We express our beliefs through language. Of course, we can also express them through our behavior, but lanaguage is another form of behavior.

Generally speaking, the later Wittgenstein questioned the claim that a belief is an inner mental state.

This is very brief and don't know if any of the above provides helpful clues. Have to get ready for work.

But this doesn't work. Like Kennethamy said, numbers are not numerals; numerals are names of numbers. I will logically prove to you that numbers are not words by a Reductio ad Absurdum argument--that is by supposing that numbers are, in fact, words.

So let's just suppose numbers are words, for the sake of argument, just like you say. Here are some words.

"Bob" is a word--it's a name.

"red" is a word--it's a predicate.

"with" is a word--it's a preposition.

"I" is a word--it's a personal pronoun.

"eat" is a word--it's a verb.

So what kind of word is a number? What else but a name? It doesn't seem to be a predicate, or verb, or a preposition. It seem to be a noun. But all nouns purport to designate an object, or a set objects. And all names, a kind of noun, actually do designate an object, one and only one object at at time. But let's just suppose numbers are not names at all, but merely some unqualified noun or other word.

Here are different instances of the same word mentioned in the quotes: "1."

"1"
"1"
"1"

How many times does the word "1" occur?

The answer is once, because I mentioned the same word three times by using the *quotes*. So suppose,

1<4
1>0
1=1

How many times does the word "1" occur? The answer is four times because I used the word four times.

So let's suppose instead of mentioning the word "1," I decide to use the word instead, when I express addition or equality, as in.

1+1=2

How many times did the same word occur in my use of it here? The answer is twice, because I used it twice.

But wait, now we have the word "2" used here as well. So how many times does the word "2" occur in my use of the word "2" in the expression of this equality? The answer is once.

So how is it that my using the same word twice equal my using the other word once?

It cannot since, if numbers were words, then

1+1=2

would be false,

because I am using, not mentioning, the words in the equality expressed, just as I am using, not mentioning, the equality expressed.

But 1+1=2 is true.

Therefore, numbers are not words.

Q. E. D.

*Further, we can prove the same result with the use/mention distiction in the philosophy of language to prove that numbers cannot be concepts or meanings, or actual physical things either. So numbers can only be abstract entities that don't physically exist, but must exist abstractly.

Thanks for trying, but this hasn't cleared up my difficulty. I don't find your use/mention distinction persuasive. Clearly I don't know what you know about these things. But now I'm aware of some things I wasn't before, so thanks again.

I wonder whether you read my post #676. It cites a Website you ought to find instructive.

You can, I suppose, see a difference between saying that the numeral "one" has three letters, and saying that the number one is odd. But that the numeral "one" is not odd, and the number one does not have three letters. If you cannot, then you don't see the difference between use and mention.

Thanks for thinking to post the link. I can understand the distinction between use and mention, but I don't find it helpful for my purposes.

What are your purposes?

By that I mean the things I am interested in. Analytic philosophy does not much interest me, though I have been learning some things about it on this forum. Different things resonate differently with different people.

I also am curious. What, I wonder, do you (or others who say your sort of thing) think that philosophy is all about? Not, I hope, resonance.

I wouldn't give this as a hard and fast definition, but I think it fair to say philosophy is about resonance.

Thanks for trying, but this hasn't cleared up my difficulty. I don't find your use/mention distinction persuasive. Clearly I don't know what you know about these things. But now I'm aware of some things I wasn't before, so thanks again.

Careful. If he does know, then it does matter. I'm not saying he does know. He doesn't. But, that's not my point. The point is that if he does know, then what he knows is true, for if one knows P, then P is true.

Thanks. But no, that doesnt' help at all.

Let me make this clear that I am not picking at you. I'm picking at Hacker, since you are having trouble giving me a straight answer to a simple question. Is my act of believing the same as what I believe or is what I believe the object of my belief distinct from my act of believing that thing?

I am not criticizing you here--but let me just say that I really get frustrated at those actual philosophers in the field at large who can't give me a straight answer to what it is they actually think....because it usually means they are holding an implicit assumption they don't want to reveal because it is typically deeply counterintuitive in some way....the dialogue becomes a bit of a wash because pragmatists will do the same stuff when you ask them really simple questions: they just skirt the question altogether....It's a kind of cognitive dissonance in the face of important questions.

To be honest I am not sure I understand your question.

If I say, "My son is over at Joe's house" most likely I am expressing my belief that my son is at that location..

After all, he told me he was going there and he usually tells the truth. But I don't think "my son is over at Joe's house' is the object of my belief.

If I believe you, then you would be the object of my belief. But that is only one use of the word 'belief'.

We often append the word 'believe' to assertions in order to indicate that we recognize that there may be some reasons for rejecting what is asserted.

I don't quite understad why you want to make it either an act or an object.

Again, so what? What reason do you have for NOT thinking it is not necessarily false. Can you give me reason? Because I have just shown that it IS necessarily false.

No, you have show that it's false. That is different.

Exactly. Stop right there. This is precisely the point I am making. You simultanesouly do two things. You deny all relational accounts of propositional-cognitive attitudes are correct based on a few substitution failures for "hoping that" or "expecting that" or "fearing that." And then in the same breath you claim you don't understand what cognitive relations to anything would look like in the first place? So how do you know what exactly it is you are pretending to refute in all relational accounts of propositional attitudes to begin with if you don't understand what a relation is? After all, you explicitly claim that no one hopes a proposition, nor fears a proposition, nor expects a proposition. So you obviously are working on some kind of implict defnition of your understanding of what that relation is that is allegedly thought to hold between two disparate objects. So your moves are just being duplicitous at their core. I feel like the discussion hasn't even started yet.

No, you haven't shown that it is necessarily false. What you have shown is that it's false. Here, I'll present it differently. Consider the following propositions (where p is words are numbers):

P1: you have shown that p is false.
P2: you have shown that p is necessarily false.

I believe that P1 is true, and you believe that P1 is true, so we both believe that p is false.

However, even though you believe P2 is true, I do not. So, not only do you believe that P1 is true (just like me), you also believe P2 is true (unlike me).