How Belief Works

Chapter 4: Belief Is Certainty​

Why there aren't degrees of belief​

It’s generally thought, including within psychology and philosophy, that we have different degrees, or strengths, of belief. For example, it can seem obvious that our belief that we’re eating an apple is stronger than our belief that it’ll rain tomorrow. However, I discovered that this apparent truism is fatally logically flawed in two ways. And the counterintuitive truth about the nature of belief has profound implications for human psychology and therefore also our lives.

The theory of degrees of belief

We have different levels of confidence in claims, with the maximum being certainty. It’s currently generally thought that our confidence in a claim constitutes our belief of it if that confidence is above a particular sub-certain level, which is perhaps most commonly thought to be half-way between zero confidence and certainty. Hence the current understanding that we have different degrees, or strengths, of belief. Some people think that the sub-certain threshold for belief is higher than 50% confidence, but it doesn’t matter for the analysis in this chapter what the sub-certain threshold for belief is considered to be.

What is confidence in a claim?

Oxford University Press's online English dictionary defines this sense of confidence – as opposed to, for example, self-confidence – as follows:

The state of feeling certain about the truth of something.

One problem with this definition is that it equates confidence and certainty in a claim, when the latter is only the highest level of confidence. The term confidence can be used to specifically mean high confidence, as in 'I can say with confidence that ...', which is what this definition must actually be referring to. But even this doesn't necessarily mean certainty. Indeed, one of the usage illustrations provided by the entry refers to high but sub-certain confidence: 'One thing I can say with a fair degree of confidence is that ...'. And the definition therefore fails to refer to confidence in the sense of any level, as in the phrase 'low confidence'.

We sometimes incorrectly refer to degrees of certainty, as when we use phrases like 'I'm fairly certain', 'I'm more certain now' or 'I have absolute certainty'. Certainty involves, by definition, an absence of doubt. And, also by definition, only the highest level of confidence involves no doubt. Therefore references to degrees of certainty are either based on the misunderstanding that certainty is a high level of confidence, rather than only the highest, or are incorrectly using the term certain to mean confident, or the term certainty to mean confidence.

Another problem with the above definition is that its reference to certainty means, given that certainty is a level of confidence, that it relies on the reader already having an understanding of what it's supposed to be defining. That is, the definition is circular.

A better wording of the above definition of confidence is:

A feeling about the truth of something.

And this definition can now seem unimpeachable.

However, as I illustrated in chapter 3, even seemingly unimpeachable claims can be false. According to this definition, our confidence in claim X is a feeling about the truth of X. But a feeling about whether X is true is a level of confidence that X is true, which is a level of confidence in the claim X is true. As I explained in chapter 3, the claims X and X is true are different claims. Therefore our confidence in claim X is different from confidence in the claim X is true. Therefore our confidence in claim X is actually a feeling not about whether X is true, but about whether X. For example, our confidence in the claim There are six eggs in the fridge is actually a feeling not about whether this claim is true, but about whether there are six eggs in the fridge.

Indeed, just as our belief of claim X is belief that X, our confidence in claim X is a level of confidence that X, which is a feeling about whether X. In the example, our confidence in the claim There are six eggs in the fridge is a level of confidence that there are six eggs in the fridge, which is a feeling about whether there are six eggs in the fridge.

For the same reason, the above definition is incompatible with the theory of degrees of belief. If our confidence in claim X constitutes belief of X if above a particular level, and that confidence is a feeling about whether X is true, which is confidence in the claim X is true, then our belief of X is belief of the claim X is true. But as I explained in chapter 3, the beliefs X and X is true are different beliefs, given that the claims X and X is true are different claims. This problem isn't recognised in the academic literature. For example, Franz Huber, an associate professor of philosopher, begins the introduction to the 2009 philosophical anthology 'Degrees of Belief' – which he edited with philosophy lecturer Christoph Schmidt-Petri – as follows: 'Degrees of belief are familiar to all of us. Our confidence in the truth of some propositions is higher than our confidence in the truth of other propositions'.

What's the origin of our confidence in a claim?

