create an undecidable statement in the process of the proof. In that case, we will never be able to prove or disprove our hypothesis. Worse, we will possibly even be unable to determine whether we hit an undecidable statement, so that we would have to keep on trying without ever knowing whether we tried enough.

In reality, the effect of undecidable statements is limited, for two reasons: First, the unprovable statements either involve self-reference or are rather complex. Thus, they are unlikely to appear in everyday discourse. Second, all deduction systems are at least correct, which means that every statement that one proves is indeed true and every statement that one disproves is indeed false. Thus, even if there exist statements for which we cannot say whether they are true or false, all those statements where we succeed are indeed true or false as predicted. Therefore, by the pragmatic principle, rationality still remains useful.

Technical: Reductive Proofs

A proof usually starts from the assumptions and derives the hypothesis (Proofs). However, we can also read the proof backwards: We start at the hypothesis (Hypotheses), we apply the rules of inference (Inference) backwards until we arrive at the proof assumptions (Pasm). Such a process is called a reductive proof.

Here is again the previous example (Proofs): Assume that I am standing in front of my office door and it is locked. I am wondering whether I left the keys inside. Technically, we want to prove the hypothesis

I have the keys of my office.
We use the following proof assumptions (Pasm):
The office door is locked
Whenever the office door is locked, I locked it
Whenever I locked the office door, I have the keys of my office

A reductive proof would start with the hypothesis. It would ask: In order to prove the hypothesis, what statements do I have to prove? It turns out that it is sufficient to prove

Prove: I locked the office door(because of 3)
This is because proof assumption number 3 tells us that, if I locked the door, I have the keys. So let's prove "I locked the office door". To prove this statement, I can equally well prove
Prove: The office door is locked(because of 2)
because then proof assumption number 2 tells us that I locked the door. Fortunately, statement 5 is a proof assumption. Therefore, the hypothesis is proven.

It turns out that reductive proofs are just the dual of constructive proofs. Therefore, we will limit ourselves to constructive proofs in the sequel.

Consequences of a rule

A proof is a process of repeated inference (Proofs, Inference). In this process, a rule can give rise to conclusions. These conclusions can be used in other rules as premises. These rules produce again conclusions, and so on. This means that a single rule can give rise to many direct and indirect conclusions.

We capture this transitivity by the notion of consequences. The consequences of a rule in a proof are all conclusions of this rule, plus the consequences of all rules in which these conclusions were used as premises. This is a recursive definition.

Good rules in proofs

A rule can be called predictive, general, and precise with respect to our knowledge (GoodRules). If it has all of these properties, it is called a good rule. This notion can be generalized to the scenario of proofs (Proofs). The proof assumptions (Pasm) take the role of our knowledge (Knowledge). The consequences of the rule (Consequences) take the role of the conclusions of the rule.

This allows us to generalize the properties of a rule to the properties of a rule in a proof process: The rule is called predictive, if some of its consequences are not in the proof assumptions. The notions of support, confidence, preciseness, and generality are defined accordingly. If a rule is not circular (CircularRules), rational in premises and conclusions (SecStat), explicative (Explicative), predictive (Predictiveness), is general (GeneralRules), precise (PreciseRules), but not too predictive (TooPredictive) under these generalized definitions of the terms, then the rule is a good rule in the proof.

Rational Arguments

A rational argument for a hypothesis (Hypotheses) is a proof (Proofs) of the hypothesis from proof assumptions (Pasm) that are founding statements (SecFounding). Thus, a rational argument is sequence of statements, where each statement is supported by one or multiple reasons — which are again statements. In the end, the argument derives the hypothesis.

Metaphorically speaking, the statements in an argument act like bricks. One statement can be the support (i.e., the reason) for another statement. We try to build up a tower with the bricks in order to reach new statements. Such a tower can be read in two ways: It can be read bottom-up, so that new statements are constructed on top of known statements. This is a constructive "usual" proof (Proofs). The tower can also be read top-down, so that a complex statement is decomposed into simpler statements (Decompose, ReductiveProofs).


This section will attempt to define the concept of truth. For this purpose, it will make heavy use of the concept of theories (Theories). These help us define the notions of truth (Truth) and reality (Reality).

Deductive Theories

A theory is a set of statements (Theories). It can contain all types of statements: simple statements (SecStat) and rules (Rules) alike.

Some theories mainly consist of rules. We call such theories deductive theories. As an example, consider the following theory:

Coke is a carbonated beverage.
If X is a mentos, if Y is a carbonated beverage, and if I throw X into Y, then X quickly catalyzes the release of CO2 from Y.
If Y is a carbonated beverage, and if X quickly catalyzes the release of CO2 from Y, then we get a foam explosion.
This deductive theory contains rules about carbonated beverages. The first statement is actually a class rule (Class).

Proof Assumptions and Deductive Theories

In this section, theories (Theories) will take two roles:
  1. A theory can serve as proof assumptions (Pasm). These are statements that we assume to be true. We will call such a theory assumptions for short.
  2. A theory can contain mainly rules. Then it is a deductive theory (DedTheories). These theories will serve to deduce statements (Inference).

In the following, we will always combine a theory of assumptions with a deductive theory. On this combination, we will perform inference to deduce new statements (Inference, Conclusions).

Conclusions from theories

Given a theory of assumptions (Pasm) and a deductive theory (DedTheories), we can draw conclusions. This works as follows: We start out with the theory of assumptions. We use it as proof assumptions. Then we add the deductive theory as additional proof assumptions. Then we apply rules of inference (Inference). This way, we derive new statements (Proofs). These new statements are called the conclusions of the deductive theory from the assumptions.

As an example, let the following be the theory of assumptions (Pasm):

m is a mentos.
c is coke.
I throw m into c
To this theory, we add as a deductive theory the theory from before (DedTheories):
Coke is a carbonated beverage.
If X is a mentos, if Y is a carbonated beverage, and if I throw X into Y, then X quickly catalyzes the release of CO2 from Y.
If Y is a carbonated beverage, and if X quickly catalyzes the release of CO2 from Y, then we get a foam explosion.
Note that line 4 is a class rule (Class). Now we can apply inference (Inference). We derive:
c is a carbonated beverage(from 2 and 4)
m quickly catalyzes the release of CO2 from c(from 1, 7, and 5)
we get a foam explosion(from 7 and 8)

The statements that we can derive from the two theories together are called the conclusions of the deductive theory from the theory of assumptions. If a conclusion was already part of the assumptions, then the conclusion is called an explanation. If the conclusion is not part of the assumptions, then the conclusion is called a prediction.

Reasonable Theories

Deductive theories can draw conclusions from assumptions (Conclusions). Even though the assumptions can be arbitrary statements, it is helpful to imagine that the assumptions are the statements that are known to be true until the present point of time. The deductive theory will then make predictions about the future.

We call a deductive theory a reasonable theory for a given theory of assumptions, if it has the following properties:

  1. Every rule is a good rule (GoodRulesP)
  2. There is no theory with less rules that is at least as correct and as supported as the original one.

Intuitively speaking, a reasonable theory is a theory that produces conclusions from assumptions. Some of the conclusions are already part of the assumptions. We call them explanations (Conclusions). The explanations tell us that the deductive theory is in tune with what we have already observed in the past. The conclusions of the theory shall not be in contradiction with our assumptions, because otherwise the theory would be incorrect. If these conditions hold, we call the theory explicative (Explicative). Other conclusions of the theory are neither part of the assumptions, nor in contradiction with them. They are new, hitherto unknown, statements. We call them the predictions of the deductive theory (Predictiveness). The predictions tell us something about the future.

Contingency of Reasonable Theories

A theory can be applied to observations of the past to make predictions about the future (Conclusions). We call the theory reasonable, if none of its conclusions is in contradiction with what we observed in the past (ReasonableTheories). As time proceeds, we gain more and more knowledge, which we add to our assumptions (Conclusions). If we apply the theory again, it might happen one day that the theory produces a conclusion that is in contradiction with our knowledge. Then the theory ceases to be reasonable. Thus, a theory can be reasonable up to a certain point of time, and it can become unreasonable after that point of time. Throughout history, this has happened many times.

Theories can also become unreasonable if we find a new, simpler theory that has the same goodness (ReasonableTheories). Then, the new theory is reasonable and the preceding, more complicated one, turns out to be redundant. Therefore, the previous theory stops being reasonable. This, too, has happened many times throughout history.

All of this shows that the notion of a "reasonable theory" is contingent. Theories can seem reasonable and become unreasonable. This even holds for theories that are considered "necessarily true" (Necessity).

The search and striving for truth and knowledge is one of the highest of man's qualities.
Albert Einstein


Commonly, a statement is seen as "true" if it corresponds to reality [Wikipedia / Correspondance theory]. However, we have no means of verifying that reality is actually the way we perceive it. Reality could be entirely different from what we think it is. This is because we can be tricked by our senses (Objective). For example, people can see an oasis in the desert, even if there is none.

It could even be that the concept of reality is inconsistent altogether (TruthExists). It could be that only we exist and everybody else is just an imagination (Zombies). It could be that everything around us is just impressions in our mind and that reality does not exist at all (RealityExists).

This essay proposes the following solution to these conundrums: I, the author if this essay, perceive myself in a stream of sensory impressions. These include the things I see, I feel, I hear, and I think. It does not matter whether these sensory impressions are real or imagined, or whether they correspond to something that exists or not. The only thing that matters is that I do have impressions. It is irrelevant whether I really have these impressions or whether just have the impression of having these impressions. Saying that I have the impression of having impressions just introduces a needless layer of indirection. Therefore, we can omit it. I will say that I perceive myself in a stream of impressions, and for ease of notation, I will see this stream of impressions as a stream of statements (SecStat).

My goal is to predict these impressions. That is: My goal is to generate the impression that I predicted that I will have a certain impression and that, later on, I do indeed have this impression. Technically speaking, I am looking for reasonable theories for my stream of sensations. Given the past sensations at any point of time as assumptions, the theory shall produce a non-empty set of conclusions (Conclusions). These conclusions shall not contradict my impressions. Some of the conclusions shall explain past sensations and others shall predict new impressions. All conclusions shall be falsifiable, rational, and there shall be no simpler theory to the same effect. In short, the theories I seek shall be reasonable theories (ReasonableTheories). I seek reasonable theories for my set of sensations. Such theories help me structure and predict my stream of sensations.

We have already seen that the notion of reasonable theories is contingent. A theory can be reasonable, and stop being reasonable at any point of time (Contingency). I will call "truth" those theories that will always be reasonable. True theories are those theories that are eternally reasonable. I cannot know these theories. I do not even know whether there is only one such theory or multiple such theories. Therefore, I approximate truth by theories that are reasonable at my current point of time. Theories that stand the test of time are closer to truth. This corresponds to our intuitive understanding of the concept of truth: If a theory makes consistently useful and correct predictions, people will call the theory "true". This use of the word "true" is justified, because the word "true" does not have any other useful definition. People who oppose the concept of "truth" usually do not offer any alternative definition of the word — let alone a useful one. Therefore, the word is meaningless unless we attach a sense to it. In this essay, I decide to use the word "true" to describe reasonable theories (Definitions). Truth is the set of theories that will always be reasonable, at all time points in my stream of sensations. Since I cannot know this set of eternally reasonable theories, I approximate it by reasonable theories based on my experience. This view of truth is, of course, itself nothing more than a theory (TheoryOfTruth).

Cogito ergo sum
(I think therefore I am)
René Descartes


I call "reality" the system of physical objects in which I perceive myself. The theory that says that reality exists turns out to be very reasonable (Truth): It allows me to predict my sensory impressions with astonishing accuracy. In contrast, the theory that says that reality would not exist (TruthExists) is unfalsifiable (Unfalsifiable): It does not make any predictions. Therefore, I abandon it.

I also have the theory that says that other people around me exist (including the reader of this essay). This theory is also reasonable: It allows to make very valuable predictions about my sensory impressions about these other people. The theory that says that other people would be mindless zombies (Zombies) is unfalsifiable (Unfalsifiable): It does not make any predictions. Therefore, I abandon it. Therefore, from now on, I will assume that reality exists (in the common understanding) and that people around me exist.

There has been considerable debate as to whether reality is pre-determined by the laws of nature or not. This essay takes no stance in this question. According to my current reasonable theories, I can neither support nor contradict this hypothesis. Thus, it remains a hypothesis (Hypotheses).

All theories are wrong, but some are useful
George Box

Free Will

I, the author of this essay, have a number of theories about reality (Reality). One theory is that people have a "free will". This is the ability to decide for or against certain actions. There is considerable debate about the exact definition of this concept (FreeWill). This essay cannot define the concept precisely. Rather, it defines the "theory of free will". This theory says two things: First, the decisions that people take cannot be predicted by current technical means. Second, the decisions that people take can often be influenced by incentives and punishments. This theory of free will allows predicting certain dispositions (Dispositions). It also allows predicting that certain things cannot be predicted. These observations are enough to make the theory of free will a reasonable theory (ReasonableTheories) — and thus an approximation of truth (Truth).

The theory of free will is a very limited theory. It does not attempt to explain any of the philosophical conundrums associated to the idea of free will. However, in this very limited sense, it is a reasonable approximation of truth. See further up for a discussion (FreeWill).

Is Truth Subjective?

This essay defines truth as the set of reasonable theories on the stream of sensory impressions (Truth). This definition, by itself, is subjective. Technically, it only defines truth for myself, the author of this essay.

However, I found that is a reasonable theory (ReasonableTheories) to assume that other people work according to the same theory of sensory impressions. This theory allows me to predict my sensory impression about what other people say about their sensory impressions. Furthermore, I have the theory that these sensory impressions are universal, in the sense that people subjected to the same conditions (Reality) experience similar sensory impressions. This is nothing more than a theory, but it turns out to be a very reasonable one: In the majority of cases, it allows me to predict what other people say about their impressions.

With these theories in place, truth becomes more objective. If reality exists, and if people in the same reality have the same sensory impressions, then they share the same concept of truth (as defined in this essay). And indeed, most people, if not all, share the theories about reality, people, and the physical world. This entails that reasonable theories are also shared. Indeed, reasonable theories are usually readily accepted. This makes truth sufficiently objective.

I never can catch myself at any time without a perception, and never can observe any thing but the perception.
David Hume

Necessarily True Statements

In philosophy, one distinguishes contingently true statements from necessarily true statements. While the former just happen to be true, the latter have always to be true in all possible worlds. For example, it is a contingent truth that the Earth has one moon. It could also have two moons. However, it is necessary truth that 4+1=5, because 5 is defined as the successor of 4.

Thus, something is necessarily true if it could not be otherwise. It is contingently true, if we can imagine it to be otherwise. This distinction between contingent truth and necessary truth is difficult, because it depends on our own imagination and on our own definitions. Our imagination and our definitions, however, are contingent. Consider the following truths:

These examples show that whether we can imagine something or not does not mean whether something can be true or not. In particular, if we are prepared to doubt everything (Truth, Objective, Reality), even the existence of reality, then we should apply this argument also to what is traditionally known as "necessary truth".
Technical Issues
The concept of "necessary truth" can be used to prove statements that are disputed. One example is a proof by Saul Kripke, an American philosopher, about the nature of human sensation. Put simply, Kripke argues that human sensation is more than a pure configuration of atoms in our head. He argues that we can imagine that human sensation is something different from a certain atom configuration. Therefore, sensation and atom configuration cannot be necessarily equal. But identity is always necessarily true or necessarily false. Hence, Kripke concludes that human sensation cannot be just a certain configuration of atoms. In this argument, Kripke deduces a fact about the world from the fact that he can imagine something. But whether or not Kripke can imagine something has no influence on the real world.

Auxiliary Notions

Our theories contain statements and rules (Theories). We use them to describe, explain, and predict our sensual impressions (Truth). Some of the statements in the theories are about sensory impressions. These are directly either true or false — depending on whether they correspond to the speaker's perception or not. They can also be unknown, if they concern the future. All other statements in our theories are not directly observable. They are auxiliary statements. Auxiliary statements can be scientific statements, legal statements, religious statements, or freely invented notions (Definitions). Auxiliary statements can be derived from rules (Rules) and can derive other statements. Words, notions, and concepts that appear in auxiliary statements are called auxiliary notions.

In our example of the theory about carbonated beverages (DedTheories), the notion of "catalyzing the release of CO2" is an auxiliary notion: It is used in the consequence and in the premise of rules, but it is not directly observable.

Auxiliary notions serve purely to bridge the consequences of some rules with the premises of other rules. An auxiliary notion that never appears in the premise of a rule is a useless auxiliary notion.

Religious truth

A religion can be seen as a set of beliefs, and thus as a theory (Theories). Some people take a religious theory as the truth (Truth). However, religious theories are often not theories in the sense of this essay (Theories). This is because there is often considerable debate about what statements make up the religious theory. Different people, times, and societies may have different interpretations of sacred sources. Thus, for some religions, it is hard to come up with a list of clear, non-redundant statements (SecStat) that would constitute the theory.

In cases where such theories (or sub-theories) exist, the theories usually contain universal abstract hypotheses (AUH). Examples are "The universe is perfect", "Everything in this world is divine", or "Every bad event will have a good consequence". Such statements are hard to nail down as objectively true or objectively false (WhatsWrong). The theory "God is good and makes this world good", e.g., predicts many "good" events in life. However, we can as well imagine that "God is evil and makes this world evil". The world offers as many arguments for "God is good" as it does for the hypothesis that "God is evil". These statements are abstract universal hypotheses (AUH), and thus not rational. This makes the religious theory not rational (Theories).

Furthermore, religious theories usually contain unfalsifiable statements (Unfalsifiable). Examples are "There exists a god", "There is an afterlife", or "God created the world" . Such statements do not produce any verifiable predictions or explications about this world. They do not predict or exclude any event in life. Thus, we are no wiser about this life if we assume such a statement. Therefore, the statement is not rational, and thus the theory is not rational (Theories).

Religious theories usually give explications for past events (Explicative). These include explications of how the world came into existence, why a certain disaster happened, or why certain fossils have been found. The explications are often of the form "God did this, therefore it is this way" or "God wanted it this way, therefore it is this way". These explications, however, can justify only known events. They cannot be used to predict unknown events. Thus, while such rules are explicative, they are not predictive (Predictiveness). To see this, we can make a thought experiment: To whatever question comes up, I (the author of this essay) will answer "Because I wanted it this way and made it happen by magical powers". This theory can explain all events of the past. It was always the author of this essay who made the events happen. Yet, this theory cannot be used to predict events, because nobody knows what the author of this essay wants next. Therefore, the theory is useless. From a rational point of view, religious explications are of similar nature. They do not make predictions and are thus not good rules (GoodRules). Therefore, the religious theory is not reasonable (ReasonableTheories).

Other religious rules do make predictions, but these concern only the future and not the past. Such rules say, e.g., that the world will be destroyed one day. Such a rule is predictive (Predictiveness), but not explicative (Explicative). Thus, it suffers from the opposite problem of the previous "God did it"-rules: We have seen no instance where the rule worked in the past. Thus, there is no reason to believe it will work in the future. Therefore, such a rule is not a good rule in the sense of this essay (GoodRules). Thus, the theory is not reasonable in the sense of this essay (ReasonableTheories). (A rational theory about the end of the world would be a theory that shows that the sun burns its material away, and that any planet left without a sun will be pulled into neighboring planets by gravitation. Both of these rules are explicative and predictive.)

Some religious theories also make outright incorrect predictions, in the sense that the theory has been used in the past to predict something that has turned out to be false (e.g., that the Earth is flat). In these cases, the theory is usually said to have been wrongly interpreted, whereas it is usually affirmed that the current interpretation is the right one. However, the theory is not changed, which would have been the adequate rational reaction to a wrong prediction (Wrong). In other cases, the religious theories make predictions that turn out to be false (e.g., that a certain person will be healed after prayer). This makes the theories incorrect from a rational point of view. An incorrect theory is not reasonable (ReasonableTheories).

Sometimes, people say that a religious theory deduces a statement that was recently discovered by science, even though that statement was not previously known to be deducible from the religious theory. Such assertions are e.g., that some fact discovered by science has been predicted by a holy book. Such assertions are not predictions in the sense of this essay, because they are made after the fact is known. They are called postdictions (NoBOD).

Last, religious theories are usually redundant, meaning that they predict something that can equally well be predicted without transcendant assumptions. It is rare that a religious theory makes a verifiable prediction about the real world that could not have been predicted by science. This makes religious theories non-minimal and thus not rational (ReasonableTheories).

That said, not every religious theory is unreasonable in the sense of this essay. For example, it is a reasonable theory that minding one's own faults before criticizing others is beneficial for a society. Religious theories (or their interpretations) also provide extensive moral frameworks (Moral). These frameworks serve a purpose from a rational point of view. Religious theories can also provide a world view and emotional comfort, even if they constitute no reasonable theory in the sense of this essay. After all, everybody is free to believe whatever he wants, no matter whether this essay defines a belief as "reasonable" or not.

The Meaning of Words

It is very hard to define the meaning of a word (Language). First, people rarely agree on the meaning of words when they start thinking about them. This is often a cause for conflict (TalkToArgueWords). Even if we succeeded to agree on a meaning, we would never be able to define all words. This is because we always define words by other words, which leads to an infinite regression (Basic). Furthermore, it might just be impossible to define a word in its entirety. "time", for example, is a notoriously difficult concept to define, as Saint Augustin once remarked. The same is true for the concept of "game", as Wittgenstein observed. It may also be true for concepts such as "carbonated beverage" — for which we have an intuitive understanding, but possibly no crisp definition (try defining what a "beverage" is).

Surprisingly, words work very well in practice, as the reader experiences while reading this text. This essay proposes the following theory (Theories) for the role of words:

Words are the constituents of statements (SecStat), and thus of rules (Rules) and theories (Theories). They serve to express and share theories. Given a theory, the meaning of a word is the set of rules that it appears in. For example, whenever we point to a flat thing with four legs, we use the word "table". The word "table" appears in other rules, such as "When we eat, we usually use a table", or "Tables usually have four legs". The set of all these rules (and situations) is the meaning of the word "table".

Thus, the meaning of a word depends on how the word is used, and what role it takes in a theory. This insight has several consequences. First, the meaning of a word is not something absolute. It depends on the theory it is used in. Second, the meaning of a word may change — with time, with context, or with users. This insight clears up a great deal of disputes about the "true" meaning of words (TalkToArgueWords).

This theory does away with the need to define words. The meaning of a word is just the set of rules that it appears in. This corresponds to our intuitive understanding of words, as follows. If someone asks us what a word means, we rarely give a logical definition. Rather, we give a set of rules in which the word appears. For example, if someone asks us what a "carbonated beverage" is, we might reply:

It has bubbles in it. A coke, e.g., is a carbonated beverage. When you shake it in a bottle, it produces lots of foam.
These explications do not have to be absolute rules. They can contain fuzzy statements, beliefs, or dispositions (SecStat). If we know other rules that contain these statements, then we can "make sense" of the explanations, even if they are fuzzy.

