(2) Wittgenstein doesn't speak for mathematics anyway. Whatever Wittgenstein wrote, it wouldn't change that fact that mathematics does not define 'infinite' as 'finite', which would be utterly ridiculous, as mathematics defines 'infinite' as 'not finite'. — TonesInDeepFreeze

You don't seem to know anything about Wittgenstein anyway from your posts. Wittgenstein's whole philosophy is about mathematics and grammar. He was also a student of Russell too, and both were deeply into mathematics and logic.

You are the one who is intellectually incompetent and ignorant, because you just keep on writing disinformation in your posts without even checking it. Just Google Wittgenstein on Math, and Wittgenstein on Infinity. It will list the whole loads of academic articles on the topic. And I am quoting one of them here.

"Abstract
The aim of this paper is to give an overview of Wittgenstein’s conception of the infinite. One focus of the paper is Wittgenstein’s rejection of what is dubbed a ‘realist’ model of our idea of the infinite. On this model our idea is the source of beliefs that we have about an independent reality. Another focus is the way in which Wittgenstein’s rejection of this model leads him to reject the idea of the infinite itself as it appears in certain mathematical contexts. I argue that these two rejections can be uncoupled: abandonment of the realist model of our idea of the infinite is consonant with full endorsement of the use to which mathematicians put the idea. There remains scope for Wittgenstein to take issue, if not with the use to which mathematicians put the idea, then with their choice of language in doing so, something that he has reason to do precisely because this choice encourages adoption of the realist model." - Wittgenstein and Infinity, by Andrew W. Moore

"Rejection of Different Infinite Cardinalities: Given the non-existence of infinite mathematical extensions, Wittgenstein rejects the standard interpretation of Cantor's diagonal proof as a proof of infinite sets of greater and lesser cardinalities." - SEP, Wittgenstein's Philosophy of Mathematics

Whether one tries to uncouple the idea or not, it was clear that W. had rejected the concept of infinity. Infinite in mathematics means "finite". Hence their discussion will end.

So what? It doesn't say that mathematics takes 'infinite' to mean 'finite'. And even if it did (which it does not), it doesn't represent mathematics or mathematicians, since they very certainly do NOT take 'infinite' to mean 'finite'. — TonesInDeepFreeze

It was just to let you know it was what Wittgenstein was saying, and he was a great philosopher of language, logic and mathematics.

You misunderstood. It meant that Wittgenstein said that mathematician's infinite means finite in his writings. — Corvus

You said that mathematics regards 'infinite' to mean 'not finite'. You didn't say anything about Wittgenstein there. If by saying that mathematics takes 'infinite' to mean 'not finite' you actually mean something different, such as that Wittgenstein notes that mathematical discussions are finite, then you need to write that and not that mathematics takes 'infinite' to mean 'not finite' and not to then blame readers for your error.

Moreover, I don't opine on what Wittgenstein meant in that quote of him, but at least, at face value, saying that discussions are finite is not the same as saying that mathematicians mean 'finite' when they write 'infinite'.

It's clear that the subject of "mathematician's discussions of the infinite are clearly finite discussions" is mathematician's discussions of the infinite, and not the infinite. Bolding, to display the distinction.
— Banno

Set your understanding out, or retract. — Banno

Please do some searches and reading on Wittgenstein's infinity.

You said that mathematics regards 'infinite' to mean 'not finite'. You didn't say anything about Wittgenstein there. If by saying that mathematics takes 'infinite' to mean 'not finite' you actually mean something different, such as that Wittgenstein notes that mathematical discussions are finite, then you need to write that and not that mathematics takes 'infinite' to mean 'not finite' and not to then blame readers for your error.

Moreover, I don't opine what Wittgenstein meant in that quote of him, but at least, at face value, saying that discussions are finite is not the same as saying that mathematicians mean 'finite' when they write 'infinite'. — TonesInDeepFreeze

I thought when I said that you would know whom I was referring to.

I asked for the textbook definition for infinite in math. — Corvus

And I gave it to you! In detail. With clear, exact explanation.

Again, if I list for you the titles and authors of the many textbooks that are currently standard, even quintessential references in the subject, will you finally admit that you are incorrect in the ridiculous claim that in mathematics 'infinite' means 'finite?

It was Frege, Russell, Quine who had reservations on it even if didn't oppose to it. — Corvus

I addressed that. You SKIPPED it.

If you have something to say specific about those mathematicians/philsophers, then please say what it is.

"Let us not forget: mathematician's discussions of the infinite are clearly finite discussions. By which I mean, they come to an end." - Philosophical grammar, p483. Wittgenstein.
— Corvus
Wasn't he saying clearly mathematician's infinite are finite? — Corvus

If he's saying that there, then he's definitely not "clearly" saying it. I don't claim to know what he is driving at. But at least at face value, the sentence does not read to be saying that in mathematics 'infinite' is taken to mean 'finite'. But you're free to provide more context and analysis to justify your interpretation.

