The Atheist Bible
Chapter on Truth
IntroductionThe question of what is “true” and what is “false” is one of the most fundamental questions in philosophy. This chapter presents my own theory of truth. It consists of the following sections:
- Introduction: Gives the running example of the ancient Greek mythological figure Persephone.
- Theories: Defines statements, rules, and theories.
- True theories: Tells us when a theory is true.
- True statements: Tells us when a statement is true.
- Theories in real life: Discusses how the theory of truth of this book translates to real life.
- Common Mistakes: Lists common fallacies that people make when they search for the truth.
- Mistakes in theological arguments: Lists common fallacies when discussing religion.
- Truth and Atheism: Links the theory of truth presented here to atheism.
- Questions: Answers objections to the theory of truth.
Strength of BeliefSome people think that truth is a matter of strength of belief. They would say that “God created the world in 7 days” and “Life took 4 billion years to develop on Earth” are both equally valid statements. Creationists believe in the first statement, and evolutionists believe in the second statement, but none is a priori more valid than the other.
And yet, there is a fundamental difference between these statements: While the first is based on belief, the second is based on evidence. This makes the first statement debatable, and the second statement verifiable, useful, and predictive. We will now discuss this difference in detail.
Persephone and the SeasonsAs a motivating example for our study of truth, let us consider a story from the Greek mythology. To explain the seasons of summer and winter on Earth, the Greeks had the following story: Hades, God of the Underworld, kidnaps Persephone, the Goddess of Spring, and negotiates a forced marriage contract, requiring her to return regularly, and lets her go. And each year, she is magically compelled to return. And her mother, Demeter, Goddess of the Earth, is sad, and makes it cold and barren. David Deutsch @ TED talks
This theory explains why winter is cold: Mother Earth is sad and shows her sadness by making it cold. Yet, is this the right explication? If not, then why is this explication wrong? Can we prove that it is wrong?
It turns out that it is very difficult to prove this explication wrong. To date, no proof has been found that Hades and Persephone do not exist. Also, the theory of Hades and Persephone makes astonishingly correct predictions to date: Every summer, the weather is hotter than in the preceding winter. Does this not prove that Persephone is still under the spell of Hades?
StatementsFor the purpose of this book, a statement is any declarative sentence. For example, the following sentence is a statement:
- Questions (“Is the Earth flat?”)
- Commands (“Go home!”)
- Interjections (“Uh!”)
- Incomplete sentences (“Well, you know...”)
RulesFor the purpose of this book, a rule is a statement of the form
If someone steals a car, then he is a thief.
If a stone is left in the air without support, then it will fall down.
A logical perspective on rules(Readers who are not familiar with logic can safely skip this article.)
From a logical point of view, a rule in the sense of this book is a clause of first order logic with positive and negative literals, only universally quantified variables, and no function symbols. This means that any first order logic formula that has only universal quantifiers in its prenex form and that does not have function symbols can be translated into a set of rules. For this purpose, the formula has to be brought to disjunctive normal form. Then, one has to pick one literal in each clause. That literal becomes the conclusion of the rule, and all others are negated and go to the premise.
The advantage of such a system is that it is decidable. This holds because the logic is a subset of Bernays-Schönfinkel’s decidable fragment of first order logic. This holds even if equality is added, because the result is the Bernays–Schönfinkel–Ramsey class Bernays-Schönfinkel-Ramsey class.
The disadvantage is that the system cannot express existential quantifiers in the conclusion. The system cannot deduce “There exists x such that...”. There are the following exceptions, though:
- If the x is an entity that does not depend on any other variables in the rule, then we can simply give a name to that entity and have it appear in the conclusion. This holds in particular if x is an entity for which we already have a name (such as “God”).
- If the x runs over a finite set of known entities (such as “the current presidents of all countries”), then the existential quantification can be replaced by a disjunction — and the system can have such a disjunction in the conclusion.
The system can deal with disjunctions in the premise and in the conclusion as follows:
A => B v C can be transformed to A ∧ ~B => C A ∧ ~C => B
If we need existential variables that depend on other variables and that run over an infinite or unknown set, then we have to use Skolem functions Skolemization. We do not go that far in this book.
A pragmatic perspective on rulesFor this book, a rule is a statement of the form “If A and B and C, then D”. In everyday discourse, rules take much less strict forms. Examples are as follows:
- “Lions roar” is an abbreviation for “If something is a lion, then that something will roar from time to time”
- “When it rains, the street gets wet” is an abbreviation for “If at some point of time it rains, then the street will be wet in the moments after that point of time”
- “When it rains, you get wet” omits some conditions. We mean “If at some point of time it rains, and you are outside without anything above you, then you get wet.”
Our rules usually contain a number of implicit conditions in the premise. Consider for example the rule:
Examples for rulesA rule consists of a premise and a conclusion. Many phenomena can be formulated in terms of rules. Here are examples:
- Scientific theories
These include for example the law of gravity. This law can be stated as a rule as follows:
If there are two physical bodies A and B
and the mass of A is m(A)
and the mass of B is m(B)
and the distance between A and B is r
then the force between A and B is proportional to m(A)*m(B)/r/r.
Regulations can likewise be formulated as rules. For example, the rule that someone is admitted to the A-levels if and only if they pass the exams in Math and English can be formalized as the following implications:
If someone passes the exam in Math and the exam in English then they are admitted to the A-levels.
If someone does not pass the exam in Math then they are not admitted to the A-levels.
If someone does not pass the exam in English then they are not admitted to the A-levels.
- World knowledge
Common sense knowledge such as “every human will die” can likewise be formulated as rules. For this purpose, the implicit type assumptions of the sentence become the conditions of the implication:
If some entity is a human then that entity will eventually die.
PerceptionsFor some statements I can immediately and incontestably say whether they are true. These are statements about my own perceptions and impressions. The following are examples:
- I feel hungry
- I have the impression of seeing something blue
- I hear a noise
These statements are not statements about the world. Rather, they are statements about my impressions. For example, I can have the impression of seeing something blue even if there is nothing blue. In that case, the statement about the impression will still be incontestably true.
My goal is now to structure and to predict these impressions.
My universe is my eyes and my ears. Anything else is hearsay.
Auxiliary statementsUp to now, we have talked only about very basic statements, namely about perceptions. We will now build more advanced statements on top of these perception statements. This works by definitions. A definition is a rule whose premise contains only perception statements and previously defined statements. Here is an example:
Auxiliary statements allow us to simplify our rules. For example, the rule
A rose by any other name would smell just as sweet.
The meaning of statementsWe have seen that statements about perceptions have a very simple meaning. We will now see what is the meaning of auxiliary statements.
The meaning of an auxiliary statement is the set of all rules in which it appears in the premise. For example, the meaning of “It is raining” is
If it is raining, and the sun shines, there will be a rainbow.
If it is raining, and I am outside, and I do not have an umbrella, then I will get wet.
The conclusions of these statements are again statements with a meaning. We can always ask for the meaning of a statement until we reach a perception statement. This way, each statement has to be grounded in reality. This definition of meaning corresponds to our everyday understanding of “meaning”. When someone asks us what we mean by “It is raining”, then we are likely to respond with a list of rules that characterize that particular state of the world.
Quite often, the definition and the meaning of a statement are just two sides of the same coin: If it rains, water falls from the sky, and vice versa, if water falls from the sky, then it rains.
From now on, we will assume that there is a set of rules that defines everyday English statements and gives them a meaning. You can think of this set as the rules that we learn during our childhood. With this in mind, we can now start using auxiliary statements in our rules.
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?”
TheoriesIn common understanding, a “theory” is a set of ideas. For the purpose of this book, a theory is a rule, together with the necessary definitions and meanings.
Examples for theories are:
- The rule “If it rains and the sun shines, then there is a rainbow”, together with the definitions and meanings of the words
- The theory of gravity, with all its rules and formulas.
- The theory that God creates life, together with the necessary definitions.
Applying a theoryA theory consists of a main rule, together with the necessary definitions and meanings. Consider, e.g., the following theory:
Def. 1: If there are droplets of water coming from the sky, then it rains.
