How Belief Works is an ongoing series of articles on the psychology of belief that's best read in sequence.

The formation of a belief is by definition us assessing that the claim concerned is true – however brief, irrational, emotional, credulous or intuitive our assessment is. This conception of belief formation can seem to be a truism. But it's actually false, because it's fatally logically flawed.

A false conception of belief formation

First, compare these two sentences:

1. 1. Humans are apes.

   2. Humans are taxonomically classified as apes.

2 is of course just a different, wordier, wording of the content of 1. That is, 1 and 2 are making the same claim.

Now compare 1 with this sentence:

1. 3. The claim Humans are apes is true.

3 can seem to also be just a different, wordier, wording of the content of 1. That is, 1 and 3 can seem to also be making the same claim. But 1 and 3 are actually making distinct claims that merely imply each other.

If two sentences are just different wordings of the same claim, then, by definition, their content must be the same. And if the content of two sentences is the same, then, by definition, neither sentence will refer to something that the other doesn’t refer to.

But whereas 3 refers to the claim Humans are apes, 1 doesn’t. That is, 1 makes, rather than refers to, this claim. 1 is about simply humans and their relationship to the taxonomic category of apes, rather than about a claim about this. Also, 3, unlike 1, refers to the concept of truth, and thereby to the relationship between a claim and reality.

In the case of 1 and 2, 2 is 1 with the addition of the words taxonomically classified as between are and apes. But this doesn't constitute 2 referring to something that 1 doesn't refer to. That is, given that ape is a taxonomic classification, the wording are apes is just a conciser wording of are taxonomically classified as apes.

The distinction between the claims made by 1 and 3 is clearer if 3 is slightly re-worded as:

The claim Humans are apes is a true claim.

That is, this wording makes it clearer that the claim being made isn't about simply humans and their relationship to the taxonomic category of apes, but is about a claim about this.

Hence, 1 and 3 are making distinct claims that merely imply each other. If humans are apes then the claim Humans are apes is a true claim, and vice versa. That is, 1 and 3 are each merely implicitly making the claim that the other is making. A sentence merely implicitly making the claim that another sentence is making isn't the same thing as a sentence making the same claim as another sentence.

1 and 3 can seem to be just different wordings of the same claim because the claim made by each follows so obviously from the claim made by the other that we can fail to notice the very basic logical step separating these claims.

In the case of 1 and 2, the fact that 2 is just a different, wordier, wording of the content of 1 means that they're not making different claims that imply each other, but are simply different wordings of the same claim.

The following sentences is another alternative wording of the claim made by 3:

It’s true that humans are apes.

Given that this sentence doesn't use the wording 'the claim Humans are apes' it might seem to be referring to simply humans, rather than to a claim about humans, and so to actually be a different wording of the claim made by 1.

However, unlike 1, but like 3, it refers to the concept of truth. And, again, this concept concerns a claim – specifically, the relationship between a claim and reality. By definition, a claim is a true claim if, and only if, it matches reality. So when we say ‘It’s true that …’ we’re saying that the claim made by the subsequent words is a true claim.

Therefore the above sentence is asserting that it's a true claim that human are apes. That is, it's asserting that the claim Humans are apes is a true claim, as 3 does, even though it doesn’t refer to this claim as a claim, as 3 does.

The difference between the claims made by 1 and 3 of course applies to any claim, X, and the claim X is true. So claim X isn’t in itself the claim that X is true, and vice versa. Instead, each claim merely implies the other.

Now compare our belief of the claims made by 1 and 3. Given that these claims are different claims that imply each other, our belief of them are by definition different beliefs that imply each other. That is, if we believe that humans are apes then we’d conclude that the claim Humans are apes is a true claim. And, conversely, if we believe that the claim Humans are apes is a true claim then we also believe that humans are apes.

But our belief of these two claims can seem to be the same belief because, again, the claims follow so obviously from each other that we can fail to notice the very basic logical step separating them and so think that they're the same claim.

The difference between these two beliefs of course applies to our belief of any claim, X, and the claim X is true. So believing X isn’t in itself believing that X is true, and vice versa. Instead, believing X merely implies that we’d conclude that X is true, and believing that X is true merely implies that we believe X.

Hence, the definition of belief that I raised at the end of the previous article – considering a claim to be true – is wrong, given that considering a claim to be true is believing it to be true. Indeed, a definition obviously shouldn't rely on the concept being defined. I'll be able to present a correct definition of belief in the next article.

The difference between believing X and believing that X is true implies that the idea that the formation of belief X is us assessing that X is true is false. That is, assessing that X is true is the formation of the belief X is true, and so can't be the formation of belief X.

It might be thought that this simply means that the formation of belief X is instead due to us assessing that X is true, given that X can be inferred from the belief that X is true. But if the formation of belief X was dependent on us assessing, and thereby believing, that X is true, then the formation of our belief that X is true would in turn be dependent on us assessing, and thereby believing, that the claim X is true is true, and so on – which implies that the formation of any belief would involve a cognitive process consisting of an infinite chain of belief formation, which is obviously impossible.

And there’s another flaw in the idea that the formation of belief X is us assessing that X is true, which also applies to the idea that the formation of belief X is due to us assessing that X is true – one which reveals the true relationship between assessing that X is true and believing X.

Again, by definition, a claim is a true claim if, and only if, it matches reality. So the only way to assess whether a claim is a true claim is to assess whether it matches reality. And the only way to assess whether a claim matches reality is to compare it with reality. But, logically, when we compare a claim with reality we can only ever compare it with what we believe about the relevant aspect of reality at the moment of the comparison, even when the comparison uses the current content of our senses.

So our assessment that the claim Humans are apes is a true claim must be based on our belief that humans are apes. That is, this assessment must be preceded by our belief that humans are apes. So the formation of our belief that humans are apes can’t ever be, or due to, us assessing that the claim Humans are apes is a true claim.

And this logic of course applies to the formation of any belief: the formation of belief X can’t ever be, or due to, us assessing that claim X is true, because that assessment is always based on, and so preceded by, our belief of X.

Although, the process of assessing the truth of X can lead to the formation of belief X, because this belief may only form during that process, the moment before we conclude that X is true.

Note also that although us assessing, and thereby believing, that X is true is belief formation that involves an assessment of truth, this belief involves the claim X is true and yet its formation involves our assessment that X, not X is true, is true.

Potential objections

Objection 1

It might be objected that even if we accept the above analysis there’s still one scenario in which the formation of belief X is due to us assessing that claim X is true.

If we read or hear claim X, and we neither believed or disbelieved X immediately before doing so, and we completely trust X’s source on the subject of X, then we can assess that X is a true claim based on that trust, and this assessment will then immediately lead us to conclude X. This sequence of events doesn’t imply the infinite chain of belief formation that I referred to earlier, given that our belief that X is true is based on our trust of X’s source and so isn’t dependent on us first believing that the claim X is true is true.

Of course, not all beliefs form via us reading or hearing the believed claim. Indeed, in the above sequence of events our belief that X is true forms via our trust of X’s source rather than via us reading or hearing the claim X is true. So the aim of this objection isn’t to show that the formation of belief X is always due to us assessing that X is true. Indeed, if it was, the objection wouldn’t provide a solution to the resulting problem of the infinite chain of belief formation.

But the objection doesn’t even succeed in its limited aim of showing that the formation of belief X is sometimes due to us assessing that X is true, because it has two flaws.

First, in the above sequence of events our conclusion that X is a true claim actually isn’t an assessment that X is a true claim.

Again, by definition, a claim is a true claim if, and only if, it matches reality. So the only way to genuinely assess whether a claim is a true claim is to assess whether it matches reality. And the only way to genuinely assess whether a claim matches reality is to compare it with reality – that is, compare it with what we believe about the relevant aspect of reality at the moment of the comparison, even if that belief is based on the current content of our senses.

So if our conclusion that claim X is a true claim is based on simply a consideration of X's source, and therefore not on a comparison of X with reality, then it’s based on a consideration, but not an assessment, of X's truth. That is, our assessment is only of X's source. So in the above sequence of events the formation of belief X is actually due to us concluding, but not assessing, that X is true.

The second flaw in this objection is that our complete trust of X’s source on the subject of X actually leads directly to us concluding X, rather than via concluding that X is a true claim.

That is, although that complete trust means, by definition, that we believe that all claims produced by the source on the subject of X can be believed to be true claims, this in turn means that we also believe that all such claims can be believed. So upon reading or hearing X we can conclude X directly, based on X's source, rather than via concluding that X is a true claim. And given that the former cognitive route to concluding X is shorter than the latter, we conclude X via the former route before we’ve had a chance to do so via the latter.

Objection 2

It might also be objected that if our assessment that claim X is true was based on our belief of X, rather than the reverse, then our belief of X would lead us to always assess that X is true and that any contrary claim is false, and so we’d never change our belief, and yet we do change our beliefs.

But this objection wrongly assumes that if we believe X then changing this belief is dependent on us assessing that X is a false claim and that a contrary claim is a true claim. Just as the formation of belief X can't be due to us assessing that X is a true claim, because that assessment is based on that belief, so the subsequent formation of a contrary belief, and hence the end of our belief of X, can’t be due to us assessing that the contrary claim is a true claim and that X is a false claim, because the reverse will be true.

Also, as I said earlier, the process of assessing the truth of X can lead to the formation of belief X, because this belief may only form during that process. Likewise, if we believe X and then assess the truth of both X and a contrary claim, we can change to believing the contrary claim during this process, and then assess that the contrary claim is a true claim and that X is a false claim. So believing X before assessing the truth of both X and a contrary claim doesn’t even mean that we’ll necessarily assess that X is a true claim and that the contrary claim is false.

The origin and prevalence of this false understanding of belief formation

The origin and prevalence of the idea that the formation of belief X is us assessing that claim X is true is likely explained by the following factors:

• Our belief of the claims X and X is true can seem to be the same belief.

• If our belief of claim X only formed during the process of assessing the truth of X, then that process was critical to the formation of this belief. And this can lead us to wrongly assume that the formation of this belief was us assessing that X is true, especially given that our belief of X will have formed only the moment before we concluded that X is true.

• When we compare claim X with reality, in order to assess the truth of X, we can easily forget that, logically, we can only ever compare X with what we believe about the relevant aspect of reality at the moment of the comparison, even when the comparison uses the current content of our senses. So when we assess that X is true we can wrongly think that we compared X with reality itself, rather than merely our belief about the relevant aspect of reality, and that our belief of X therefore formed upon us forming that assessment.

• When we conclude that claim X is true based on our complete trust of X’s source on the subject of X we can wrongly think both that this is us assessing that X is true and that it's the formation of our belief of X.

So how do beliefs form?

There’s actually yet another flaw in the idea that the formation of belief X is us assessing that claim X is true.

We obviously can only begin to assess the truth of a claim after it has entered our mind. But concluding X involves claim X entering our mind upon it being generated by reason, and a conclusion is by definition a belief. So we can believe X before we’ve had a chance to even begin to assess the truth of X.

The fact that a conclusion is by definition a belief can also seem to answer the question of how beliefs do form. That is, the formation of belief X is us concluding X – however brief, irrational, emotional, credulous or intuitive our reasoning is.

It might be thought that the formation of a belief about our surroundings or body via sensory perception doesn't necessarily also require reason, and so isn't necessarily a conclusion. For example, it might be thought that to see rain is in itself to believe that it's raining. But belief formation via sensory perception actually always also requires reason.

Belief involves a claim. In the example, the belief that it's raining involves the claim It's raining. And the formation of any belief involves thinking the believed claim. In the example, the formation of the belief that it's raining involves thinking 'It's raining'. So the formation of a belief about our surroundings or body via sensory perception involves the generation of a claim about the physical world, and us thinking that claim.

And yet the output of a perceptual process is in itself simply a perceptual experience of the physical world. In the example, the output of the visual process is in itself simply our visual experience of rain. That is, the output of a perceptual process is the content of one of our senses, not a thought about that content.

When we form belief X about our surroundings or body via sensory perception claim X is generated by reasoning based on our perceptual experience, with our thinking X being the output of that reasoning. But such reasoning is often so basic and therefore brief that the resulting belief can seem to be a direct product of the perceptual process.

Note that the term perception can be used to refer to an understanding – as in, for example, Different people can have different perceptions of what constitutes living morally. And a perception in this sense is by definition in itself a belief. But this is a different sense of this term from sensory perception.

The idea that the formation of belief X is us concluding X can seem true by definition and therefore irrefutable. But so can the idea that the formation of belief X is us assessing that X is true. And, incredibly, even the former is fatally logically flawed. To understand why, it's necessary to first understand the real truth about how beliefs form – which is the subject of the next article.

Next article: How Beliefs Form – Part 2

How Belief Works