Clear Language, Clear Mind

I noticed a small dissimilarity between the two words. As I have pointed out numerous times in the past, the phrase “I don’t believe that p” is ambiguous between belief in not-p and lack of belief in p. However the similar phrase for knowledge, “I don’t know that p” is not similarly ambiguous. It is however ambiguous in another way; between lack of belief in p and in not-p, and lack of knowledge that p.

For some reason some people get these wrong.

And so on for a great deal of other concrete entities. However for abstract objects it becomes more difficult to translate into believe-that phrases. Consider:

I believe in democracy

What are we to translate this into? Some ideas:

I believe that democracy is good

I believe that democracy is the best

Other examples include:

I believe in freedom of speech

I believe in myself

I believe in you (this does not mean anything similar to the above even though the phrases are quite similar, the object of belief is a personal pronoun)

I believe in love

Quote from The Web of Belief

“Rather, believing is a disposition that can linger latent and unobserved. It is a disposition to respond in certain ways when the appropriate issue arises. To believe that Hannibal crossed the Alps is to be disposed, among other things, to say “Yes” when asked. To believe that frozen foods will thaw on the table is to be disposed, among other things, to leave such foods on the table only when one wants them thawed.” (p. 6 in the online version.¹)

Main argument

One dispositional account of belief may seem to imply that we have an infinite number of beliefs. The reasoning goes like this: Suppose that if (if one is asked “Do you believe that P?”, then one is disposed to answer “Yes.”), then one holds a belief that P. So the disposition to answer “Yes” to such questions materially implies belief. If that’s true, then it could seem that such a dispositional account of belief implies an infinite number of beliefs in persons. It seems that regardless of what number n is, one will always answer in the affirmative to the question “n is a number”.

Some numbers are so large that it will take more than a life time to pronounce them therefore no question will ever be asked. This does not however disprove the material implication; it actually proves it. Recall that if the antecedent is false, then the implication is true.

The liar objection

One objection to m. implication is that one’s answering “Yes” to such a question does not imply belief in P because it is sometimes the case that one lies, and therefore there are cases where one answers “Yes” to believing something but does in fact not. It is easy to amend the implication to avoid this objection. Simply add a clause about sincerity: If one is disposed to answer sincerely “Yes” to the question “Do you believe P?”, then one believes P.

The brain objection

Beliefs are stored in the brain and they take up space. Moreover the brain is finite in size. Thus, an infinite number of beliefs would take up an infinite amount of space. Since there is not an infinite amount of space in the mind, then there is not an infinite number of beliefs stored in the brain. This holds for all humans, thus, no human holds an infinite number of beliefs.

This objection may seem forceful, but it is begging the question against the dispositional account. Basically it says that if this other brain-physical account of belief is true, then the dispositional account is false. That of course proves nothing since it would need the premise that the brain-physical account is true and that would be question begging.

There is often some confusion surrounding the terms: belief, disbelief, agreement and disagreement when used in a philosophical context. We need to keep in mind that normal dictionary definitions are often not precise enough to be used in a philosophical context where precision and clarity are essential. (For analytic philosophy.) In this article I will explain the terms ‘belief’ and ‘disbelief’, and ‘agreement’ and ‘disagreement’. Then I will suggest a new way to define the terms in the name of clarity.

Belief and disbelief

I’m not going into some advanced theory of how humans believe things. I’m merely going to the contrast between believing something and disbelieving something. The confusion lies not with the word ‘belief’ but with the word ‘disbelief’. Some take ‘disbelief’ to be a mere lack of belief in something. Others take ‘disbelief’ to be a belief in the negation of something. It is this latter meaning that is usually meant in philosophical context. Going by the normal meaning of ‘belief’ and the second meaning of ‘disbelief’ we should then be able to see that this is a false dichotomy; One does not either believe something or disbelieve in something. There is a third option, that is, that one has no belief at all on the matter.¹ Here’s a table that shows trichotomy along with a symbolic logic representation of the options:

Note: Replace ‘something’ in the table with some particular proposition. Philosophers usually just write p which is what I have done in the formalization to the right.

The confusion is often between row number two and row number three. Especially when the ambiguous phrase “I don’t believe that something” is used. Taken literally this phrase means the first part of the second row² but people usually mean the third row when they say it.

I suggest that, for the sake of clarity, that one ought to use “I believe something” to mean the first row, “I have no opinion about something” to mean the second row, and “I disbelieve in something” to mean the third row. To mean a lack of belief in something I suggest using the phrase “I have no belief that something”. Avoid using the phrase “I don’t believe that something” because it is ambiguous.

Agreement and disagreement

Having understood the above we can move on to the second part of this article. I suggest that we define agreement and disagreement in an analogous way to the above defined words. This means that to be in agreement about something with someone is to believe the something that the other person believes. To disagree with someone about something is to believe the negation of what the other person believes. Note that the common usage of ‘disagree’ is to merely not believe the something that the other person believes. I suggest that if one wants to say that one does not believe the something it is that the other person believes, then one ought to say “I don’t agree”. If one accepts this redefinition in the context of philosophy, then one should see that the dichotomy between agreeing and disagreeing is false. It is possible to not hold an opinion at all about something.

1I mean ‘the matter’ in a strict sense. Here’s an example. Suppose the matter is ‘one ought to vote for the republican party’. Then the matter is only that. Beliefs about whether one ought to vote or note, or to vote for the democratic party are not relevant.

2That one has no belief in something. [¬B(p)]

I was just discussing this over at FreeRatio.org. I made the claim, which seemed intuitively true to me, that knowledge (JTB+) is a kind of belief. This caused some controversy. I made this simple illustration clarify how I intuitively grasped the idea.

A flaw was discovered in the above. It implies (wrongly) that there are no true or justified things which one does not belief in. This is false. Here is an extended diagram: