What is a Belief? (Part 1: "Solving" Moore's Paradox)

a thought with the property of "true"

Consider the sentence:

“It is raining, but I don’t believe it is raining.”

At first read, this statement appears coherent. But what does it mean? If it conveys meaning, then what is it? If it has none, then it’s meaningless. But how could such a coherent sounding sentence be meaningless? This problem is known in philosophy as “Moore’s Paradox”.

Moore’s paradox (or “Moorean sentences”) arises when a proposition is said alongside a speaker’s belief that they don’t believe that very same proposition. Many have tried to resolve this paradox by shifting the context of each clause, either forcing coherence or dismissing the sentence as absurd (but not contradictory).¹ It should make sense, so it should be read in a way that makes sense (silly, but could still make sense). But forcing a meaning onto a sentence is clearly misguided.

Yet to understand the paradox, we need to know what a “belief” is. Once we do, we can see that Moore’s paradox is a straightforward contradiction, and its proposed “solutions” are just inserting meaning where none exists.

In summary, a belief is just a relationship between a thinker and a thought, where the thinker gives the property of “true” with respect to that thought. That thought doesn’t actually have to be true for the subject to believe that thought as so. So long as a thought is considered true, then it’s believed.

This article isn’t motivated by semantics. It’s not an exercise in definition-making solely for the sake of analytic philosophy; the concept of “belief” plays a broader role.

With a clear understanding of what “beliefs” are, we can take a peek at the relationship between “thoughts” and “truth.” You can’t understand “truth” without first understanding what a “belief” is. And we can’t yet understand the PSR's self-evidence without understanding truth itself, as these next few articles will make clear.

2 What is a Belief

To repeat, belief is a mental state in which a subject assigns a thought the property of “true.” When we believe, we, as thinkers, have " truth-giving” relationships with a thought, regardless of whether the thought is actually true. 

How much “truth” must a thinker assign to a thought for it to qualify as a belief? That depends on the standard of truth in a given context. It’s an annoying answer, but there is no objective amount of “truth,” we need to give to beliefs. Different situations have different “belief” confidence level requirements.

The fact that a subject assigns some degree of truth to a thought is enough for it to count as a belief in some contexts, depending on how the term “belief” is used.

Beliefs have two defining properties:

1. Mental State: A belief exists within the mind.

2. Truth Assignment: A belief attributes a truth value to a thought.

To preview this Substack, “truth” itself is grounded in reasons. However, we are still free to assign the property “true” to whatever thoughts we so desire. We can even believe every proposition, as trivialists do. We may not be able to give “reasons” for such truth properties when pressed by others, but we can still “believe” them nonetheless.

Beliefs don’t even need to be grounded in reasons. A belief without justification is still a belief. Just take a thought and add “true,” and you got a belief.

But I expect there are questions and hesitations about reducing beliefs to a subjective truth assignment onto thoughts (including partial or implicit truth assignments). Like any definition, we may believe this account to be too broad or too narrow, especially one that is foundational in philosophy as “beliefs.”

I’ll discuss the below potential objections (but more are welcomed in the comments):

1. Contradictory Beliefs: The fact that people can hold contradictory beliefs at the same time.

2. Assumptions: We can assume some thoughts to be true for certain purposes, without actually believing them to be true.

3. Degrees of Truth: A truth assignment does not have to be absolute; beliefs can exist along a spectrum of certainty.

4. Unconscious Beliefs: We can hold beliefs without them being in conscious thought.

But first, why is a belief a mental state about thoughts?

3 A Belief is a Mental State

It’s nearly self-evident that “beliefs” relate to internal mental states rather than external physical states. Beings without mental states can’t have beliefs.

We could ascribe beliefs to them based on their actions (e.g., anthropomorphization), but beliefs can only ever exist in the conscious mind. If a thing lacked consciousness, it couldn’t have beliefs.

Meanwhile, humans in mental states can have as many beliefs as possible. We don’t even have to act on our beliefs. Our internal beliefs and external actions can be completely out of line. 

We can sometimes ask, “What do you really believe?” because we understand that beliefs are internal and can be concealed. 

Some try to reduce beliefs to only external dispositions or actions. But this is deeply unintuitive and at odds with the term's common use. Defining a “belief” as something physical is more of a bullet the materialists are forced to bite, while the metaphysical stance I take here allows for the existence of mental states.

Moreover, “beliefs” are not with respect to reality itself, but with respect to our thoughts about reality. Reality is true by definition. It doesn’t need us assigning truth to it.

And we don’t need direct access to “reality” to have beliefs. Rather, as we have direct access to our “thoughts” (propositions, abstractions, forms, senses, etc.), these are the units to which we can assign truth values. Even brains in vats can have beliefs.