Def. 2: If there is extremely bright round shape on the sky, then the sun shines.
Meaning of “rainbow”: If there is a rainbow, then I can see colors in the sky.
Grounded theoriesWe have seen that a theory can be used to make predictions. This works only if
- all statements in the premise are well-defined, i.e., for every statement, there is a rule (or a sequence of rules) that allows deducing this statement from perception statements.
- the conclusion is meaningful, i.e., there is a rule (or a sequence of rules) that allows deducing perception statements from the conclusion.
I never can catch myself at any time without a perception, and never can observe any thing but the perception.
Truth in a caseA theory can be applied to a particular scenario and yield a prediction. If the theory is grounded, this prediction can always be reduced to a perception statement. There are two cases:
- The predicted perception is correct
- If the predicted perception corresponds indeed to our perception, we call the theory “true in this case”.
- The predicted perception is incorrect
- If the predicted perception does not happen as predicted, we call the theory “false in this case”.
Both notions of truth and falsehood apply only to one particular case at hand. It can also happen that we have a case where we cannot verify the prediction of the theory. Furthermore, it can happen that the theory makes no prediction whatsoever — either because it is not applicable or because its conclusions are not grounded. In all of these cases, the theory can be called neither true nor false.
Truth of a TheoryA theory is a rule with accompanying definitions and meanings. We have seen how to determine the truth of a theory in one particular case. Now a theory is called “true” (in general), if it is true in all cases. This means in particular:
- There are cases where the theory is applicable.
- The theory is grounded.
- All of its predictions in all cases are true.
The problem is, of course, that we do not know which rules are true in eternity. Even if we have observed quite some number of cases in our lives, and others have also observed quite some number of cases, a theory that seems to be true can still turn out to be wrong one day. Take, e.g., the theory “If water is heated to 100 degrees Celsius, it boils”. This theory is generally considered true. However, it may happen that the theory makes a false prediction. For example, in environments with higher air pressure or more gravity, the theory may turn out to be incorrect. There is no guarantee that reality behaves according to the theories that we build.
This is the main insight of this chapter: We do not actually know the truth. We just approximate it by our theories. Once a theory behaves nearly perfectly, we assume that it is the truth — but we can never be sure.
Proving the truthA theory is true if it will always make correct predictions. As an example, take the theory of gravity: If an object is not held in place, it falls down. This theory is most likely true — in the sense that it will most likely make correct predictions in eternity.
And yet, we cannot prove that the theory is true. The only way to prove the theory would be to use another theory — which we could again not prove. And the reason why we cannot prove these theories is that there could be a case, one day, where the rule makes a wrong prediction. For the theory of gravity, this has actually happened: Objects do not fall “down” in outer space. The theory is actually not true in general.
No matter how many instances of white swans we may have observed, this does not justify the conclusion that all swans are white.
ValidationWe cannot prove that a theory is true. All we can do is observing whether it makes correct predictions. If the theory has made a number of correct predictions in the past, and has made no incorrect predictions, we start to trust the theory. We say that the theory is “validated”. We assume that it is part of the truth.
Consider an example: We hire a violinist to play at an art exhibition. The violinist says that all of her performances so far have been very well received. The theory is thus “If this violinist gives a performance, then that performance will be great”. This theory predicts that the violinist will do a good job at the exhibition. However, even if all of the performances so far have been great, our trust in this prediction will depend on how many performances the artist already has already given. If, e.g., the artist has given only 2 performances so far, then it does not mean much that all of them have been well received. If, on the contrary, the artist has a long career of hundreds of performances (all of them great), then we are more likely to trust the prediction. The rule “This violinist gives great performances” is validated by a large number of correct predictions. (This works only if we are willing to trust the perceptions of the violinist.)
If a theory has delivered a large number of correct predictions in the past, we say that the theory has been validated. Even a validated theory may go wrong in the future. However, the performance in the past turns out to be the best predictor for the performances in the future.
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.
RejectionA theory can make correct and incorrect predictions. If the theory makes lots of correct predictions, we call the theory “validated”, and we assume that it is part of the truth. If, on the contrary, the theory makes lots of incorrect predictions, then it cannot be part of the truth. We call the theory “false”, and reject it. We have already seen that a theory cannot be “proven” true. However, it can be proven false: False predictions mean that the theory is false.
In principle, a single wrong prediction shows that a theory is false. In practice, however, we know that all of our theories are mere approximations of the truth. Thus, we are willing to accept some few wrong predictions. In the example of the violinist, we are willing to tolerate some number of not-so-good performances of the violinist, and still say that “This violinist gives good performances” — if the vast majority of the performances were well received.
Life can only be understood backwards
but it must be lived forwards.
Unknown truthIf a theory always makes correct predictions, we assume that the theory is a good approximation of the truth. Some theories have not yet made any predictions at all. Consider again the theory that a certain violinist would give only great performances. Now assume that this violinist has so far not given any performances at all. In this case, the theory has not yet been applicable. There has not yet been a case where we could see whether the theory makes true predictions or false predictions. Thus, we cannot say that the theory is true, because truth presupposes true predictions. The theory is not false either, because falsehood follows only from false predictions. Thus, it is just unknown whether the theory is true or not. A large number of theories are actually of unknown truth.
What are we to do in such cases? Allen Kardec responds:
In the absence of facts, the wise man suspends his judgment.
Useless theoriesOne condition of a true theory is that it must be applicable, i.e., there must be cases where the it makes predictions. The theory may not yet have made a prediction in the past, but it has to make a prediction at some point in time. If the theory cannot make any prediction on principle, then the theory is useless.
As an example, consider again the violinist whom we wanted to hire for our art exhibition. Assume that the violinist promises that “If she gives a public performance while in her shower, her performance will be great”. This theory is not applicable. Under reasonable meanings of the words, there cannot be a case where she gives a public performance in her shower, because the public does not fit in her bathroom. Hence, this theory is not true (because it does not make true predictions). It is also not false (because it does not make false predictions). It is not of “unknown truth” either, because truth presupposes applicability, and we know that the theory is not applicable. The theory is just useless.
Unfalsifiable theoriesA theory can only be true if it is grounded, i.e., if all premises of its rules are well-defined, and if their conclusions are meaningful. It is not always easy to see whether a theory is grounded. Consider again the example of the violinist whom we want to hire for playing at our art exhibition. Assume that she says:
Technically speaking, the premise is not well-defined: We cannot determine whether someone is a “true music connoisseur” purely from known data. We cannot even arrive at this conclusion after the performance, because someone may like the perfomance even if he’s not a music connoisseur. Thus, the premise of the rule is ill-defined. The rule is not grounded.
A simple way of checking whether a theory is grounded is to see whether we can imagine a situation where the theory makes a false prediction. For a grounded theory, we can imagine a situation where the rule goes wrong: The theory of gravity, e.g., says that masses attract each other. We can easily imagine a situation where two masses do not attract each other — even if this is unlikely to happen. If there could be, at least hypothetically, a case where the theory makes a false prediction, we say that the theory can be falsified. Now consider the theory with the violinist. It cannot be falsified. If this theory ever predicts that someone loves the performance and it turns out to be wrong, then that person was simply not a true music connoisseur in the first place. The theory cannot go wrong.
Falsifiability explainedThe concept of falsifiability was advocated by the philosopher Karl Popper Falsifiability. A theory is falsifiable, if we can imagine a case where the theory makes a wrong prediction. If a theory is falsifiable, then it is grounded. To see this, consider the rule “If A then B”. We are looking for a statement X such that
If B then X is wrong.
The second rule, “If B then X is wrong” asks for what we can deduce when B becomes true. In other words, it asks for the meaning of B. Falsifiability is thus equivalent to having (1) a well-defined premise and (2) a meaningful conclusion. Thus, falsifiability is a way to ensure that the theory is grounded in perceptions.
If a theory is not falsifiable, it is not grounded, and thus not meaningful. Such meaningless theory typically take one of the following forms:
- If someone is a real hero/Christian/American/..., then...
- If you do it right, then...
- If ..., then something that cannot be seen/understood happens.