Given that our confidence in claim X is a feeling about whether X, it arises from our belief about the probability that X, with our particular level of confidence corresponding to the apparent probability that X. For example, our confidence in the claim There are six eggs in the fridge arises from our belief about the probability that there are six eggs in the fridge. And our high but sub-certain confidence in the claim There are six eggs in the fridge arises from our belief that it's highly likely that there are six eggs in the fridge. We sometimes think more precisely about both the probability of a claim's content and our resulting level of confidence in the claim. For example, we may think that there's a 90% probability that there are six eggs in the fridge, and that we therefore have 90% confidence in the claim There are six eggs in the fridge.

Our certainty in claim X therefore arises from our belief that it's certain that X. That is, the first reference to certainty in the previous sentence concerns the highest level of confidence, which is a mental state, whereas the second reference concerns the highest level of probability, which is a mathematical concept.

Our confidence in claim X – our confidence that X – is indeed a different mental state from our belief about the probability that X. Whereas that confidence is confidence in claim X, that belief is belief of the different claim There's probability P that X. In the example of having high but sub-certain confidence in the claim There are six eggs in the fridge, our belief about the probability that there are six eggs in the fridge is belief of the different claim It's highly likely that there are six eggs in the fridge. Even our certainty in claim X – our certainty that X – isn't our belief that it's certain that X, given that X and It's certain that X are different claims.

Also, given that our confidence in claim X is a feeling about whether X, rather than a feeling about whether X is true, it indeed arises from our belief about the probability that X, rather than our belief about the probability that X is true. For example, given that our confidence in the claim There are six eggs in the fridge is a feeling about whether there are six eggs in the fridge, rather than a feeling about whether this claim is true, it arises from our belief about the probability that there are six eggs in the fridge, rather than a belief about the probability that this claim is true.

Also, it might be thought that our feeling of confidence in claim X doesn't always depend on us forming a belief about the probability that X, because it can instead be a product of our intuition, which is understood to be a kind of sixth sense. That is, our feeling of confidence in X can simply be an instinctive feeling about whether X. We often attribute a feeling or belief to our supposed intuition when it doesn't seem to be the product of perception or reasoning. However, the occurrence of any mental phenomenon is the product of a cognitive chain of events, whether or not we're aware of those events. For example, when an apparently random memory suddenly enters our mind it is in reality always triggered, however indirectly, by something in our current experience, even though we're not aware of what it was. In the case of feelings and beliefs that don't seem to be the product of perception or reasoning, we invented the concept of intuition to bridge this explanatory gap. In the case of our apparently intuitive feeling of confidence in X, the only cognitive chain of events that can lead to this feeling is one that involves the formation of a belief about the probability that X. But given the speediness of the brain which works on the timescale of milliseconds – our consideration of this probability was so brief that we're subsequently only aware of the feeling of confidence in X that arose from it.

Also, it might be thought that our confidence in claim X could actually be the basis of, rather than arising from, our belief about the probability that X. For example, perhaps our high but sub-certain confidence in the claim There are six eggs in the fridge is actually the basis of, rather than arising from, our belief that it's highly likely that there are six eggs in the fridge. However, the problem with this idea is that the only possible explanation for the origin of our level of confidence in X is a belief about the probability that X. That is, given that our supposed intuition is a fiction, a particular level of confidence in X must arise from a particular belief, of some kind, about the content of X. And the only belief about the content of X that could be the basis of a level of confidence in X is a belief about the probability that X. And that belief can obviously be the product of our assessment of that probability.

Why degrees of belief are logically impossible

The two key points so far are:

  • Our confidence in claim X – our confidence that X – is a feeling about whether X.

    • For example, our confidence in the claim There are six eggs in the fridge – our confidence that there are six eggs in the fridge – is a feeling about whether there are six eggs in the fridge.

  • Our confidence in X arises from our belief about the probability that X.

    • For example, our confidence in the claim There are six eggs in the fridge arises from our belief about the probability that there are six eggs in the fridge.

Again, the theory of degrees of belief states that our confidence in X constitutes our belief of X if that confidence is above a particular sub-certain level, which is perhaps most commonly thought to be half-way between zero confidence and certainty. There are two fatal logical flaws in this theory.

First, the theory implies that the formation of a belief is, impossibly, dependent on an infinitely long process that involves the formation of an infinite chain of other beliefs. Our confidence in claim X arises from our belief about the probability that X. Therefore if that confidence constituted our belief of X then this belief would be dependent on the prior formation of our belief of the claim There's probability P that X. But that prior belief would constitute confidence in the claim There's probability P that X, and that confidence must have in turn arisen from our prior belief of the claim There's probability Q that there's probability P that X – and so on, indefinitely.

The second logical flaw in the theory of degrees of belief is that confidence and belief are different kinds of mental states, and so no level of confidence in a claim, even certainty, can itself constitute our belief of the claim. Our confidence in claim X is a feeling – a feeling about whether X – and therefore an emotional mental state. But our belief of X is, as I defined in chapter 2, an understanding of part of reality, and an understanding is in itself a purely intellectual mental state. As I explained in chapter 2, when a belief arouses an emotion this is one mental state leading to another – although, given the speediness of the brain, such an emotion can arise within an unnoticeable fraction of a second of the formation of the belief, and so these two mental states can seem to be the same mental state. The difference between confidence and belief is also another reason why our confidence in X is indeed a different mental state from our belief about the probability that X.

It might be countered that our degree of belief of X could instead be merely based on, rather than the same mental state as, our level of confidence in X, when that confidence is above a particular sub-certain level. Or our degree of belief of X could arise directly from our belief about the probability that X, but separately from our level of confidence in X, when that apparent probability is above a particular level. However, although our belief of X can't be the same mental state as our confidence in X, the idea that a particular degree of belief of X doesn't in itself involve a particular level of confidence in X also doesn't make sense conceptually. Also, this idea doesn't get around the first flaw, given that it still involves the formation of our belief of X being dependent on the prior formation of our belief of the claim There's probability P that X.

It might also be thought that, whereas our confidence in claim X arises from our belief about the probability that X, our degree of belief of X could actually be our belief about the probability that X, when that apparent probability is above a particular level. If so, a belief wouldn't be dependent on the prior formation of an infinite chain of other beliefs. However, this idea still has the problem of separating our confidence in X and our belief of X. Also, I explained in the previous section that our confidence in claim X – our confidence that X – is indeed a different mental state from our belief about the probability that X, given that that belief is belief of the different claim There's probability P that X. Likewise, our supposed degree of belief of X couldn't be our belief of the different claim There's probability P that X. Whether or not beliefs exist in degrees, our belief of different claims constitutes, by definition, different beliefs. Therefore our supposed degree of belief of X and our belief of the claim There's probability P that X would merely be consistent with each other. For example, a high but sub-certain degree of belief of the claim There are six eggs in the fridge would merely be consistent with belief of the different claim It's highly likely that there are six eggs in the fridge.

It might also be thought that, whereas our confidence in claim X arises from our belief about the probability that X, our degree of belief of X could actually be the basis of our belief about the probability that X. For example, perhaps our high but sub-certain degree of belief of the claim There are six eggs in the fridge is actually the basis of our belief that it's highly likely that there are six eggs in the fridge. Indeed, if our belief There's probability P that X was dependent on the prior formation of our belief of X, then that wouldn't imply an infinite chain of past belief formation. However, again, this idea still has the problem of separating our confidence in X and our belief of X. Also, it has the same kind of problem as the idea that our confidence in X could actually be the basis of, rather than arising from, our belief There's probability P that X: the only possible explanation for the origin of a degree of belief of X is a belief about the probability that X. That is, given that our supposed intuition is a fiction, a particular degree of belief of X would have to be dependent on the prior formation of a particular belief, of some kind, about the content of X. And the only belief about the content of X that could be the basis of a degree of belief of X is a belief about the probability that X. And that belief can obviously be the product of our assessment of that probability.

In sum, degrees of belief are logically impossible. The logic of this analysis applies not just to the concept of sub-certain degrees of belief, but even to the concept of the highest degree of belief. Again, even our certainty in claim X can't itself constitute our belief of X. And the idea of a highest degree of belief of X not in itself involving certainty in X also doesn't make sense conceptually. So the concept of degrees, or strengths, of belief is a fictionbeliefs are non-degreed.

The true relationship between confidence and belief

To understand the true relationship between confidence and belief, consider first sub-certain confidence in a claim. Our sub-certain confidence in claim X arises from our belief of the different claim There's sub-certain probability P that X. And this belief is our only belief regarding the content of X that's implied by our sub-certain confidence in X, given that we can't have a sub-certain belief of X. For example, if we have high but sub-certain confidence in the claim There are six eggs in the fridge then the only belief regarding the content of this claim that's implied by that confidence is our belief of the different claim It's highly likely that there are six eggs in the fridge.

It might be thought that sub-certain levels of confidence in X above a particular level could be associated with a non-degreed belief of X. However, any degree of uncertainty about X, however small, is incompatible with a non-degreed belief of X, given that the latter implies that the content of X is a certainty. Indeed, non-degreed belief of X is incompatible with non-degreed belief of the claim There's sub-certain probability P that X, given that they can't both be true. For example, non-degreed belief of the claim There are six eggs in the fridge is incompatible with non-degreed belief of the claim It's highly likely that there are six eggs in the fridge, given that the first claim implies that the existence of six eggs in the fridge is certain, whereas the second claim implies that it's uncertain. If degrees of belief were possible then these two beliefs would be compatible if the second belief was held with certainty and the first was held with high but sub-certain confidence. Also, again, if our belief of X was dependent on us having a particular level of confidence in X, then that belief would be dependent on the prior formation of our belief about the probability that X, which implies an infinite, and therefore impossible, chain of belief formation.

Now consider certainty in a claim. Our certainty in X arises from our belief of the different claim It's certain that X. Again, the first reference to certainty in the previous sentence concerns the highest level of confidence, which is a mental state, whereas the second reference concerns the highest level of probability, which is a mathematical concept.

I explained in chapter 3 that the claims X and X is true can seem to be claiming the same thing, and therefore to be just different wordings of the same claim, but are actually different claims that merely logically imply each other. And the same is true for the claims X and It's certain that X. For example, the claims There are six eggs in the fridge and It's certain that there are six eggs in the fridge can seem to be claiming the same thing – that there are six eggs in the fridge – and therefore to be just different wordings of the same claim, but are actually different claims that merely logically imply each other. That is, if there are six eggs in the fridge – the first claim claim – then, logically, it's certain that there are six eggs in the fridge – the second claim. Conversely, if it's certain that there are six eggs in the fridge then, logically, there are six eggs in the fridge. The claims X and It's certain that X are different claims because whereas the first claim simply asserts X, the second asserts the probability of the content of X. But, as with the claims X and X is true, the claims X and It's certain that X can seem to be just different wordings of the same claim because they each follow so obviously from the other that we can fail to notice the basic logical step separating them.

Therefore our belief of the claim It's certain that X, which gives rise to our certainty in X, isn't itself belief of X, given that these are different claims. However, our belief of the claim It's certain that X at least implies that we believe X.

Our belief of X can't be dependent on the prior formation of our belief of the claim It's certain that X, given that that implies an infinite, and therefore impossible, chain of belief formation. Therefore our belief of the claim It's certain that X must instead be based on our belief of X. I explained earlier that a particular degree of belief of X would have to be dependent on the prior formation of a particular belief, of some kind, about the content of X. And the only kind of belief about the content of X that could be the basis of a degree of belief of X is a belief about the probability that X. But a non-degreed belief of X, as opposed to the highest degree of belief of X, can form simply upon the generation of X by a chain of reasoning about the subject of X, and therefore before the formation of a belief about the probability that X.

Whatever our level of confidence in a claim, there’s actually a sense in which our belief regarding the content of the claim involves in itself certainty. I've been referring to the mental state of certainty as being the highest level of confidence in a claim, which is a feeling. However, the mental state of certainty can instead simply involve an absence of doubt about a claim, which is the absence of a feeling. Indeed, Cambridge University Press's online English dictionary defines certainty, in the sense of the mental state, as 'the state of being completely confident or having no doubt about something'. And just as the mental state of belief can't in itself involve confidence, so it can't in itself involve doubt. That is, whereas our belief of claim X is an understanding of part of reality, and therefore an intellectual mental state, our doubt in X is a feeling about whether X, and so an emotional mental state. Also, doubt in X can't even exist separately from our belief of X, given that, as I explained, any degree of uncertainty about X, however small, is incompatible with a non-degreed belief of X. Therefore belief is certainty in the sense of an absence of doubt.

To recap the main points of the true relationship between confidence and belief:

    • Our confidence in a claim is a difference mental state from our belief of a claim.

    • And whereas we have levels of confidence, we don't have degrees of belief.

    • If our feeling of confidence in claim X is certainty, then what we believe regarding the content of X is It's certain that X and X.

    • If our feeling of confidence in X is sub-certain, then what we believe regarding the content of X is There's sub-certain probability P that X, with our level of confidence corresponding to that probability.

    • Whatever our level of confidence in X, our belief regarding the content of X involves in itself certainty in the sense of an absence of doubt.

The idea that there aren't degrees of belief, and that belief is certainty in the sense of an absence of doubt, doesn’t imply that we can't doubt any of our beliefs – which we obviously can – but that doing so constitutes the end of the belief – although, we may then at least believe that the content of that past belief is highly likely.

I stated in the introduction that it can seem obvious that our belief that we’re eating an apple is stronger than our belief that it’ll rain tomorrow. In reality, if, as we're eating the apple, we feel certainty in the claim I'm eating an apple and only sub-certain confidence in the claim It'll rain tomorrow, our beliefs regarding the content of these claims are separate mental states from these feelings of confidence. And whereas our belief regarding the content of the claim I'm eating an apple is non-degreed belief of either this claim or the different claim It's certain that I'm eating an apple, our belief regarding the content of the claim It'll rain tomorrow is non-degreed belief of only the different claim There's sub-certain probability P that it'll rain tomorrow.

The logical necessity of the certainty of belief

The conclusion that there aren't degrees of belief, and that belief is always certainty in the sense of an absence of doubt, is counterintuitive not just because it can seem obviously contrary to our experience. The above theoretical argument consists solely of conceptual analysis – that is, the chain of logic doesn't at any point depend on observational evidence. It therefore reveals not only that there aren't degrees of belief, and that belief is always certainty in the sense of an absence of doubt, but also that this is so not because of the nature of the human brain, but simply by logical necessity.

As I mentioned in chapter 1, the central tenet of the field of psychology today is that how the human mind works is solely due to the wiring and chemistry of the human brain, which is in turn determined by a person’s genes and experiences. Therefore all mainstream theories about any aspect of the functioning of the human mind involve that aspect being due, in some way, to the nature of the human brain. However, although our capacity for belief is obviously due to the nature of the human brain – rocks can't hold beliefs – there isn’t anything about the human brain which prevents degrees of belief and leads to belief always being certainty in the sense of an absence of doubt. Instead, the certainty of belief is simply a logically inherent, and therefore inevitable, feature of belief, for any form of intelligence.

The origin and dominance of the theory of degrees of belief

Again, the idea that we have different degrees, or strengths, of belief is widespread, including within psychology and philosophy. For example, the previously mentioned philosophical anthology 'Degrees of Belief' contains twelve essays by different academic philosophers on degrees of belief, and none argues against their existence. The origin and dominance of this theory of the nature of belief is due to the combination of the following factors:

  • As I explained, our confidence in claim X isn't itself confidence that X is true, just as our belief of X isn't itself belief that X is true. However, high but sub-certain confidence in X and belief of X are both mental states that are at least implicitly positive about the truth of X. Therefore the former can be mistaken for sub-certain belief of X, with the implication that certainty in X is the highest degree of belief of X. Certainty in X can be mistaken for being the highest degree of belief of X also because both concepts involve an absence of doubt about X, and because certainty in X so obviously implies belief of X that we mistakenly conflate them. We're especially likely to mistake confidence for belief given that our confidence in X can, given the speediness of the brain, form within an unnoticeable fraction of a second of the formation of our belief regarding the content of X, and so the formation of this confidence can seem to be the formation of a belief regarding the content of X. Also, we can subsequently switch between these two actual mental states so quickly that our confidence in X can continue to seem to be a belief regarding the content of X.