So which discussion is not finite in that case? — Corvus

What? Are you trolling?

Banno didn't say that discussions are not finite. He is saying that "discussions are finite" doesn't mean that mathematics takes 'infinite' to mean finite'.

It was Frege, Russell, Quine who had reservations on it even if didn't oppose to it.
— Corvus

I addressed that. You SKIPPED it. — TonesInDeepFreeze

It was me who addressed at the very first, which was ignored.
I addressed it again. I still have the details of the reasons somewhere.

If you have something to say specific about those mathematicians/philsophers, then please say what it is. — TonesInDeepFreeze

I don't. I have been just responding to your posts making my points.

It is not just mathematician's discussions which end. All discussions end. That is too obvious.

What Wittgenstein must have meant was the concept of infinity in mathematics. — Corvus

That might be the case. That might be part of Wittgenstein's argument against the notion of infinity. I don't know. But even if it is, it still is not saying, at least at face value, that mathematics regards 'infinite' to mean 'finite'.

What? Are you trolling? — TonesInDeepFreeze

No time for that. You just call anyone trolling if you haven't understood something?

Banno didn't say that discussions are not finite. He is saying that "discussions are finite" doesn't mean that "mathematics takes 'infinite' to mean finite'. — TonesInDeepFreeze

He seemed to be saying discussions are finite, and all discussions end. What he seems to be saying was that it has nothing to do with mathematics infinity. I didn't agree with that. I will read him again. Are you speaking for him too?

That might be the case. That might be part of Wittgenstein's argument against the notion of infinity. I don't know. But even if it is, it still is not saying, at least at face value, that mathematics regards 'infinite' to mean 'finite'. — TonesInDeepFreeze

To me, it was clear that Wittgenstein meant infinite in mathematics means finite, hence mathematician's discussions will end. - He denies the concept of infinity in mathematics.

Banno said, it is nothing to do with the infinity in mathematics, but mathematician's discussions will end, like all discussions. I thought that was nonsense.

I have.

I’ve addressed your post and comments directly.

More misrepresentation. Pathetic.

You don't seem to know anything about Wittgenstein anyway from your posts. — Corvus

I haven't made any claims about him, other than that, at least at face value, "discussions are finite" does not mean that mathematics regards 'infinite' as meaning 'finite'.

He was also a student of Russell too, and both were deeply into mathematics and logic. — Corvus

So what?

As I said, Wittgenstein does not speak for mathematics. Mathematics speaks for itself when it defines 'infinite' as 'not finite' and not, ridiculously 'finite'.

you just keep on writing disinformation in your posts without even checking it — Corvus

You've not shown any disinformation in what I posted.

it was clear that W. had rejected the concept of infinity — Corvus

That doesn't entail that in mathematics 'infinite' means 'finite'. What in all creation is wrong with you?

Infinite in mathematics means "finite". Hence their discussion will end. — Corvus

You are claiming again that in mathematics 'infinite' means 'finite'.

You have a bizarre idea that because Wittgenstein was critical of the notion of infinity in mathematics that therefore mathematics takes 'infinite' to mean 'finite'. Amazing.

↪Corvus I have.

I’ve addressed your post and comments directly.

↪Corvus More misrepresentation. Pathetic. — Banno

Your claim was out of point from the start, because you see the discussion in the quote as discussion in talking. It is the concept of infinity in Mathematics he was meaning, which doesn't exist, hence not speakable and is meaningless. If you are still hanging on that "discussion" and make song and dance about it, you are not in the game.

I haven't made any claims about him, other than that, at least at face value, "discussions are finite" does not mean that mathematics regards 'infinite' as meaning 'finite'.

He was also a student of Russell too, and both were deeply into mathematics and logic.
— Corvus

So what? — TonesInDeepFreeze

You sounded as if Wittgenstein was irrelevant in math. That sounded not intelligent or read in philosophy.

Infinite in mathematics means "finite". Hence their discussion will end.
— Corvus

You are claiming again that in mathematics 'infinite' means 'finite'. Amazing. — TonesInDeepFreeze

You keep misunderstanding which was the part of the main problem here. It was said by Wittgenstein, and I just used his sayings to support my own point.

it was clear that W. had rejected the concept of infinity
— Corvus

That doesn't entail that in mathematics 'infinite' means 'finite'. What in all creation is wrong with you? — TonesInDeepFreeze

You better ask Wittgenstein what he meant by that. I have my own point. What with you?

So what? It doesn't say that mathematics takes 'infinite' to mean 'finite'. And even if it did (which it does not), it doesn't represent mathematics or mathematicians, since they very certainly do NOT take 'infinite' to mean 'finite'.
— TonesInDeepFreeze
It was just to let you know it was what Wittgenstein was saying, and he was a great philosopher of language, logic and mathematics. — Corvus

First, you said that mathematics takes 'infinite' to mean 'finite'. You didn't say anything about Wittgenstein there. Then, you said that you expected me to infer that you meant Wittgenstein, though there was no hint even about him there. Then, you mentioned a post in another thread where you quoted Wittgenstein commenting that discussions about infinity are finite. While, it may be that he meant that as part of his argument against the notion of infinity, at least at face value, it is not an assertion that mathematics regards 'infinite' to mean 'finite'. Finally, even if that was what he meant, he does not speak for mathematics, which speaks for itself when it defined 'infinite' as 'not finite, and not ludicrously as 'finite'.

And then your quoting of Chat GPT as part of your bizarrely specious attempt to dispute my explanation of how mathematics actually does define 'infinite'.

And your really foolish dispute against the fact that modern, current, authoritative, standard and widely referenced textbooks in the main areas of mathematics define 'infinite' as 'not finite'.

And that's all just recent posting by you, not mentioning all the other garbage you've posted in this thread and at least another.

And that's all just recent posting by you, not mentioning all the other garbage you've posted in this thread and at least another. — TonesInDeepFreeze

You don't seem to even know who said what, and what was whose points, and just get into ad hominem all the time. Would you say your postings are high standard? Read them yourself. They are full of disrespects to the others. You don't even know what Wittgenstein was up to. If you thought he had little to do with math, then it tells you where you are in the discussions.

it was clear that W. had rejected the concept of infinity
— Corvus

That doesn't entail that in mathematics 'infinite' means 'finite'. What in all creation is wrong with you?
— TonesInDeepFreeze
You better ask Wittgenstein what he meant by that. I have my own point. What with you? — Corvus

You are amazing!

You said that mathematics takes 'infinite' to mean 'finite'. Then you said that actually you meant that Wittgenstein said that. Then when you are offered that you can provide any context or explanation to support that, you say that I should I should ask Wittgenstein rather than indeed, you providing an argument that when Wittgenstein said that discussions about infinity are finite, he implied that mathematics takes 'infinite' to mean 'finite'. And then you totally reversed to say as much as that whatever Wittgenstein's point is, you have your own point. So which of these things that you've already said not is that you mean?:

(1) Mathematics regards 'infinite' as meaning 'finite'.

(2) Wittgenstein implies that mathematics regards 'infinite' as meaning 'finite' and you agree with that.

(3) Maybe Wittgenstein did not imply that mathematics regards 'infinite as meaning 'finite', but that you do claim that mathematics regards 'infinite' as meaning 'finite'.

And it's not been at issue that Wittgenstein was critical of the notion of infinity in mathematics.

Your claim was out of point from the start, because you see the discussion in the quote as discussion in talking. It is the concept of infinity in Mathematics he was meaning, which doesn't exist, hence not speakable and is meaningless. If you are still hanging on that "discussion" and make song and dance about it, you are not in the game. — Corvus

It's difficult to make anything sensible from this. The point I am making is simple, you misrepresented Wittgenstein's view. He is saying that mathematical discussions are finite, not that infinity is finite - an absurdity that seems peculiar to you.

You are amazing! — TonesInDeepFreeze

"Incorrigible" would be more accurate.

You don't seem to even know what said what, and what was whose points — Corvus

You have not shown that I've failed to know what has been said.

and just get into ad hominem all the time. — Corvus

When you say "just", you're lying.

I post extensive arguments that are not ad hominem, and give extensive information and explanation that is not ad hominem.

Anyway, I do comment on the ignorance, confusion and dishonesty of cranks, but not as an ad hominem argument in the sense of something like "you are [fill in the personal remarks here] therefore your argument is not sound." Rather, I have given you fulsome information, explanation, counter-arguments and refutations, no matter what else I have to say about your ignorance, confusion and dishonesty. Pointing out that you are a crank is merely lagniappe to my substantive comments.

Would you say your postings are high standard? — Corvus

They're never good enough for me, for a number of reasons. But they do provide a lot of information, explanation, and cogent arguments, and sometimes have other virtues too. Posting is hard, because it's impromptu and usually under the constraint of being time diverted from other things one wants and needs to do. So, that considered, all and all, I think I've written some really good posts, while others are just okay, but in just about all cases, I wish that I had time to make them a lot better still. And too many typos in them.

You don't even know what Wittgenstein was up to. — Corvus

You don't know what I know about Wittgenstein, including what I've forgotten and would need to refresh myself on. And it's aside the point anyway, as my arguments are not about Wittgenstein, not even to try to dissuade you from sharing his views about mathematics. Whatever the case about Wittgenstein, it is not the case that mathematics regards 'infinite' as meaning 'finite', for example.