This is because, as I've discussed previously, our access to reality is mediated by “thoughts.” This lens of reality is in the form of beliefs that we take as true. These beliefs and truth values are always subject to change based on new information (at least, they should be). 

In sum, “beliefs” can be described as a “truth-giving” relationship between a thinker and a thought. But why is a belief truth-giving?

4.1 A Belief is a Truth-Assignment

Belief is inherently tied to truth. When we hold a belief, we assign a truth value to a thought—however justified or unjustified that assignment may be. An assertion of one’s belief and one’s truths are practically identical (the problem with Moore’s Paradox, to be discussed below).

Of all possible thoughts, only the ones taken are true can be beliefs. The mental states no one takes as true could not count as beliefs for anyone.

And because certain true things cannot be true along with other true things (i.e., there are no true contradictions), there are sets of beliefs that have contradictions. And people can hold these sets of contradictory beliefs, which is how we are able to describe some people as irrational, as we’ll now turn to.

4.2 The Role of Contradiction in Beliefs

Take a vegan activist who believes that consuming animals is unethical but finds nothing unethical about himself eating meat.

In fact, some might even defend this vegan activist on utilitarian grounds. If the negative effects of his meat-eating are outweighed by the lessened animal suffering from his activism (and he would only be a vegan activist if he could still eat meat), then the utilitarian could have no critique.

Yet, from a reason-based standpoint, we could still criticize the activist for bad reasoning. It's illogical to hold two inconsistent beliefs in mind. The vegan activist can be reprimanded as unreasonable, rather than immoral.

However, hypocrisy isn’t the only way we can be irrational; human cognition has its limits. We might hold certain beliefs that we aren’t even aware don’t go together. Instead of trying to force coherence into our beliefs, we should accept that they are sometimes illogical and revise our belief set accordingly.

However, sometimes, it’s rational to hold inconsistent beliefs. We don’t routinely update our knowledge to remove contradictions. Reconciling our internal inconsistencies may require too much effort. So, at times, our beliefs can be contradictory without us noticing.

The limitation of human cognition gives context for our irrationality. But it doesn’t make certain contradictory beliefs any less contradictory. We can spot the contradiction objectively without assuming blame.

4.2 Belief vs. Assumption

Sometimes, we just “assume” certain things to be true without actually believing them. But these wouldn’t be “beliefs " but “assumptions.” We don’t need to believe our assumptions. 

We can assume something is true without actually believing it.

For example, a lawyer representing a guilty client would still assume that his client’s innocence when he speaks to the court. 

A moviegoer would describe events in a movie, on the assumption that they happened, without believing that they really did.

And we may assume certain religious myths as true during religious events, regardless of whether we actually take these myths to be true.

How we act on the outside may not reflect what we truly believe. To qualify as a belief, the truth assignment must be genuine, rather than purposeful. And we’re free to act in a way that doesn’t reveal our true beliefs.

This is the problem with Eric Schwitzgebel's “dispositional” view of beliefs. Humans can hold and play with certain ideas without accepting their truth. Beliefs exist only in the mind and don’t have to align with actions. Our dispositions don’t necessarily determine our beliefs. 

4.3 Degrees of Truth

Truth assignments aren’t binary. In fact, we can give beliefs degrees of truth. Probabilities represent just this. We can still believe things to be true and have different confidence levels.

And we can also believe things with certainty. Analytic truths like 1+1=2 could be true with maximum confidence. Meanwhile, synthetic truths (i.e., “truths about the world”) may carry a lower degree of certainty depending on the probability assignment.

We can make statements of beliefs about events in the world like, “It will rain today,” “My Amazon delivery will arrive by 9pm,” and “There will be heavy traffic into the city today,” with different confidence levels based on relevant circumstances.

Truth as probability confidence isn’t new. It was notably discussed by Frank Ramsey’s “Truth and Probability” back in 1926, referred to as “degrees of belief.”

And our level of confidence would vary based on the relevant facts and circumstances.

If I don't care too much about making the bus, I could say, “I believe the bus will come at 5:00 p.m.,” based on my review of bus schedules from some months prior. 

But if I have an important flight to catch, I could still say, “I can’t say that I believe the bus will come at 5:00 p.m., so I should look at the latest schedule before I believe anything.”

Probability is a massive topic, as is only being discussed in passing here.² Yet, as long as we understand probability as subjective confidence levels rather than objective entities, we can see how this definition accommodates beliefs of different degrees.

4.4 Unconscious Beliefs

Another possible challenge is whether unconscious beliefs could still count as beliefs.

In short, yes. Beliefs don’t have to be immediately present in working memory. We can be ascribed beliefs that are in our long-term memory. Most of our beliefs are “stored” in long term memory.

Consider someone who grew up in a community where cooperation was highly valued. Even if they never consciously reflect on this fact, they might unconsciously hold the belief that "people are generally trustworthy and willing to help one another." This belief, while stored in their long-term memory, nonetheless influences their behavior (being cooperative, honoring contracts, being polite, etc) even though they're not actively thinking, "I believe people are trustworthy." In this case, the belief exists unconsciously, yet it still guides their actions and judgments.

It doesn’t matter whether a belief is in our conscious or unconscious minds. So long as they contain a positive truth value for a subject, they count as beliefs.

5 Understanding Moore’s Paradox

Now that we have a definition of “belief,” we can return to Moore’s paradox.

"It is raining, but I don’t believe it is raining."

On initial review, while both prongs appear contradictory, they still seem consistent. Yet once we apply the above definition of “belief,” we can see the contradiction more clearly.

Now let’s remember that “truth” qualifiers to statements are useless (as discussed in my article on the Liar’s Paradox). In language, adding “truth” as a property to a proposition would not change its meaning.

"Snow is white,” and “It is true that snow is white” both mean the same thing (see the deflationist theory of truth).

Just prefacing all of our statements with “It is true that,” would be totally redundant.

So “it is true that it is raining,” has the same meaning as “it is raining.”

And because a belief assigns “truth” to a proposition, statements of belief and of propositions are logically equivalent.

So “I believe that it is raining” = “It is true that it is raining” = “It is raining.”

Therefore, if you say that it is raining, you must also believe that it is raining (“belief doesn’t include assumptions, as discussed above”).

See the below to clarify. Let’s label each clause of the statement of: "It is raining” as P (as in proposition) and “I don’t believe it is raining” as B (as in belief).

1. Moorean sentences state B and P.

2. P’s meaning is equivalent to “It is true that P.”

3. B is equivalent to “It is not true that P.”

4. Moorean sentences state both “It is true that P” and “It is not true that P” (or both P and -P)

5. If a statement contains a contradiction (both P and -P), then the statement is meaningless.

6. Therefore, because Moorean sentences that both P and -P, Moorean sentences are meaningless.

Moore’s paradox has been nonsense this whole time.

“Solutions” to Moore’s paradox have been all over the place. Some interpret the statement in entirely different ways or find it to be merely absurd rather than straightforward contradictions.

Yet the fact that the meaning of a Moorean sentence is so subjective, such that no one can agree to it, is proof of its subjectivity. Moorean sentences fail to convey a thought on account of contradiction. As discussed previously, contradictions have no objective meaning since their language can only be private.

If everyone has a different, subjective, interpretation of what a statement means, then the statement doesn’t convey a thought. It lacks an objective mind-independent meaning, making the statement meaningless. It’s not an intelligible thought.

However, like the Liar’s Paradox, it only takes a bit of analysis to see the contradiction clearly.

6 Implications

“Beliefs” help explain the relationship between our minds and truth. As skeptics rightly point out, we don’t have direct access to truth. There is no “truth” label on things in the world. Rather, our minds assign truth using beliefs and we decide what beliefs to have (and at what degree of confidence) using reasons.

Explaining what “ beliefs” mean may seem like a pedantic exercise in analytic philosophy, as everyone just knows what a belief is. But a clear definition is vital for a systemic philosophy and a proper understanding of truth.

Of course, our beliefs aren’t directed at the world but at thoughts or “propositions,” those non-spatial, non-causal, non-temporal entities whose existence is self-evident, as I’ve discussed here.

Our model of truth is built with thoughts that we label with “truth,” and we use “reasons” to make these assignments. As reasons and evidence shape our beliefs, our beliefs can be subject to rational inquiry.

The next articles will spell out more clearly the relationship between reasons, beliefs, and truth. But if anything is unclear, do not hesitate to raise it or else criticize it. A philosophy is only as strong as its foundations and the definition of “belief” is an important part of that foundation.

Conclusion

A belief is nothing more than a thought that a subject assigns the property of “true.” Under this definition, any sentence that contradicts its own truth assignment—such as a Moorean sentence—is inherently meaningless. And with this definition, we can see how truth is something our minds impose on thoughts.

As we continue to explore how beliefs ground objective truth, we must base our analysis on clear definitions and logical consistency, including an analytically true definition of “beliefs.”

1. See Green, Mitchell S., and John N. Williams, eds. 2007. Moore's Paradox: New Essays on Belief, Rationality, and the First Person. Oxford: Oxford University Press, for arguments on the nature of Moore’s paradox. See a few examples of philosophers’ thoughts on Moore’s paradox, here, here, and here.

2. See Pearl, Judea, and Dana Mackenzie. The Book of Why: The New Science of Cause and Effect. Basic Books, 2018 and Clayton, Aubrey. Bernoulli’s Fallacy: Statistical Illogic and the Crisis of Modern Science. Oxford University Press, 2018 for a discussion on the nature of probability.