Does this analogy about translations illuminate, or obfuscate, the nature of belief?

Question

I'm engaged in a discussion with somebody about the nature of belief. I've been arguing that belief is an attitude toward a proposition, and that in order to believe something, you necessarily have to have some concept of the proposition in mind(whether consciously or not). He disagrees(!), however, and believes that its possible to believe something without having any concept of the proposition at all. The example he gave me was of a trusted friend who can write in a foreign language(let's say arabic) and that upon asking him to write a true statement in arabic, you end up believing the proposition written in arabic to be true. This is a terrible analogy of course, you're really believing B about A, rather than A itself. I'm having a hard time of convincing him of this however, as he's stubborn and intellectually naive. any suggestions?

Answer 1

Let us say that the Arabic sentence in question is S, and that the proposition expressed by that sentence is p. Your friend is equivocating between

• the belief that the proposition expressed by S is true

and

• the belief that p

They are different: you can have the former belief without having the latter, and you can have the latter belief without having the former.

One way to see that you can have the former without the latter: suppose that p is the proposition expressed in English by the sentence "the Earth is round". The beliefs that the proposition expressed by S is true, and that the Earth is flat, are not contradictory. The beliefs that the Earth is round and that the Earth is flat are.

You can have the latter without the former, for example, if you have never encountered S.

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What about the following objection:

If you believe that the proposition expressed by S is true, then you must believe that p. This is so because, first, that the proposition expressed by S is true implies that p; and because, second, if you believe A and A implies B, you therefore believe B.

To begin with, the second premise in this argument is false: One can believe all of the Peano axioms, and these axioms jointly imply all of the truths of arithmetic. This doesn't make one arithmetically omniscient.

Apart from false, the second premise is also irrelevant: that the proposition expressed by S is true does not imply p in the logical sense. S could have expressed a different proposition.

Answer 2

I've been arguing that belief is an attitude toward a proposition,

That's not necessarily the case, as your friend has pointed out. One can have a belief in the general trustworthiness of a person, and thus be inclined to believe any future propositions made by that person, without any regard to the propositions in question.

However, this is still operating at the level of folk epistemology. If you want to move this discussion to a more properly philosophical domain, you're going to have to make reference to a particular epistemological school of thought.

Answer 3

Belief in the fact X is a probability assessment that roughly corresponds to your willingness to bet money on X being true.

This is the Bayesian definition of belief. It furthermore says that if you observe X false, you should adjust your probability downwards (not discard the belief as Popperian epistemology would have you think), since you might have read the measurement apparatus wrong, or you might have another chance to observe the phenomenon in the future. Correspondingly if you observe X being true, you increase your probability assessment.

Now note from this definition that a belief can be useful: It lets you anticipate things. If you believe that a certain racehorse is quicker than another, you can bet on that racehorse, and if your are right, you win money. This should motivate you to create true beliefs.

The thing about humans is that we are not perfect Bayesians, and so we have some weird behaviours. For example we can believe that a belief is beneficial in itself and not because of predictions. Also many people tend to conflate reasons why it is beneficial to believe something and reasons why the belief is true.

Answer 4

The root of the paradox in your analogy is essentially the same as in Gödel's first incompleteness theorem — not that your paradox is equivalent to it, but in that both are seeming paradoxes involving encodings of propositions.

The crux is that if you were to write down a proposition P in English — and call that written expression e — then you don't believe e; you believe the proposition encoded in e. And if you were to express P in speech, that would be a different encoding e'. You may decode such encodings reflexively, but it is indeed a process performed by reflex, and this is what we mean by the meaning of a piece of written or spoken language; the attributing of propositions to these expressions. In the case of writing and speaking, there is a recognized way of translating between the two encodings: for instance, transcription and reading aloud. But these are translations rather than decodings, and the encodings are not the propositions.

Similarly, if your friend expresses the proposition P by something written in Arabic a, you don't believe a; you believe the proposition expressed by a — although only by accident, or rather because you trust that a is an encoding of a proposition (it doesn't matter which) that you believe in anyway, because you lack the ability to decode a, either directly or by computation to obtain a hopefully-equivalent expression e in English.

In this case the problem is precisely that we are ignoring the representation of the proposition, which is pertinent. Analogously, we have in Gödel's Incompleteness theorem a proposition P, which is of the form

P  :=  p is an integer ⟨which is a Gödel encoding of a proposition⟩ is not contained in the recursive set T ⟨consisting of those integers which encode theorems⟩

where it turns out that p is the Gödel encoding of P itself. Within the formal system S expressing P, the proposition is true only if S is consistent. From an external formal system T, we can prove P — which is why it's called an Incompleteness Theorem — because the external formal system can explicitly incorporate the fact that the logical structure of S can be encoded in number theory, so that propositions about integers are on the same logical level as propositions about P ∈ S. But the integer p is not itself a logical proposition, which is true or false; it is an encoding of a proposition. And in the meta-theory T, P ∈ S isn't a proposition either; it is an object within a mathematical structure, just as p is, and in T we have a specification of an isomorphism between S and a sturcture of the natural numbers.

