Chapter 1 - Why Belief ‘X’ Can’t Be Due to Assessing That ‘X’ Is True

The surprisingly basic logical flaw in this idea

This is part of an archive of an old version of my book ‘Belief’ — the new version is available at https://medium.com/belief-farnell .

Previous: Introduction

An earlier version of the below argument first appeared in my article ‘How Belief Works’, which was published in the journal Think.


Why do we believe what we believe?

The answer may seem obvious: we believe something because we’ve assessed that it’s true, however brief or unsound our reasoning.

Indeed, the Oxford English Dictionary defines ‘believe’ as ‘to consider to be true’. And both the American Psychological Association Dictionary of Psychology and Stanford Encyclopedia of Philosophy define belief likewise.

However, as the following argument shows, the idea that we believe something because we’ve assessed that it’s true is, as a matter of surprisingly basic logic, false — and is therefore yet another incorrect way of defining belief.

The difference between the claims ‘X’ and ‘“X” is true’

Consider these two claims:

It rained yesterday.
The claim ‘It rained yesterday’ is true.

They can seem to be saying the same thing, and therefore to be simply different wordings of the same claim — but they’re not.

Truth, and falsity, are properties of claims. Therefore, a claim about the truth, or falsity, of something is necessarily a claim about a claim, as the second claim above is.

Therefore, whereas the immediate target of the first claim is simply yesterday’s weather, the immediate target of the second claim is a claim about yesterday’s weather:

That is, the content of these two claims is different:

And if the content of two claims is different, then they’re, by definition, different claims, and therefore not simply different wordings of the same claim.

The above two claims are instead ‘logically equivalent’. That is, they directly imply each other: if it rained yesterday, then the claim ‘It rained yesterday’ has the property of being true, and vice versa.

These claims can seem to be saying the same thing because they each follow so obviously from the other that we don’t notice the logical step separating them.

And the above applies to any two claims of the form ‘X’ and ‘“X” is true’:

‘X’ ≠ ‘“X” is true’

This includes self-referential claims, like ‘This is a sentence’ and ‘This sentence consists of six words’. That is, although, for such claims, the target of ‘X’ and ‘“X” is true’ is the same — ‘X’—the first claim is about itself, whereas the second claim is about a claim about itself.

The difference between the beliefs ‘X’ and ‘“X” is true’

As stated in the book introduction, a belief is one’s understanding of an aspect of reality, and the content of a belief is a claim that expresses that understanding.

Therefore, if the claims ‘It rained yesterday’ and ‘The claim “It rained yesterday” is true’ are different claims, then our belief of these claims are different beliefs:

That is, believing that it rained yesterday merely implies that we would conclude that the claim ‘It rained yesterday’ has the property of being true. And believing that the claim ‘It rained yesterday’ has the property of being true merely implies that we believe that it rained yesterday.

These beliefs can seem to be the same belief because they each so obviously imply the other that we don’t notice the logical step separating them.

And the above applies to our belief of any two claims of the form ‘X’ and ‘“X” is true’:

belief ‘X’ ≠ belief ‘“X” is true’

Therefore, contrary to the definitions of belief mentioned in the introduction, to believing something isn’t, in itself, to believe that it’s true.

This also applies to believing that the content of a claim is real, or the case, given that these are simply alternative ways of saying that the claim is true. A belief is one’s understanding of an aspect of reality, but one’s understanding that it rained yesterday is different from one’s understanding that the content of the claim ‘It rained yesterday’ is real or the case.

Of course, the distinction between the beliefs ‘X’ and ‘“X” is true’ doesn’t, in itself, undermine the idea that our belief of ‘X’ is due to us assessing that ‘X’ is true. However, there’s a surprisingly basic logical flaw in this idea.

The true relationship between belief and an assessment of truth

Again, truth, and falsity, are properties of claims.

And the formal definition of truth is:

‘X’ is true if, and only if, X.

For example, by definition, the claim ‘It rained yesterday’ has the property of being true if, and only if, it rained yesterday:

And if the sole condition for the claim ‘It rained yesterday’ having the property of being true is that it rained yesterday, then our conclusion that this claim has the property of being true must be based on our belief that it rained yesterday:

And, by definition, and logic, our belief of the basis of one of our conclusions precedes that conclusion, even if the former formed only a fraction of a second before the latter.

Therefore, our conclusion that the claim ‘It rained yesterday’ has the property of being true must be preceded by our belief that it rained yesterday.

Therefore, contrary to the current understanding, our belief ‘It rained yesterday’ can’t, as a matter of logic, be due to us assessing that this claim is true.

And the logic of this point applies to our belief of any claim:

Belief ‘X’ can’t, as a matter of logic, be due to assessing that ‘X’ is true.

And there’s actually another surprisingly basic logical flaw in the idea that we believe something because we’ve assessed that it’s true, given that ‘X’ and ‘“X” is true’ are different claims.

If our belief of ‘X’ was dependent on us believing that ‘X’ is true, then believing that ‘X’ is true would in turn be dependent on us believing the claim ‘“X” is true’ is true, and so on, indefinitely. Therefore, belief formation would be impossible, and yet we do form beliefs.

To be clear, if we believe ‘X’, and then assess that ‘X’ is true, although our latter belief is due to an assessment of truth, it isn’t due to assessing that its own content is true — that is, its content is ‘“X” is true’, and our belief of it formed via our assessment that ‘X’, not ‘“X” is true’, is true.

Possible objection

It might be objected that although we indeed can conclude that claim ‘X’ is true on the basis of our belief of ‘X’, it can sometimes be the other way around.

For example, someone who neither believes or disbelieves ‘X’ could assess that this claim is true on the basis that they heard it being made by someone who they think can’t be wrong regarding the subject of ‘X’. And they’ll then infer, within a fraction of a second, ‘X’ from ‘“X” is true’.

However, as stated, by definition, the claim ‘It rained yesterday’ has the property of being true if, and only if, it rained yesterday. That is, by definition, claim ‘X’ is true if, and only if, X.

Therefore, by definition, we can only assess that ‘X’ is true if its content is found to match reality — that is, what we believe to be reality — and therefore not for any other reason. That is, we can only assess that ‘X’ is true if we first believe ‘X’.

Therefore, in the above scenario, when the person hears or reads claim ‘X’ being made by the trusted person, the formation of their belief of ‘X’ must precede their assessment that this claim is true.

Consider another scenario in which it may seem that a belief is due to assessing that the claim in question is true.

If we believe that it rained yesterday, but someone says that it didn’t, and we then assess the truth of these contrary claims, which leads us to changing our belief, then it may seem that our new belief is due to us assessing that the other person’s claim is true.

However, what actually happens is this.

In assessing the truth of these contrary claims, we consider what evidence exists regarding whether it rained yesterday. This may involve considering what led each of us to our contrary belief. Did we observe it raining yesterday, or did someone merely tell us, at some point, that it was raining? Or we may seek information about yesterday’s weather.

If, for example, we remember that we didn’t actually observe it raining yesterday, but was merely told that it was, and we then find weather data from yesterday that shows zero rainfall, we may thereby form the belief that it actually didn’t rain yesterday, with the formation of this belief constituting the end of our belief that it did rain yesterday.

Only after forming this new belief do we conclude, albeit possibly within a fraction of a second, that our original belief was false, and that the other person’s claim, which we now believe, is true.

That is, although the formation, and ending, of beliefs may occur during an assessment of the truth of the claims in question, this occurs before the conclusion of that assessment — albeit possibly only a fraction of a second before — rather than being due to that conclusion, which is actually due to the change of belief.

The origins of this misunderstanding

As stated, the logical flaw in the idea that we believe something because we’ve assessed that it’s true is surprisingly basic. That is, given that, by definition, claim ‘X’ is true if, and only if, X, our conclusion that ‘X’ is true is obviously dependent on our belief of ‘X’, not vice versa.

It therefore might seem implausible that this flaw in this theory of belief formation hasn’t been pointed out before.

However, the definitions of belief mentioned in the introduction illustrate the current lack of awareness of the flaw. And there doesn’t seem to be mention anywhere in the philosophical or psychological academic literature that we can’t, as a matter of logic, and contrary to the current understanding, believe something because we’ve assessed that it’s true.