TestabilityA theory is testable, if we can trigger its premises at will. Consider for example the theory that Peter has a crush on Sarah. This theory says:
Testable theories have a huge advantage over non-testable ones: We can repeatedly trigger the premises, and thus see whether we can validate the theory. If a theory is testable, we commonly say that there is a causal relationship between the premise and the conclusion. In the example, we would say that Peter blushed because Sarah entered the room.
CompressionSo far, we have only talked about the truth of a theory. However, there is something more that we expect from a good theory, other than being true. To see this, consider the high tides of the ocean as an example. There was a high tide in New York on Saturday the 3rd of June 2017 at 17:02, and at 5:16 the next day. Hence, we build the following theory:
Now consider the following theory instead:
If a part of the ocean is in line with the moon and the Earth at some time X, it will also face the moon at 12:25 hours after X.
If it is Saturday the 3rd of June 2017 at 17:02, then the ocean close to New York faces the moon.
A theory compresses information, if it talks about events in a way that is shorter than listing all the events. In that case, the theory generalizes the events. It captures a pattern whose significance goes beyond the cases at hand.
Compression is the key to making a theory satisfactory. If a theory compresses events, we do not have to memorize the events, but just the theory. If needed, the events can be reconstructed from the theory. Compression is the basis of good predictions and explanations. It is so quintessential to a good theory, that it has been suggested that it is tantamount to comprehension.
Comprehension is compression.
EvidenceFor some statements, we can immediately see or feel whether they are true. These are perception statements. For others, we cannot. For example, the truth of the statement “There will be an solar eclipse in 2030” cannot be decided in the year 2014. For these statements, we have to use evidence.
Evidence for a statement is a true theory that predicts this statement. In the example: If we have a true theory that tells us how the Earth orbits around the sun, and how the moon orbits around the Earth, and if this theory predicts that moon, sun, and Earth will be in line in 2030, then this theory counts as evidence for the statement that 2030 will see a solar eclipse. If a true theory predicts the statement, we say that the statement is true.
Whatever is not deduced from the phenomena is to be called a hypothesis.
Counter-EvidenceA statement is true if it is predicted by a true theory. Now let us see how we can determine whether a statement is false.
A statement is false if there is a true theory that predicts the negation of the statement. Take for example the following theory:
There is an alternative way to prove a hypothesis false: A hypothesis is false, if it appears in the premise of a true rule, and if that rule makes a false prediction. As an example, take the following rule:
Modus tollensSuppose that the rule “If it rains, the street gets wet” is true. Then the following rule is also true:
If the original rule has several conditions in the premise, then we obtain as many rules as there are conditions.
Joint inferenceA statement is true if it is predicted by a true theory, and it is false if its negation is predicted by a true theory. Now assume that there is a theory that predicts the statement, and another one that predicts its negation. By definition, this cannot happen if all theories are true. However, in reality, we do not know which theories are true. Therefore, we often find ourselves in situations with contradictory evidence. In that case, we can only hypothesize about the truth of the statement.
If, on the contrary, two theories predict the same thing, then the conclusion is more likely to be true. Sometimes, a more special theory overrides a more general theory. For example, birds can generally fly. So the theory is “If something is a bird, it can fly”. Penguins, however, cannot fly. Here, a more special theory overrides a more general one. We see that if we want to believe in a conclusion, it is not sufficient that one theory predicts it. We also have to check that no other theory contradicts or overrides it.
This means that predicting the future is a complicated business. We have to know lots of theories, weigh them against each other, and combine their conclusions. This is why few people can look into the future. Those who say they can usually can’t.
The UnknownA statement is true, if it is predicted by a true theory, and it is false if its negation is predicted by a true theory. Now suppose that no theory predicts the statement or its negation. For example, assume that we have theories about physics, chemistry, and biology. These theories contain the law of gravity, the chemical reactions of substances, and the functioning of human organs. Now suppose that our question is “How does Sarah feel about Peter?”. None of our theories can deliver a conclusion that would be remotely relevant.
In such cases, something very simple happens: The answer to the question is unknown. This means that there could be an answer, but that we do not know it. Thus, the right thing to say is “I do not know”. That is nothing to be ashamed of. In fact, the vast majority of things are unknown to us.
I was gratified to be able to answer promptly. I said I don’t know.
FalsifiabilityThe concept of falsifiability was advocated by the philosopher Karl Popper Falsifiability, and we have already seen how to apply it to theories. It can also be applied to statements: A statement of a theory is falsifiable if we can imagine a situation in the present or future that contradicts the statement or its meaning. The following statements are falsifiable:
- The Earth has only one moon.
- Let us imagine that one day we see two moons orbiting the Earth. Then this situation would prove the statement wrong. Therefore, the statement is falsifiable.
- 4 + 2 = 6
- Let us imagine that I have an empty table, and that I put 4 matches on that table. Then, I put 2 more matches on the table. If I count the matches on the table, and the number is not 6, then the statement is wrong. Thus, the statement is falsifiable.
- Bob is angry.
- If Bob actually appears to be very happy and, when asked, says that he is not angry, then this statement is wrong.
- Reality does not exist, everything is just a dream that you cannot quit.
- What could prove this statement wrong? What would have to happen so that we see that reality is no a dream? Since we cannot “wake up”, there is no way to show that the statement is wrong — even hypothetically. Thus, the statement is not falsifiable.
Now let’s look at the statements that are not falsifiable, such as “Reality is a dream”. These statements cannot be proven wrong. This has an interesting consequence: It means that we can come up with several contradictory non-falsifiable statements. For example, I can say “Reality is a dream“, and you can say “No, reality is a trick that is being played to our mind by extra-terrestrials”. These statements are contradictory. However, since they are both non-falsifiable, there is no way to show that one of them would be wrong. Hence, we have two statements that cannot be true together, and yet none of them is wrong. Therefore, each of us can defend our respective statement without ever giving in. We can literally argue forever. This is indeed what people do.
Falsifiability and MeaningA statement is falsifiable if we can imagine a situation that would prove it wrong. Falsifiability asks for a perception statement X, such that the following rule holds:
Non-falsifiable statements typically take one of the following forms:
- It is claimed that something is the case, but this something cannot be seen, understood, or verified.
- It is claimed that something is the case in a very abstract form.
- It is claimed that something is the case, but not in the usual meaning of the word.
Falsifiability in a nutshell:
If it cannot be false, then it cannot be true.
ExplanationWe can now formally define what constitutes a good explanation for a fact. We say that a theory explains an event of the past if (1) the theory is true, (2) the theory predicts the event, and (3) the theory is compressive. As an example, consider again the theory about the high tides:
If a part of the ocean faces the moon at some time X, it will also face the moon at 24:50 hours after X.
Now consider the following theory:
PredictionWe can apply a theory to known cases, and thus get an explanation. We can also use the theory make predictions of which we do not yet know whether they are right or wrong. This is the interesting case where the theory predicts something unknown. For example, take again the theory about the high tides, and assume we’re in New York. We look at our watch, and we see that it’s 17:55 on June 4th, 2017. So the theory predicts there should be a high tide. We don’t know yet, but we walk to the waterfront to see that, indeed, there is a high tide. The theory has made a correct prediction.
Just as with explanations, compression plays a crucial role here. If the theory just gives us a finite list of times when there are high tides, then it cannot predict any high tides beyond that list. Only if the theory compresses information, it can make satisfactory predictions.
Prediction is very difficult, especially about the future.
Theories in real life
Learning theoriesWhen we wander through life, we see things, we hear things, and we feel things. That is: we perceive ourselves in a continuous stream of perceptions. We would like to structure these perceptions, to understand them, and (most importantly) to predict them.
And so we start to build theories about these perceptions. These theories are rarely verbal and explicit. Rather, they are a body of knowledge about the patterns that we observe in this world. For example, we pretty quickly build the theory that if we touch a hot oven then we will feel pain. This theory helps explaining past instances of pain, and is very effective in preventing future instances of pain. And this is the goal: We want to build theories that explain past experiences, and that predict future experiences.
We build theories about everything around us, possibly starting as a baby. The baby’s job [...] is to [...] discover the patterns that govern how the physical world works, and encapsulate them in theories that can be used to predict what will happen in new situations [Ian Witten: Data Mining]. One of the first theories a baby builds could be about objects. Objects always move around as a whole. If there is a face, a body, legs, and arms, then these form a whole and move around as a whole. This theory separates the continuum of sensations around us into distinct entities. Then we build basic physical theories: Objects fall down if they are not supported. If it is dark, we cannot see. We also learn theories about the consequences of our own actions. If I touch an object, I can feel that object. If I collide with an object, I feel pain. Then we build theories about people. When I smile, the other person smiles back. When I cry, people come and help me. Then we build theories about words and language. Whenever we eat, people say “food”. Whenever we meet, people say “hello”. Later in life, we build theories about what we learn in school: If I multiply two negative numbers, I get a positive one. If someone says “bonjour”, he is speaking French and wants to say “hello”. We learn the basic rules of human interaction. By the time we are adult, we have built up a corpus of theories. These theories can pretty accurately give a structure to our past and predict much of the immediate future.
Wisdom is not the product of schooling, but of the lifelong attempt to acquire it.
Fundamental theoriesThis book argues that all we do is learning theories about our perceptions. This means that, in principle, there is no universal truth. It could even be that the universe does not exist, that I do not exist, or that other people do not exist. It could all just be happening in my head.
During my learning process, I have relatively early built the theory that if I see a solid physical object (including the Earth, myself, or other people), then I cannot walk through it. This rule has proven correct over and over again. I call this property of the physical object “existence” — but you can call it in any other way if you like. The theory of existence has made so many correct predictions in the past (I could never walk through a person) that I assume it to be the truth. Another fundamental theory of mine is that the people around me perceive similarly to myself. They see what I see. They hear what I hear. Again, this theory has made so many correct predictions in the past that I believe it to be the truth. Now comes the trick: If other people hear and see what I hear and see, then my definition of truth implies that they hold true what I hold true — at least in the physical world. Thus, truth is universal.
There are a number of other theories that I (and my fellow humans) hold true. These include the laws of nature, or the identity of objects. These have made so many correct predictions in the past, that we all believe that they are the truth. We would be willing to revise that assumption only if we are shown cases where they make a prediction that does not correspond to our perception.
ScienceThis book argues that throughout our life, we build up theories that help us structure our experiences. We seek those theories that are “true”, i.e., that will eternally make correct predictions. The more correct predictions a theory makes, the more likely it is that the theory is true. In that sense, science is an extrapolation of that process: Science continuously builds theories and tests them to see if their predictions are consistently correct. When scientists propose a new theory, they conduct experiments to show that the theory makes predictions that correspond to reality. Other scientists try to build experiments that show that the theory makes false predictions. If a theory turns out to make consistently correct predictions, it is accepted into the corpus of scientific truth.
This does not mean, however, that the theory would be the real truth. A theory can always make a wrong prediction one day. This is why scientific theories are called “theories”. Even universally accepted laws, such as the law of gravity, are still called theories. If, one day, any theory is found to make a false prediction, then the theory will no longer be considered an approximation of truth.
This entails that science never “proves” anything. Science just builds models of reality.
Physics is like sex. Sure, it may give some practical results, but that’s not why we do it.
CorrectionTheories yield explanations and predictions. If a theory has consistently yielded correct explanations in the past, we trust its predictions also for the future. Now what happens if a theory has made thousands of correct conclusions in the past, but then one day, it delivers a false prediction? For example, consider the theory that speed adds up. If I walk at 6km/h in a train that runs at 100 km/h, then my speed relative to the ground is 106 km/h. This theory makes lots of true predictions. Now assume that there is a screen at the end of the rails, some kilometers down in the direction of travel. Assume that I point at that screen with a laser pointer from the train. You stand at the station and also point at the screen with a laser pointer. Then my laser beam should travel faster than yours. If we both switch on the laser pointer at the same time, in the very moment the train passes the station, then my dot should show up on the screen slightly earlier than yours. Yet, it does not. Both dots appear at the same time. The speed of both laser beams is the same, no matter whether it is measured relative to the ground or relative to the train. This is confusing and contradictory.
In such a case, the prediction of the theory is wrong. This is surprising, because the theory has made zillions of correct predictions in the past. Still, its prediction in the case of the laser beam is wrong. No matter how plausible this theory sounds, and no matter how many correct predictions it has made in the past, it is wrong. Importantly, it is not reality that is wrong. It is the theory that is wrong. Thus, it has to be abandoned.
This is indeed what happened to the theory. Albert Einstein had the courage to say that, if the theory does not correspond to the facts, then it had to be changed. He set up a new theory that permits light to always have the same speed. This theory entails all kinds of weird things, such as objects gaining infinite weight when they approach the speed of light. Despite its ridiculous conclusions, this theory turned out to make consistently correct predictions. It is the special theory of relativity.
The ability to see that a theory is wrong, and the readiness to abandon it if it does not correspond to the facts, is one of the cornerstones of rational thinking.
I would never die for my beliefs because I might be wrong.
The theory of truthThis book argues that we constantly build theories to explain our past perceptions and to predict our future perceptions. In this view, we humans have a rather humble position in this universe: We perceive, and we try to model what we perceive. At any moment, our theories may turn out to be wrong. Then we have to abandon what we thought was true. That is all there is to truth.
Interestingly, this view of truth is itself nothing else than a theory. This theory says that we judge the truth of a theory by comparing its conclusions to our experiences. If the conclusions consistently correspond to our experiences, we trust the theory — and we assume it to be part of “the truth”. In such cases, we will just say “The theory is true”. This theory of truth predicts what a person on the street calls “true”. This theory is true, because by and large, this is indeed what the person on the street calls “true”. Then again, the theory is only true by its own definition.
Science may be described as the art of systematic over-simplification — the art of discerning what we may with advantage omit.
BeliefsA statement is true if we have evidence for it — i.e., if it is predicted by a true theory. A statement is false if we have counter-evidence for it — i.e., if there is a true theory that predicts its negation. In real life, our evidence for or against a statement is often very weak: We do not have a set of theories at hand that predicts our hypothesis. And even if we had, we would probably not have the statistics to show that these theories are validated. And even if we did, we would have to perform joint reasoning to arrive at the most likely conclusion. Since we usually cannot do all of this, we often just believe a statement.
This does not mean, however, that the Theory of Truth elaborated in the present chapter would be useless. On the contrary. The first thing that the Theory of Truth allows us to do is to exclude unfalsifiable statements. These can never predict anything, and they are thus meaningless in the sense of this book. If we accepted such statements, we would open the door to accepting all other kinds of meaningless statements: religious fanatics’ arguments, conspiracy theories, and pseudo-science. They all have in common that we would never be able to find out whether they are wrong. Falsifiability is the bulwark against such nonsense.
The second thing that the Theory of Truth allows us to do is to exclude theories that have consistently clashed with our perceptions — these are the wrong theories. In our search for truth, wrong theories are as important as correct theories. Knowing them allows us to dismantle bogus claims and to avoid drawing wrong conclusions.
Finally, and most importantly, the Theory of Truth tells us at least what we would have to do if we wanted to check the truth of a hypothesis: We know that we have to find evidence, i.e., we know that we have to find a true theory that predicts the statement. This is a fundamental insight: It allows us to weigh our confidence in a statement by the evidence that we have for it. We should not believe strongly in a statement for which we have only weak evidence. In particular, we should not make life-changing decisions based on weak evidence.
From an evolutionary perspective, humans are not a kind of smarter two-legged antilope, but the species that outsmarts the antelope. Thus, there is a strong selection pressure for humans to develop explanations that are true.
Common MistakesIn the previous articles, we have elaborated a theory of truth: Humans build hypotheses to describe and to predict what happens around them. The perfection of this endeavor (the hypotheses that always make correct predictions) is what we call “the truth”.
We will now look into common mistakes that people make when trying to approach the truth. We will illustrate each mistake by an example. We will then apply the theory of truth to find out what the problem is in the example scenario. As we will see, the theory of truth allows us to identify and rebuke the mistakes reliably.