  • Although we can refer to confidence in claim X versus belief of X, we can also instead refer to confidence that X and belief that X. For example, our confidence in the claim There are six eggs in the fridge can be referred to as confidence that there are six eggs in the fridge, and our belief of the claim There are six eggs in the fridge can be referred to as belief that there are six eggs in the fridge. And this identical grammar accords with the idea that the mental states are identical, and that levels of confidence above a particular sub-certain level are therefore degrees of belief.

  • Given that the claims X and There's high but sub-certain probability P that X are both implicitly positive about the truth of X, but the latter is less so, belief of the latter can be mistaken for sub-certain belief of X. And this mistake is especially likely if we already mistake belief of the claim It’s certain that X for the highest degree of belief of X.

  • If we believe that the content of claim X is to some degree likely, and we consider that we therefore don’t disbelieve X, we can assume that we must therefore believe X to some degree, even though it’s actually possible to neither disbelieve or believe a claim.

  • If we believe that the content of claim X is to some degree likely, and we consider that we therefore neither disbelieve or believe X, we can be motivated to describe this belief as our sub-certain belief of X in order to avoid our non-belief of X being misinterpreted by others as disbelief – and we may even end-up believing this description ourselves, especially given the other points in this list.

  • Our experience of non-degreed belief is actually similar to what we imagine the experience of degrees of belief is like. For example, the experience of being certain, in the sense of an absence of doubt, that it's highly likely that there are six eggs in the fridge is similar to what we imagine it's like to have a high but sub-certain degree of belief that there are six eggs in the fridge. Likewise, the experience of being certain, in the sense of an absence of doubt, that there are six eggs in the fridge is similar to what we imagine it's like to have the highest degree of belief that there are six eggs in the fridge. Whether we have certainty, in the sense of an absence of doubt, that there's sub-certain probability P that X, or a sub-certain degree of belief that X, we’re equally uncertain about X. And whether we have certainty, in the sense of an absence of doubt, that X, or the highest degree of belief that X, we have an absence of doubt about X.

Previous arguments against degrees of belief

The idea that there aren't degrees of belief isn’t new. The previous arguments against degrees of belief are presented in the 2017 paper 'Belief does not come in degrees', by assistant professor of philosophy Andrew Moon.

The first argument is based on an analysis of how we refer to beliefs. However, I won’t go through the argument because its implicit premise is false. We can’t reasonably form conclusions about the nature of something based on how we refer to it. Even when we’re being honest, how we refer to something is simply a reflection of our current understanding of it, which may be false. The only way to reasonably form conclusions about the nature of something is to perform a deliberate and careful analysis of it, and then form a conclusion based on that analysis. Moon also presents, and objects to, a linguistic argument in favour of degrees of belief, which fails for the same reason, although Moon of course objects to it for a different reason.

Before presenting the second argument against degrees of belief, Moon presents a counterargument to the argument that levels of confidence in claims necessarily imply degrees of belief. He first considers the idea that belief is simply confidence in a claim, and its implication that at least some levels of confidence are degrees of belief. He points-out that this idea is always presented without a supporting argument and is therefore merely an assumption. However, he doesn't question the current understanding that belief involves in itself confidence. He states that confidence is a property of belief, and points-out that 'Although a property of something might come in degrees, the thing itself might not'. He gives the example of trees and their property of height: although tree height comes in degrees, trees themselves don't. That is, something is either a tree or it isn't. Therefore, he argues, even though confidence is a property of belief, levels of confidence don't necessarily imply degrees of belief. For example, our high but sub-certain confidence in claim X could imply that we have a non-degreed believe of X that involves in itself that confidence. This non-degreed belief would therefore not necessarily involve certainty in the sense of an absence of doubt, given that a sub-certain level of confidence involves a level of doubt.

However, Moon doesn't provide a supporting argument for his premise that confidence is a property of belief. He instead merely states that references to particular beliefs involving, in themselves, particular levels of confidence are 'beyond reproach'. Therefore this premise is itself merely an assumption – and the analysis in this chapter shows that it's actually logically impossible.