If you thought he had little to do with math — Corvus

You're lying about me. (Though you weasel with 'if'.)

I never said that Wittgenstein has little to do with mathematics.

It's overwhelmingly the case that Wittgenstein is one of the very most central philosophers in the subject of logic and mathematics.

That I say he does not speak for mathematics in the sense that mathematics speaks for itself in its definitions, I am not at all saying that it is not relevant to mention what he says about mathematics. He has things to say about mathematics, but he cannot be fairly regarded as speaking for mathematics, especially as the fact that he was critical of the notion of infinity in mathematics does not imply that mathematics regards 'infinite' to mean 'finite'.

"Incorrigible" would be more accurate. — Banno

Amazing in the forms of incorrigibility.

You [Banno] haven't even explained what "infinity" means. — Corvus

I don't speak for Banno, but I have said that there is no set named with the noun 'infinity', but rather there is the adjective 'is infinite' defined:

x is infinite iff x is not finite

How can one admit error when he is not in error but the other party is? — Corvus

Even if the other party were in error (which is not the case here anyway), if you are also in error, then you could admit it.

Actually, it seems you can't.

You compound your errors now by claiming that you've not been in error, when its overwhelmingly clear that you have been, and in so many ways.

We’re not saying that the symbol “A” is identical to the symbol “B”. This is where I think you are misunderstanding. — Michael

Of course, we are not talking about the symbols, we are talking about what the symbols represent. In your example, "A" represents something, and "B" represents something. The issue is, what "=" represents

In the context of maths, when we say that A = B we are saying that the value of A is equal to the value of B. The value of A is equal to the value of B if and only if A and B have the same value. — Michael

Right, A=B means that the value of A is equal to the value of B. This does not mean that A is identical to B, so the "=" signifies a relationship of equality, it does not signify a relationship of identity.

A non-identical but equal value makes no sense. — Michael

How could this be true? Two dollar bills are non-identical, but equal value. There is however, a very special relationship, which a thing has with itself, expressed by the law of identity (a thing is the same as itself), which is known as the identity relation.

Would you agree with me, that every identity relation (the relation a thing has with itself as expressed by the law of identity) is also an equality relation, such that a thing is equal to itself, but not every equality relation is an identity relation? In fact, in the vast majority of cases when things are said to have equal value (like two different dollar bills) they are two distinct things, and it is very rare, because it is rather useless, for a person to say that a thing is equal with itself.

We can skip right to the matter at hand, if you're prepared. Let's propose your example in slightly different terms, unambiguous terms which might better expose the issue. instead of saying "the value of A", and "the value of B", let's simply say that "A" represents "a value", and "B" represents "a value". Then when we say "A=B" we might claim that A and B both represent the same identical value.

But this creates a procedural problem in practice. Let's take the example "1+1=2". The value represented by "1+1" would be exactly the same, identical, to the value represented by "2". The problem is that "1+1"contains the representation of an operation, and "2" does not. And in order that an operation can fulfill what is intended by the operator, the operation must have a very special type of value. Because it is necessary to recognize this special type of value, that signified by the operator, it is impossible that "1+1" signifies the exact same value as "2", because there is no operation represented by "2". In other words the value represented by "1+1" consists of an operation, and the value represented by "2" does not, therefore they are not representations of the exact same value.

By a 'mathematical antirealist' I meant someone who thinks maths is invented, not discovered. Or someone who thinks that your "objects" in set theory only exist in our minds, or as pebbles or ink or pixels, etc. — GrahamJ

The issue is a complex one, but here's the simple explanation. If a numeral such as "2" signifies an object, then every time that symbol is used it must refer to the exact same object. However, if a "mathematical antirealist" believes that math is invented and these concepts exist only in human minds, then one must accept that the conception of "2" varies depending on the circumstance, or use. This is very evident from the multitude of different number systems. So for example, when a person uses, "2" it might refer to a group two things, or it might refer to the second in a series, or order. These are two very distinct conceptions referred to by "2". So, since "2" has at least two referents, it cannot refer to a single object. We could however propose a third referent, an object named "2", but what would be the point in that? The object would be something completely distinct from normal usage of the symbol.

"Incorrigible" would be more accurate.
— Banno

Amazing in the forms of incorrigibility. — TonesInDeepFreeze

Pure nonsense from the pair. You two have been degrading the whole discussions into a comedy.

Even if the other party were in error (which is not the case here anyway), if you are also in error, then you could admit it.

Actually, it seems you can't.

You compound your errors now by claiming that you've not been in error, when its overwhelmingly clear that you have been, and in so many ways. — TonesInDeepFreeze

You speak for Banno, and now trying to speak for me?
It seems obvious your whole purpose of coming into the forum is forcing people to admit errors when the error is on your side.