The examples that we will use are quite abstract — even absurd, you may say. And yet, they appear in very similar form in the world’s major religions. We will make this link in a footnote in each article, thereby anticipating the discussions in the later chapters of this book.
Unclear theoriesThe Inkas had an elaborate system of myths and collective wisdom. One of their omens was as follows: “And that day will be a great day. After that day, no one will be as they were before. And that day will show the grandness and glory of the God of the Sun.” This theory seems to be making predictions. Yet, it is completely unclear when the theory fires. Was today a great day? Should we expect the God of the Sun? And if so, what does it mean that the day will “show the grandness” of that god? Will he actually appear? Or is the grandness rather shown implicitly? The theory is just not clear.
The criterion that helps us here is falsifiability: The theory is not falsifiable. There is nothing that we would accept as a proof that the theory is wrong. Therefore, the theory is nonsense. Such theories can be poetic and beautiful, but they cannot be true.
Science is the journey to the truth.
Religion is pretending you’re already there.
PostdictionsConsider the story of the seer in the book of Asterix (illustrated on the right). The seer finds shelter in the village of Asterix during a thunderstorm. He says that he knew that the thunderstorm would be coming, and he knew that he would find shelter in that village. Asked how he knew all of this, he replies “I’m a seer”.
However, the seer just claims he foresaw whatever happened. He waits until something happens, and then says he knew that it would happen. Therefore, the seer is not actually making “pre-dictions”. He is making “post-dictions”.
The real challenge is to build theories that predict not just the known, but also the unknown. The essential quality of a true theory is that it is true not just for the case at hand, but for all cases in the future.
Counting the HitsChelsea drives to work this morning. Her dad warns her that he has the bad feeling that Chelsea might have an accident. Indeed, that day, Chelsea has an accident. Predictably, his dad says that he told her so. Chelsea reminds him that he has been warning her about accidents every morning for the past 2 years. Thus, the theory that her dad can predict accidents was correct in only 1 out of 712 cases. That ratio is too bad to call his theory true. The theory is just false.
Technically speaking, the theory has failed the test of validation. It has delivered numerous false predictions in the past, and has hence to be rejected. Even a false theory can make a true prediction from time to time, but that still does not make the theory true. Looking only at the cases where the theory makes a true prediction is a fallacy called “Counting the hits”.
Bad compressionYour superstitious friend Sara has the theory that on Friday the 13th there will be car accidents. This theory has made correct predictions in the past, and it continues to do so. Is Sara finally right with her superstitions?
Yes and no. The theory that there are car accidents on Friday 13th is true, but it is unsatisfactory for a different reason: The prediction “There are car accidents” is true no matter whether it is Friday 13th or not. The premise of the theory does not add any insight. For such theories, we can develop arbitrary variations. For example, we can construct the theory that “On Tuesday 17th, there will be car accidents”. This theory is a true as the Friday 13th theory — or indeed as true as the theory “There are car accidents”. Consequently, some countries take 17 as the unlucky number, and others take 13. It is clear that with this argument, we can take any number as an unlucky number — or as a lucky number, for that matter.
In the Central Park in New York, a man jumps around on one foot.
People ask him why he’s doing that.
“To scare away the rhinoceroses!”, he answers.
“But there are no rhinoceroses here!”, people tell him.
“You see”, he says, “it works!”
Wishful thinkingBill is a very happy person. One day you talk to him, and you ask him why he is always so happy. He pulls you aside and whispers: “It’s because I am rich!” You are surprised, because Bill doesn’t look particularly rich, and from what you can tell, he seems to possess only a single pair of trousers. You ask “What do you mean, you are rich?”. Bill whispers: “Look, I believe that I have a treasure hidden in my garden!”. You say that this is great, and you ask him whether he checked. He says no, he didn’t check. You ask then why he believes he has a treasure in the garden if he didn’t even check. Bill replies: “Would you want to be poor? No, right?”.
You are perplexed. From the fact that Bill does not want to be poor, it does not follow that there is a treasure in his garden. Such a rule is just plain wrong, meaning that it produces conclusions that do not correspond to reality. Such thinking is called “Wishful thinking”.
Happy thinkingYour friend Bill believes that he has a treasure hidden in his garden. As this is obviously very unlikely to be true, you are worried, and you talk with a common friend of yours. He tells you: “So what, if this makes Bill happy, just let him believe he has a treasure in the garden!”. You ask: “So if that makes him happy, is it true that he has a treasure in the garden?”. And your friend is wise enough to say: “If a belief makes you happy, it doesn’t mean it’s true”.
While you are still pondering this wisdom, your friend suggests: “You look as if you could use some happiness in your life, too! Why do you not also start believing that there is a treasure in your garden?”. You are perplexed: It does not make sense to believe something wrong or unknown just to be happy. Believing something that is wrong will lead to wrong conclusions. Such belief is thus ultimately treacherous.
The prettiness of a falsehood does not make it any less false.
Meaningless statementsYou are inviting your friend Sandra over for dinner. Sandra is very happy to join you. However, as soon as she steps into your place, she starts looking around and seems to be worried. You ask whether everything is alright. Sandra replies yes, everything is alright, but: “There is something here”. You ask: “What do you mean, there is something here?”. Sandra says “I don’t know, I just feel there’s something here”. She continues to walk around, looks behind the door, checks the kitchen sink, and verifies the place under the table. You are worried and ask her “Sandra, what is it? Are you OK? Do you need anything? Did you see anything? Is there a smell?”. But she just says that yes, she’s OK, she doesn’t need anything, she didn’t smell anything, and she didn’t see anything. It’s just that “There is something here”. Later, to your relief, she seems to have forgotten about it and the evening turns out to be really nice.
After she left, you still wonder what she meant by “There is something here”. It did not mean that she was uncomfortable, that she would need something, or that she would smell or see something particular. In fact, the statement didn’t seem to mean anything.
You try to fit Sandra’s statement into the theory of truth that you read in this book, and you find that, from the fact that “There is something here”, you cannot deduce anything. There is no rule that has this statement in its premise. Thus, the statement is literally meaningless. It does not have any sense.
Pumpkin statementsAndy is your friend from highschool, and you still meet him from time to time. One day, Andy pours out his heart to you, and tells you how he suffers in his relationship. You listen attentively, and comfort your friend. Andy is very grateful, and tells you that you are really the best friend he has. You are happy that you could help, and that he appreciated it.
A week later, you meet another acquaintance, and you find out that you both know Andy. The other person tells you that he gets along really well with Andy, and that Andy calls him his best friend. You are surprised, but do not say anything. A few days later, you go with Andy to a bar. Andy is still sad, and orders a beer. The waitress sees that Andy is having a difficult time, and pities him. She brings peanuts on the house and tells him to cheer up. Andy smiles at her, and tells her that she is really the best friend he has. She smiles back. Later that evening, a client who has drunk too much gets rude and aggresses the waitress. Andy seems visibly uncomfortable and proposes that the two of you should leave the bar quickly.
At this point of time, you understand two things: First, Andy actually calls everybody “best friend”. Second, this word does not mean anything to him, as he does not even consider helping the waitress. Technically speaking, you cannot deduce anything from the fact that Andy calls you best friend. Neither that you are the only “best friend”, nor that Andy will do anything more for you than he does for a random person on the street. There is no rule that has “X is Andy’s best friend” in its premise. Thus, the statement “you are Andy’s best friend” is technically meaningless.
This is different from the usual semantics of the word “best friend”. If a normal person calls you “best friend”, then you can deduce a number of things from this. First of all, you are the only best friend. Second, that person will give you special treatment, and help you when you are in trouble. Andy, in contrast, uses the word in another way. The way Andy uses the word is like the merchant who gives you a hollow pumpkin. It looks like a pumpkin, but it is empty inside.
Using a statement or word in another meaning than the common meaning is treacherous. It will mislead any listener. It may even mislead the speaker. To see this, assume that Andy decides to call everybody “the greatest idiot” in the same way that he called everybody the greatest friend before. In both cases, the statement does not have any meaning, because Andy simply applies it to everybody. And yet, Andy will probably hesitate much more to tell people they are “the greatest idiot” rather than “his best friend”. This is because, in his heart, Andy knows what the statements mean and how they are understood. It’s just that he uses them in a different way. This makes his use deceptive.