The likely reason for this strange lack of awareness is that there are at least four different factors which lead us to think that we believe something because we’ve assessed that it’s true.

First:

As explained, we can wrongly think that to believe ‘X’ is, in itself, to believe that ‘X’ is true.

Again, the claims ‘X’ and ‘“X” is true’ can seem to be saying the same thing because they each follow so obviously from the other that we don’t notice the logical step separating them.

And this misunderstanding reinforces itself via our language, as illustrated by the definitions of belief mentioned in the introduction.

We often refer to our, or someone else’s, belief of a claim, when we’re actually trying to refer to the belief that the claim is true.

This particular confusion is strengthened by the fact that we often refer to our belief that someone’s claim is true by simply stating that we believe that person.

Also, when we’re trying to refer to a belief — whether ours or someone else’s — we often refer to the believer believing the claim in question. For example, in referring to our belief of someone’s account of a past incident, we may refer to ourselves believing that account.

And this wording suggests that belief, in itself, involves thinking about the believed claim, which tallies with the idea that to believe ‘X’ is, in itself, to believe that ‘X’ is true, given that the latter involves thinking about ‘X’.

However, in the example, our belief of the account simply consists, in itself, of the content of the account being our understanding of what happened during the past incident, rather than being a thought about this claim about what happened. Indeed, instead of expressing our belief of the account by referring to our belief of this claim that A, B and C happened, we can do so by simply referring to our belief that A, B and C happened.

A belief, in itself, is simply one’s understanding of an aspect of reality, rather than a thought about the claim that expresses that understanding.

Second:

As also explained, the process of assessing that a claim is true can stimulate the formation of our belief of it, and therefore seem to be the origin of that belief, even though the belief actually formed before the conclusion of the assessment.

Third:

When we consider that, by definition, claim ‘X’ is true if, and only if, X, we easily forget that, in order to compare a claim with reality, we ultimately can only ever compare it with what we believe to be reality.

Also, as explained in the next chapter, contrary to the current understanding, we don’t have different degrees, or strengths, of belief — we can only believe with certainty.

Therefore, when we assess that claim ‘X’ is true, on the basis of our belief ‘X’, we’re likely to forget that the content of our belief ‘X’ is indeed merely that, and think that we’re comparing the claim directly with reality, and then believing the claim upon our assessment being positive.

Fourth:

Even when we distinguish between believing ‘X’ and believing ‘“X” is true’, the latter belief obviously logically implies the former belief, and we may then commit the error of confusing this logical link for a causal link, even though the causal link is actually the reverse.

So why do we believe what we believe?

There’s yet another problem with the theory that we believe something because we’ve assessed that it’s true.

By definition, we believe a conclusion of our reasoning upon that claim being generated by that reasoning. Even if we merely conclude that claim ‘X’ is a possibility, we, by definition, believe the claim ‘“X” is a possibility’ upon it being generated by our reasoning. And even if we doubt, or even disbelieve, a conclusion just after its generation, we, by definition, at least believe it at the moment of its generation.

However, we obviously can only begin to assess the truth of a claim after it has entered our mind via our reasoning.

And this point may also seem to provide the answer to the question of why we believe what we believe: we believe claim ‘X’ not because we’ve assessed that it’s true, but because we’ve concluded ‘X’.

For example, we believe that it rained yesterday not because we’ve assessed that the claim ‘It rained yesterday’ is true, but because our reasoning has generated this claim. That reasoning could be based on a memory of it raining yesterday, or a memory of someone reporting, yesterday, that it was raining.

Indeed, even the formation of beliefs about our surroundings that are gained via perception involve at least some reasoning about the content of our perceptions, given that the content of a belief is a claim — such as ‘There’s a chair in front of me’ — and the perceptual process produces perceptions, not claims. Such reasoning is often so basic, and fast, that we don’t recall it, and so such beliefs can seem to be formed from our perceptions without reasoning.

So it seems that we believe ‘X’ because we’ve concluded ‘X’ — however brief, or unsound, our reasoning. However, chapter 3 shows that even this theory is wrong.

Next: Belief is Certainty