If we want to communicate our theories to other people, we have an interest (Goals) that other people understand our words. The standard way to do this is to use a commonly accepted theory that defines (or describes) the words: a dictionary. A dictionary contains exemplary sentences with the word. In the terminology of this essay, the dictionary contains rules with that word. These constitute a subset of the meaning of the word. By an (implicit) inclusion statement (Inclusion), a dictionary can become part of our argument. It provides rules that narrow down the meaning of the words. It is good rational practice to use these definitions as founding statements in rational arguments (WordMeaning). If we do not find the word in a dictionary, if it is ambiguous, or if we require it in a different meaning, we can describe the word ourselves, together with our interlocutor (Definitions).

If we know in which rules words and statements appear, then we know how to use them — we understand them. Thus, the logical definition of a word is unnecessary for the use of the word. A great deal of philosophical discussions becomes superfluous (in this sense). Most notably, a great deal of cantakerousness becomes superfluous, too (TalkToArgueWords). If we still strive for a crisp definition of a word by other words, then we should first see in which rules the word appears. This step, however, is usually omitted — although it is the basis for the understanding of a word. So, before trying to define "soul", "self", or "sense of life", we should ask ourselves in which regularities or rules these terms appear. We may then decide to accept the set of these rules as the definition of the term.

The meaning of a word is its usage in language
Ludwig Wittgenstein

The Theory of Truth

This essay has defined truth as the theories that are eternally reasonable (Truth). It has introduced auxiliary notions as ways to describe and model sensory impressions (Aux). This viewpoint on truth is of course by itself nothing more than a theory (Theories). In this theory, "truth" itself is nothing more than an auxiliary notion.

This theory of truth does not claim that this is the way humans think or the way humans perceive truth. Most notably, the theory depends on a concept of statements and thus of language. To what degree humans model reality with or without language is a matter of ongoing debate. Humans also lack the capability to perform the consistent reasoning that the theory requires. Rather, the theory of this essay is to truth what grammar is to language: It is a way to formalize the phenomenon, without claiming that humans work that way. Every child can speak grammatically correct sentences without knowing the grammar. Yet, we use the grammar to model the language. In the same way, every child perceives reality and builds up knowledge about reality without knowing logical rules. Yet, to describe this phenomenon, we use logical rules. This is what the theory of truth of this essay does.

The theory of this essay offers a framework to define the notion of reality (Reality). It also gives answers to the questions of existence and zombies. The theory also gives a meaning to words, without having to define them (Mean). Thus, it breaks the vicious circle of infinite regress. The theory also connects the notion of reality with the notion of scientific inquiry, as follows: Scientific inquiry aims to find and verify rules. This essay defines truth as the extrapolation of this search. Science driven to ideal perfection is truth. Science in its current state is an approximation of truth. In a nutshell, this essay's theory of truth tells us that we have to be ever more precise, and ever more careful if we want to approach truth.

And so this is what we do: We build theories of reality, we see where they fail, and we build new ones. And with each step, we understand this world a little bit better.


This essay proposes the following theory (Theories) on truth (Truth, TheoryOfTruth), words (Mean), and morality (Moral):

In this theory, truth, words, and ethics are purely human artifacts. They are things that we construct to cope with reality, to share theories, and to structure our lives. This implies that these items have no foundation in nature. Rather, they are human constructions. They have no value per se. Rather, they gain their value through human consensus. They are not eternal or immutable. Rather, they evolve according to human decisions.

 all our science, measured against reality, is primitive and childlike and yet it is the most precious thing we have.
Albert Einstein


This section will introduce some common techniques of rational thinking.

Proofs in the real world

We have seen how to formally prove the truth of a statement (Proofs). Proving a statement is a very tedious and complicated process. It is close to impossible to prove all our statements formally — not least because we lack a formalization of the world in the form of rules (OtherRules). Yet, this tedious process is needed if we want to establish the truth of a statement with certainty (as far as this is possible (Truth)). Therefore, proofs are used in several domains of human activity. First and foremost, proofs are the backbone of mathematics. Mathematics is again the backbone of a large number of domains and applications, such as the engineering sciences, data analysis, and computer science. Proofs are also used in the sciences in general, to convince fellow scientists of the correctness of a theory (Conclusions). This applies to the science of physics as well as to computer science. It applies to micro- and macro-economics, and even to philosophy. Proofs are also used in the legal domain, to show whether or not a certain law applies in a certain case. This reasoning is known as subsumption reasoning. In all of these cases, people have developed a (more or less complete) formalization of their domain in the form of a theory of rules (OtherRules).

In everyday thinking, proofs play a smaller role. In most cases, we have an intuitive idea of what statements we want to see as true. Then we come up, a posteriori, with an argument to convince ourselves (and others) of the truth of that statement. In many cases, rules are just invented on the fly (RuleInvention). This leads to a type of informal proofs, which we will discuss in this section.


Proofs can use simple statements to arrive at complex statements (Proofs). Proofs can also be used, vice versa, to decompose a complex statement into simpler statements. The hope is that, by repeated decomposition, one arrives eventually at very basic statements that require no further decomposition (SecFounding). Thereby, the decomposition proves the complex statement. Technically, such a proof is a reductive proof (ReductiveProofs).

To see how far one can go with the decomposition, let us assume a sample discussion. Assume that Alice thinks that everybody in our country can read and write. To prove the contrary, one could cite the scientific studies that give evidence for the illiteracy in our country. If Alice still has doubts, even the statements made in the scientific studies can be decomposed and questioned. If the doubts still remain, Alice could redo the study by herself. She could pick a random sample of people and check whether they are literate. This process will prove or disprove the hypothesis about the literacy rate in our country. Thus, the complex theory that there exist illiterate people in this country has been decomposed into basic statements about whether a certain respondent could write his name. Note that rationality emphasizes the right to decompose and question any statements, even those of scientific studies.

Decomposition is a type of reverse argument (Arguments), which will eventually reduce a hypothesis to founding statements (SecFounding).


Grounding is the process of making statements explicit and thus admissible in rational arguments. It is the prerequisite for any argument or formal or informal proof (Arguments, RealProofs). Grounding means:

It is good practice to ground all statements before starting a rational argument.

Naming facts, assumptions, and goals

In everyday reasoning (RealsProofs), it is easy to lose track of assumptions, facts, goals, and hypotheses. Therefore, it is a good strategy for the purpose of approaching truth to make these statements explicit. That means: If you want to make sure that you are aware of these ingredients, try formulating each of them in your head before you start an argument — or even write them down. Being clear about these statements will allow us to make more correct and more convincing arguments (Arguments).

Modus Tollens

The Modus Tollens is an axiom schema (Axioms, LogicalAxioms) that says
(X => Y) => (~Y => ~ X)
The Modus Tollens is usually universally assumed to be true (LogicalAxioms). It allows us to make, e.g., the following proof.
(X => Y) => (~Y => ~ X)(Assume Modus Tollens)
If it rains then the street is wet (Assumption)
The street is not wet(Assumption)
If the street is not wet then it does not rain(by Rule Application from 1 and 2)
It does not rain(by Rule Application from 3 and 4)

Thereby, the Modus Tollens allows us to "turn around" an implication (Implications): If the consequence is not fulfilled, the condition cannot be fulfilled either. This reflects in the ways we can negate rules (NegRule) and in the idea of necessary conditions (Necessity). It is used in the Reductio ad Absurdum (Reductio).

Reductio ad Absurdum

The Reductio ad Absurdum is a proof strategy that works as follows: Assume we want to prove that some statement X is false. For example, we want to prove that the following statement is false:
The Earth is flat.
The reductio ad absurdum will then assume that this statement were true. In the example, we would assume that the Earth is indeed flat. For this, we would build a hypothetical scenario (Scenarios) in which the Earth is flat. Then, we would elaborate all consequences of that statement (Consequences). In particular, we aim to find a consequence that looks implausible. In the example, we could build the following argument:
The Earth is flat(Assumption)
...(Many intermediate steps)
If someone travels continuously westward, he finds the end of the world(Intermediate conclusion)
If Ferdinand Magellan travels continuously westward, he finds the end of the world(Instantiation)
Ferdinand Magellan continuously traveled westward(fact)
Ferdinand Magellan finds the end of the world(Modus Ponens)

We know that Magellan did not find the end of the world. Therefore, the Earth cannot be flat. People will usually find this line of argumentation sufficiently convincing.

To be logically correct, however, we need a precise argument that shows that the Earth is not flat. For this, the reductio ad absurdum proceeds as follows: From the hypothetical scenario, we build an implication:

The Earth is flat => Ferdinand Magellan finds the end of the world
Then, we use the Modus Tollens Principle (ModusTollens) to turn this implication around:
Ferdinand Magellan did not find the end of the world => The Earth is not flat
Then, we exploit that we know that Magellan did not find the end of the world. By rule application (Inference), it follows immediately that
The Earth is not flat

These last 3 steps are always the same for the reductio ad absurdum. Thus, to prove a hypothesis wrong, it is usually sufficient to build a hypothetical scenario that leads to a false conclusion.

Shortened Evaluation

There are two cases in which we can avoid checking an implication in its entirety (Implications).

The first case works if we have an implication as follows:

A & B & C => D
If we know that one of the premises is known to be false, then we do not need to check the other premises. This is because, in any case, the rule will not be applicable if one of the premises is false. For example, assume that, in order to serve in the military, you have to be at least 20 years of age and physically fit. If someone is younger than 20 years of age, then there is no use checking his physical fitness, because in any case he will not be able to serve in the army.

The second case works if we have two implications with the same conclusion:

A => C
B => C
If we know that A is true, then we do not need to evaluate B in order to arrive at C (Knowledge). We already know that C holds. For example, we should call emergency services if a building is in flames. We should also call emergency services if someone suffers from a major injury. Hence, if we see that a house is in flames, we can immediately call emergency services without running into the building to see whether someone suffered major injuries.

Using shortened evaluation, we can avoid checking unnecessary statements. This strategy, however, can also be misused (DecDuc).

Making a moral analysis

A moral analysis means deducing whether someone did something "wrong". In the framework of rationality, a thing is never wrong by itself. It is only wrong in the opinion of a person, an authority, or a law (Moral). Thus, we first have to make up our mind about what we consider "wrong". The list of things we consider "wrong" is called a moral framework (MoralFrame). It can be the national law of our country, a religious list of dos-and-donts, a liberal framework [Thoughts on Ethics] , or our own list. A moral framework can say, e.g.:
If X takes away something that belongs to someone else, then X is a thief.
If X is a thief, then X acts in a morally wrong way according to this framework.
This moral framework will allow us to deduce that someone who steals does something wrong. We can use such rules as proof assumptions in a proof (Proofs, Pasm). This allows us to deduce whether someone did something wrong. If we find that someone has done something wrong, we may reproach him and take appropriate action (UseMoral).

Hypothetical scenarios

A hypothetical scenario is an argument (Arguments) that is based on the assumption (Assumptions) that something happens. Hypothetical scenarios can be useful to figure out the consequences of an action or an event. Speaking in the brick metaphor (SecProofs), hypothetical scenarios are towers that one builds on the side, just to see where they go.

Hypothetical scenarios can be used to figure out whether a hypothesis is wrong. For this purpose, one constructs a scenario in which the hypothesis is true. If this scenario leads to a contradiction with reality, then the hypothesis is false (Reductio).

It is often much easier to prove a hypothesis wrong than to prove it right (Popper). Therefore, once we have a hypothesis, rather than accumulating evidence for it, we should try to prove it false. Simply pursuing more and more positive evidence just isn't useful (NegEv).

Rule invention

Rule invention is one of the less elegant, but more frequent techniques of rational thinking. In the vast majority of cases, we do not possess a sufficient number of rules to prove a hypothesis right or wrong (RealProofs, OtherRules). Therefore, we often invent the required rules on the fly. These rules form a theory (Theories) that we use as proof assumption (Pasm).

In order to arrive at true conclusions (Truth), the invented rule has to be true. For this essay, this means that the rule has to be a good rule (GoodRules), so that the theory of invented rules is a reasonable theory (ReasonableTheories). Only reasonable theories make good on-the-fly inventions. All other theories will most likely not yield true conclusions.

This means that the invented rule has to make predictions other than the one we want to prove. A rule that simply predicts our hypothesis is not convincing (and most likely false). The predictions of the theory have to be not incorrect, and verified in the past. They may not be in contradiction with other reasonable theories. The rule may still turn out to be wrong (Contingency). However, rules that consistently make correct predictions will be reasonably close to truth (Truth). See further down for an example (ArgFalse).

Using intuition

If one has a good intuition, then the outcome of a rational argument should conform to one's intuition (Arguments). Therefore, one strategy of building a rational argument is to start with the hypothesis that one expects intuitively to be true (Hypotheses). One can try to prove this hypothesis with rational methods (Proofs). This may fail, of course, if the intuition is wrong. If the intuition is right, then the proof will succeed. For example, we have a strong intuition that it is a bad idea to cross a railway line if the barriers are down. Starting from the standard goal of staying alive (StdGoals) and some very basic rule inventions in the domain of physics (RuleInvention), we can quickly construct a rational argument that supports this intuition.

If one has a strong aversion against one of the possible conclusions, it is worth examining why one has this aversion. The reason may be either a fact with which one feels uncomfortable (and tries to brush aside) or a line of thought that is worth considering in the argument. In both cases, it is good to be aware of one's aversions and note down possible reasons. They might turn out handy in our line of reasoning.

Education is what survives when what has been learned has been forgotten.
B. F. Skinner

Presenting the argument to other people

Rational arguments rely on transparency and verifiability. If one wants to validate an argument, it is a good idea to share it with another person. This helps check the assumptions one is making and the conclusions that one draws. If there is nobody who would listen to the argument, it is a good idea to imagine presenting the argument to somebody. In the ideal case, one imagines presenting the argument to someone who has a different opinion. This helps spot the weak points of the argument. It also helps see reasons and statements that we did not know about. This is essential in a world where additional information can make theories incorrect (Contingency, AAP, NegEv).

Notwithstanding privacy issues (Private) and potential negative consequences of airing one's opinion, one should be able to present one's argument to anybody. What you say to one person you should be able to say to any other person. If you find yourself saying contradictory things to different people, you are not being rational. Transparency and consistency across different interlocutors are the safeguards of rational arguments.

Getting a second opinion also helps assessing the truth of what other people tell us. If one person says one thing, and another person says a contradictory thing, then one of them is lying.

— What would you do if your doctor told you that you had only 3 more days to live?
— I would immediately go to another doctor.

Empathizing with other people

One way to check a rational argument is to put ourselves into the place of the person who is concerned by the argument. In other words: We imagine that we are the person about whom we are talking. Then we can use intuition (QIntuition) to check the validity of our argument.

The process of imagining oneself in another person's shoes is called empathizing. Empathizing is one of the most powerful means to check the emotional consequences of our argument. For example, when arguing that we have the right to do something to another person, we can sidestep for a moment and imagine that someone did that something to us. This will help us assess the effect of our behavior on the other person. If we decide that that effect is too negative, we may refrain from what we were planning to do.

Imagining one's future opinion

In order to check the validity of an argument, we can imagine how we would think about the argument in some years' time. We can imagine different courses of time and see whether the argument maintains its validity in retrospect. A good rational argument will remain valid over time.

It may also be useful to look back at the arguments that one has built in the past and see if they are still valid. If one has built arguments that have become obsolete over time, one can try avoiding such reasoning in future arguments.

Consistency across time is a characteristics of correct rational arguments (Contingency, Truth).

Having a plan B

To make a rational argument water-tight, it is useful to check to which degree the argument relies on assumptions. To find out how important the assumptions are, we can use hypothetical scenarios (Scenarios). We can build a hypothetical scenario for the case that an assumption is wrong and see if we can still get to the conclusion. If we can, the argument is stable (and the assumption is superfluous). If we cannot, we should consider making an argument for the case where the assumption is wrong.

A hypothetical scenario for the case where one of the assumptions is false is known as a "Plan B". To maximize the probability that our conclusions are correct, we should start making a plan B with the assumptions that are most likely to be wrong.

If Plan A did not work out, stay cool. The alphabet has 25 more letters.
an anonymous on the Web

Finding negative evidence

Some hypotheses that seem true can become false if more evidence appears (Contingency). For example, assume that you learn that your girlfriend has pictures of another guy in her room — all in frames, and with personal drawings by him for her, and that she even got in touch with his parents. You might want to deduce that your relationship is in danger. However, if you then learn that this guy is her god-son, 4 years of age, you might reconsider your conclusion (AAP).

Therefore, we should never rely just on the positive evidence. We should always try to find also negative evidence against our hypotheses.

Unfortunately, we have a tendency to accumulate only the positive evidence for what we want to believe. In the interest of truth, we should stop accumulating positive evidence at some point of time and start looking for negative evidence [Toolkit / How does this help]. Only if we have analyzed and rejected all negative evidence shall we accept our hypothesis as true. Talking to other people helps find negative evidence (QPerson).

You're only as young as the last time you changed your mind.
Timothy Leary


Backtracking is the process of reconsidering the assumptions that we made in an argument (Pasm, Arguments). Backtracking means abandoning one assumption, and redoing the argument without that assumption.

Backtracking can be useful,

  1. if we found out that one of our founding statements was wrong (SecFounding)
  2. if we want to find out what would happen if one of our founding statements were wrong (PlanB)
  3. if our argument produces conclusions that are in contradiction with reality (Reality)
  4. if certain goals cannot be fulfilled (Backtracking)

Backtracking is essential in a world where things that appeared true can turn out to be wrong (Contingency).


This part covers arguments with other people (SecArg), fallacious arguments (SecNonRatArg) and dealing with non-receptive people (SecNonRec).

Technically, the types of behavior presented here are patterns (Patterns). This means that they are abstract descriptions of hypothetical behavior that might or might not appear in reality. The responses suggested to counter the behavior are theories in the sense of this essay (Theories). This means that they are not guaranteed to work.


Sometimes, we wish to present our rational argument to other people (Arguments). This section explains ways to do this convincingly.

Arguing that a statement is true

If we want to show our interlocutor that a statement is true, then the most convincing way to do this is usually a rational argument (Arguments). To make a rational argument, it is useful to first make all assumptions, facts, and goals explicit (Name). If we are making assumptions, it is helpful to ask our interlocutor whether he agrees. Once we agree with our interlocutor on the founding statements (SecFounding), we conduct a proof for our hypothesis (Proofs). We might have to come up with some additional rules on the way (RuleInvention). It is useful to check each of this rules for plausibility with our interlocutor. If he agrees, we can build our proof on these rules and deduce the hypothesis.

Throughout our discourse, is useful to use grounded language (Grounding).

Arguing that a statement is wrong

To argue that a statement is wrong, we have to prove (Proofs) that its negation is true (Negations). Thus, an argument against something (Arguments) follows the same structure as an argument for something (ArgTrue): We first make all assumptions, facts, and goals explicit (Name). Then we show that the negation follows from the founding statements (SecFounding).

In reality, such a proof is often shortened. It is often sufficient to name just one founding statement that will allow us to deduce the falsehood of the claim. This statement is called a counter-argument. The proof that uses this statement is usually left implicit.

As an example, consider the following discussion:

Alice: Yesterday, I stayed at home all day to work for school.
Bob: But I saw you at the tennis court in the afternoon!
It seems that Bob has a valid counter-argument to Alice's claim. The full proof looks as follows: We first come up with the following rules (RuleInvention):
  1. If someone sees something, then that something is true
  2. If someone is in one place at some point of time, he cannot be in another place at that point of time.
  3. If something happens all day long, it also happens in the afternoon.
Then the proof proceeds as follows: With the first rule, we deduce that Alice was at the tennis court in the afternoon. With the second rule, we deduce that Alice was not at home in the afternoon. With the Modus Tollens (ModusTollens) applied to the third rule, we deduce that Alice was not at home all day long. This is the negation of the claim. Therefore, Bob has found a valid counter-argument to Alice's claim.

Arguing for the truth of a rule

Logical rules are an essential part of rational discourse (Rules). Unfortunately, some rules are so predictive that we may never hope to prove them true in eternity (Popper). Yet, rules that have certain properties (GoodRules) are often acceptable as approximations of eternal truth (Truth).

In order to show that a rule is "true" in this approximative sense, we have to show that it is a good rule (ReasonableTheories, GoodRules). This means in particular that it is rational (SecStat), supported (Support, EstablishRule), general (GeneralRules), precise (PreciseRules), and predictive (Predictiveness). If we succeed in showing these properties, then the rule is a reasonable approximation of truth.

Intuitively, there are three important properties of a rule: (1) it has predicted true things in the past, (2) it never predicted something false, and (3) it makes predictions about the unknown. If it has predicted a large number of true things in the past, then chances are good that it will predict true things in the future. There is no guarantee for that, though (Contingency).

Arguing for the falsehood of a rule

It is often impossible to argue for the truth of a predictive rule in eternity (Popper, ArgForRule). In contrast, it is easier to argue for the falsehood of a rule. More precisely, it is possible to argue that the rule is incorrect. It suffices to find an instantiation (Instantiations) where the premise of the rule is true in our knowledge (Knowledge) and the conclusion is false.

To make such an argument watertight, it is useful to first clarify with our interlocutor what the rule is supposed to mean (Name). We cannot argue agains a general valuation (GenVal), an abstract universal hypothesis (AUH), or an unfalsifiable claim (Unfalsifiable). If the rule falls into one of these categories, then we should concentrate on showing that the rule is not rational.

If we want to prove the rule wrong, then we can proceed as follows:

  1. Ask which statement our interlocutor would accept as a proof that the rule is wrong
  2. Prove that statement
Equivalently (Reductio), we can
  1. Ask for a prediction that the hypothesis makes
  2. Show that the prediction is wrong

For example, to prove that a certain superstition is wrong, we can ask "What would you accept as evidence that the superstition is wrong?". When our interlocutor says that failure to follow the superstition leads to, say, illness, then we can prove the superstition wrong by (1) not following it and (2) not falling ill.

The problem is that our interlocutor will most likely not be willing to produce anything that he would accept as counterevidence for his rule. Here are two strategies that we can use in this case:

Arguing that we should so something

Sometimes we wish to show our interlocutor that it is good for them or both of us to do something (Good). The most convincing way to do this is usually to establish the following facts:
  1. We have a certain goal X (Goals). It is helpful to reassure ourselves that our interlocutor agrees with this goal.
  2. A certain action Y will lead to that goal X (Good).
  3. The action Y is the only one that leads to X without violating other goals.
  4. Therefore, it is good to do Y

Point 4 follows from the definition of "good" (Good, Advice). This line of reasoning is a general blueprint for an argument for doing a certain thing. The drawback is that the argument works only if the condition in line 3 is fulfilled. If this condition is not fulfilled, then we cannot make an easy argument for doing something. We have to go through a full fledged decision process to figure out the best thing to do (SecDec).

Reactions of our interlocutor

Once we have made our argument (SecArg), it is our turn to listen (Listen). The other person may now say something in reply. We distinguish the following cases:
  1. The other person does or says something that is unrelated to our point. This problem is discussed further down (SecNonRec)
  2. The other person acknowledges our point (Ack). In this case, the argument is over.
  3. The other person produces a valid objection to our point, e.g., by a method outlined in this section (SecArg). In this case, it is our turn to reply (Reac).
  4. The other person produces an invalid objection. We will discuss this case in the following section (SecNonRatArg).