Mistakes in theological arguments
Theological MistakesIn this section, we will continue our journey from the previous section, and list more mistakes that people commonly make in their search for the truth. We shall now concentrate on mistakes that are more frequently encountered in arguments about religion and gods.
It makes senseWe have a tendency to accept theories if they “make sense” to us, i.e., if they appear somehow plausible. This, however, does not make a theory true. As an example, consider the practice of bloodletting Bloodletting: In historical times, people thought that certain illnesses were caused by “bad blood”. Hence, they reasoned, the illness could be cured by removing the bad blood. Therefore, they punctured the arm of the ill person, and let the blood come out. This practice was widespread from the ancient Greeks to the 18th century. It made a lot of sense to people. However, it did not have any positive effect. On the contrary, in the overwhelming majority of cases, the historical use of bloodletting was harmful to the patients [ibid].
This shows us that a theory can be wrong even if it “makes sense to us”. A theory does not become true if “ it makes sense”. It becomes true if it makes correct predictions. The failure to see this, and the reliance on the intuitive “sense” instead of on concrete and correct predictions is one of the bedrocks of religious belief, as we shall see in the Chapter on Proofs for Gods and in the Chapter on Gods.
Know how to rank beliefs not according to their plausibility, but by the harm they may cause.
Narrative FallacyThe narrative fallacy, according to Nassim Taleb, is the human tendency to add causality to unrelated events. Consider the following example: When the US captured Saddam Hussein in Iraq in 2003, the oil price initially fell. Hence, newspapers ran stories explaining that the capture gave confidence that the war would be over, which would lower the price of oil in the long run. Shortly thereafter, however, oil prices rose. Hence, newspapers ran stories explaining that the capture has created new conditions for the mission in Iraq, and that this insecurity has driven up oil prices. In reality, there was possibly no causal relation whatsoever, as oil prices tend to fluctuate in any case. However, humans tend to add causality to unrelated events (Daniel Kahneman: “Thinking fast, thinking slow”).
This tendency to “storify” may have a very simple reason: It is easier to remember events if they are connected in some way. As an example, consider the sentence “The king died and then the queen died”. Now compare it to “The king died, and then the queen died of grief”. It is somehow easier to remember the second story, because it seems to contain just a single piece of information with its consequence, rather than two unrelated events. Rephrasing the initial story as a causal sequence may thus be a technique of “dimensionality reduction”, i.e., of data compression. This may explain why people have a tendency to consider the second sequence more probable than the first — even though the second actually implies the first (Nassim Taleb: “The Black Swan”).
GhostificationMany ancient peoples believed that inanimate objects were inhabited by spirits. They might well have believed, e.g., that fire was kept alive by fire demons. Based on this, they could have built the following theory:
If the fire demon is chased away, the fire dies.
If you are not kind to them, they may refuse to be chased away.
Abductive ReasoningA rule is a statement that allows us to draw certain conclusions if certain conditions are true. For example, we can have a rule such as
This type of reasoning is called abductive reasoning. In general, abductive reasoning does not lead to true rules. That is, conclusions drawn by abductive reasoning usually do not correspond to reality. Abductive reasoning can only help us find possible reasons for a fact.
John F. KennedyJohn F. Kennedy was the president of America from 1961 until 1963, when he was assassinated. The murderer could never be found, and the case remains one of the greatest mysteries of modern history John F. Kennedy. Nobody knows who killed Kennedy.
Now, Robert has long been suspecting the Russians behind the assassination. He comes up with the following rule:
It is true that nobody can explain how Kennedy died. It is also true that the theory “Russian spies killed Kennedy” could explain why Kennedy died. However, this reasoning is still false. It could be Russian spies, Chinese spies, or American spies who killed Kennedy, and nothing tells us it was the Russians. In order to accept a hypothesis as true, we need a rule that has the hypothesis in conclusion, and not in the premise. In other words: We need evidence for the hypothesis.
Contradictory conclusionsNobody knows who assassinated John F. Kennedy. Robert, a US citizen of Chinese descent, came up with the rule
Now, something very interesting happens: When Robert and Vladimir meet, they will start arguing about who killed Kennedy. Since both of them believe in abductive reasoning, neither can invalidate the claim of the other. The line of reasoning used by one of them can be used to support the hypothesis of the other. Each of them has an equally convincing argument, but the claims are contradictory.
Of course, neither argument is correct, because in order to assert a hypothesis, we need a rule that implies it. In other words, in order to believe that any spies killed Kennedy, we would need evidence for this hypothesis. However, if people do not subscribe to the necessity of evidence for hypotheses, they can go on arguing forever.
Unfalsifiable conclusionsIn the wake of the terrorist attacks of September 11, 2001, Chris has come to the conclusion that all Arabs are terrorists. When Chris is confronted with lots of friendly Arab people, Chris argues:
Does that mean that Chris’ hypothesis is right? After all, it cannot be proven wrong... As the attentive reader will have noticed, this immediately makes the hypothesis unfalsifiable. That is, we cannot find a condition X such that
In the terminology of this book, the phrase “Arabs have terrorist intentions that cannot be seen” has no meaning. There is no perception statement that follows from this hypothesis. The phrase is literally meaningless. A meaningless phrase does not help at all in understanding this world, in explaining the past, or in predicting the future. It is just not worth debating.
DisputesIn our example, Chris believes that all Arabs have terrorist intentions, but that they hide them so that they cannot be detected. We have seen that this hypothesis is nonsense, because it cannot be falsified. One day, Chris meets Mohammed. Chris explains his world view to Mohammed, and Mohammed gets very offended. He counters that, in fact, all Arabs are friendly and peaceful people. Chris objects that the terrorists of September 11, 2001, were Arabs. Mohammed explains that these terrorists are not real Arabs. Real Arabs would never kill innocent people.
However, Chris is unable to see that Mohammed’s hypothesis is nonsense. This is because if he were able to see this, he would have to accept that his own hypothesis is nonsense, too. This means that both Chris and Mohammed are falling prey to the same fallacy — a bit like in the case of abductive reasoning. The case of unfalsifiable claims, however, adds an interesting twist: The claims are contradictory, but on principle, neither of them can be proven wrong. This means that neither Chris nor Mohammed can ever show that the other’s claim is mistaken. At the same time, the nature of their hypotheses also forbids them to ever predict anything about the real world. Thus, their argument is futile, and their hypotheses are nonsense.
Truth and Atheism
Revisiting PersephoneWe started our discussion of truth from the ancient Greek story of Persephone. Persephone is the Goddess of Spring, and she returns to Hades each year. This leaves her mother sad and so she makes it cold. This explains why winter is cold.
Now let’s look at the story of Persephone in detail. It goes roughly as follows:
If someone is forced to go somewhere, then that person goes there.
If Persephone is in Hades, her mother Demeter is sad.
If Demeter is sad, then it is cold.
Summary on the concept of truthThis book argues that we perceive ourselves in a continuous stream of perceptions. Our goal is to predict these perceptions. For this purpose, we build theories of the form
The problem is, of course, that we never know whether a theory will always correspond to our observations. This is why we humans take a rather humble position in this universe: We try to describe our reality by theories, we validate the theories, and we hope that they are the truth — but in the end we have no guarantee that nature behaves as we predict. Therefore, we find ourselves in a continuous process of improving our theories.
When a true theory makes a prediction, we call that theory “evidence” for the prediction. Evidence distinguishes myths from facts. But our theories cannot predict everything. Some things are just unknown. In that case, it does not help to just invent an explanation. Even if the explanation is beautiful, that does not make it true. It is better to believe only the validated theories, and continue searching for validated theories in what is the unknown today. In everyday life, our evidence for or against a statement is often weak. In such cases, we tend to just believe the statement. This is fine, as long as our confidence in the statement is proportional to the evidence.
Believing in truthThis book defines truth as the set of validated theories. The question remains why we should believe in these theories and not in others.
The reasons why it is advantageous to believe in this theory of truth are as follows:
- If this book calls a theory “true”, then you can use it to predict parts of the future.