In this case, however much you may think to yourself in your native or adoptive languages, English and Arabic are not the languages of evaluating truth or falsehood, but rather more-or-less formalized systems for encoding truth or falsehood, in which it may be easier to arrive at logical conclusions; and you encode and decode propositions from those languages to some mental model in which you evaluate propositions as either true or false. The encodings and decodings to and from various languages are more or less like recursive predicates E and A on the expressions e, e' in English and a, a' in Arabic repectively, where if you are skilled there is a truth-preserving and reversible map t such that E(t(a)) ≡ A(a). But unless you have been taught how to evaluate A, you will be unable to evaluate any expression a of a proposition in Arabic as true; you will only be able to evaluate

• F is a trustworthy friend who is able to perform meaning-preserving translations between English and Arabic;

• F knows you well enough to know one or more expressions e in English which will correspond to propositions you believe in;

• a is what F produced as an Arabic translation of some proposition e that you believe in.

On the strength of this, you can believe that a is an expression in Arabic of a proposition that you believe in; though you cannot confirm this directly, as you do not know which proposition a expresses.

Answer 5

I work in a quite technical field, that my wife knows nothing about. When I am trying to explain something that happened at work that day that involves something technical, there's two ways I can approach it:

1) I can try to explain to her the basics around what happened, which I will do when it is fairly simple or close to something I can easily analogise.

2) I can give her some absolutes to work from that explain the situation I am in without imparting an understanding of the underlying tech.

When I do 1) she understands the issues, and hence believes the conclusions that I lead her to. When I do 2) she agrees to just "take it on faith" because she trusts my knowledge of the area. "Taking it on faith" is very different from "believing" it (as we are using the terms here), even if religion has merged the two to mean the same for its own purposes.

I guess I do the same when reading about quantum physics break-throughs and similar. There's a lot I need to accept without understanding to understand the stories. When I later learn enough to fill the gaps, I gain belief.

Answer 6

I can speak Chinese by imitatation. I can speak the Chinese with full conviction that it is the right thing to say, for whatever reason. I couldn't know if I believe any of what the meaning of the Chinese was, unless I understood it

So I don't believe the Chinese , I believe it's the right Chinese to say. Likewise, in the analogy, he doesn't believe the statements meaning, he believes the trusted friend wrote down a true statement, and he's not aware of the meaning of the statement.

He requires the concept of a trusted friend, and that the trusted friend wrote down a true statement, so effectively the analogy is just more evidence that you must have a concept of the belief in order to believe it.

A better argument might be when you look at multiple personality disorder, does the person believe their name is x or y? In the case , the same person believe 2 contradicting things, depending on the time of the day(for example), and for no rational reasons, and you can wonder if at any split second point in time, did the person believe their name changed, before they conceptualized it.

Answer 7

Beliefs are the statements that need no proof. In other words, basic statements. Of course, we need some beliefs, because there are some statements we must take for granted (for example, the statements that are proving something, and the concept of truth and false themselves).

Do we need some concept of what we believe in? Yes, of course. But there is the word 'some' in your statement. Taking it literary, 'some' is anything of concept, no matter how small. To say if you believe in something or not, you must be able to say something about that object. The mind is bound to its own categories, and as Kant have stated, it's impossible to think about something that is out of this categories (absolute nothingness, for example). So, if you can think about something, you HAVE some concept of it (this is, it fits to some categories of your mind).

Let's say, do you believe that dkjafdioe fdjoiwefof? You can't, because you have no idea what is dkjafdioe and what means fdjoiwefof. But you can believe that there are fdafdas on the bubu. You can, because you have some concept what are fdafdas (some objects) and the bubu (some place).

Answer 8

I think the problem lies with the term "some concept". It is not well defined.

As an example, you could believe in a second proof for Fermat's Last Theorem (a famous math problem).

Now some concept of that depends on a lot on what you mean by concept and by some. Does it mean you know a lot about math and have a sketchy idea about how that proof should look like? Is that what you mean by concept? Or is it more? Or less?

It seems clear that the definition of concept and some depends on the example too, so that makes it harder to define.

And what is "some"? you understand 40%? or 90%? And then again how do you define understanding something x% objectively?

Also if your understanding of the subject changes, does your believe change?

What is "some concept" of god? What is "some concept" of reality?