This model does not apply in all cases. We can imagine discussions with more than two people, asynchronous discussions or verbal interactions that are not discussions in the rational sense (TalkToArgue). In particular, this discourse model assumes that every valid statement deserves an acknowledgement.

Bad arguments

When people argue, one person usually tries to bring a counter-argument to the other person's opinion (ArgFalse). There are a number of counter arguments that look rational, but that are wrong.
These bad counter arguments are so numerous that it would exceed the frame of this essay to list and explain them all. Therefore, this section explains only some of the more frequent such arguments.
Technical issues
In slight redundancy, some of the fallacies covered here appear again in other sections. The organization is as follows:

Non Sequitur

The most universal fallacious argument is the non-sequitur argument. It takes the following form:
Therefore, B.
In such an argument, there is no rule that allows us to go from statement A to statement B. In other words, a non-sequitur argument is just a listing of the premises, followed by the word "Therefore" and the hypothesis. The examples for non-sequitur arguments are numerous; here is one:
I am older than you.
Therefore, I should keep the money, not you.
Although non-sequitur arguments sound "logical", they are in fact not valid arguments in the sense of rationality (Arg). That means that, if A is true, then B can still be false. B remains nothing more than a claim.

A valid rational argument has to use rules, e.g., as follows:

A => B.
Therefore, B.
The rule, A => B, should be a good rule (GoodRules). More generally, the theory that is used to deduce B should be a reasonable theory (ReasonableTheories).

If the theory between the proof assumptions A and the hypothesis B is missing, then the argument is not a rational argument at all. There is no reason to believe that the hypothesis would be true. Thus, a standard reply to a non-sequitur argument is always:

Yes, A.
But this does not mean B. / But why should that mean B?
In the example:
Yes, you are older than me. But why should that mean that you should keep the money?

Him as well

A him-as-well argument assumes that something is good, because someone else did something bad. For example:
Alice: The US is a peaceful country
Bob: But the US invaded Afghanistan!
Alice: But Al Qaida bombed the World Trade Center buildings!
In this discussion, Alice claims that the US is a peaceful country. Bob brings a counter-argument. His counter-argument is valid, because peacefulness commonly implies not invading other countries. Alice tries to counter the counter-argument. Her argument is that the US invasion cannot be so bad, because Al Qaida also did bad things. But one bad thing does not cancel out another bad thing (GoodNoBad). The fact that the US invaded Afghanistan remains a valid counter-argument to the claim that the US would be peaceful (whether the invasion was justified or not).

One standard response to a Him-as-well argument is:

Yes, I agree. But this does not change the fact that X.
In the example:
Yes, I agree. Al Qaida bombed the World Trade Center. But this does not change the fact that the US invaded Afghanistan. Thereby, the US is not a peaceful country.

Conspiracy Theories and Insinuation

An insinuation is the hypothesis that something is not as prima facie evidence suggests, but caused by someone with bad intentions. Examples are:
Such statements are often conspiracy theories.

Insinuations are valid rational statements. They are dangerous, because they claim that someone did something with a bad intention. This could be an insult in the moral framework (Moral).

In a discussion, an insinuation is often used to prove that the prima facie evidence is false. Yet, an alternative explanation for something does not make that explanation true. The prima facie evidence remains the most plausible explanation until the alternative explanation can show some evidence for it.

A possible reply to an insinuation is:

That's an insinuation. There is no evidence for it. Hence, it's more reasonable to believe in the most plausible explanation for now.

Yes, but apart from that

An apart-from-that argument implies that since there is only one argument against a thing, that argument is not strong enough. As an example, consider the following discussion:
Alice: Your proposal to invest in this fund is against the policy guidelines of our company.
Bob: Yes, but apart from that, is there anything you can say against it?
This argument implies that the counter-argument that Alice brought up would not be sufficient. Yet, in fact, it is a killer argument (Killer). In general, one correct argument is enough to prove something wrong.

One way to deal with an apart-from-that objection is to say:

I already gave you a counter-argument.

True but irrelevant argument

A true-but-irrelevant argument presents a statement that is true or not falsifiable, but irrelevant. Since it is assumed that the interlocutor agrees on this statement, it is assumed that he gives up his previous objection. This technique is a particular case of the non-sequitur argument (NonSeq).


The true-but-irrelevant argument is not a valid counter-argument. The original hypothesis is not refuted. This type of argument can be seen as a special form of missing acknowledgement, a non-receptive behavior (MissingAck).

If confronted with a true-but-irrelevant argument, we can say:

That is true, but irrelevant.
It does not change the fact that (repeat your point)

Worse things have happened at sea

A worse-things argument says that there are things that are much worse than those observed by the other person and that, therefore, these things are not so bad after all. Example:
Alice: What you are doing to your wife is not nice, Bob!
Bob: Well, come on. Other couples are already divorced!
Bob's statement is true, but does not address Alice's reproach. Such an argument is a special case of the true-but-irrelevant argument (Irrelevant).

When confronted with a worse-things argument, we can say

That may be true, but it does not change the fact that
(repeat your point here)


A strawman argument is an argument that misrepresents or exaggerates the position of the opponent and then argues against it. For example:
Alice: We should liberalize the laws on beer.
Bob: No, any society with unrestricted access to intoxicants loses its work ethic and goes only for immediate gratification.
In this example, Bob exaggerates Alice's position and refutes that exaggerated position — but not the original one. (Example from [Wikipedia / Straw man]) This strategy is similar to distracting (Distracting).

One standard way of dealing with such an exaggeration X' of the original argument X is to say:

Nobody claimed X'. I was just saying X.
In the example:
Nobody claimed we should grant unrestricted access to intoxicants in general. I was just saying we should liberalize the laws on beer.

One particular instance of the strawman argument misportrays the original hypothesis as necessary or perpetual:

Alice: I would like to go swimming today.
Bob: I don't see why you always have to go swimming!
In this example, Bob implies (through a loaded question (Loaded)) that Alice feels a perpetual necessity to go swimming. This exaggeration is (most likely) false. It is also often obviously false, so that it is most likely not ment literally (ReasonBehind). Therefore, we can safely ignore the literal content of the statement. One way to answer is to point out that you have the right to do what you wish:
Alice: I can do as I wish, no?

Reason as excuse

The reason-as-excuse argument presents a reason for something as an excuse for that something. However, a reason for something does not necessarily make that thing any better (Good). A reason for something also does not make that thing morally correct (Moral). A reason for a behavior does not automatically justify that behavior. In particular, a reason why a statement is false does not make that statement true.

Here are some examples for this fallacious argument:

If confronted with such a reason-as-excuse argument against our statement X, we can say

OK, so we both agree that X.
In the example, Alice can say:
OK, so we both agree that you cannot help me with my problem.
Technical issues
Here are some unproven thoughts about this phenomenon (Theories): The reason why we are taking explanations as excuses may be that we have a tendency to automatically associate guilt, intention and damage. If the intention is missing, we assume no guilt and we assume no damage. Still, these components are independent (WrongRules).

False Dichotomy

This argument wrongly assumes that we have the choice between only two options, which exclude each other. For example:
Alice: To counter the problem of youth criminality, we can either use harder penalties or try to prevent the crimes in the first place, for example by investing more in education.
Bob: I think we should invest more in education!
Alice: OK, so you think that the current laissez-faire attitude of the courts is OK.
In this argument, Alice says that we can either upgrade penalties or education — but not both and nothing else. As Bob favors education, Alice concludes that he does not want harsher penalties. Yet, the two options do not exclude each other: One can implement harsher penalties AND invest in prevention. (This is an insight that political parties rarely have, as they identify either with one or the other, while a country may need both.)

If we are confronted with a false dichotomy, we can say

These options do not exclude each other.

Wrong rules

A wrong rule is a rule (SecRules) that does not hold in reality. Such wrong rules are, for example: See [Thoughts on Ethics / Misconceptions] for a further list of common errors in the area of morality. See here for a list of wrong rules as found on Wikipedia [Wikipedia / List of fallacies]

Technically, a wrong rule is a rule that produces incorrect predictions on our knowledge (Confidence). Therefore, it will most likely produce wrong conclusions. A wrong rule that someone uses to "prove" a statement X can be countered either by discussing the underlying wrong rule (ArgAgainstRule) or by saying

Yes, but that does not mean that X
For example:
Yes, it is quite normal that animals are mistreated in husbandry, but that does not mean we should tolerate it.

I read it

If someone makes an I-read-it argument, he supports a statement by saying he read somewhere that this statement is true. Typical examples are advice on food ("You should not eat sausages because it is bad for your health") or on certain behaviors ("You should not use dish soap to clean the bathroom"). As evidence for such statements, the person typically cites Web pages, friends, or newspaper articles.

Newspapers, friends, and Web sites, however, may report false information. It is not sufficient that someone thinks or writes something to make it true. General statements (SecRules) are only true if they have made true predictions in the past, and if they make predictions for the future (SecTruth). The safest way to validate a general statement is through a scientific study (EstablishRule, Authority). Scientific studies about health effects can only generalize from the subjects of the study to the world population if at least a hundred people participated in the study (EstablishRule). Studies about the health effects of medical drugs, for example, have to have thousands of participants in order to prove that the medicine is harmless and that it has the desired effect. Studies with less participants can only yield a hypothesis (Hypotheses). They are not statistically significant.

Even if the claim has been scientifically validated, the newspaper, Web site or friend my may still misinterpret the study. Scientific studies usually come with a caveat that more research is needed to validate the hypothesis — a note that is often omitted in news articles. Lastly, the newspapers, friends, and Web sites may also be misinterpreted themselves. Therefore, care is necessary with "I read it" arguments. If we follow wrong or useless advice, we just complicate our life needlessly. We discuss this in NoBOD. Therefore, we should take care and avoid gullibility.

To counteract the I-read-it arguments, I have created a Web page that also makes all sorts of claims. The reader is invited to have a look at this page, and next time someone makes an I-read-it argument, this argument can be countered by an equally plausible I-read-it argument. The page is here.

Wer nichts weiß muss alles glauben
(If you don't know anything, you have to believe everything)
Marie von Ebner-Eschenbach

I know someone

The I-know-someone argument seeks to reject a guarded generalization (Guarded) by naming a counter-example. However, a guarded generalization remains valid even if we find a counter-example, because the generalization makes a claim only about the majority of cases, not about the single instance. Example:
Alice: In general, men are more likely to become criminals than women.
Bob: Well, you cannot really say that. I read about a woman who stole a car. So it all depends.
Bob's objection to Alice's statement is not valid: A single example does not contradict the general observation that there are more male criminals than female criminals. In general, it is easy to attack guarded generalizations, because in most cases we can find counter-examples. Still, the only valid counter-argument to a guarded generalization is an observation that the claim is not true in the majority of cases.

If confronted with an I-know-someone argument, we can reply, e.g.:

Yes, but I was talking about the general case.

Why not?

The why-not argument implies that, if we do not have a reason against something, then we should do that something. Consider the following sample discussion:
Alice: Why don't we simply go watch a movie?
Bob: er...
Alice: OK, let's go watch a movie.
In this discussion, Alice asks for reasons against watching a movie. Since Bob does not come up with any, Alice deduces that they should go watch a movie. However, it is a fallacy to assume that, just because we have no argument against something, we should do that something. To do something, we need positive reasons in favor of that something (KnowReasons).

There are some standard arguments against doing a thing X. We are usually just too lazy to enumerate them. These standard counter-arguments are:

Thus, a standard reply to "Why don't you do X?" can be:
I do not feel like it.
This argument does not need justifications (EmotionalState).

Rhetoric questions

A rhetoric question is a question with an obvious answer. When the listener gives that obvious answer, the asker assumes that the listener agrees with him on some hypothesis. Examples are:

The rhetoric question forces the listener to give a predetermined answer, which is wrongly seen as a proof for the hypothesis. This proof happens through a wrong rule (WrongRules). Therefore, a rhetoric question is a bad argument. A rhetoric question that asks X to imply Y can be countered, e.g., as follows:

That is a rhetoric question. Even if X, that does not mean that Y.


Not all people strive for truth. Sometimes, people strive mainly to establish their own viewpoint, no matter whether it is right or not. It can take considerable effort to determine and counteract such behavior.


Non-receptiveness in the sense of this essay is conversational behavior that does not give due attention to an argument brought by the interlocutor or that prevents the interlocutor from giving arguments altogether.

Non-receptiveness is not necessarily intended. Sometimes people are just too busy or too lazy to take into account an argument. In some cases, however, non-receptiveness is a sign of disrespect, cantankerousness or arrogance. Non-receptiveness may be deprecated behavior under your moral framework (Moral).

If someone does not give due respect to the arguments of his interlocutor, this means that he is not interested in revising his position. Therefore, non-receptiveness means that the person may be talking without the aim of speaking truth. Therefore, such behavior is not rational (SeekTruth). Worse, the fact that the person does not have his thoughts checked by other people entails that he may be saying things that are wrong (OpReal). If someone says things without caring whether they are true or not, this person becomes untrustworthy. This section will make proposals of how to detect and counteract non-receptiveness.

I disapprove of what you say, but I will defend to the death your right to say it.
Evelyn Beatrice Hall, attributing it to Voltaire

What non-receptiveness is not

Non-receptiveness in the sense of this essay (NonRecDef) does not cover the following cases:

When to counteract non-receptiveness

Non-receptiveness (NonRecDef) implies talking without the aim of speaking truth. In general, everybody is free to talk with whatever aim he wishes (if he follows his respective moral rules (Moral)). We are not obliged to change how a person is talking. We are also not obliged to help someone approach truth if he does not want to (Teach). Therefore, there is no reason to counteract non-receptiveness per se. On the contrary, we may decide to just listen (Listen).

However, we might wish to counteract non-receptiveness, if we have an interest in the other person's opinion. This can be because our own goals depend on the other person's opinion (Goals). It can also be because we feel challenged by the other person or because we feel the desire (Desires) to show that what he says is wrong. In these cases, we have to counteract non-receptiveness.

Know what statement you want to get through

Non-receptiveness is a state in which the other person does not acknowledge what we want to say (NonRecDef). If we want to counteract non-receptiveness, we have to know exactly what we want to say. If we do not know what we want to say, then, by definition, there is no problem of non-receptiveness. If we do not want to say anything, we can just listen (Listen).

Now assume that we want to say something. Then we have to know exactly what we want to say. This is not trivial, since non-receptive people often do their utmost to distract us from what we want to say. Therefore, before even thinking about counteracting non-receptive behavior, we have to be very clear in our mind about the message that we want to get across. It helps to repeat this message at the beginning of the discussion ("My main concern is that..."). It also helps to repeat this message from time to time — for ourselves and for the other person. We shall not let go of the message, and we shall not let ourselves distract to different messages.

How to counteract non-receptiveness

This essay proposes a strategy to counteract non-receptiveness (NonRecDef). This proposal is a theory (Theories), meaning that the strategy is not guaranteed to work. If the reader has his own strategies, he is free to use them (and invited to share them with me).

The basic strategy that this essay proposes is:

  1. Identify non-receptiveness
    This is not trivial, because not every argument that we do not like is necessarily non-receptive (NonRecNot).
  2. Ignore its content
    This is often hard, because non-receptive talking still distracts us.
  3. Repeat your argument until you get it acknowledged by your interlocutor
    Getting it acknowledged means: Having your interlocutor react to it.

As soon as our interlocutor becomes non-receptive, we are no longer bound to follow his arguments. We may require him first to acknowledge our point. The following articles treat specific instances of the general procedure to that end.

Missing acknowledgement

A missing acknowledgement is a situation where we bring an argument, but our interlocutor does not react to it. More precisely: Our interlocutor says something that he could also have said if we had said the contrary. Here is an example:
Alice: We should get the tickets for the cinema.
Bob: The movie will be awesome, I have read so many good things about it!
This is missing acknowledgement, because Bob could have said the same thing if Alice had said the contrary:
Alice: We should get the tickets for the cinema.
Alice: We already have the tickets for the cinema.
Bob: The movie will be awesome, I have read so many good things about it!

Such behavior is non-receptive (NonRecDef) and thus not rational. It may be combined with distraction (Distracting) or flooding (Flooding). This essay proposes the following procedure to counter missing acknowledgement:

  1. Identify the missing acknowledgement.
    You can do this by checking if the other person could have said the same thing if you had said the contrary.
  2. Acknowledge what the other person said (Ack).
    Alice: Great, I am really looking forward to seeing that movie!
  3. Repeat your point
    Alice: But I still think we should get the tickets now
  4. Point out the missing acknowledgement
    If the other person is still does not acknowledge, point out that you are talking about different things. Then ask the other person to acknowledge explicitly.
    Alice: Bob, we are talking about two different things! I know the movie is great, but we do have to get the tickets now if we want to watch it tonight. Do you understand that?
Here is the same scenario in a more poetic setting:
- Je ne puis pas jouer avec toi, dit le renard. Je ne suis pas apprivoisé.
- Ah! pardon, fit le petit prince.
Mais après réflexion, il ajouta:
- Qu'est-ce que signifie "apprivoiser"?
- Les hommes, dit le renard, ont des fusils et ils chassent. C'est bien gênant! Ils élèvent aussi des poules. C'est leur seul intérêt. Tu cherches des poules?
- Non, dit le petit prince. Je cherche des amis. Qu'est-ce que signifie "apprivoiser"?
Antoine de Saint-Exupéry in his book "Le Petit Prince"

Shooting down

Shooting down an argument happens by discrediting the other person's position without giving a proper counter-argument (ArgFalse). This is non-receptive behavior, because such a reaction does not depend at all on the other person's argument (NonRecDef). Examples for such shooting down sentences are:

Such a phrase ends the discussion, but does not give due respect to the other person's view. To counter such behavior, we have (at least) two options:

  1. If we would like to pursue our point, we can break the stop sentence by saying
    So did you understand my point or not?
  2. If we are no longer interested in the discussion, we can just reply with any other stop sentence. This will end the discussion without our admitting defeat.
Shooting down can be combined with distraction (Distracting) or flooding (Flooding).


Flooding is the process of bringing so many arguments and saying so many things that it is impossible to answer them all. This conveys the impression that the original argument is definitively dead — even though it has not been given due attention. Flooding often follows missing acknowledgement (MissingAck) or shooting down an argument (ShootingDown).

Flooding is non-receptive behavior (NonRecDef), because it does not give due respect to the other person's argument. This essay proposes the following procedure to counter flooding:

  1. Identify flooding
    Flooding is happening if you feel that your argument has not been given due attention, and the other person talks about so many other things that you could not summarize them in one sentence.
  2. Ignore what the other person said
    This can be hard, because among the many things the other person said, there may be some that challenge you. Still, ignore them!
  3. Point out the flooding
    You can do this, e.g., by saying
    Now you have said many things, but I am afraid you still have not answered my point. Could you please say why my argument is wrong?
  4. Repeat your point
Flooding is similar to distracting (Distracting). Both try to seal off the previous argument without giving it due attention. There are people who habitually flood their interlocutor. They are not interested in the interlocutor's view and just keep talking. They are just like a radio. They are radio-people.


Distracting is the process of raising a point that is different from the original argument. Often, the new point is challenging, controversial, interesting or phrased as a question. The danger is that the participants of the discussion jump on the new topic, forgetting about the original argument. Distracting usually follows missing acknowledgement (MissingAck) or shooting down an argument (ShootingDown).

Distracting is non-receptive behavior (NonRecDef), because it ignores the other person's argument completely. This essay proposes the following procedure to counter distractions:

  1. Identify the distracting behavior
    The other person is distracting you if he could have said the same thing if you had not brought up your point (MissingAck). At the same time, he brings up a new, interesting topic.
  2. Ignore what the other person said
    This can be hard, because, by definition, distractive behavior aims at distracting you.
  3. Destroy the distraction
    You can do this, e.g., by saying
    That may be true, but you are talking about something different. Let's go back to what I said before.
  4. Repeat your point

In email communication, distraction can happen if the interlocutor inflates one topic to 3 or 5 topics (possibly with provoking hypotheses or insults). If you respond to each of the topics, your interlocutor will inflate each of your answers into again 3 or 5 topics. This way, the original point suffers an exponential decline. In these cases, it is best to ignore all topics raised by the interlocutor, respond not inline, but above the interlocutor's text, and address only the topic that you raised, until it is acknowledged.

Slamming the door

Slamming the door means making a point and then ending the discussion. This can happen, e.g., by leaving the room.

Slamming the door is a very explict means of being non-receptive (NonRecDef). Therefore, it is worth considering whether the other person is possibly angry with a reason (ReasonBehind). Maybe we have been non-receptive ourselves (NonRecDef), or maybe we have offended them. In these cases, it is up to us to resolve the problem.

The reason may also be that the other person cannot counter our argument. In this case, we can consider the battle won. If we were just interested in showing that we were right, that goal is achieved (NonRecWhen). We can save our energy (StdGoals).

However, if we need an explicit acknowledgement from the other person, we will have to contact them again later (not necessarily in person). It may be that the other person already regrets having slammed the door, so we should generally assume good intentions (AssumeGood).

Staying silent

Sometimes a person does not reply at all to an argument, but just stays silent. This is non-receptive behavior (NonRecDef), because the argument is not given due weight.

Just like slamming the door (SlamDoor), staying silent is a very explicit way of being non-receptive. Therefore, we should ask ourselves whether the person is possibly angry with a reason (ReasonBehind). We can, for example, ask why the person is not talking to us.

If it becomes obvious that the other person simply does not want to admit defeat, we can say that we assume that the other person agrees. If the other person does not object, we can consider the argument won.


In this scenario, the other party simply says that the issue is not worth discussing. They will say, e.g.,

It might be true that the issue is indeed not worth discussing. Therefore, we should spend a second to think whether we really want to continue defending our point (ForgiveForget, TalkToArgue). If we agree that the issue should simply be abandoned, we should say so.

In general, however, the other party's behavior is non-receptive, because it ignores our original argument (NonRecDef). In this case, we should insist that the point is worth discussing:

  1. Emphasize the importance of the point, e.g., by saying
    Don't swipe it under the rock.
  2. Repeat your point

Accusing of overreaction

In this scenario, one party accuses the other party of overreacting. Instead of answering to an argument, they imply that the other party is taking the disussion way too serious ("Don't get your panties in a bunch!", "Hey, reg dich ab, Mann!"). Such behavior is non-receptive, because it ignores the original argument (NonRecDef). The behavior is particulary unpleasant, because the accusation makes you angry, but getting angry would be exactly the overreaction that you have been accused of.

If someone accuses us of overreaction, we should first verify whether that reproach could be true. If we have been insisting on a detail or if we have offended the other person, we should backpedal. There may also be some hidden reason behind the accusation (ReasonBehind).

If it turns out that the other person merely seeks to hide that they cannot answer our argument, we can simply ignore the reproach:

  1. Repeat your point


Deflection is a technique to react to a reproach (Reproaches). Instead of talking about the content of the reproach, one talks about the person who makes the reproach. This can take the form of a generalization about that person (Generalizations) or of an insult, so that the statement acts as a distraction (Distracting). Examples are:
Bob: You did not do the shopping as you promised!