- This is an immense advantage over alternative definitions of truth. It is a very constructive and useful property.
- Given two theories, it is easy to see which theory is more likely to be true.
- Any theory is measured by what it predicts. Thus, there is a clear yardstick for the quality of theories. This implies that two people who search for truth will converge onto the same theories — which is what happens in science.
The criterion of validated evidence helps us distinguish between myths such as Persephone (whose existence is not predicted by a validated theory), and objective facts such as the spherical Earth (whose truth is established by many validated theories).
You are entitled to your own opinions.
But you are not entitled to your own facts.
Non-True StatementsBelieving theories that are true in the sense of this book has a number of advantages. At the same time, believing in theories that are not true in the sense of this book has a number of disadvantages. If we abandon the requirement for validated evidence for theories, we run into the following problems:
- We make wrong predictions.
- If we no longer judge a theory by the proportion of correct predictions, then we may make predictions that do not correspond to reality. If our mental model of the world is not accurate to predict what happens in the world, then we simply cannot achieve our goals effectively.
- We open the floor for arbitrary theories.
- If we abandon the need for evidence, then we can come up with arbitrary theories. For example: To guarantee the survival of humanity, we should all become Scientologists. There is no evidence for this, but, hey, who needs evidence?
- We can easily claim the opposite of a theory.
- If our theory is non-falsifiable, or if we abandon the need for evidence, then anybody can claim anything. For example, instead of claiming that the abrahamic God created the world, I can also claim that the goddess Gayatri created the world. The result is endless disputes (and sometimes even war), because if we abandon the requirement for falsifiability and evidence, then no theory can be shown provably superior to any other theory.
- We blur the distinction between reality and nonsense.
- If we accept wrong or unfalsifiable theories as readily as true theories, then this is a sign that we are unable to distinguish the two. This means that we will accept other wrong theories, too. We develop justifications, explications, reinterpretations, or view points to justify the false theories.
- We inhibit the search for truth.
- If we accept a wrong or unfalsifiable theory as an explanation, we block the way for scientific enquiry. If we do not know something and assume we know it, then we will never know.
- We give undeserved credit to the inventor of such a theory.
- If we believe in theories not because they are validated, but because they are presented convincingly, then we give a blank cheque to any charlatan to tell us whatever he wishes. He may use this trust for his own advantage and/or for our disadvantage.
- We risk curtailing our freedom.
- If the faulty theory requires us to do or abandon something, and if we follow, then we are needlessly wasting our time, restricting our liberty, renouncing part of our property, or worse.
- We risk harming others.
- If the faulty theory requires us to reprimand other people, to harm them, or to attack them, then we are unjustly causing damage to other people. This is where it’s no more fun.
- We perpetuate the problem for our children.
- If we do not teach our children to distinguish between validated evidence and myths, then the very same problems will be perpetuated in the next generation (← this is a recursive reference).
It is always better to have no ideas than false ideas;
to believe nothing than to believe what is wrong.
The SupernaturalBased on our theory of truth, we can now formally define the supernatural: A supernatural statement is any statement that, on principle, cannot be validated by a direct observation, and that cannot be predicted by a validated theory. Note that, with this definition, being supernatural is a property of statements, not of entities. Supernatural statements can be “God exists”, “There is life after death”, or “We will be reborn after death”.
A statement about the supernatural is unfalsifiable. However, not every unfalsifiable statement is about the supernatural. For example, the statement “A true music connoisseur will love this violin performance” is unfalsifiable, but not a statement about the supernatural. A statement is supernatural only if it is, on principle, shielded from our observations and from grounded theories. In this sense, communism, too, is not a religion. Some people may adhere to it with almost religious fervor, and they may accept nothing as a proof that communism is wrong, but it remains an ideology that is, in principle, open to our observations.
Truth and AtheismThis book has laid out a theory of truth that is based on perceptions. Now what has this to do with atheism?
Atheism is the rejection of belief in the supernatural. Before, we only had a very vague description of “the supernatural”. With our definition of the supernatural, we can now explain what that means: When we say that atheists do not believe in the supernatural, we mean that atheists will not believe supernatural statements.
Based on this, this book will build up a set of validated statements about the natural world. Most notably, how this world came into existence (Chapter on the Universe), how moral values developed (Chapter on Morality), and how religions work (Chapter on Memes). This book will also argue that believing non-validated statements can be dangerous (Chapter on Criticism of Religion).
Is truth subjective?The definition of truth put forward in this book says that we judge the truth of a theory by comparing its conclusions to our experiences. If the conclusions correspond to our experiences, we call the theory “true”. Since nothing guarantees that other people have the same perceptions as I, this means that someone else can have a completely different truth from my truth.
Indeed, it is a long-standing philosophical conundrum whether truth is absolute or subjective. There is no reason to assume a priori that other people perceive like I do. The idea that truth is objective is just a theory. This theory, however, has made an impressive number of correct predictions in the past. In fact, for every single case that I have come across in my life, other people have perceived physical input just the way I did. There may be people with different perceptual capabilities or incapabilities (such as color blindness or deafness), but while I may observe different sensitivities to stimuli, I rarely observe contradictions: When I cannot walk through a wall, other people cannot, either. When I see a mountain, other people also see a mountain. When I hear noise, they hear noise. These experiences continue every hour of my life. Therefore, I consider these observations a validation of the theory “Other people perceive physical observations the way I do”.
Now comes the interesting part: If my assumption is true, then other people will evaluate the truth of a given theory in a given case in the same way as me. For example, if some theory predicts a rainbow and if I observe that the theory makes a correct prediction on a given day, then other people in my vicinity will also make this observation. Thus, if we wanted to determine whether a given theory is true, we would just have to validate or reject the theory together by making the same observations together. My assumption then tells me that we will come to the same conclusion. This, in turn entails that truth itself, as defined in this book, is objective.
The claim “Everything is subjective” must be nonsense, for it would itself have to be either subjective or objective. But it can't be objective, since in that case it would be false if true. And it can't be subjective, because then it would not rule out any objective claim, including the claim that it is objectively false.
Science is not everything!The approach to truth that this book puts forward may look rather scientific. It is based on theories, evidence, and testability. Indeed, this book’s notion of truth is just an extension of the scientific principle itself. And yet, as the reader might object, science is not everything.
This book does not claim that everybody would have to follow the proposed way of thinking, let alone that it would be the only one. It does claim, however, that most people consider trustworthy that which has made true predictions in the past. And that most people mistrust that which has made no predictions, or bad predictions in the past. To see this, consider an example: In a casino, someone tells you that he can predict the outcome of the roulette. You trust him and bet the money as he says. It does not work. You try again. Again, it does not work. You have already lost a substantial amount of money. Would you trust his predictions again? Probably not. This guy was just plain wrong. But by not trusting him, you act “scientific”. Shame on you!
The bottom line is that we all work mostly according to this principle whenever it comes to trusting people or theories. It is true that we are vulnerable to bias and error. However, clearly not all of us are vulnerable all the time — otherwise we would not even be able to say that we are vulnerable to bias and error. The human brain is capable of reason, given the right circumstances. The goal is to identify those circumstances, and to put them more firmly in place (Stephen Pinker: Enlightenment Now).
By nature, I am an engineer. I am more interested in solving problems than in wallowing in the emotions that they incur.
You can’t prove everything!This chapter proposes that evidence for a hypothesis is a true theory that predicts this hypothesis. Now, unfortunately, we do not have evidence for all hypotheses that we make. In fact, for the vast majority of hypotheses, we do not have any evidence at all. Even if we have evidence, there may be counter-evidence. This means that, strictly speaking, we would have to go through a process of joint reasoning before deciding the truth of that statement. And yet, in everyday life, we rarely do that. Thus, is the theory of truth put forward in this book not just absurd?
However, we rarely believe just “anything”. Rather, we usually judge the likelihood of a hypothesis by our experience — as in the previous example of the roulette player. Technically speaking, this “experience” is nothing else than the set of theories that we have accumulated in our life time. It’s just that we rarely make these theories explicit. When we are asked why we believe in something, then we will certainly have our reasons. Again, technically speaking, these reasons are explanations in the sense of this book. Thus, by and large, we do use the methods of this book — just in a watered down variant that is way less formal than presented here.