The second argument against degrees of belief tries to show that it's actually our intuition that there aren't degrees of belief. However, again, I won’t go through the argument because its implicit premise is false, and for two reasons. First, again, our supposed intuition is a fiction. Second, even if our supposed intuition was real, we couldn’t reasonably form conclusions about the nature of something by uncritically following our intuition, given that our intuition would fallible, and often wrong. Indeed, most people's supposed intuitive response to the idea that we don't have different degrees, or strengths, of belief is disbelief – a fact which not only illustrates the unreliability of our supposed intuition, but also contradicts the argument's sub-conclusion that it's our intuition that there aren't degrees of belief. Again, the only way to reasonably form conclusions about the nature of something is to perform a deliberate and careful analysis of it, and then form a conclusion based on that analysis – although, the cognitive chain of events underlying our supposed intuition can be a valuable source of ideas during this process.

The third argument against degrees of belief is a metaphysical argument – metaphysics being the branch of philosophy that examines the fundamental nature of reality. The argument involves an analysis of the concept of degrees of something. Given that the chain of logic consists solely of conceptual analysis, the implication of its conclusion that there aren't degrees of belief is that this is so not because of the nature of the human brain but because degrees of belief are simply logically impossible – although, Moon doesn't actually make this point. I'm not enough of a philosopher to be able to assess the argument. However, even assuming that it isn't flawed, it's inferior to my argument in one sense. Its reliance on an analysis of the concept of degrees of something, rather than on an analysis of the concepts of confidence and belief, and their relationship, means that it doesn't provide, like my argument, an understanding of why the nature of confidence and belief, and their relationship, means that degrees of belief aren't possible. And it therefore also doesn't provide, like my argument, an understanding of the true relationship between confidence and belief. That is, it doesn't reveal that confidence and belief are actually separate mental states, and that our sub-certain confidence in claim X actually means that what we believe regarding the content of X isn’t X, and that belief is always certainty in the sense of an absence of doubt. It therefore also fails to reveal the falsity of Moon's conception of non-degreed belief as involving in itself a variable level of confidence in the believed claim.

The above issues with the previous arguments against degrees of belief partly explains why even awareness of the counterintuitive theory of non-degreed belief is low today, even among researchers in psychology and philosophy, and interest in it is even lower, and support for it is lower still. Regarding interest, there doesn’t seem to have been any experimental research into the theory. However, as I explained in chapter 1, the past absence of a good theoretical argument is ultimately much more an effect than a cause of the poor status of the theory within academia. That is, the more fundamental cause of its poor status is the combination of its counterintuitive nature and insufficient open-mindedness within academia. This has led most academics who’ve encountered it to not take it seriously, which has in turn resulted in academia not giving it sufficient attention to develop a good argument for it.

Why the certainty of belief matters

If Moon's theory of non-degreed belief were true, its replacement of the theory of degrees of belief wouldn't actually have any significant theoretical or practical implications, given that belief would still be considered to involve in itself a variable level of confidence in the believed claim. And it might be thought that the replacement of the theory of degrees of belief by the true theory of non-degreed belief also doesn't actually have any significant theoretical or practical implications. Again, whether we have certainty, in the sense of an absence of doubt, that there's sub-certain probability P that X, or a sub-certain degree of belief that X, we’re equally uncertain about X. And whether we have certainty, in the sense of an absence of doubt, that X, or the highest degree of belief that X, we have an absence of doubt about X. Also, the fact that the non-existence of degrees of belief isn't obvious to us might itself be assumed to imply that it has no significant practical implications. However, the replacement of the theory of degrees of belief by the true theory of non-degreed belief actually has profound implications for human psychology and therefore also our lives.

In the next chapter I show that, counterintuitively, the mere entrance of a claim into our mind, whether via reasoning, comprehension, imagination or recollection, causes us to believe it. If there were degrees of belief then our belief of a claim upon it entering our mind could at least sometimes have been an uncertain belief, and that uncertainty could have motivated us to investigate the truth of our new belief. And the same applies if Moon's conception of non-degreed belief were true. But the reality of the nature of belief means that we always believe the claim with certainty, in the sense of an absence of doubt, upon it entering our mind.