Alice: You never do the things that you promise either!
Alice: You seem to think about that a lot.
Alice: You are not very good at shopping anyway.

Deflection can also happen preemptively by attacking the speaker already before he makes the reproach — to kill the reproach before it gets on the scene. A deflection is non-receptive behavior (NonRecDef), because it does not give any consideration to the reproach. It deflects the attention from the addressee of the reproach to the other person.

The main difficulty in countering a deflection is to ignore the deflection. This is difficult because the deflection is deliberately provocative in order to distract (Distracting). So one strategy to counter it is:

  1. Identify the deflection
    The other person is deflecting your statement if you suddenly find yourself urged to explain or excuse yourself.
  2. Ignore what the other person said
    Deflection is a trick. Ignore it.
  3. Destroy the deflection
    You can do this, e.g., by saying
    This is about you, not me.
    You are just trying to distract from yourself.
  4. Repeat your point

Accusing of dispute

In this scenario, one party accuses the other party of aiming for dispute. Such a reproach can take several forms: The original argument is ignored. Therefore, such behavior is non-receptive (NonRecDef).

When confronted with such a reproach, we should verify whether the other party is possibly right. Is the issue we are talking about really important enough to spend our time on it? Or are we just arguing for the sake of it? (TalkToArgue) It might also be that we already convinced the other party (DontAssumeRatStat). If it turns out that the other party merely seeks to hide that they have no more argument, we can react, e.g., as follows:

  1. Break the accusation
    This can happen, e.g., by saying
    Well, if you understood my point, we would not have to argue.
    Yes, if we have different opinions, we have to argue.
    I am not arguing. I am explaining why I'm right [Global Secular Humanism Movement].
  2. Repeat your point

What to do if you cannot counteract non-receptiveness

There may be cases where we just cannot get the other party to react to our argument. It may be that we have to give up on convincing our interlocutor (Loss).

If our goal was to convice the other person, we can say that we have the impression that the other person does not want to question his views. If that is indeed the case, then there is no use arguing (Teach). If that is not the case, we might be offered a chance to make our argument heard.

If we are in a dispute with the other person and cannot resolve it, we have the option of asking someone else to arbitrate. If there is an authority, we can consider asking that authority to arbitrate (Outsourcing). If the argument concerns work, the authority may be our boss (or theirs). If the argument is of legal nature and of significant importance, the authority may be the jurisdiction.


Goals and Problems

This part introduces the notion of a goal (SecGoals). It defines a problem as a goal that is not fulfilled. It goes on to cover different classes of problems (SecProb) and decision problems in particular (SecDec).


This section defines the notion of goals. Goals give a purpose to rationality. They allow us to label things as "good" and "bad". They are also the basis for the study of ethics.

Statements about Goals

A goal is a long-term desire (Desires). For example, a goal can be to be rich, to have a dog or to visit Napels. In a rational argument, goals can be expressed for example by statements of the form "My goal is...":
My goal is to become a teacher one day
Like desires, goals are personal preferences and thus can rarely be justified or explained (EmotionalState). Still they play an important role in rational arguments because much of rationality is about finding ways to achieve goals (SecProb).

Even though the concept of goals may sound egoistic, goals do not necessarily have to be selfish. For example, it can be a goal to make another person happy. Parents the goal of giving their children a good upbringing. A husband has the goal of having a harmonious relationship with his wife. A friend has the goal of comforting a friend. Goals can be altruistic.

We can assume that some goals are shared by most people (StdGoals).

If you want to do evil, science provides the most powerful weapons to do evil; but equally, if you want to do good, science puts into your hands the most powerful tools to do so. The trick is to want the right things, then science will provide you with the most effective methods of achieving them.
Richard Dawkins
Technical issues
If one state of the world is a necessary condition for a goal, then this state necessarily becomes a goal. For example, since a university degree is a necessary condition for being a teacher, we deduce:
My goal is having a university degree.
Since necessary goals are necessary conditions for the goal, we have to achieve the sub-goal in order to achieve the goal.

There are also sufficient sub-goals, i.e., states that are sufficient conditions for a goal. For example, if giving somebody chocolate is sufficient to make him happy, then giving him chocolate is a sufficient sub-goal for achieving his happiness. It may not be the only sufficient sub-goal, though.

Problem Statements

A problem is a difference between the desired state or goal (Goals) and the current state of the world. Since different people have different goals, different people have different problems. Rationality expresses problems by saying "For X, it is a problem that...". For example, we can say:
For Bob, it is a problem that there is no chocolate left in the fridge.
Such a statement means that there is a desired state (involving chocolate) and that the actual state of the world is different. Much of rational thinking serves the purpose of problem solving. Rational arguments are used to find ways that push the real state of the world towards the desired state, thus eliminating the problem (SecProb).

Statements about good and bad

An action is "good" with respect to a goal (Goals), if it pushes the state of the world closer to the desired state. An action is "bad" if it pushes the state of the world farther away from the desired state. (See [Thoughts on Ethics / Formalizing the World] for a formal model of states and actions.). For example, if it is a problem that there is no chocolate in the fridge, then it is "good" to go shop some chocolate:
For the goal of having chocolate, it is good to go shop chocolate.
The notions "helpful", "useful", "reasonable" and the like are synonymous with "good" in this context.

The notions of good and bad are always tied to a particular problem. An action is never good or bad by itself, but only with respect to a desired state. If we say that ethical behavior according to some moral framework is a goal (Moral), then the notions of "morally good" and "morally bad" are special cases of "good" and "bad".


An advice is a friendly instruction. Rationality allows expressing advice by statements of the form "You should". For example, we can say
You should not take away his bicyle.
Such an advice means: For one of your goals, this action will be useful (Good). Much like the notions of good and bad, advice is only admissible in rational arguments in conjunction with a goal:
If you do not want him to get mad at you, you should not take his bicyle.

Nothing allows us to prove that the addressee of this advice will follow the advice. Human behavior is unpredictable in this strict sense (FreeWill). Still, advice is a useful outcome of a rational argument. It is possible that a rational argument produces two contradicting advices. Then, these advices have to be weighted against each other (BestAdvice).

Best Advice

An advice is a friendly instruction (Advice), telling someone that one particular action will bring the state of the world closer to one particular goal:
If you do not want him to get mad at you, you should not take his bicyle.
However, people usually have multiple, conflicting goals. In the example, you might have the goal to be in time for your math exam, after having missed the alarm you set. His bike might be the only option you have:
If you want to be in time for the math exam, you should take his bicyle.
Such conflicting goals have to be weighted carefully against each other. This essay dedicates a section to this process (SecDec). Once a decision process has determined which action is the best to take in view of all goals, this action becomes the best advice. The best advice is an advice that fulfills the most important goals in a trade-off with the others. In our case, this may well be:
The best thing to do for your goals is to take his bicyle.

Moral Labels

The question of what is right and what is wrong is one of the oldest philosophical conundrums. In the framework of rationality, we distinguish three types of behaviors:
  1. morally wrong behavior
    These are immoral behaviors that we want to avoid and punish. For example, most people agree that theft is morally wrong.
  2. morally obligatory behavior
    These are the things that we are morally obliged to do. For example, calling the police when we see a crime.
  3. morally allowed behavior
    These are the things that we may do. For example, most people will agree that it is morally OK to eat chocolate.
These terms are labels for behavior. A moral statement is statement that says that a certain person or authority gives a certain moral label to a certain action. For example, a moral statement is:
I call George W. Bush's invasion in Iraq morally wrong.
A moral statement can take other forms, such as "I find that the invasion in Iraq is morally wrong" or "For me, the invasion in Iraq is morally wrong".

There is no universal agreement on which behaviors are morally right or wrong. It cannot be proven from the laws of nature which behaviors are wrong and which are not (see [Thoughts on Ethics / Ethics and Nature] for a discussion). Therefore, the moral quality of a behavior is not an intrinsic property of the behavior itself. We cannot say that a certain behavior is objectively morally wrong. Such a statement would be unfalsifiable (Unfalsifiable). We can only say that certain people find certain actions morally wrong. These statements are what we call moral statements. Such statements are personal statements (Personal). Thus, "I find the invasion in Iraq morally wrong" is of the same type as "I find Alice beautiful". They express a valuation of an action by a person. Such statements are falsifiable (it suffices to ask the person about their opinion). Moral statements typically come in the form of moral frameworks (MoralFrame).

Moral Frameworks

Moral statements are statements that attach a moral label to a behavior (Moral). Typically, moral statements come in the form of a whole package of moral statements. These packages are called moral frameworks. Examples for moral frameworks are:

Moral frameworks label certain behaviors as morally bad, others as morally obligatory, and again others as morally allowed (Moral). For example, the national criminal law can say something like

Theft is a crime.
Technically, this statement is an abbreviation for a rule that has a moral statement in its conclusion:
If X steals something at time point T, then the national criminal law of this country calls X's action at time point T morally wrong.
From now on, we will see moral frameworks as theories (Theories) of such rules (Rules). In most cases, the moral framework itself appears as a moral authority, i.e., as the "person" who labels certain behaviors good or bad. For example, the moral framework "National Criminal Law of Germany" is a set of rules that say that the national criminal law of Germany condemns certain actions.
Doing the right thing means having no regrets.
Edward Snowden

Properties of Moral Frameworks

Moral frameworks label certain behaviors as morally bad, others as morally obligatory, and again others as morally allowed (Moral). In a contradiction-free moral framework, all obligatory behaviors are also allowed behaviors. Both obligatory and allowed behaviors are disjoint from bad behaviors. Moral frameworks may also offer degrees of judgements, saying for instance that certain behaviors are desirable, but not obligatory. Most moral frameworks define only morally bad behaviors. They do not define what "morally good" behavior is. If something is not morally bad, this does not mean it is "morally good". For example, most moral frameworks are silent about the consumption of chocolate. Therefore, the consumption of chocolate is not morally wrong. But it is not explicitly "morally good", either. It falls in the class of morally allowed behaviors.

When using a moral framework, we usually assume completeness. This means that we assume that everything that is not defined as wrong in the framework is morally allowed. For example, if we assume the Ten Commandments with completeness, then we can deduce that slavery is allowed, because the Ten Commandments do not condemn it. If we assume the Ten Commandments without completeness, we cannot say anything about slavery.

Moral frameworks typically require that the same framework be used to judge your own behavior and other people's behavior. They may also require that the framework used to judge your own behavior be stricter than the framework used to judge other behavior (Asymmetry). Yet, not all systems require equality of rights and duties. Societies that allow slavery, for example, have different standards for slaves and free people, as do societies that implement the caste system. Note that we do not discuss here whether one morel framework is "better" than another one. That is technically impossible anyway without a reference framework (Good). Here, we limit ourselves to the definition of moral frameworks. See [Thoughts on Ethics] for a deeper discussion of moral values.

Liberal moral frameworks, such as [Thoughts on Ethics], label only behaviors as bad that harm somebody else. There are other moral frameworks that go beyond this minimalistic liberal view. These are, e.g., religious sources or advice books. They aim to be more comprehensive and define "good life" in general. This may include the educational, social and political aspects of life.

Moral frameworks come into existence if someone defines them. This is done mostly by writing them up. The creators of the criminal law, for example, gathered and produced a document that contains rules with moral statements. Such a moral framework comes into effect if people vow to adhere to it. For example, the government of the country decides that from now on, it wishes to enforce its criminal law, and to use its jurisdiction and executive power to prosecute people who behave morally wrong according to this law. This does not make the law "true" or "good" in any sense. It just means that the law is enforced.

If a moral framework got approved by a government, it becomes a legal framework. The rules of such frameworks are called laws. Something is legal, if the legal framework deems it morally acceptable. The concept of legality is often opposed to the concept of morality. While the former refers to the laws of a country, the latter refers to the "natural" or "true" moral quality of actions. We have already seen that there exists no such "natural" or "true" moral quality of actions (Moral). All moral frameworks are just lists of human preferences. Therefore, when people criticize a law as "immoral", they usually mean that it contradicts their own personal moral framework.

Using Moral Frameworks

In rationality, a moral framework is a theory of rules that condemns certain behaviors as morally wrong (MoralFrame). This theory can serve as a proof assumption (Pasm) in a proof (Proofs). We can use inclusion to incorporate the moral framework into our proof (Inclusion). For example, we can say:
We assume the Ten Commandments.
This inclusion statement expands to a list of moral statements:
If X kills a person, then X's behavior is morally wrong according to the Ten Commandments
If X prays to more than one god, then X's behavior is morally wrong according to the Ten Commandments
We can now add more proof assumptions, e.g.:
Bob prays to more than one god.
By rule application, we can derive (Inference):
Bob's behavior is morally wrong according to the Ten Commandments.
The Ten Commandments say that praying to more than one god is morally wrong. Bob's behavior is an instance of that behavior. Therefore, Bob behaves morally wrong according to the Ten Commandments. People have a tendency to omit the specification "according to the Ten Commandments". They often believe that a behavior by itself is morally wrong. Therefore, they will object to such a conclusion if it does not fit with their personal beliefs of morality. However, an action is never wrong or right by itself (Moral). A proof such as the above will never conclude that a behavior is wrong. It will only conclude that a certain moral framework declares it wrong. We do not have to agree with that moral framework.

In reality, people rarely know what framework they agree with. They just call anything "morally wrong" that goes against their interests. See [Thoughts on Ethics / Perpetrator's justice] for a discussion on the subjectiveness of moral statements. We can, however decide to explicitly agree with the moral framework, by adding as a proof assumption:

If X is morally wrong according to the Ten Commandments, then I find X morally wrong.
This allows us to deduce
I find Bob's behavior morally wrong.

Once we have concluded that a certain moral framework (or ourselves) deems a certain action morally wrong, we can make a reproach (Reproaches). This does not mean that something would happen. If someone does something bad, usually nothing happens. Something happens only of some authority (be it the government, some activist group, or ourselves) decides to enforce the moral framework — and to impose a penalty or consequences on the perpetrator.

Social Norms

A social norms is a behavior that is expected in a certain society. For example, the British society expects you to queue at a bus stop. Rationality can express social norms by a statement that says that a certain behavior is the social norm in a given society:
In the British society, it is a social norm that people queue at the bus stop.
Behaviors are never expected per se. Behaviors are expected by people. A society expects people to behave in a certain way. If the society is clear from the context, it can be omitted in the statement (Context).

Stating that something is a social norm does not mean that the speaker appreciates this norm. A social norm is neither good nor bad by itself. It can be judged only with respect to a moral framework (Moral) or with respect to goals (Good). Some moral frameworks enforce social norms. In this case, not respecting the norms is a morally bad thing (Normal).

Classes of Problems

One of the main applications of rationality is problem solving (Problems). Every problem requires a different solution and it is hard to find generally applicable solutions. Still, there are certain classes of problems that appear again and again in life. This section will list some of them, together with proposals of what to do. The classes of problems presented here are patterns in the sense of this essay (Patterns), i.e., they do not necessarily happen in reality. The proposals are theories in the sense of this essay (Theories), i.e., they are not guaranteed to work.

Becoming aware of a problem

The most important step in solving a problem (Problems) is becoming aware of the problem. This is not always easy. We tend to ignore our problems, to distract ourselves from our problems, to burden the fault for the problems on someone else, to refuse to accept that we have a problem, or to assume that the problem is not where it is in reality. Another mistake is to assume that there is only one problem, while, in reality, there are several. If we want to solve the problems, we have to pinpoint them first.

To pinpoint the problem, we have to allow ourselves an honest analysis of ourselves and of the facts. This is a conscious step to take. It is also a very reasonable step to take, as we are arguably our most trusted friend. To find out where the problems lie, we can use self-analysis (SelfAnalysis): We imagine different situations, of the past and of the future, and note down the ones that make us feel uncomfortable. These are most likely those that define the problem.

By nature, I am an engineer. I am more interested in solving problems than in wallowing in the emotions that they incur.
Edward Snowden in on 2014-05-27, translated

Loss problems

A loss is a problem (Problems) where a desired thing or a circumstance is invariably no longer available. Specific instances of this problem are

Losses are among the hardest problems in life, because they correspond to a net decrease of life quality. Often, they cannot be "solved", i.e., often, the original state cannot be restored. Therefore, one way to deal with a loss problem is the following:

  1. Check whether it's real
    Check whether the loss really happened. In some cases, we are just afraid that the loss happened or we suspect it, but we are not sure. In such cases, it is not reasonable to act as if the loss had already happened (DontWorry).
  2. Check whether it can be undone
    Check whether the loss can be undone at reasonable cost. Can the object that we lost be found? Can the injury be healed? If the loss cannot be undone, seek alternatives (Orange). Can we replace the object we lost? Can we send our application elsewhere? This is a how-to problem (HowTo).
  3. Quantify the loss and live with it
    If no alternatives can be found, we have to learn to live with the loss. We have to accept that life will not be as it was before. There is no use complaining. Rather, we have to make the best out of what we still have. For this purpose, we should quantify the loss: We should become aware of what exactly we lost and what we still have (LimitLoss). Then we should write off the part we lost. We should write off exactly the part we lost — nothing more and nothing less.

In addition, it is always reasonable to take care that the loss is not repeated (SeeMetaProblem). We can also decide to help other people avoid the loss. Such altruistic endeavors are often perceived as comforting. There are a number of other things that we can do to recover from the problem (PostProb).

Technical Issues
When counseling other people, we might be tempted to point out the "positive aspects" of the loss. Such a view is not always helpful. It will push the other person into emphasizing the importance of the loss. It might be safer to ask the person to quantify and bound the loss — and then to accept it.

How-to problems

A how-to problem is the problem (Problems) of figuring out how to transform the current state of the world into a desired state (Goals). Specific instances of this problem are:

Generic approaches to how-to problems are:

  1. Ask yourself
    Try to figure it out by yourself. Try to remember whether you solved this problem or a similar problem before. See whether there is documentation available (forms often carry instructions; printers often have explanations printed on them; the stain cleaner comes with a manual etc.)
  2. Ask the Internet
    Search the Internet for a solution. It is often surprising to see how many other people have bumped into the same problem — and have proposed solutions for it.
  3. Ask others
    Ask someone who has experience. To be respectful, ask the person that is lowest in the hierarchy who can answer your question.

Once the problem has been solved, it is reasonable to take care that the problem does not appear again (SeeMetaProblem). For example, it can be reasonable to write down the solution we found. We can use this solution next time we have the problem. We can also be altruistic and provide the solution to other people who might run into the same problem — e.g., by posting a note on the printer or by publishing the solution in an online forum. This is one of the main strategies to pursue after a problem in general (PostProb).

Overstrain problems

Overstrain is a problem (Problems) where more things are demanded from an individual than he can deliver. Specific instances of this problem are

In addition to the things that are demanded explicitly, there are always the natural needs of happiness, health and well-being (StdGoals). If these natural needs are not met, this will also lead to overstrain. Overstrain problems can be addressed, e.g., in the following way:

  1. Become aware
    Become aware of the overstrain (Aware). This is not trivial, because people often think that they can handle the situation when, in fact, they cannot.
  2. Reduce obligations
    Identify items that are less important and that can be given up savely (DecProb). Give them up (Loss).
  3. Postpone obligations
    Identify items that can be dealt with at a later time, if you know that you will have the necessary resources later on. Postpone these items. Postpone only if you know that you will have the resources later on.
  4. Be more efficient
    Organize your work and resources so as to be more efficient (HowTo).
  5. For the rest: fail
    Fail on the items that you cannot deliver. Do so early (FailFast, Loss).

In addition, it is always reasonable to take care that the overstrain is not repeated in the future (SeeMetaProblem, PostProb).

Remorse problems

Remorse is the problem of regretting that we have done something to someone. Examples are: Remorse can be a painful experience. We long for forgiveness or for a way to undo the damage we did. This may not always be possible.

In general, immoral behavior and remorse fall in the domain of the moral frameworks (Moral). Moral frameworks define what is "wrong" behavior. They also define what to do if such behavior has happened. A religion, e.g., can provide answers to remorse problems.

Here is a proposal of how to deal with remorse under a liberal moral framework [Thoughts on Ethics]:

  1. Check whether there is a problem
    See whether the thing you did was really as bad as you think it was (DontWorry). See whether damage occurred [Thoughts on Ethics / Damage]. Compare with previous similar instances (Normal). Check whether you can undo the damage you did. Can you still stop the mail or undo what you did wrong? If the damage is real and irreversible, the following process will be painful. Stay firm and go the painful way, there is a light at its end.
  2. Apologize
    Figure out who are the people that you made angry. Try to imagine what they feel. Present your apologies to the people you hurt. Apologize fully and whole-heartedly, with more than just set phrases (AckWrong). Compensate for the damage you did (Loss). Take care that the problem will not appear again. If this works out, you're off the hook.
  3. If necessary, insist
    If your apology is not accepted, try harder. Show that you feel remorse and that you are ready to make efforts. If the other person categorically refuses to accept your apologies and does not offer alternatives, then the other person does not want to resolve the issue. There is no use trying to resolve an issue against the will of the person affected [Thoughts on Ethics / Sulking , Way out] . If you did your best, then nothing more can be asked from you. You are free.

In general, an apology should be backed up by a compensation for the damage [Thoughts on Ethics / Compensation]. In addition, we have to take care that the problem is not repeated in the future [Thoughts on Ethics / Penalty]. (SeeMetaProblem). Without these two components, an apology is just worthless words.

If we find ourselves on the receiving side of the remorse, and if we want to accept the apology and make the other person happy, we should say that we know that the other person did not act with bad intentions. What people often fear most is that other people think badly of them. By saying explicitly that we believe in the other person's good intentions, we can destroy that fear. Remorse and forgiveness in tandem can even strengthen a human relationship. See further down for general ideas on what to do after a problem is solved (PostProb).

Fear problems

Fear is the state of anticipating a severe problem (Problems). This can be, for example Fear is a very unpleasant state that cannot always be resolved — in particular if the fear is justified. Here is a generic proposal to deal with fear:
  1. Find out what you fear
    We should first formulate the anticipated problem clearly, possibly by writing it down. In particular, we should check whether the real cause of our fear is not something else than we think (ReasonBehind). Once we have established what we fear, we should estimate how likely it is that this event happens. We have a tendency to fear things, even if they are unlikely to materialize. This is counter-productive (DontWorry).
  2. Take measures
    If the problem is real and likely to occur, we should take all possible counter-measures. This is a how-to-problem (HowTo).
  3. Stop being afraid
    Once we have taken all necessary counter-measures, there is no use fearing anymore. We have to wait patiently and accept whatever will finally happen. What finally happens may be a loss (Loss).

In addition, it is always useful to ensure that such problems will not happen again (SeeMetaProblem). This is one of the main strategies to counteract insecurity, along with others (PostProb).