That is all fine, of course. Things are different when it comes to more serious questions: When it comes to constructing a sky scraper, for example, it would be foolish to rely just on the “experience” of the architects. You would want engineers to thoroughly verify that the building is stable and safe. In that case, you would insist on formal methods. The same is true when it comes to anything that influences your life. Say, for example, that your doctor prescribes you a new medicine. If he tells you that this medicine has never been tested, you would certainly hesitate to take it. It would be of poor comfort to you if the doctor assures you that “If you really deserve the healing, this medicine will not be lethal”. Even if you are not familiar with the principle of falsifiability, you would realize that there is something wrong with this doctor. You would insist on taking only medicine that has been tested thoroughly beforehand. And so this is the compromise that we use: In our everyday lives, we use some informal methods to decide what we believe in. These informal methods are vaguely related to the theory of truth of this chapter. For anything that engages our lives crucially, we insist on formal methods — as presented in this book.
This book will argue in the Chapter on Criticism of Religion that anything that restricts people’s lives drastically, anything that impacts the lives of others, and anything that claims absolute truth falls in the second class of cases: It requires the formal type of methods. At the very least, it should be falsifiable. That is the minimal condition for even just being considered in earnest.
It’s in the very nature of an argument that people stake a claim to being right. As soon as they do, they have committed themselves to reason — and the listeners they are trying to convince can hold their feet to the fire of coherence and accuracy.
I don’t want theories, I want facts!This book puts forward the idea that everything we do is building theories about our perceptions. The reader might wonder where this view accommodates facts.
If you wish, you can see your elementary perceptions as facts. Statements such as “I feel hungry”, “I see red color”, or “I feel happy” are undoubtable facts. This book says that everything that goes beyond these elementary perceptions are theories that we build to explain these perceptions: The concepts of hunger, of red objects, and of happiness are theories that we build on top of these perceptions in order to structure them and to predict them.
What about moral truths?This book says that truth is whatever makes correct predictions. This leaves us to wonder whether a moral statement such as “Theft is wrong” is true.
In fact, according to this book, such a statement is not true. It is not even wrong. This is because it is not falsifiable. (It took my quite some time to put moral statements into the framework, but here we go:) For this book, moral statements are not absolute truths. Rather, they are subjective opinions about behaviors. Thus, we can never say “Theft is wrong”. We can only say “I find theft wrong”. That makes sense: There are cultures where theft is not considered wrong. In an ideal communist world, for example, the notion of theft is entirely meaningless. Thus, “I find theft wrong” is on the same level as “I find Alice beautiful”. Such theories do make predictions: For example, if you steal something from me, I will get angry, because I think that theft is wrong. Thus, these theories are falsifiable.
On this insight, we can build an entire moral theory, which we discuss in the Chapter on Morality.
What is the meaning of love?The meaning of a statement is the set of rules in which it appears. So here we go:
If you love someone, you feel happy when that person is around.
If you love someone, you want to help that person wherever you can.
What is the meaning of mathematical concepts?Mathematical concepts are labels for real-world phenomena. For example, when I say “There are 5 apples”, I mean “There is one apple for each finger of my right hand”. Thus, “5” is simply an abbreviation for the fact that a group has as many elements as we have fingers. When we say “5+5=10”, then this is an abbreviation for “When you have as many apples as you have fingers on your right hand, and you have as many bananas as you have fingers on your right hand, then you have as many fruits as you have fingers on both hands”. It is way more convenient to say “5+5=10”.
Based on this, we can come up with plenty of rules in which these labels appear:
If x+x=y then 2*x=y
These theories make predictions. In the simplest case, they make predictions about the real world, as in “If you have 2 apples and you add 1 more, you will have 3 apples”. In the cases of more abstract mathematics, the theories still make predictions. However, these may concern the process of calculus only. As an example, consider the rule “If x=log(y), then 10^x=y”. This rule predicts that if x is the logarithm of y, and if I compute 10^x, then I will obtain as result y. This prediction rarely finds its uses in everyday life, but it is undoubtedly a prediction — and a true one.
You can’t believe in math. You have to understand it.
You can’t understand religion. You have to believe it.
What about historical facts?How do we know that Cleopatra was queen of Egypt Cleopatra? Is that falsifiable?
Historians reconstruct past events from human artefacts, written accounts of events, archeological sites, and other sources. Technically speaking, they have a number of theories, such as “If a person appears on a coin, then that person was a ruler of a state”, or “If a contemporary historian wrote a book, then things happened as written in that book.”. These theories are not always correct. They may make wrong predictions. For example, a person on a coin could be a deity instead of a ruler. However, in a large part of the cases, the theories are known to be correct. Thus, historians basically have a set of imperfect rules. From these, they try to deduce what most likely happened in the past. If several rules predict the same thing, and no rule predicts the contrary, then the historian accepts this thing as the most likely course of history.
This thing, however, may turn out to be wrong. For example, it was widely assumed that Cleopatra committed suicide by an asp bite. Nowadays, some historians are questioning this version of history, based on the fact that an asp bite could not have caused the quick death claimed by most sources Cleopatra. As the reader may have noticed, we have just presented evidence that could suggest that the common assumption about Cleopatra’s death is wrong. Thus, we have shown that a historical conviction can be falsified. Therefore, historical facts are not meaningless. They have their role in the physical course of time.
This limits your view of the worldThis book defines truth by building on perception statements. It cuts away anything that does not ultimately talk about perceptions. This raises the question whether this view of truth is not too limited. All metaphysical concepts, for example, are cut off.
It turns out that there are theories that are grounded in perceptions and theories that are not. The first class of theories can make tangible predictions, whereas the second one cannot. This holds no matter how you define truth. The first class of theories is the stuff of science. This holds by definition, because science is what is concerned with the natural world. Science encompasses not just physics. It encompasses also psychology, biology, history, or sociology.
The second class of theories is not about perceptions. This does not mean that this class of theories would be useless. Such theories can make up stories, metaphors, or poems. These can provide entertainment, consolation, or inspiration. Most atheists enjoy such products of human culture. Several atheists produce them, and a few atheists are even extremely successful at it. So an atheist’s view is not limited to what can be falsified. It’s just useful to keep the distinction in mind.
There is no society in human history
that ever suffered because its people became too reasonable.
There is divine truth!Some people define truth through God. Truth is what God says.
The problem with this definition is that it never allows to make any tangible predictions. If you assume that God is the truth, then you do not know anything more about this world than if you don’t. To see this, assume that God is the truth. Now, who killed John F. Kennedy? You don’t know. How many species exist on Earth? You don’t know. Who will win the lottery? You don’t know. It turns out that you know exactly as much as everyone else, as far as concrete predictions are concerned. And what everyone else knows is what we commonly call “the truth”. No need to use God for this.
We may say that you know at least that the Earth was created by God. That the species were created by God. And maybe that the lottery winner was chosen by God. However, you can know this only after the fact. Whatever happens, you say that it was God’s will. But you can never know in advance what will be God’s will. Thus, such a theory of truth is useless. It is just a story that is put on top of whatever happens. Technically, it is non-falsifiable, and thus literally meaningless.
If the test tube turns green, God wanted it. Oh, sorry, it actually turned blue. No worries, God decided that in the first place.
Truth is a false conceptIt has been argued that we cannot be sure whether the physical system in which we perceive ourselves really exists (most famously in the movie “The Matrix”). There could be no physical system at all. There could be also multiple such systems. Then, our sensations would be just impressions that have nothing to do with any physical world. We could be living in a dream world.
We observe that this assumption cannot be falsified. There is no way to prove that we are not living in a dream. This entails that the theory does not tell us anything about our perceptions. When we assume that we are living in a dream, we are no wiser than before. Thus, the theory is literally meaningless. It is completely irrelevant for our life. I could as well claim that you are dead and what you think is your life are in fact just hallucinations of some surviving neurons in your brain. Such theories lead nowhere. They do not talk about our perceptions, and thus do not even qualify to be considered for being true.
This theory is not only not true.
It is not even false.