Also, I discovered that, as I'll show in later chapters, the certainty of belief and our extreme credulity together explain cognitive biases, which are universal biases in our reasoning. Since the early 1970s, researchers have discovered a large number of these biases. A Wikipedia page currently lists around two hundred of them, and the list keeps growing. I mentioned three of these biases in chapter 1: illusory superiority, confirmation bias and availability bias. Again, illusory superiority is our cognitive bias towards overestimating our qualities and abilities relative to those of other people. And confirmation bias is our cognitive bias towards interpreting, seeking and recalling information in a way that confirms, or helps to confirm, what we currently believe. And availability bias is our cognitive bias towards making a judgement on the basis of whichever relevant information happens to be most readily available to our mind, instead of suspending judgement until we’ve checked for other relevant information. Confirmation bias and availability bias permeate all reasoning. However, illusory superiority is specific to a particular type of reasoningjudging our qualities and abilities – however frequent such reasoning may be. Another example of a cognitive bias that's specific to a particular type of reasoning is hindsight bias, which is our bias towards judging that a past chain of events was objectively predictable. Cognitive biases account for all of our consistent reasoning errors – including our consistent mathematical and statistical errors, and those which occur when our reasoning is affected by our emotions – and so together account for the whole of human irrationality.

There are many theories about why cognitive biases exist. Some theories only concern a single cognitive bias, whereas others concern several. However, there are only three types of such theories.

One type states that a cognitive bias is the product, or a by-product, of a supposed cognitive heuristic, which is a rule-of-thumb reasoning shortcut that has become either hard-wired into our cognitive processes through evolution, or ingrained in those processes through learning. Cognitive heuristics develop in order to somewhat compensate for our cognitive limitations, which are due to our finite amount of processing power, information, and time, and to our imperfect information storage and retrieval processes. Evolved cognitive heuristics developed to counter these limitations in way that tended to be optimal in the ancestral environment in which we evolved, when we lived as hunter-gatherers, but which doesn't necessarily tend to be optimal in the modern world.

A second type of theory states that a cognitive bias is simply a direct manifestation of our cognitive limitations. And a third type of theory states that a cognitive bias is due to our reasoning being affected by a particular emotion.

The cognitive heuristics explanation for cognitive biases has been dominant since the first biases were identified. Jonathan Baron, a psychology professor at Pennsylvania University, subscribes to this explanation in his popular 2008 textbook on rationality, Thinking and Deciding, which, according to the blurb, is 'the required text and important reference work for students and scholars of human cognition and rationality'. Baron suggests that a cognitive heuristic can be responsible for multiple cognitive biases, but also states that ‘We have no good reason to expect a single account to apply to all [cognitive] biases that have been discovered’. However, although we indeed have no good reason to 'expect' such a single unifying explanation, we equally have no good reason to expect there not to be one. He points-out that cognitive biases '... were not discovered by looking for examples of any particular mechanism ...'. But what leads us to discover a natural phenomenon is irrelevant to its cause. He also points-out that cognitive biases '... could arise for many reasons'. But they equally could arise for the same reason.

And there are two good reasons to think that a single unifying explanation for cognitive biases is a reasonable possibility which should therefore be explored. First, all of the many different cognitive biases have one obvious but unique thing in common: they're cognitive biases. Second, a central theme in the history of science is the development of theories that can simultaneously explain apparently separate phenomena. For example, the 19th-century physicist James Clerk Maxwell showed that the apparently separate electric and magnetic fields actually form a single electromagnetic field, and it's now known that many different forms of radiation – including light, radio, X-ray, microwave, infrared and ultraviolet – are simply different wavelengths of ripples in the electromagnetic field. And in the same century the biologist Charles Darwin showed that the myriad different species of plants and animals that exist today are all the product of the same process – evolution by natural selection – and are the tips of the living branches of a single tree of life, with the tips of the dead branches being extinct species.

I'll show in later chapters that all cognitive biases are actually simply manifestations of the certainty of belief and our extreme credulity. And given that these two aspects of the psychology of belief are logically inevitable, for any form of intelligence, cognitive biases are simply logically inevitable aspects of the psychology of reasoning, for any form of intelligenceand are therefore not due, in our case, to the nature of the human brain. So the certainty of belief and our extreme credulity together provide a single unifying explanation for all cognitive biases, and therefore for the whole of human irrationality.

As I explained in chapter 1, given that belief is the centre of human psychology, the theories of the certainty of belief and our extreme credulity will together revolutionise the field of psychology, and therefore also have equally profound implications for every aspect of our lives.

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