Social problems

A social problem (Problems) is a state where we entered into conflict or misunderstandings with other people. This may be, for example, in the following cases: Social problems are hard to deal with because they center on something that is intrinsically beyond our own control (another person). Even more that the other classes of problems, social problems have no generic solution. Here is a proposal that might help:
  1. Check whether it is a problem
    Check whether there is really a problem or whether you are just fearing there could be one (DontWorry). Check whether you want to solve the problem or whether you can actually live with the status quo (ForgiveForget). Check whether you are not assuming bad intentions without reason (AssumeGood). Also check whether the problem is serious enough to consider it at all.
  2. Check whether you did something wrong
    Check whether the problem is that you think you behaved badly with the other person. If so, treat it as a remorse problem (Remorse).
  3. Talk it out
    Talk to the other person (MakeStep). Make your point clear (Clear). Make sure you act with the goal of finding a consensual solution (ConflictResolution, TalkMeHappy).
    If the other person refuses to talk, the problem splits into two parts: First, there is your desire to talk. Check whether you really need to talk. Do you care about the opinion of someone who does not care about your opinion? If so, making a point with a person who does not want to talk is covered in a different Section (SecNonRec). Second, there is the uncomfortableness that the other person feels. However, as the other person shows no interest in resolving that uncomfortableness, there is nothing we can do about it. The issue can safely be ignored (MakeStep, Remorse).

Talking about the problem is just one way to deal with it. However, it has proven one of the most effective ones. If done rationally (Def), talking about a problem benefits from all the advantages that rationality offers (WhyUse). In particular, talking resolves misunderstandings, shows good intention and brings both persons closer to truth (SeekTruth). Doing the first step towards the other person can be very helpful in general (MakeStep). However, not all people prefer talking it out (DontAssumeRatStat, DontAssumeRationality). Note that your moral framework (Moral) may decide that if a person does not want to co-operate in resolving the issue, he loses the right to any claims [Thoughts on Ethics / Sulking].

There are a number of things we can do to recover from a social problem (PostProb).

Decision problems

A decision problem is the problem of choosing between different options. Such a choice may be painful, in particular if none of the options appears really attractive (BestNotGood). A decision problem may also induce insecurity or fear (Fear). Examples for decision problems are:

It is not possible to give a general solution to these decision problems. Still, there are some general techniques that can be applied. This essay covers them in the section about decision taking (SecDec).

Post-Problem Measures

After a problem solving process (SecProb), we do not necessarily feel good. There are several things that we can do:
  1. Develop safety strategies that avoid that the problem appears again (SeeMetaProblem). It will comfort us to know that at least the problem happened only once.
  2. Help others avoid the problem — e.g., by writing about it on the Internet. Altruism makes us feel good.
  3. Work. Work distracts us, gives us the feeling of being useful, and gives us appreciation. If we channel our anger, fear, or sadness into work, we can hardly do anything wrong.

Decision Taking

Decision taking is the process of weighting the benefits of different options choosing one of them. Unfortunately, rationality cannot give a definite recommendation in all cases. This is because the perceived utility of an option does not necessarily behave like a numeric quantity. However, rationality can help rule out certain options and it can help assess them. Formally speaking, a decision question is the problem (Problems) of choosing the option that best satisfies our goals (Goals). Advice in this section (Advice) is to be understood with respect to this goal.


A decision process is the process of assessing the values of different options. For example, if we are offered multiple jobs, we can use a decision process to figure out which job offer we want to accept. A criterion in a decision process is a property of the options that the decision taker is interested in. For example, the criteria in the job decision may be the prospective salary, the location of the job and the type of job. Technically speaking, a criterion is a goal statement (Goals) that can be fulfilled to a certain degree.

It is useful to think of the options and the criteria in form of a table. Here is an example table for the job search problem. The columns are the different options. The rows are the different criteria:

(= job offers)
CriteriaMacrosoft Banana Inc.Moogle
Salary High High High
Location Nice Nice Bad
Job type Nice Bad Dumb (factory line)
Decision problems can also aim to satisfy different people. In this case, the criteria are the people, and the options are the different actions. Suppose for example that a group of friends wants to go to the cinema. The options are different movies. The criteria are the preferences of the people:
(= movies)
CriteriaLife of Brian Titanic Inception
Alice dislikes likes likes
Bob likes dislikes dislikes
Carl likes dislikes dislikes

In general, it is not trivial to weight the criteria against each other, because it is difficult to compare across different dimensions. However, there are some cases in which we can simplify the equations.

Undistinctive Criteria

An undistinctive criterion in a decision process (Criteria) is a criterion that all options fulfill equally well. Such a criterion does not help in the decision process. Hence, it should be ignored.

In example with the job offers (Criteria), all job options yield the same salary. Therefore, the salary plays no role in the decision. Hence, it should be ignored. In the example where we want to choose a movie that makes everybody happy, a person that has the same opinion on all movies should be ignored.

This obvious principle is not always observed. Some people argue, for example, that nuclear energy is good, because the danger of a nuclear accident is minimal. Strikingly, this criterion is also fulfilled for all alternative sources of energy. Hence, it cannot count as an argument for nuclear energy.

Quantifiable Criteria

In a decision process, we may be able to quantify some of the criteria (Criteria). A quantified criterion is a criterion that has a number associated to it. For example, the financial cost of something can be expressed by help of a number. The quantified criterion should come with a preference for small numbers (e.g., in the case of effort) or a preference for large numbers (e.g., in the case of financial gain). If all criteria are numeric on the same dimension (e.g., all criteria are financial), we can simply compute the benefit of each action and choose the most preferable one.

We can also resort to a whole domain of systematic analysis of choices, called Decision Theory [Wikipedia/ Decision theory].

Killer arguments

A killer argument in a decision process is a negative criterion that is stronger than all other criteria combined (Criteria). That is, a killer argument is a problem that has to be avoided at all cost. If one of the options produces such a problem, while other options don't, then this option is no longer a choice.

In our example of deciding for a job offer (Criteria), we may say that a "dumb job" is a killer argument. Thereby, Moogle is out of the game — no matter how good the salary or location are.

If you know that something is bad, do not waste time figuring out how bad exactly it is.

Tie breakers

A tie breaker in a decision process (SecDec) is a weak criterion (Criteria) in favor of one of the options that are otherwise equally beneficial. Quite often, the tie breaker may be a pure personal preference (Preferences).

In the example of choosing a job offer (Criteria), assume that all options score equally well on all important criteria: All jobs offer the same salary, are equally interesting, and are in an equally good location. Assume furthermore that your husband likes one of the options most. Even though this is surely a weak argument, it may become the decisive one if it is the only one.

Tie breakers serve no other purpose than tipping the scale if all other criteria are balanced between the options. Thereby, tie breakers allow making decisions even if all other criteria are deadlocked.

Coin flipping

If two options in a decision process fulfill all criteria equally well (Criteria), then there is no rational argument for one or the other. In these cases, one usually invents other, minor citeria to reach a decision between the two (TieBreaker). However, it may happen that there is no such tie breaker, because it is impossible to state a personal preference. Consider, for example, the choice between two wedding cakes that are equally expensive and equally nice. Or consider the decision of which movie to watch, if all people have the same preference for all movies (Undistinctive). It may also be socially inadequate to state a personal preference. Consider for example the decision of whom of your children may sleep in the upper bed.

In these cases, we may invent an artificial criterion: a coin flip. For this purpose, we associate one option to "tail" and the other option to "head". Then, we flip a coin. The criterion says that the option that corresponds to the coin face shall be preferred. Thereby, a coin flip serves as an artificial tie breaker.

Technical Issues
If there are more than two options, the coin flip can be generalized as follows:
  1. Be n the number of options.
  2. Number the options from 1 to n
    (in the job offer example (Criteria), we could say Macrosoft=1, Banana Inc.=2, Moogle=3).
  3. See how often you can divide n by 2 until you get below 1. Be c this number.
    (i.e., c=log 2(n), rounded up to the next integer)
  4. Flip the coin c times. For each flip, note "1" if the coin shows a head and "0" if the coin shows tail. We will refer to these numbers as f1, f2, ..., fc.
  5. Compute
       r=f1 * 1 + f2 * 2 + f3 * 4 + f4 * 8 + ... fc * 2c-1
    where the coefficients are the powers of two.
  6. The coin flip criterion favors option r+1. If this option does not exist, repeat the process.

Dominant Criteria

The killer argument (Killer) and the tie breaker (TieBreaker) are just the two extreme instances of a broader decision scheme. This scheme works if one criterion is strictly more important than a set of other criteria. If this criterion is fulfilled for one option and not for another, then the dominated criteria have no longer to be considered in the comparison of these two options.

In the job choice example (Criteria), we may decide that the location is more important than the type of job and the salary. If one option has a good location, while another one does not, then the type of job and the salary need no longer be considered when comparing these two options.

Dominant Options

An option dominates another option in a decision process, if it is better than the other option on all criteria (Criteria). In this case, the dominated option can be discarded.

In the job choice example (Criteria), we may find that one employer pays a higher salary, has a better location and offers a better type of job than one of the other options. In this case, the other option should no longer be considered.

Technical issues
Interestingly, people are easily influenced by dominated options. For example, if people are given the choice between
  1. A free trip to Rome, including hotel and all food
  2. A free trip to Paris, including hotel and all food
then they will split roughly 50/50 on these options. However, if we introduce a third, dominated option
  1. A free trip to Rome, including hotel and all food, but without breakfast
then people have a tendency to favor option 1. This is because the dominance of option 1 over option 3 makes option 1 look much more attractive — not just more attractive than Rome without breakfast, but also more attractive than Paris [Wikipedia / Asymmetric dominance effect]. This is a totally irrational behavior, because dominated options do not change the quality of other options.

Certainty of Criteria

We may not always be able to say whether a criterion in a decision process (Criteria) will be satisfied for sure (Uncertainty). In this case, it becomes very difficult to weight the criteria against each other.

If the criteria are quantifiable (Quantifiable) and if the probabilities of the outcomes are known, then the criteria can simply be multiplied by their probabilities to give an estimated value. For example, if we have the choice between two equally expensive lotteries, one with a prize of $10 and a chance of 50% of winning and the other with a prize of $1000 and a chance of 1% of winning, then the expected outcome of the first lottery (50% * $10 = $5) is lower than the expected outcome of the second lottery (1% * $1000 = $10). Therefore, we should choose the second lottery.

This calculus, however, does not take into account the risk associated to the options. The first lottery has a chance of 50% of winning and is therefore much "safer" than the second lottery. The second lottery has a higher expected gain, but it is less probable that this gain materializes.

This risk can be an additional criterion. This criterion cannot be weighted easily against the criterion of the expected gain. There may even be cases where there is an infinitely high expected gain for one option — but the option should still not be chosen [Wikipedia / St Petersburg paradox].

If the criteria cannot be quantified, they have to be handled differently (AsmCrit, CertainUncertain).

Assuming criteria

Some criteria in a decision process (Criteria) may be uncertain (Certainty). It is very hard to deal with uncertain criteria. It can be reasonable to assume that the criterion is fulfilled or not fulfilled (whatever is more likely). For example, if one criterion in the job search scenario (Criteria) is that we enjoy the work at our future employer, and if it is likely, but not certain, that we will enjoy work at Macrosoft, then we should simply assume that this will be the case. This makes the decision process more risky, but ultimately simpler.

We may also choose a conservative approach and assume that all criteria about which we are uncertain will not be fulfilled ("Hady's Law"). For example, if a good salary is promised, but not certain, we may choose to assume that the salary is bad. This may degrade the option and waive the chances for a better salary there, but nobody knows whether the salary would really have been as good as promised. By being pessimistic about the uncertain criterion, we can at least be sure to optimize the certain criteria.

Too many assumptions may lead into the fallacy of Decision Ducking (DecDuc).

Certain and Uncertain Options

Assume that we have two options in a decision process (SecDec). Assume that each of them fullfills a criterion equally well (Criteria). If the first option is certain to fulfill the criterion, while the second option is uncertain to fulfill the criterion, then the first option is better than the second option for this criterion.

For example, consider again the scenario where we have to select a job offer (Criteria). Assume that both companies, Macrosoft and Moogle, offer a good salary. However, if Macrosoft has already made a written offer, while Moogle has just outlined possibilities, then Macrosoft dominates Moogle for the salary.

Analogously, if the first option does certainly not fulfill the criterion, but the second option could fulfill the ceriterion, then the second option is better than the first for this criterion. For example, if Macrosoft has definitively excluded a higher salary, but Moogle does not rule out this possibility, then Moogle dominates Macrosoft for this criterion.

Moral Evaluation

One of the criteria (Criteria) in a decision process can be (in fact: should be) its morality. For each of the options, we can construct a hypothetical scenario (Scenarios). For each scenario, we can make a moral evaluation (MakeMoral). If one of the actions turns out to be morally objectionable, this can be a killer argument (Killer).

Considering Alternative Options

In a decision process (SecDec), it may be useful to think of alternative options that have not yet been considered. Quite often, the choice in a decision process is not limited to the options that one first thinks of.

The classical example is as follows: Two sisters both want to have an orange, but there is only one orange left. It seems that only one girl can have the orange and the other one will get nothing. After some litigation, it turns out that the elder sister wants to have the orange to make a juice, while the younger sister wants the peel of the orange for a cake. The solution is obviously that the elder sister makes the juice and then gives the peel to the younger sister for the cake. This way, both are happy.

In the example of which movie to choose (Criteria), we observe that all guys prefer "The Life of Brian", while all girls prefer Leonardi di Caprio movies. In this case, it may be reasonable to split up and have everybody see her or his favorite movie.

In other words, we should not limit ourselves to the options that first came to our mind. Quite often, the best solution to a decision problem is a completely different alternative. We might have to backtrack (Backtracking).

Taking future benefits and disadvantages into consideration

In a decision process (SecDec), it may be useful to develop the hypothetical scenarios for the options further into the future (Scenarios).

For example, assume that a company has to decide whether to invest into a new generation of products. Given that this generation of products will be out-lived soon therafter, the company ponders whether to skip this generation and to invest directly into the next-next generation of products instead. Imagining the hypothetical scenario, though, it turns out that clients would turn to a competitor if they cannot find the next-generation products at the company. They might not come back when the company comes up with the next-next generation product. Therefore, it may be reasonable to invest in the next generation product, even if it will be out-lived soon thereafter.

Another example is the choice between working in industry and doing a PhD. While working in industry may yield a much better salary than a PhD position, the PhD may lead to a better job later. Thus, the PhD might ultimately lead to a higher living standard.

Making Personal Preference a Criterion

Personal preference (Preferences) should always be a criterion in a decision process (Criteria). The reason is that, if we ignore personal preference, we might not be happy with the option we choose. If we are not happy with the option we choose, the other criteria may lose their value.

Personal preference can even become a killer criterion (Killer). For example, in the job decision scenario (Criteria), we may discover that we have a strong aversion against the Banana Inc.. In this case, it is fully legitimate to note down this aversion and to decide against Banana Inc.

Admitting personal preference as a criterion will also allow us to see the other criteria more clearly. This is because, if we ignore personal preference, our inner preference will subconsciously distort the other criteria. By giving our feelings (Feelings) an appropriate place in the decision process, we make sure that we give every criterion its due weight.

It may also happen that, by consciously admitting personal preference as a criterion, and by consciously allowing ourselves to choose according to that preference, we may yet decide to override the preference and do what is better on the long run.

Taking repetition into account

If we have to take the same decision (SecDec) multiple times, we can choose different options each time. This may be a way to satisfy all criteria on the long run, even if each instance of the decision satisfies only one criterion (Criteria).

In the cinema example (Criteria), where a group of friends disagree about which movie to watch, the friends may decide to watch one movie this time and another movie next time. This will make all of them happy. Or take as an example a group of colleagues who want to go for lunch. They have one Indian food lover, two Chinese food addicts and two Burger fans. The solution is to go to an Indian restaurant once a week, and to a Chinese place and a Burger place twice a week, respectively. This will maximize the group's happiness.

Using Self-Analysis

Rational arguments may tell us which option to choose in a decision process (SecDec). However, if we secretly favor another option, then we should not ignore this feeling (Feelings). Rather, we should analyze our intuitive aversion or our intuitive preference. Maybe our preference is due to one of the following factors:
At some point of time, you have to choose between what is easy and what is right.

Imagining one option

We can use our imagination to help with a decision problem (SecDec). For this purpose, we have to imagine that we choose an option. Then we have to see how we feel and, in particular, whether we spot feelings of regret. If we do, then we can use self-analysis (SelfAnalysis) to see whether we weighted our criteria correctly or whether we forgot a criterion.

In the job search example (Criteria), we would first determine which job we should choose under the current criteria. Say rationality tells us to choose the Banana Inc.. Then we imagine that we choose the Banana Inc. We imagine how it would be to work there and how we would feel about that. In particular, we would have to watch out for any feelings of regret. If we feel regret, then it is likely that our criteria are not weighted correctly.

Assuming equivalence of criteria

It can be very hard to weight the criteria of a decision process correctly (SecDec), in particular if it is not clear whether one option really fulfills a criterion better than another option. For example, in our job search scenario (Criteria), one criterion could be that we want to minimize the likelihood of being laid off by our future employer. This criterion, however, is very hard to estimate.

In such cases, it can be reasonable to assume that all options fulfill the criterion equally well. In the example, we would assume that all candidate employers have an equal probability of laying people off. Thereby, the criterion becomes an undistinctive criterion (Undistinctive) and can be ignored. Thereby, assuming equivalence of criteria serves to prune the space of criteria. It ultimately simplifies the decision.

Out-Sourcing and Up-Sourcing

For some decision problems (SecDec), we may not have the necessary knowledge to make a good decision. In these cases, it is helpful (or even obligatory) to have somebody else decide. This holds in particular if the decisions are important.

Here are examples for decision problems that are important, but where we might lack the necessary knowledge to decide by ourselves:

In these cases, it can be unhelpful (StdGoals) or even dangerous if we decide on our own. Therefore, we should not hesitate to out-source the decision process to experts or to up-source it to senior people.


In a decision process (SecDec), satisficing means deciding for an arbitrary option that fulfills the most important criteria — without caring whether this option is really the optimal one [Wikipedia / Satisficing]. In our example of the job search (Criteria), we might decide for the Banana Inc., because this company fulfills the basic criteria of good salary and good location. If we satisfice, we decide to ignore certain other criteria (such as work environment etc.).

Satisficing may lead to an option that is not optimal. In our example, Macrosoft is better than Banana Inc. Still, satisficing may choose the Banana Inc.. The main advantage of satisficing is that is saves time deciding. It may well be that the time and resources used to find the optimal solution are so costly that it is inefficient to find the optimal solution. In these cases, satisficing is a good tradeoff between a good option and a fast decision process. Consider for example the decision of what places to visit in a city. The time spent to figure out the "optimal" places to visit might as well be invested in visiting these places. Or consider the decision of what train connection to take. We might well waste more time figuring out the best connection than we gain in the end by taking this connection.

As a general guideline, it can be reasonable to limit the time and effort spent on the decision process and take whatever option looks most reasonable after this time is up.

The best is not necessarily good

When we have to choose between several options in a decision process (SecDec), we hope for an option that satisfies all our criteria (Criteria). However, such an option does not necessarily exist. All of our options may have their downside. More likely than not, none of the options will be perfect. Hence, the choice we make is not necessarily a good choice. Still, it may be the best choice. Therefore, we should accept making a choice that does not satisfy us entirely.

In the job search example (Criteria), it may be that the only company that offers us an interesting field of work and a good location pays the lowest salary. If we choose this company, the choice may be a bad choice in the sense that it does not satisfy all criteria, but still the best choice in the sense that it is the optimal thing to do.

If one thing is bad, that does not make another thing good (GoodNoBad).


Backtracking is the process of re-considering assumptions that we made (LogBack). In a decision process (SecDec), backtracking means re-considering whether it is really necessary to take a decision in the first place. If a decision proves hard, it can be useful to think again why we have to take the decision and whether we can possibly avoid it altogether.

In the job search scenario (Criteria), backtracking could mean to re-consider whether we really need a job in the first place. Alternatives could be to spend a year abroad for a charity or to spend more time with our family instead. In the cinema example, backtracking could mean to choose a completely different joint activity with our friends, such as going for a drink or going ice skating. This way, backtracking can avoid the decision problem altogether.


This part contains advice on how to become more rational (SecMore) or less rational (SecLess). It also contains advice on how to talk (SecTalk). The distribution of the topics across the sections is to a certain degree arbitrary. There is also overlap with the section on reasoning techniques (SecTec). In general, the section SecLess addresses readers who think they are rational. Section SecMore is intended for readers who are not particularly inclined to rationality as understood by this essay.

How to talk

Much of our social interaction revolves around talking. Talking with the goal to convince someone was discussed in a previous chapter (ChapDisc). Here, we discuss the general verbal interaction with our fellow humans.

Why we talk

Talking consumes effort and time — both for ourselves and for our partner. Therefore, we should make sure that our talking serves a goal (KnowReasons). Unfortunately, we are often unaware of the goals that we are serving with our talking. To be rational, we should be aware of why we talk (Rational).

We can have different goals while talking. Here are some:

There can be many more reasons for talking. It is good to know them.
Do you know why you are talking?

Talking for ourselves

When we talk, we usually assume that we are helping our interlocutor understand something. However, in many cases, the truth is that we are talking just because it makes us feel good. Put differently: In many cases, the only goal that we are serving with our talking is our own happiness (Goals). These cases are in particular

It is fine to do something with the goal to feel good. We do many things because we want to feel good (StdGoals). Then, however, we should not pretend that we are doing it to enlighten or entertain the other person. That would be wishful thinking (NoWish). In other words: When you are talking, be aware that you might be doing it just for your own pleasure.

If we want to become aware of why we talk, we should ask ourselves:

We may also talk to sort out our own thoughts. This is one way to check the correctness of our thinking (QPerson). If we want to be polite, we can ask our interlocutor just to listen to us. Thereby, we give them a role in the conversation (TalkToTalk).

Talking to talk

When talking, we can pursue different goals (WhyTalk). Sometimes, we talk just to talk. If we want to detect such cases, we can ask ourselves whether the other person has a role in our conversation. This role can be

The other person may also do us a favor by listening. He may also be morally obliged to listen (Moral). He may also be expected to listen in a discussion, if he would be non-receptive otherwise (SecNonRec). If we talk and the other person has no such role, then we are like a radio (Flooding): We produce noise without caring about the other person. This way, we are mainly consuming our friend's time. We are actually talking to ourself (TalkMeHappy).

Talking to praise ourselves

Most of us like it if we are appreciated. If we are not appreciated, we sometimes help a bit, by mentioning some good thing that we did or showing what we know. We hope that this generates a bit of admiration and then a bit of praise, which makes us happy.

However, if we overplay it, the effect may well be counter-productive. People who praise themselves a lot are usually not admired — on the contrary. People who praise themselves give the impression that they need the praise, which might be because they do not get enough praise, which might be because they do not have much to be praised for. For example, assume that a singer introduces himself as "the well-known Metal Bob". This raises suspicions: If Metal-Bob were really well-known, why would he have to say it? In general, people who praise themselves raise this suspicion. This holds in particular if people or organizations ascribe particular attributes to themselves. For example, those countries that carry the word "democratic" in their official name are usually the least democratic. Or, as Margaret Thatcher remarked for both the attributes of "being powerful" and "being a lady":

Being powerful is like being a lady. If you have to tell people you are, you aren't.

In contrast, People who do not praise themselves are considered modest — and thus praiseworthy. The thinking goes that people who have enough to be proud of do not need to long for other people's admiration.

If we want to follow this avenue of reasoning, and if we want to be modest, we should think, before each thing that we say about ourselves, whether this thing serves any other purpose than showing off. If the only effect of our statement is showing what good thing we did, we should consider omitting that statement.

Wahre Größe rühmt sich nicht.
La vraie grandeur méprise la gloire.
Honest grandness needs no praise

Talking to teach

Rationality has the goal of approaching the truth (SeekTruth). This, however, does not mean that we have to help other people achieving this goal — in particular if the other person has no such desire (Desires). Teaching other people about the truth (or about what we think is the truth) can be a very strenuous enterprise. This is in particular true if our interlocutor is radio-person, focusing primarily on getting thoughts out of his head rather than into his head (Flooding).

Fortunately, in general, nothing forces us to change our interlocutor's mind. If our interlocutor is not interested in what we have to say, then there is no need to say it (WhyTalk). If our interlocutor makes statements with which we do not agree, and if we do not want to engage in a discussion, then we can say things like:

If that leads our interlocutor to ask about our point of view, we have a reason to talk and may also expect our interlocutor to listen. Otherwise, if our interlocutor is not interested in what we have to say, then, under most moral frameworks (Moral), there is no obligation on our side to talk and none on his side to listen. We can just listen (Listen, NonRecWhen).

Technical issues
These considerations do not apply if our interlocutor's statements contradict moral standards (Moral). In this case, we have a moral obligation to contradict. They also do not apply if our interlocutor's statement acts against our (or somebody else's) goals. Finally, these considerations also do not apply if we simply have the goal of changing our interlocutor's mind. These cases are discussed further up in this essay (SecNonRec).

Talking to Argue

Usually, we may assume that a person who initiates a conversation is looking for feedback from the listener. If the speaker did not want to receive feedback from the listener, then it would be easier for him (StdGoals) to talk, e.g., to a teddy bear — or not to talk at all. Therefore, we may assume that the speaker aims at some kind of feedback (TalkToTalk). Usually, the person who initiates a conversation is looking for confirmation, information, admiration, consolation, attention or entertainment.

Many of these types of feedback benefit from rational thinking. Confirmation and information, for example, are much more valuable if thought through with rational means. Other types of desired feedback, such as consolidation, admiration or attention, may benefit less from rationality (NoUse). Worse, rationality may lead us to think that the speaker wants information, if in fact he is looking for admiration or simply for attention.

Therefore, if we want to serve the goal of making our interlocutor happy (WhyTalk), we should not automatically assume that he would be looking for advice (Advice), valuations or information. That is, we should not automatically

Maybe our interlocutor is not looking for this type of feedback. He may be looking for confirmation, admiration, consolation, attention or entertainment. If we want to consider this possibility, we should consider giving deep feedback instead (TalkYouHappy, DeepFeedback).

Talking to make the other person happy

When we talk, we can have the goal to make our interlocutor happy (Goals). Clearly, it is a purely personal choice to have this goal in a given conversation or not. Usually, however, making our interlocutor happy lays the ground for a harmonic interaction, which can also be beneficial for ourselves (MakeStep). It should be well understood at this point that "making our interlocutor happy" cannot mean just telling him what he wants to hear. Rationality in the sense of this essay remains committed to the principle of truth (SeekTruth). Rather, it can mean some of the following:

If we want to make our interlocutor happy, we should talk only if we know that our interlocutor is interested in what we are saying. Lecturing our interlocutor, for example, or telling them stories, should happen only if our interlocutor expresses sincere interest in our discourse (i.e., interest that goes beyond pure politeness). If we are talking for a long time without being asked for it, then it is likely that our discourse does not serve the goal of making our interlocutor happy. In all likelihood, it serves more to make ourselves happy (TalkMeHappy).

Acknowledge what the other person says

When people talk, they usually aim for some kind of feedback (TalkToArgue). If that feedback is not received, the person is likely to repeat what he said, because he has the impression that the other person did not understand. Here is a sample discussion:
Alice: Let's not go watch this movie, it is raining and cold outside.
Bob: Oh, no, let's go, the movie will be awesome! I talked to a friend, he says the cast is fantastic!
Alice: It's raining like crazy...

In this example, Alice is concerned about the rain. Bob does not respond to her concern. Therefore, Alice repeats it.

Common expected acknowledgements are:

If this reply is not given, then the other person feels let down, repeats their point, or loses interest in the conversation.

A special case of this phenomenon is a situation where two people each want to receive feedback from the other person, but no one is ready to yield such feedback to the other person. Therefore, both keep repeating their argument. In the sample discussion, neither Alice nor Bob got their concerns acknowledged. Therefore, the discussion is likely to continue:

Alice: Let's not go watch this movie, it is raining and cold outside.
Bob: Oh, no, let's go, the movie will be awesome! I talked to a friend, he says the cast is fantastic!
Alice: It's raining like crazy...
Bob: But the actors are just so good!
Such discussions usually do not make the interlocutors happy. They will complicate the understanding and the strife for truth (MissingAck). If we want to break such cycles, we should acknowledge what the other person says. This can be done, for example, by (1) paraphrasing what the other person said and (2) taking his point into consideration:
Alice: Let's not go watch this movie, it is raining and cold outside.
Bob: Oh, no, let's go, the movie will be awesome! I talked to a friend, he says the cast is fantastic!
Alice: It's raining like crazy...
Bob: Oh, that is true. Very nasty, in fact... I would still really love to see the movie. Would you come with me in spite of the rain?
Note that a simple "yes" is not enough of an acknowledgement. This is because it could be the reply to any true statement. An honest acknowledgement is the reply to the other person's statement — and to no other statement. By taking the other person's point serious, we can not only learn new things, but also free the way for our own argument.

If, beyond making the argument proceed, we also have the goal of making our interlocutor happy (TalkYouHappy), we can consider giving deep feedback (DeepFeedback).

Give deep feedback

This essay argues that, for an effective communication, it is useful to listen to our interlocutor (Listen) and to acknowledge what he says (Ack, MissingAck). If, beyond this goal of effective communication, we also have the wish to make our interlocutor happy (TalkYouHappy), we can consider giving deep feedback.

Deep feedback is a reaction to our interlocutor's statement that shows that we grasp the factual and emotional consequences of that statement. Deep feedback is context-sensitive, in the sense that it is tailored to what the other person said. Crucially, deep feedback avoids changing the topic, withdrawing attention from our interlocutor, or playing down what he says.

To give deep feedback, we can, e.g.,

Such a reaction shows our interlocutor that we are taking seriously what he says. This is likely to give him emotional and intellectual satisfaction.

Here is an example:

Alice:I broke my leg yesterday!
Don't say: OK.(no emotional feedback)
Don't say: Well, that's not so bad. Other people have their legs amputated. (downplaying)
Don't say: Oh, my grandma also broke her leg! (withdrawing attention from Alice)
Don't say:Yes, could you bring cheese when you pass by the supermarket? (changing topic)
Say: Oh, you broke you leg? (paraphrasing)
That is aweful, I am so sorry! (emotional feedback)
How did that happen? (asking)
Deep feedback shows that we care about the other person. Taking the time to respond in a context-sensitive manner sends the message that the other person is important to us. Obviously, we should only give deep feedback when we mean it.

Listen and learn

One goal of rationality is approaching the truth (SeekTruth). For this goal, it is helpful to learn what other people have to say. Unfortunately, we have a tendency to talk more than we listen. We have a tendency to be in radio-mode, concentrating on getting across our thoughts instead of concentrating on learning our interlocutor's thoughts (Flooding). For our own goal of approaching truth, however, this behavior is counter-productive. This is because we already know the things we say, but in most cases, we do not know what the other person wants to say.

To get to know our partner's thoughts, we need sincere listening. This is an art that few people master. It involves

The following behaviors do not serve the goal of getting to know our partner's thoughts on a particular topic:

Apart from serving the goal of learning, sincere listening is also very likely to make our interlocutor happy (TalkYouHappy). This is because sincere listening is a form of expressing interest in our partner, which in turn is often perceived as a signal of appreciation. Thus, sincere listening can serve the goal of making our partner happy (WhyTalk). We should not, however, do sincere listening just because we want to make our partner happy. This is because listening without true interest means giving a false impression, which will make our partner unhappy. We should use sincere listening only if we are sincerely interested in his thoughts.

In general, it is hindering to the goal of exchanging knowledge if one party talks without end. If we find ourselves talking for more than roughly a few minutes in a row, it is likely that we are counter-acting the goal of exchanging knowledge with our partner in a balanced fashion.

The present discussion is not to be understood in the sense that we should always be interested only in our partner's thoughts. Obviously, it would be impossible to implement this simultaneously for both partners. Rather, the present discussion aims to make us more sensitive as to how to serve the goal of learning. Balanced discussions can have the partners listen in alternation.

It is the province of knowledge to speak and it is the privilege of wisdom to listen.
Oliver Wendell Holmes
Technical issues
The techniques of sincere listening can also be used to steer the discussion with a radio-person to topics that we are interested in, thus combining our interlocutor's joy of talking with our own desire for knowledge.

To read about what subjective effect listening can have, see [TinyBuddha].

Be precise about your statements

Many conflicts arise because people make and defend vague statements, thereby allowing a margin of interpretation and thus inducing a potential for dispute. Consider for example the statement "Germany is a peaceful country". This is surely mostly true today, but it has not always been true. Saying that Germany is a peaceful country may raise objections concerning her peacefulness during the World Wars. It may also rise objections concerning her involvement in the war in Afghanistan.

If we want to avoid this, we should rather make a statement such as

During the last 50 years, Germany has not been involved in a war of aggression.
This statement is precise — and true. Of course, we use the first sentence as a convenient shorthand for the second. But if it comes to an argument, we should not try to defend the first sentence, but rather defend the second sentence.
Technical Issues
If we are too lazy to use such complicated statements, we can define shorthands:
Germany is a peaceful country. By "peaceful country", I mean a country that has not been involved in a war of aggression in the last 50 years.
See above for a discussion of definitions (Definitions).

Use plain language

In order to transmit our message in the most efficient way, it is useful to use simple, straight-forward and matter-of-fact language. This style of language is called Plain Language. It is language that has no confusion about meaning, is free of cliché and unnecessary jargon, and is easy to understand. [Wikipedia / Plain English].

This implies making simple sentences with as few nestings as possible (Simple). It also means grounding our statements (Grounding), i.e., avoiding for example colored language (ColoredLanguage) and empty phrases (Empty).

Make your point clear

If we have the goal (Goals) of informing somebody else about something we intend to do or about something that the other party should do, then the following structure is helpful:
  1. state the relevant facts (Name). Be sure to use grounded statements (Grounding).
  2. if you are making any assumptions beyond the standard assumptions (StdAsm)
    1. list your assumptions (Name).
    2. ask whether the assumptions are correct.
  3. if you have any goals other than the standard goals (StdGoals), name them (Name) .
  4. state in what way these goals are currently not fulfilled (Problems).
  5. explain which actions lead to the goals in the best manner according to your view (SecDec).
  6. say that you will perform these actions unless the other party proposes a better method or ask the other party to perform these actions.
  7. ask the other party for their view (Listen).
Throughout this discourse, it is useful to use plain language (Plain).
A good scientific theory should be explainable to a bar waitress
Ernest Rutherford

Be more rational

This section will give advice (Advice) on how to become more rational (Rational). In all of the following, it is assumed that approaching truth is a goal (SeekTruth). It is also assumed that moral behavior is a goal (Moral). Different topics in this section will also presume different other goals. The section will propose techniques for achieving these goals in a rational way (Advice, Rational). Technically speaking, the techniques are theories in the sense of this essay (Theories), i.e., they are not guaranteed to work.

Make sure you know why you are doing something

People sometimes find themselves doing something with which they are unhappy — even though there is no reason why they should be doing it. This unhappiness can be avoided.

The following are rational reasons (Rational) for doing something:

If none of these items apply, then our action is not rational (Rational). The following items are not rational reasons for doing something that we don't like:

For example, assume that someone on the street stops you to raise funds for animal welfare. After having talked with that person for 15 minutes, you feel that it would be ungrateful if you decided simply to walk away. Hence, you reluctantly sign a membership with the animal welfare group. Rationally speaking, the pressure you feel is fully your own. Unless you really want to support animal welfare, or you sincerely want to make the guy happy, none of the above justifications applies. You have every right to walk away, even if you talked for an hour with that person.

It matters not how strait the gate
how charged with punishments the scroll,
I am the master of my fate:
I am the captain of my soul.
William Ernest Henley in his poem "Invictus"

Do not duck decisions

Decision Ducking is the fallacy of assuming that there is only one option in a decision process (SecDec). The option that one sees is usually only the safest option. This option may not be the best one.

One particular instance of decision ducking is mutual decision ducking, where each of the two partners in a joint decision process assumes that the other partner has a preference for the safest option. Therefore, the partners opt for the safest option, even though they would both have preferred a different option.


Decision ducking is irrational because it misrepresents truth (SeekTruth) and does not serve our interests (Rational). Decision ducking is related to our tendency to avoid responsibility (BeResponsible). In both cases, we impose boundaries on ourselves, and then say that we did not have the choice. But:
Choosing your boundaries is a choice.
Technical Issues
Here is a theory about decision ducking and avoiding responsibility (Theories): When we take decisions, we take over responsibility. If the decision was wrong, the consequences of that decision fall back on us. Therefore, decision taking is risky. Therefore, people try to avoid it. They limit their own decision taking capabilities by submitting themselves to other people, to rituals, to conventions, to frames and to self-imposed boundaries. This liberates them from the need to decide. When something goes wrong, they can point out that they did not have a choice.

Be responsible

We sometimes feel pressure from our family, our society, or our convictions to do a certain thing. Then we have the tendency to assume that we have no choice but to to that thing. That assumptions is nearly always wrong. In most cases, we have a choice. Here are examples: In all of these cases, it is reasonable to ponder the options thoughtfully. Obedience, too, shall be given due consideration: Social norms usually serve a purpose, our parents have more experience than us, moral frameworks are the basis of our actions for a reason, our decisions for our convictions were based on certain arguments, and also our friends' interests deserve attention. Therefore, all options deserve thought. This is true in particular since choosing disobedience can be a very difficult, and sometimes even immoral endeavor (Moral).

There are cases where we do indeed not have the choice. One class of cases is physical necessity or inability [Thoughts on Ethics / Possible event]. This includes the case where the decision is in the hand of another person, and not in ours (such as being accepted for a job or not). There is no talk of choice here. The other class of cases is where we are forced by illegal or unethical means to do something. This includes threat by other people [Thoughts on Ethics / Threat], obstruction by other people [Thoughts on Ethics / Obstruction], mobbing, social pressure, or other types of manipulation. In these cases, our prime attention should be on (1) condemning the threatening behavior and (2) opposing it. If we find ourselves put under undue pressure, then we should become aware of this pressure, object to the person who manipulates us, and seek help. However, way too often, people do not condemn the threatening behavior, but they accept it. This leaves us to conclude that they did, indeed, make a choice.

If we have a choice, then we may opt to do just nothing and let things go their way. This is a choice. We may also choose to opt for one particular option. In both cases, we have to acknowledge that we made a conscious decision, and that we did ponder (or at least could have pondered) the alternatives. This entails that we have to take full moral responsibility for our choice (Moral). We may not blame our decisions on higher orders, if it is us who choose to obey these higher orders.

If we find ourselves repeatedly in such conflicts, then we should take this problem seriously (SeeMetaProblem). Maybe we should talk to our parents, to our friends, to our boss — or to ourselves. If it is a systematic problem, it deserves a systematic solution (EmTraps).

Man is condemned to be free; because once thrown into the world, he is responsible for everything he does.
Jean-Paul Sartre

Give yourself the right to change yourself

We have a tendency to assume that we should keep being as we are. We should not change our attitudes, habits, and way of being. After all, we should be the person that we have always been.

The past, however, does not define the future. It is a fallacy to assume that, just because we have been in some way, we have to stay this way (WrongRules). There is nothing that prohibits us from changing ourselves. Our habits, attitudes, and decisions are not God-given — they are given by ourselves. It is a mistake to assume that we could not develop other attitudes or habits (DecDuc). In fact, if we find out that our view of the world is wrong, then we should do our utmost to change it (OpReal). If we find out that what we are doing is suboptimal, then we should do something else.

Life isn't about finding yourself. Life is about creating yourself.
George Bernard Shaw


We have a tendency to bury past problems and to avoid thinking about them. We also have a tendency to avoid thinking about present problems. This might be because they remind of us something unpleasant, because we have a bad conscience, or because we want to suppress this issue as well as possible. Yet, thinking about a problem helps us understand it better. Thinking also often leads to a solution. In fact, rational thinking is one of the safest ways to arrive at a solution for a problem (Use).

Therefore, we should not hesitate to think about a problem. As Immanuel Kant put it, you should

Have the courage to use your brain.
He was of the opinion that we are prisoners of our own inability to think. We should also not hesitate to speak about a problem (SayIt). This applies even if the problem belongs to the past, because thinking and talking can help us avoid the problem in the future (SeeMetaProblem).

The appeal to think may seem highly superfluous. Yet, people do not always think.

Chew before you swallow.

Reserve your right to think

It is very hard to find truth (Truth). Everything can be contested and questioned (LogBack), and everything we thought was true can turn out to be wrong (Contingency). Nobody knows for sure what is the truth. Therefore, if we want to approach truth, we should always continue seeking the truth (SeekTruth).

If a philosophy or ideology claims to find truth or to have found the truth, then it has to allow us to listen to other opinions, to doubt the ideology, to question it, and to change our mind about it. If the ideology is true, then it has nothing to fear: It will prove robust to all questions and doubts. If the ideology is faulty, then doubts and questions can help the ideology improve. Thus, the ideology should welcome the criticism. If the ideology does not welcome criticism, then this indicates that it fears being proven false. Its goal is probably not to find the truth, but something else. We should not adhere to such an ideology.

This means:

Reserve your right to think. For even to think wrongly
is better than not to think at all
Hypatia of Alexandria

Do not commit logical fallacies

We have a tendency to believe things that sound logical. Yet, not everything that sounds logical is logical. There are only few ways in which one statement logically implies another statement (SecRules). Other ways of deducing new statements are fallacious: They may lead to false conclusions.

There are many wrong ways of deducing a statement. This essay reproduces the list of fallacies as found on Wikipedia [Wikipedia / List of fallacies] here. Most of these fallacies are subsumed by the non-sequitur argument (NonSeq). Here is an example for such a wrong argument:

You brought the chair here
Therefore, you also have to bring it back
This looks like a perfect logical conclusion. However, it is not. The first statement does not logically entail the second argument. To see this, consider the following argument. It plays on the distribution of work (you did something, so I will do something, too):
You brought the chair here
Therefore, I will bring it back
This argument also looks like a perfect logical conclusion — but the result is the opposite of the previous conclusion. Both arguments are fallacious.

The only way that one statement logically follows from another one is through logical deduction (SecRules). In most cases, statements will not follow logically. Then, logic will not help us. In the example of the chair, we might decide to bring the chair back out of goodwill (MakeStep). We might also ask the other person to do that, if we are doing something else (SayIt).

There are many more ways to do something wrong than there are to do something right.

Expect multiple reasons

When something happens, we have a tendency to assume one single reason for it. That is not always true. Many things have multiple causes that came together and amplified or enabled each other. Therefore, it is not rational to assume that, once we have identified one reason, there is no other (FalseDich). It is also not rational to start an argument saying that, since there is this reason, all other reasons must be wrong.

Examples are:

Do not mix independent events.

We have a tendency to have our mood influenced by bad events and then transfer that bad mood to other (unrelated) events. For example, if we get a bad grade at school, we feel bad and we have a tendency to see any following events that day also in a slightly darker light. This is not rational, because the other events do not change in their quality if we get a bad grade.

One example (from a Loriot movie) is a customer in a restaurant, who tries to eat a steak. Whenever he brings the fork close to his mouth, someone asks him whether the food is alright. He is obliged to answer and looses his bite. Different waiters and other customers all keep asking, so that the poor guy never gets a single bite of his steak. In the end, he is so unnerved that he yells at the waiter. Yet, each of the waiters and customers asked him only once, and so none of them can understand why the guy is angry. Difficult as it is, we have to separate different events.

A good thing does not make another thing bad

When we encounter two comparable things, and we like the first, we have a tendency dislike the second. Vice versa, when we dislike the first, we have a tendency to think that the second is good. This is not necessarily so: Both things can be good or both things can be bad.

Look at these examples:

This advice echoes in other parts of this essay (NoGen, BestNotGood).

Steer clear of general valuations

General valuations are statements that assign a judgement to a thing, such as in "Bob is annoying" or "Life in Italy is great". As we have seen (Valuations), general valuations have no place in rational arguments. There is no point arguing about them (NoArgGenVal).

This obversation applies not just to arguments with others, but also to personal reasoning. Very few things are really completely "great" or completely "bad". If you do not like a person (Personal) or if that person has hurt you, then there is still no need to assume that everything about that person is bad. On the contrary, by assuming this, you close the door with that person (ConflictResolution). Likewise, if you do like another person, there is no need to assume that this person is totally "great". That person will have his weaknesses, too. Thus, instead of remembering that someone is "great" or "not great", we should be aware both his negative traits and his positive traits. If you ever find yourself admiring something or someone, be sure to find at least one not-so-great characteristics as well. If you ever find yourself hating someone or something, try also to find a positive trait of that something. This will help maintain a realistic picture of the world (SeekTruth).

One particular instance of this pattern is the fact that even an evil person can do good things, even a dumb person can say smart things, and even a bad ideology can have good aspects — and vice versa (DontId).

A general valuation is rarely true in its entirety (Valuations). Therefore, someone who defends a general valuation defends something that is partially wrong. Such a person becomes untrustworthy, because we get the impression that he says things not because they were true, but because he enjoys believing them. If, in contrast, a person presents both sides of the coin, then it becomes clear that he values truth more than his personal preferences. Thus, he will appear trustworthy.

Technical issues
Here are some unproven thoughts concerning general valuations (Theories): General valuations simplify our lives. Classifying people, situations and things into "good" and "bad" speeds up our decisions. For example, if we decided that a certain person is "bad" and another person is "good", then choosing with whom to spend an evening is very easy. This mechanism might have been developed in early humanity, where fast classification of people into "friend" and "foe" was essential to survival. It is no longer today. Today, we have the life conditions and the brain power to draw more differentiating conclusions.

Do not give a theory the benefit of doubt

We have a tendency to believe in supersticious theories (Theories) that claim to predict events or that suggest that we should do something in order to avoid harm. Such theories are for example astrology, clairvoyance, the theory that certain things should only be done during certain phases of the moon [Wikipedia / Moon astrology], superstitions or Internet hoaxes [Wikipedia / Hoax].

People are very vulnerable to such theories, because they see proofs that the predictive theories actually work. However, these proofs are rarely valid (SecProofs). This essay dedicates a section to true theories (SecTruth) and an article to good rules (GoodRules).

Here is a list of scenarios where a proof for a predictive theory is not valid. The first four scenarios appear to be especially frequent.

(adapted and extended from [Wikipedia / Postdiction])

Theories that are "proven" by these means should not be considered valid. These theories are false. That is, they cannot predict reality and they cannot avoid harm (GoodRules). Therefore, believing in such a theory is not rational (Def). Furthermore, the problem with believing in such a theory is that the theory may cause us to do something that conflicts with our goals — and be it only to waste our time (StdGoals). Worse, such theories may lead us to believe that a certain person or ideology is trustworthy, leading us to follow even more of their teaching, while the person or ideology actually deserves no such credibility.

The thing about statements on the Internet is that you cannot verify their validity
Abraham Lincoln

Do not engage in wishful thinking

Wishful thinking is the belief that something is true because we like it to be true. Obviously, things do not become true just because we want them to be true (Desires). Therefore, wishful thinking is not rational (Def). It is a particular variant of mixing up independent properties (WrongRules). It is also a logical fallacy (DontFall) [Wikipedia / Wishful thinking]. By obscuring the truth, wishful thinking may actually prevent us from obtaining the thing that we wish for.

Wishful thinking deserves particular attention here, because people have a tendency to not just believe what they want to be true, but also to justify it with pseudo-rational arguments. That is, they use rationality to reinforce their wishful thinking. This usually happens through wrong reasoning (SecNonRatArg) or invalid assumptions (WrongRules). For example, you will hear people say "I am sure that the Bible prohibits slavery. The Bible is a good book.". This is wishful thinking, because out of the conviction that the Bible is a good book, the person deduces that it bans slavery (while it does not [Thoughts on Atheism / BibleMoral]).

The goal of rationality is approaching the truth — no matter whether the truth is what we want or not (SeekTruth). But our desires (Desires) have a tendency to influence our rational thinking. Therefore, we have to be particularly attentive with our rational arguments if we know that we prefer one outcome of the argument.

Do not let a small thing have a big effect

We have a tendency to take every event as a confirmation of our beliefs (NoWish). This is particularly misleading if we take a "small" event that was caused by chance as a basis for major decisions. If we want to be rational (Rational), we should thoroughly verify any circumstance that we base a major decision on.

Here are some examples:

One particular instance of this problem is short messages such as e-mails or text messages. These can easily be misinterpreted, seen as offensive or aggressive — even when, in fact, the author had no such intention. This danger is particularly imminent when we have rare contact with the other person, so that a single message may be all we know about them. We should never base our opinion about someone on too few samples.
A wise man, therefore, proportions his belief to the evidence.
David Hume

Do not identify with bad or untrue things

We have a tendency to defend people, ideas or values if we feel close to them. That is unreasonable. To approach truth, we should defend truth, no matter where it is or who advocates it (SeekTruth). We should not identify with something that is morally bad or untrue (Moral).

Examples are:

To find truth, we must have a differentiated picture of reality — where things are rarely simply "good" or "bad". Most things have upsides and downsides. This is an appeal that repeats itself in this essay: GenVal, NoGen, NoArgGenVal, OpReal.

I'm for truth, no matter who tells it.
I'm for justice, no matter who it's for or against.
I'm a human being first and foremost,
and as such I am for whoever or whatever benefits humanity as a whole.
Malcolm X

Do not insist on subjective statements as if they were objective.

Subjective statements are statements that cannot be proven from universally agreed facts. Examples for subjective statements are faith statements, personal preferences (Preferences) or desires (Desires).

We should not claim that subjective statements are the absolute truth. Most likely, they are not. Therefore, it is not rational to present subjective statements as objective truth (Def). We should also avoid entering into a dispute about subjective statements, because it is unlikely that we will come to a conclusion. We should save the effort (StdGoals). We have to be particularly careful with subjective statements that talk badly about somebody else. This is because, in many moral frameworks (Moral), statements that dishonor somebody else are insults unless they can be proven to be true (e.g. [Thoughts on Ethics / Insult]). Subjective statements, however, can never be proven to be true. Hence negative subjective talk about other people is always an insult in these frameworks. If we want to play safe, we should not say something about someone that we would not say if that person were present (QPerson, TalkWell).

In the interest of speaking truth, we should use subjective statements only

Do not try to contradict if there is no contradiction

People often start arguing even though there is no contradiction in their views. As an example, take a discussion between a man and a woman on vacation in Paris. She says "Paris is full of dirt". He says "But Paris has wonderful buildings". She says "But look at all the rubbish in the streets." — and a dispute is on the way.

Objectively, though, there is no need for dispute, because there is no contradiction. The statement that Paris has dirt in the streets and the statement that Paris has wonderful buildings are both true. What causes the dispute is that the two squabblers assume that the woman defends defends the statement "Paris is horrible" and the man defends the statement "Paris is wonderful". These are the implicit statements that we hear (Implict) — and these statements are indeed contradictory. However, neither her nor him stated these claims. Therefore, the claims should not be assumed. Then, the cause of conflict vanishes immediately. Furthermore, both claims are general valuations (Valuations). Thus, they have no place in a rational argument anyway.

If we want to resolve such a conflict, we should first become aware of it. Then we should stop acting as if we were contradicting. We can acknowledge what the other person said, if we share their view ("Yes, indeed, Paris is very dirty", (Ack)). Then, we can say what we wanted to say. The magic words are

This is not a contradiction to what you were saying

Do not say something that you do not know

Sometimes, out of the desire to help or to impress, we sell things for certain that we do not know for sure. Saying things that are not sure counteracts the goal of approaching truth (SeekTruth). Particular instances of this problem are The bolder the statement, the more impressive it seems. But the bolder the statement, the more likely it is to be wrong. Therefore, we should resist the temptation to impress other people and carefully ponder what exactly we want to say (WhyTalk).

We can make weaker statements instead, for example by

I was gratified to be able to answer promptly. I said I don't know.
Mark Twain

Say it

Many problems appear because people do not say what they know. Rationality, with its emphasis on explicitness and clarity (Speak), favors saying what you know, if this advances knowledge. The following scenarios are cases where it is rational to say what you know, because it brings discussion participants closer to truth (SeekTruth):

For example, assume that a group of friends wants to go to a movie. Everybody thinks that the others want to go, and so everybody feels obliged to join in. If these people talked about their reasons for going, they might well figure out that everybody just thinks the others want to go — while nobody really wants to go (DecDuc).

In general, there is no harm in assuring that you and your interlocutor start from the same founding statements. [Wikipedia / State the obvious]

You won't have to watch what you say if you watch what you think.
Bill Johnson
(a person whom I rarely cite — but credit where credit is due.)

Say what you want and say what you don't want

People are often too shy or too complicated to say what they want. This may cause problems (Problems) when other people assume that they like something. These problems can be avoided if we clearly say what we want. Particular instances are:
He who knows does not speak.
He who speaks does not know
Lao Tzu

Do not say you are doing something for someone else, if it is for you

Some people avoid saying what they want (SayWant). One particular form of this phenomenon is saying that one does something for the other person, when, in reality, one does it for oneself. Examples are

Such statements misrepresent reality. Therefore, they are not rational, in the sense that they counteract approaching truth (SeekTruth). Such statements will put the other person into a defensive position, even though the burden of explanation lies plainly with the speaker. Therefore, it is more rational to make one's wishes explicit (SayWant).

In some cases, the speaker may intentionally misrepresent reality in order to achieve his own goals. Then, it can be rational (in a sense) to speak falsehood. This is a machiavellian view of things, which is discussed further up (Machiavelli).

Give reasons for your statements

Nobody is forced to give reasons for his statements or behavior. However, in the following cases, it is helpful to give reasons:
It's not that people dislike rationality. They just don't like the conclusions.

Watch out for emotional traps

An emotional trap is a pattern (Patterns) in which a person voluntarily tries to fulfill expectations of another person, group, or ideology to such a degree that he suffers continuous discomfort. The person is unaware of the misery that he is causing to himself, because he desires emotional rewards such as love, recognition, forgiveness, friendship, respect, or salvation in return for his behavior. Particular instances of this pattern are:

Emotional traps are different from classical bullying or abuse, because the victim voluntarily sticks to the abuse. This entails, unfortunately, that liberal moral frameworks (MoralFrame) will not be able to protect the victim. The frameworks will point to the principle of "Volenti non fit iniuria" and thus not condemn the abuse [Thoughts on Ethics/ Volenti]. Therefore, it is of utmost importance for the victim's well-being to become aware of his misery. The safest indication for an emotional trap is continuous emotional discomfort. Should we become aware of such a feeling, we should immediately start asking ourselves whether we are in an emotional trap. Talking with friends can help us compare our life to what is normal (Normal, QPerson).

Do not assume that this period of life is special

We have a tendency to assume that the current period of life is exceptionally stressful. We are tempted to take this as an excuse to neglect resolutions or to take less care of ourselves. Yet, every period of life is stressful in its own way (Fuzzy): Therefore, we are probably wrong in assuming that the current period of life would be exceptionally stressful. Therefore, such an assumption is not rational (Def). As soon as a stressful period lasts longer than a few weeks, we should accept that period as part of our lives and not as an exception.

If a problem appears, also see the meta-problem of why it appeared

If a problem appears, it always means that there is a meta-problem as well, namely the problem of why the first problem appeared. For example, assume that you find a notification in your letter box that a parcel is waiting for you at the post office. This is a problem because the current state of the world (with the parcel at the post office) does not correspond to the desired state of the world (with the parcel at home) (Problems). This problem is easy to solve, it suffices to go to the post office and pick up the parcel.

The meta-problem, however, is that the parcel was not delivered in the first place. This may be because the letter box is too small for parcels. If this meta-problem is not solved, then the original problem will appear again and again. Therefore, it is useful to spend some time thinking how the meta-problem can be solved (e.g., by putting a note that asks the postman to deposit parcels in the court yard). Thereby, future instances of the original problem disappear. Usually, people avoid solving the meta-problem, because the effort does not seem justified if the original problem occurs only once in a while. However, the solution of the meta-problem often takes little longer than the solution of one instance of the original problem. Thus, the effort is justified as soon as only two more instances are expected.

This seems a very simple technique, but people do not always apply it:

Limit the losses

When an endeavor does not work out as we want, we have a tendency to chuck the entire endeavor. We start believing that the endeavor failed and that there is no use continuing it. Yet, in many cases, only part of the endeavor failed. More often than not, it is possible to save and continue the part that did not fail. It might even be possible to rescue the part that we considered failed.

Therefore, it is not rational to abandon an entire endeavor when only part of it did not work out. The partial endeavor can still be more beneficial than no endeavor at all (by the Pragmatic Principle).

A similar observation applies to losses (Loss): When we lose something, we have a tendency to assume that we lost everything. That is not reasonable, in the sense that we should not assume it unless it is true (SeekTruth). It is more rational to be aware of what we lost and what we still have. This will also help us make use of the part that we still have (DontWorry).

Do not postpone if postponing it costs more effort than doing it

We have a tendency to postpone things that we do not like. In some cases, though, postponing a thing takes as much effort as doing the thing. In these cases, it is more reasonable (StdGoals) to do the thing rather than to postpone it.

Here are examples:

You cannot change your future, but you can change your habits, and surely your habits will change your future.
Abdul Kalam

If something is sure to get worse, get out

Sometimes, we find ourselves trapped in a situation that only gets worse with time. We should immediately head out of such a situation, because the longer we wait, the worse it will get. This is true even if getting out comes at some cost. ("cost" and "worse" are to be understood with respect to our goals (Goals).)

Here are examples:

Besser ein Ende mit Schrecken als Schrecken ohne Ende
Better an end with horror than a horror without end
Sophie Scholl

If you can have a huge gain for a small effort, make the small effort

If we want to serve our goals efficiently, we should trade off effort with gain (Goals, Rational). Unfortunately, we have a tendency to avoid effort, even if the effort is small compared to the gain. In these cases, it is useful (Good) to force ourselves to make the effort.

Examples are

Section SecDec gives proposals about how to trade off effort with gain.
If you dont ask, the answer is always no.

Don't worry

When we run into a problem (Problems), we worry. In most cases, our worry helps us take the problem seriously. It also tells other people that this problem is important to us. Worrying sends an implicit call for help to other people. In some cases, however, the worry just aggravates the problem. This happens, e.g., In these cases, it is more comforting to decide not to worry.

Specific instances of this phenomenon are:

In such cases, it is more reasonable to decide not to worry (Fear).
In your life expect some trouble /
when you worry, you make it double.
Bob Marley (among others)
Unproven thoughts
It seems that much of the suffering from a problem comes from Each of these feelings have their purpose (see the respective topics). However, together, they may actually cause more suffering than the problem itself. This avenue of reasoning seems to call for control of our feelings, the abandon of fear, and the restrain of anger — which are concepts often found in religions.

Be happy

Happiness is a standard goal (StdGoals). Beyond that, happy people are likely to make other people happy. Folk-psychology teaches us that happiness triggers positive thoughts. It also teaches us that positive thoughts can trigger happiness. Therefore, if we want to be happy, we can contribute ourselves to our happiness:

Happiness is not always the appropriate way to go (DontWorry, NoAnger). However, if we have no serious problem (Problems), we can sweeten our life by being happy. A particularly rich source of happy thoughts are positive experiences in the past. Nobody can take away our memories:

Don't worry, be happy
Bob Marley (among others)

Be responsive

Being responsive means reacting to your interlocutors statements. A responsive person will acknowledge what the other person said, answer a question that is asked, and reply to a concern that is raised. If confronted with multiple questions, a responsive person will take each of them seriously. A responsive person will react swiftly and avoid any unnecessary delay in the response.

Being responsive is generally highly appreciated. So if we want to be nice to our fellow humans (StdGoals), being responsive has a good benefit/cost ratio. Being responsive is also highly helpful (Good) if we have a personal interest in the resolution of the issue at hand. It will also encourage our interlocutor to be responsive towards ourselves, which benefits us on the long run. Last, it will establish trust, because our interlocutors learn that they can rely on us.

Being responsive means in particular

Do not reproach in hindsight

When someone annoys us, we do not always feel ready to tell him that he annoys us. Rather, we have a tendency to accumulate the anger in ourselves. At some point of time, the accumulated anger comes out and we accuse the other person of all the bad things that he supposedly did to us. We might also consistently use sideswipes (Sideswipes) to hint at what angers us. This has the following effect: Our interlocutor learns that, even if we say nothing, we might still be tacitly accumulating anger against him. Therefore, our interlocutor can never be sure whether he currently annoys us or not. This induces a feeling of insecurity on his side. Our interlocutor cannot trust us if we signal peace, because he knows that if we are angry, we might not say so. This ultimately undermines his trust in us.

Therefore, for the goal of being a trusted person, it is more reasonable to speak out if we feel annoyed. We should speak out immediately if we feel uncomfortable (Sayit) — or forget the issue forever (ForgiveForget). This will allow the people around us to be sure that everything is alright unless we say so.

Do not talk badly about other people

Gossiping is talking about other people. As it is the case with every other behavior, our moral framework decides whether gossiping is morally acceptable or not (Moral). Liberal frameworks will most likely permit gossiping, if we do not insult or lie.

However, it can be in our own interest not to overdo gossiping. If we present other people in an unnecessarily bad light, if we judge them prematurely, if we do not seem to care about them, if we disrespect their interests, or if we behave badly towards them, then our interlocutor will assume that we will do the same thing to him when we talk to other people. This, in turn, will discourage him to trust us. Therefore, if we want other people to trust us, it is in our own interest not to talk badly about third parties.

If we want to guard against this kind of behavior, we can proceed as follows: If we do not like something that the other person did, we always talk first to the person himself, before talking to others. In many cases, this will eliminate the reason for discontent.

Who gossips to you will gossip about you
Judging a person does not define who they are. It defines who you are.
Technical Issues
Talking badly about other people is frowned upon in society. Therefore, doing so gives us a weakness. This weakness can also be interpreted as a proof of trust in our interlocutor. This trust can produce reciprocal trust. Therefore, paradoxically, talking badly about others can also generate trust between two people. This seems to have to do with some group mechanisms that unite people if they share a common enemy.

If you fear you cannot do something, say so early

Sometimes, we are unable to fulfill our promises. Technically, this is a problem (Problems), because the actual state of the world is not the desired state of the world (the one we promised). This makes us feel uncomfortable. We have a tendency to avoid talking about this problem. However, ignoring the probem does not solve it. On the contrary, the longer we wait, the less likely it is that someone else can do the work that we cannot do. Therefore, we should tell people as soon as possible if we know that we cannot fulfill a certain expectation. This is the fail fast principle [Wikipedia / Fail fast]:
If you fail, fail fast.

Here are examples:

In all of these cases, the fact that we cannot fulfill the expectation is deplorable, but the fact that we say so too late makes it even more deplorable (because it is less likely that the desired state of the world is achieved). Therefore, we should at least minimize the damage and "fail fast".

Failing fast also makes us more trustworthy. This is because people will learn that they can rely on us — and that we will tell them when they cannot.

As a corollary, we should aim to give reasonable time estimates rather than too optimistic time estimates. The reason is that it is easier to manage expectations upfront than to deceive them later.

Have a conflict resolution mechanism

In conflicts with other people, we have a tendency to insist on our view. We have a tendency to sulk, to hate the other person and to brand them as lifelong enemy. This is not a rational mechanism to resolve the conflict. The reasons are as follows:

Conflicts will always appear in life. They will appear with friends, with colleagues, with our partners, with the family or even within ourselves. It is impossible to avoid conflicts in general. Rather, we should have a way to deal with conflicts. The most rational way of dealing with conflicts is to talk them out (SocialProb). Talking about conflicts resolves misunderstandings, makes the problem more precise and allows both participants to learn.

A friend is someone who is there when life is unfriendly.

Do not assume a reproach

When we speak, we transmit much more than the content of the actual statements: We transmit connotations, appeals, valuations and information about ourselves. These are implicit statements (Implicit). When listening to a statement, we infer these implicit statements.

Two classes of statements are particularly prone to appear in the hidden layer rather than in the explicit layer: reproaches (Reproaches) and negative assignments. A reproach is a statement that someone else caused something bad according to some goals (Desires) or moral standards (Moral). The reproach also acts as an appeal to act. A negative assignment is a statement that says that a person has a trait that is commonly regarded as bad. Nobody likes receiving reproaches or negative assignments. Therefore, we often frame them in the hidden layer of our speech. As a result, we are used to spotting implicit reproaches and negative assignments in other people's statements.

The problem is that we might at times spot such an implicit statement even if it was not intended. For example, assume that a man and a woman are eating a homecooked meal together. The man says: "There is something green in the soup.". The woman reads: "I do not like what you cooked", "The soup is bad" or even "You cannot cook". Understandably, she gets annoyed [Wikipedia / Four sides model]. But if she starts arguing with him, he may say that he just wanted to draw attention to something green in the soup — without making any of these reproaches.

The solution to these kinds of problems is to ignore any reproach or negative assignment if it is not explicit. The rationale is that if someone wishes to make us a reproach, we may expect it to be explicit. If our interlocutor does not dare making the reproach explicit, he does not deserve our attention to it. We may also decide to uncover the implicit statement (Uncover).

Technical issues
Here is a proposal for figuring out whether an inference was intended:
  1. Use the principle of simplicity (Simplicity): Collect possible meanings of the statement, from the innocent ("There is some strange item in the soup") to the malicious ("You do not know how to cook"). Then, ask yourself whether there is any way to express these meanings in a simpler way. If one of the meanings can be expressed in a simpler way, then this is likely not the intended meaning. In the example, the reproach "You cannot cook" can be expressed in a much simpler way (namely by saying "You cannot cook"). Therefore, we may assume that it was not the intended meaning. The meaning "There is a strange item in the soup" cannot be expressed any simpler. Thus, if the man really wanted to state just this, then the way he did it was the best way to do it. Therefore, this meaning is likely the intended one [Thoughts on Ethics / Declaration].
  2. Once you have guessed an intended meaning this way, do not assume that the statement has any negative or reproaching content beyond what was said explicitly. Close your ears to what was not said. In the example, the woman would understand that there is something strange in the man's soup — and not draw any further inferences about her cooking.
  3. If you decide that the statement does carry a reproach or a negative assignment, ask whether this is the case (Uncover): "Do you mean, you do not like the soup?"

Uncover implicit statements

In discussions, we sometimes argue against implicit statements (Implicit). This is always a mistake, because implicit statements are not rational statements. They may even trap us, as in this example:
  1. Our interlocutor says something, e.g., "This book did not even make it into the top 10!"
  2. We hear an implicit message, e.g., "This book is not worth reading"
  3. We contradict the implicit message ("Well, the book is not so bad!")
  4. Our interlocutor can insist that we did not contradict his thesis ("Whatever. It did not make it in the top 10")

In many cases, the best solution to this problem is to ignore the implicit statement completely (NoReproach, NoContradiction). In the example, we can simply acknowledge the statement (Ack) by saying "Yes, true...".

Otherwise, we can uncover the implicit statement, and make it explicit. This can be done by stating that the implicit statement is not implied:

Yes, but this does not mean that the book would be bad.
However, with this statement, we might be bringing a strawman argument (Strawman). Therefore, the safest way to counter an implicit statement is to ask whether the other person believes in it:
Do you think that the book is bad?

Do not assume bad intentions

When other people do something that we do not like, we have a tendency to believe that they do so in order to harm us. This is not always the case. In fact, assuming that they want to harm us is in most cases an unsupported hypothesis.

It is more reasonable (and more beneficial to inter-human relations) to assume the more frequent case, namely that other people have good intentions. They may do something not because they want to harm, but because they do not know that what they are doing harm.

Never attribute to malice that which is adequately explained by stupidity.
the principle of Hanlon's Razor

Assume good reasons

Sometimes other people do something that we do not understand. We have a tendency to assume that these people do not know what they are doing. This, however, is not true in the majority of cases. Rather, in most cases, it is us who do not know the full picture. There may be some facts we do not know or some private reasons (Private) that we do not know. Therefore, we should assume that people have their reasons to act the way they do.

One example comes from a Karl May book. It is about a man and his son who climb up a church tower to repair the bell of the tower. The ladder they have to climb is several dozen meters high. Shortly before they get to the bell, the crowd sees father and son struggle with each other on the ladder. To the horror of the crowd, the father then kicks his son and the son falls off the ladder into his death. As the father returns, the crowd is ready to lynch him for murder. But the father explains himself: When they climbed the ladder, the son panicked out of fear of heights. He grabbed the leg of the father. The father tried to calm him, but instead, the son panicked more and more, threatening to pull both of them into their death. In order to save his own life, the father had to kick his own son off the ladder. The wise men of the village are consulted and confirm that, if someone panicks on the ladder, there is no way to save his life. The crowd lets the father go.

Be less rational

Too much rationality can be poisonous to human relations (NoUse). This holds in particular if rationality is applied badly or against its principles. This section will give advice (Advice) for achieving certain goals (Goals) that are usually considered "irrational". As usual, we assume the goal of approaching truth (SeekTruth). We also assume the goal of avoiding unnecessary dispute, and the goal of saving effort (StdGoals).

Ask if you feel offended

When we feel offended, we have a tendency to argue back. Yet, in many cases, the best thing to do in order to resolve the conflict is to ask a question instead. One standard question is
Why do you think that X?
...where X is whatever the other person said. Here are examples for such offenses:

Asking a question will allow us to understand what the speaker wants. Thus, it helps us approach truth (SeekTruth). It will also help take out the sting of disputes — if the speaker realizes he is wrong, or if we realize he is right. Thus, asking a question is usually a good reply for these goals.

Do not explain when you have no explanation

If it appears that we did something wrong, we feel inclined to explain ourselves. In most cases, this is useful. In some cases, it may even be morally required (GiveReasons). However, if the reason is mainly that we were mistaken, and if time is pressing, then we should save everybody's time and not explain (StdGoals). An acknowledgement and/or apology may do the job.

For example, assume that we are late for a meeting because we did not plan our trip well. There is no use explaining which buses exactly we missed because of which bad planning. An apology for misplanning will do the job (ReasonExcuse).

Extremes invite extremes

Whenever someone has an extreme opinion, it is tempting to start arguing for the other extreme. It seems that an extreme opinion provokes us to defend the other extreme, because we feel that this other extreme is unfairly disregarded. In this process, however, we tend to forget that both extremes may be true to some degree. In reality, the truth is nearly always somewhere in the middle (GoodNoBad, NoGen, GenVal, FalseDich). By arguing for an extreme, we provoke needless conflict (NoProv) — and most likely we are as wrong as our interlocutor (SeekTruth).

This holds in particular for politically correct opinions. Since most opinions we hear in the media and in public are politically correct opinions, we have a tendency to fight for the opposite opinion. That desire is understandable. It is even in the interest of truth. However, but we should not forget that an opinion can have truth in it, or even be entirely true, even if it is politically correct. Here are examples:

In the end, a thing is always true or false by itself, no matter how we present it (Truth).

Do not get caught by the temptation to contradict

Some people have a way to talk that is perceived as so provocative that we feel the urgent desire to contradict the person. This holds in particular if the other person is acting in a bluntly non-receptive way (SecNonRec), if the person makes general statements (NoGen, Extremes), or if he does not give you a role in the conversation (TalkToTalk).

However, contradicting makes only sense if the other person makes a statement to which we have a valid counter-argument (DontArgue). If we do not like the way the other person talks, we often think we do have a counter-argument — while, in reality, the other person may just be saying true things in an unpleasant way. Then, we have no foundation to attack the content, and hence we should not do it (SecNonRec). It may be more reasonable to unpack implicit statements (Uncover).

Passion [in an argument] is inversely proportional to the amount of real information available.
Gregory Benford

Don't argue about the meaning of words

A great deal of cantakerousness finds its nurture in disputes about the right meaning of words. That is a pity, because language should be a tool and not an object of dispute.

Words acquire their meaning by convention (Language, Mean) and mutual goodwill (ReasonableMeaning). People can also use a word with any meaning, as long as they and their interlocutors agree on the meaning and as long as no reference to other sources is made where the word is used in another meaning (Definitions).

When interlocutors cannot agree on the meaning of a word, then it is more efficient for an argument (Arguments, StdGoals) to use another word in order to approach truth. For example, it is useless to argue whether the term "Europe" should include Russia or not. If the interlocutors cannot agree on whether "Europe" should include Russia or not, they should use the terms "Europe with Russia" and "Europe without Russia" instead. Then, it does not matter what "Europe" means.

Do not argue against personal preferences

As their name suggests, personal preferences are personal by nature (Preferences). They can rarely be justified. In fact, they do not require justification (EmotionalState). Therefore, it is futile to argue against them. If someone likes Coca Cola with salt in it, then there is nothing we could say against it.

The only judgement we can make is pointing out that a personal preference is in conflict with moral standards or with someone's goals (Evaluations, Moral). For example, if someone has stated that he wants to start a healthy life, then this goal is in conflict with the preference of drinking Coca Cola (with or without salt). In this case we may bring this conflict to our partner's attention (WhyTalk). His culinary preferences, however, cannot be challenged.

Accept all arguments for a personal preference

People sometimes feel urged to justify what they do. They will come up with reasons in order to make their behavior or their decisions more palatable to others. In reality, however, they may just wish to behave in a certain way (Preferences) or they may have private reasons for their behavior (Private). If we suspect that this is the case, then there is no use asking for reasons. Instead, we should accept whatever unconvincing reasons our interlocutor enumerates — knowing that these reasons are just a silent request to accept a personal preference.

The classical example is the girl who is asked out for a date. If she does not want to go, she will come up with a stack of excuses. Instead of arguing about these excuses, we should accept that the girl just does not want to go for a date.

Anything that is in the world when you're born is normal and ordinary and is just a natural part of the way the world works. Anything that's invented between when you're fifteen and thirty-five is new and exciting and revolutionary and you can probably get a career in it. Anything invented after you're thirty-five is against the natural order of things.
Douglas Adams in "The Salmon of Doubt"

Understand proxy arguments

People do no necessarily always say what they want (SayWant). If they want something for a certain reason, they might keep silent about that reason and put forward a different reason instead. Then they defend this different reason. We call this different reason a proxy reason. Examples are:

If we want to know the truth, we should be prepared for these kinds of proxy reasons. We should try to understand what people really want.

Do not burn the bridges behind you

It is embarassing to argue vigorously for a hypothesis, only to find out that one of our assumptions was wrong or that we did not know a crucial fact (OpReal). Therefore, in all discussions, we should always consider the possibility that we are wrong (PlanB). This means that we should Such behavior will help us stay as close to reality as possible (SeekTruth).
I would never die for my beliefs because I might be wrong.
Bertrand Russell

Acknowledge when you are wrong

Rationality aims at discovering the truth. For this purpose, it is helpful to admit when we are wrong. It is useful to admit that we are wrong as soon as we notice that we are wrong, because the longer we discuss, the more we will lose face when we finally admit we are wrong (FailFast). We should admit our fault quickly, explicitly and wholeheartedly. Example phrases are We should not get stuck with an opinion just because we do not want to admit defeat.

The same applies if we find a part or statement of our partner's argument convincing. Even if we have a general opinion about something (e.g., that the USA often act immorally), we can still acknowledge statements that go in the other direction, if they are true (such as the idea that the USA played a vital helpful role in the Second World War). We should not fight off these statements just because they go in a direction we dislike (DontId). Rather, we should acknowledge them if they are right. Acknowledging explicitly that a certain statement is right will get it off the table and avoids needless dispute.

In all of these cases, it is most helpful to acknowledge the facts wholeheartedly — i.e., without the "but" already at the tip of the tongue or in our minds. Spend a few seconds just acknowledging what is right. Acknowledging what is right will make you more trustworthy. That is because people will learn that you have the desire to discover and acknowledge the truth.

There is nothing wrong with being wrong, if you don't stick to it

Be alright with not having an opinion

We have a tendency to think that we should have an opinion on everything. That is wrong. Nothing forces us to have an opinion on all issues. In fact, for the goal of approaching truth, having a wrong opinion is worse than having no opinion (SeekTruth). This essay proposes various ways to express that we do not have an opinion on something (DontKnow, Unknown, AvoidIKnow, Theories).

Not having an opinion may also avoid needless disputes. It will allow us to listen in an unbiased way to what other people say (Listen). This, in turn, may help us form an opinion.

I try not to think with my gut. If I'm serious about understanding the world, thinking with anything besides my brain, as tempting as that might be, is likely to get me into trouble. Really, it's okay to reserve judgment until the evidence is in.
Carl Sagan

Be ready to give up your convictions

It has become quite fashionable to claim to be open-minded, tolerant and not attached to particular convictions. In reality, however, people are rarely ready to give up what they have been taught [Wikipedia / Confirmation bias]. If we want to approach truth, however, we should be willing to seriously question even what we think are constants in our world (SeekTruth).

Here are some examples for convictions that are upheld with great vigor, but that should be open to discussion:

If we want to approach truth, we should always be ready to search it even where we do not suppose it. Play the devil's advocate and see where you can go. This is a call that appears repeatedly in this essay (PlanB, DontBurn, OpReal, GiveUp, AAP, AssumeRight, NegEv).
Believe those who are seeking the truth. Doubt those who find it.
André Gide

Make sure that what you believe corresponds to reality

It may seem obvious that we should take care that what we believe is true (SeekTruth). Yet, this is not always easy to uphold this principle.

The principle boils down to 3 components:

  1. We should not form a belief prematurely, but only if we have solid evidence for it (SmallBig).
  2. The strength of our belief should correspond to the strength of the evidence (AvoidIKnow, NoSubjective). If we are not sure of something, we should not believe we know it.
  3. We should be ready to reconsider, abandon, downtune or change our belief whenever we have doubts whether it still corresponds to reality (DontBurn, NegEv).

Even though it makes us reliable if we stick to our beliefs, it makes us unreliable if we also stick to false beliefs. People who always stick to their beliefs, no matter whether they are true or not, lose trustworthiness. This is because we learn that these people value consistency more than truth (SecNonRec). But our goal should always be to find the truth, and not to show that we are right.

Adhere to a principle not because you decided for it, but because it is good
François de La Rochefoucauld

Audiatur et altera pars

Some statements seem true at first glance, but turn out to be false if additional information becomes known (Contingency, NegEv). As an example, consider the statement that introducing the minimal wage increased the gross domestic product by 2%. This makes the minimal wage look economically reasonable. However, if we learn that the gross domestic product has been growing by 10% per year in all the years before, we might want to reconsider our conclusion.

The most effective guard against this type of false conclusions is talking to people who have a different opinion. These people will be able to contribute the facts that we do not know. It is one of the principles of rationality to make our arguments open to verification by others and doing so is good practise (QPerson).

The same applies if our interlocutor tells us what bad things somebody else did. This is known as gossipping (TalkWell). Unless we have also heard the viewpoint of the other person, we are unable to tell whether that person acted right or wrong (Moral). Therefore, we should not adopt a conclusion.

In general, founding statements are safe and will not change with additional information (SecFounding). Likewise, logical deductions are safe over time (QTime). Basic statements by other people can also be considered safe [Thoughts on Ethics / Dixit principle] under common assumptions (StdAsm). However, the following statements are vulnerable to additional information:

Such statements may become wrong if additional information becomes available. Therefore, such statements should never be made or trusted without having heard the other side.
The shining spark of truth cometh forth only after the clash of differing opinions.

Do not generalize

Generalizations are absolute statements about a large set of people or events or a longer time (Generalizations). Examples for generalizations are "Germans are blond", "The postal service is slow", "Bob is not doing well in his job" or "Alice is unpunctual". Due to their generality, these statements allow a wide range of conclusions — some of which are almost certainly wrong. Furthermore, if the statement is pejorative, it may actually insult people (assuming the definition of [Thoughts on Ethics / Insult]). Therefore, we should avoid these statements unless we have solid evidence for them. The statements can be avoided, e.g., by If a generalization is not watered down, it is likely to lead to a needless dispute. A special case of this phenomenon are general valuations (Valuations, NoArgGenVal). These should be avoided in all cases in rational thinking.

Do not argue against general valuations

As we have seen, general valuations, such as "America is great" are not rational statements (Valuations). General valuations cannot be used in a rational argument, neither as assumptions nor as conclusions (Arguments). Therefore, we should not let our thinking be influenced by general valuations (GenVal).

This observation applies also to arguments with other people. When someone makes a general valuation, we should not start arguing against it (TalkToArgue). This is because there is no hope that such an argument will prove the valuation true or false. Rather, we should ask for more details ("How do you mean that?"). We can ask, for example, for concrete reasons that make our partner believe in the general valuation (Listen). This will help us get to know his point of view. Thus, a general valuation should be seen not as a hypothesis (Hypotheses), but rather as an invitation for discussion.

If we find the general valuation too strong, and feel the desire to argue against it, we may paraphrase it into a concrete statement. ("You think America is great. Does this mean that you think it always acts morally right?"). Once our interlocutor accepts this more concrete statement, we can then argue against that concrete statement (Abstract).

Assume the most reasonable meaning

Most statements in everyday discussions are ambiguous and can be understood in many different ways (Language, Mean). Many conflicts arise because people are being overly pedantic about the meaning of statements. These conflicts are not necessary. If we have the goal of advancing our knowledge (instead of the goal of being pedantic), then we should always take the meaning that seems most consistent with reality and with which we agree most (Abstract). For example, assume that our interlocutor states
Communism is practically inexistent today
This can be read as "There are no communist countries today". This statement is false. However, it can also be read as "There are only few nominally communist countries today and those that call themselves communist are less communist than they were before". This statement, in contrast, can be considered true. By assuming the latter meaning instead of the former, we avoid an unnecessary argument.

If our preferred meaning seems to be not the intended one or if the preferred meaning deviates a lot from the actual statement, we can always opt to make our interpretation explicit (Grounding, Plain). For example, we can say something like "You probably mean that..." or "I agree that...", followed by the presumed meaning.

Make everything as simple as possible, but not simpler.
Albert Einstein, paraphrasing the principle of Occam's Razor

Assume that your interlocutor is right

Unfortunately, we have a tendency to think that what we believe is right and that what other people believe is wrong. This is counter-productive for the goal of approaching truth (SeekTruth).

If we really want to approach truth, we should

It may actually turn out that our interlocutor is right and we were wrong. To practise true openness, imagine how your interlocutor tells you something really implausible, such as "Flowers breathe air through their leaves.". Then practice to react in an open-minded manner. (Example by Mouna Kacimi)
If you don't know and you think you know, you will never know.
Mouna Kacimi

Do not assume that people use rational statements

Rationality favors making clear-cut statements (SecStat, Plain, Clear). While clear statements are useful for rational arguments, we may not assume that everybody makes such statements. Some people do not like making such statements, others see their benefit, but are too lazy to shoulder the effort, and again others do not bother (Sorry, Cannot). We have no right to expect that other people would talk the way we would like them to talk.

If our interlocutor does not make clear statements, but we need a clear statement, we can often enforce such a statement by paraphrasing what the other person said and asking for confirmation. Here is an example:

Other person: "Well, you know, Alice is... I mean, she does not understand my kind of... you see?"
We can ask: "Do you mean that Alice does not understand your feelings for her?"

Things that are often said only implicitly are

Even though it is rational (Def) to use clear statements, we cannot expect everybody to use clear statements.

Do not assume that people behave rationally

Even though rationality has its benefits (Use), not all people behave rationally (Sorry, Cannot). Thus, it is fallacious to assume that whatever our interlocutor says is meant in a literal and rational way.

Here are some examples:

Even though it is rational (Rational) to behave in a consistent way, it can be a fallacy to assume that other people do. People often act by irrational motives (ReasonBehind).

Find the true reasons behind someone's behavior

Sometimes, people act in very irrational ways, insist on very irrational theories, make very unfounded reproaches, or get angry with apparently no solid reason. In many cases, such behavior is just a sympotom of the true underlying problem (Problems). Therefore, we should do the following if we want to help our partner: As soon as we are convinced that our partner's behavior is unfounded, we should stop fighting against this behavior. We should seek the true reasons behind it and talk about them. Talking about these reasons will likely be the best thing to comfort our partner.

Here are some examples:

If a behavior is strongly irrational, then it often has a true reason behind it. There is no use fighting the irrational behavior. Rather, one should go find that true reason behind it.

Learn what is normal

Some things are very normal in a certain society, while others are very normal in another society. If we happen to come to a different society, we can have a hard time estimating what is normal in that society and what is not. The same applies if we come to a different social community, a different age group or to people with a different background. Knowing what is normal is useful (Good) in the following cases:

The concept of "Normality" is a fuzzy and extremely context-dependent property (Fuzzy, Context) — but it has quite a number of implications in everyday life.

Do not get angry.

Anger is useful to make other people see the urgency of an issue. However, if our anger is directed against a thing, if no other people are around, or if the other people around have nothing to do with the issue, then our anger does not serve that purpose. It just portrays us as a violent-tempered person.

Anger may also underline our conviction in an argument. However, more often than not, anger is seen as an indication that we lack solid arguments. Thus, anger may actually turn out to be a weakness.

Anger may be also useful to motivate us to solve or to avoid problems [Wikipedia / Anger]. However, if the issue is minor, or if a solution is anyway on the way, then anger does not serve that purpose. In these cases, anger just consumes energy (StdGoals). Worse, it may hinder us to think rationally. Therefore, it is more reasonable to abstain from anger in these cases.

Be nice towards other people

Very often, conflicts arise because one party assumes bad intentions of the other party. We should not assume bad intentions (AssumeGood). We can also help other people to avoid assuming bad intentions. We can show other people that we do not have bad intentions by being nice to the other people.

This can be done, e.g., as follows:

These little things help avoid that other people assume bad intentions. They also help avoid that other people think badly of you or talk badly about you. They also create a general climate of harmony and well-being. It is clear that these things should only be done if we sincerely feel them (SeekTruth), and not to expect benefit. The benefit is not guaranteed either (MakeStep).

Make the first step towards the other person

In many cases, conflicts arise not because there would be a fundamental incompatibility of goals, but because the other person feels misunderstood, not taken seriously or exploited. If we want to resolve such a conflict, it is useful to send a first sign of goodwill to the other person. The other person might then follow with concessions from his side.


In many cases, this first step is the one that gets things going. The first step also makes sure that no one can reproach you that you did not try (Reproaches). However, this magic "first step" should not be done just because we want the other person to do the second step. The first step is valuable in itself.

If nobody does the first step, then it means the neither of the parties is interested in resolving the problem. If nobody is interested in solving the problem, then, by definition, there is no problem (Problems). The moral frameworks may see it the same way: If the victim of an offense does not actively help resolve the offense, then he loses his right to concern [Thoughts in Ethics / Sulking].

Forgive and forget.

When somone does un an injustice, we have the right to expect an apology. Moral frameworks regulate what constitutes an injustice and what is acceptable as an apology (Moral). An apology is usually perceived as humilating for the other person. Therefore, if we want to do the other person good, we can consider to refrain from insisting on an apology. This holds in particular if the three components that are commonly required for a proper apology are minor (Remorse) [Thoughts on Ethics / Resolutions]. That is the case if In these cases, it can be beneficial for the social interplay to drop the issue altogether — silently forgiving the other person's faux pas.
Und der Mensch heißt Mensch, weil er mitfühlt und vergibt.
And man is called man because he empathizes and forgives.
Herbert Grönemeyer in his song "Mensch" ("Man")

Give more than you expect to be given

By definition, it is good to follow good principles (Good). Depending on your goals (Goals), good principles may be moral principles, rational principles, or altruistic principles. At the same time, we may not always expect other people to follow the same principles. In fact, other people will not always follow the same principles (Sorry, Cannot). This, however, should not prevent us from still following the good principles (Pragmatic Principle). If we want to follow good principles without expecting other people to follow the same principles, we have to implement social asymmetry, i.e., the following policy (Policies)
Give more than you expect to be given

This means in particular


This concludes the philosophical part of the present essay.

The following appendix contains only questions about this essay (About), references (Bib), and acknowledgements (Acknowledgements).


Why do you think you can prescribe how people should think or talk?

This essay lists a number of thinking techniques (SecTec, SecMore). It also lists a number of talking strategies (ChapDisc). This could be understood as if this essay tried to tell people how to talk or how to think.

However, this is not the case. This essay describes the tool of rationality. It does not request people to use it. Everybody is free to use or to disregard the techniques outlined in this essay. I do not expect people to do what I call reasonable.

This essay also describes a number of ways to achieve certain goals (SecLess). This does not mean that everybody would have to share these goals. Nor does it mean that the techniques outlined in this essay would be the only ones that lead to these goals. The essay just outlines some possible ways to achieve certain goals. Whether the reader has this goal or not, and which way the reader chooses to achieve it, is his own decision.

People are also free to use the term "rationality" in a different manner or in a different implementation (Definitions). This essay describes "rationality" in just one particular sense (SecDef). The methods outlined in this essay (SecMore) are helpful (Good) for achieving the goal of approaching truth. If a person has no such goal or if a person prefers another way to approach truth, this essay will not stand in that person's way.

Why do you always refer to Wikipedia?

[Wikipedia] usually provides a good set of sources and justifications for its claims. This makes it a verifiable and trustworthy encyclopedia. Furthermore, it is constantly edited and corrected by thousands of volunteers. This minimizes biased descriptions.

Last, Wikipedia is freely and readily available to every Internet user. Everybody can contribute to articles in Wikipedia. If you disagree with some statement in Wikipedia, you can enter a discussion with the editors and even write an article by yourself.

This essay says nothing new

Some people say that this essay says nothing new. To their mind, the essay just summarizes the viewpoint of any normal rational person. The things said here appear obvious to them.

I am very happy that there are people who think that the ideas presented here are obvious. They are not obvious, and even debatable, to a large number of people. This essay serves both to make the rational point of view explicit (SayIt), and to explain it to people who may not find it so obvious after all.

Does this essay make anybody happier?

Yes. Several articles in this essay are directly concerned with making people happy (TalkYouHappy, Asymmetry). Other articles are concerned with solving problems, which usually also makes people happy (SecProb). These suggestions have a direct positive impact on us or our fellow humans.

Beyond these more concrete suggestions, this essay elaborates the theory of rationality in general. To certain readers, this theory gives intellectual satisfaction (thus making them happy). The theory itself has a number of advantages (WhyUse), and pocketing these may also make you happy.

Is this essay, together with your other ones, a religion?

A religion is commonly defined as the belief in and worship of a superhuman controlling power [Oxford Dictionary / Religion]. This essay is not concerned with the supernatural. Likewise, the essay on Ethics [Thoughts on Ethics] is not concerned with the supernatural. The essay on Atheism [Thoughts on Atheism] argues against the existence of something supernatural. Therefore, these essays do not form a religion. They are also not divine in nature. They have been written by a human. Unlike religious texts, they change whenever I discover that something can be improved.

However, the essays do offer some components that religions also commonly offer: A proposed approach to truth (this essay), a moral code [Thoughts on Ethics] and a view on the universe and the sense of life [Thoughts on Atheism]. In this sense, the essays can be seen, in a misuse of terms, as a religion without gods — or, more aptly, as a philosophical life stance.

Are you done with writing essays now?

No, I am not done. My further plans are essays on Links to these essays will appear here once I have started writing.

I have read this essay to the very end, but I am not convinced of your approach.

Thank you for reading this essay. Rationality, as defined in this essay, is nothing more than a tool. It is sometimes useful (Use) and sometimes not (NoUse). In general, people are free to use or disregard this tool as they like (Prescribe). Therefore, the purpose of this essay is not to convince you, the reader, to use rationality. Rather, the purpose of this essay is to inform you about my view on it. If you would like to learn more about this view, please keep on browsing the essay! If you would not like to learn more about rationality, please feel free to stop reading this essay at any time.



Here are cross-references to the other essays, concerning



The following people deserve my thanks