Finitism can get simply ridiculous at some point.

Regarding the fact that mathematics is not even isomorphic to a system of physical objects:

It's not intended to be, and it's not required for the efficacy of mathematics. Detailed explanations of that point have been given over the years in this forum.

By the way, the distinction between the countability of the naturals and the uncountability of the reals doesn't, in a certain important sense, even require infinitistic assumptions.

Even if there is no set of all the natural numbers and no set of all the real numbers (and even if real numbers are not infinitistically conceived as equivalence classes of Cauchy sequences or Dedekind cuts), still we may note that there is no procedure such that its outputs are increasingly longer finite sequences of real numbers (however real numbers are finitistically conceived or represented such as a real number itself as a procedure for outputting increasingly longer finite decimal sequences) and such that, for any real number, it will eventually be an output. (I think that's right, but perhaps there could be objections?)

Another common crank fallacy is claiming that mathematics is false by way or arguing that mathematics uses words in ways different from their ordinary meanings or different from their meanings in certain other fields of study.

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. — Metaphysician Undercover

??

Of course there are many conceptions of "2". I don't know what you mean by objects, why you're talking about objects, or what point you are attempting to make. I don't know what you mean by the normal usage of "2".

(I think that's right, but perhaps there could be objections?) — TonesInDeepFreeze

I think it's right. But anyway, even the notion of reals would go against this argument that mathematical objects "cannot be carried out, cannot be completed" and hence are "nonsensical". And when you throw out real numbers as "nonsensical", your mathematics is quite illogical. We do need number like pi!

Another common crank fallacy is claiming that mathematics is false by way or arguing that mathematics uses words in ways different from their ordinary meanings or different from their meanings in certain other fields of study. — TonesInDeepFreeze

The most irritating answer type is that if you ask something about mathematics and mathematical objects, people answer by referring to physics and for instance quantum physics. No, an observation of the physical reality, that we model by a mathematical model, doesn't tell if a mathematical object is true or false.

We start from the need to move something and then build a carriage to move it, not that we just build a carriage without requirements and then try to find something that can be moved with it. Furthermore, it's even more wrong to start arguing that our primary task, need to move something in the first place, is wrong, we shouldn't even think of it, because our carriage can't move it.

You may try for, literally, years and he will not understand. — TonesInDeepFreeze

Indeed; I did; he doesn't.

Way back, I wrote of @Corvus:

But you will double down, again. — Banno

Even I was not expecting such recalcitrance. That was 24 hours and three pages ago. Those three pages are replete with Corvus' squirming and flailing.

There are interesting and controversial ideas in Wittgenstein's anti-platonism, which could make an excellent thread. But an attempt at any such conversation in these fora would quickly be derailed by those who cannot grasp equality and those who misattribute and fabricate willy-nilly.

That's a limitation on @Jamal's otherwise excellent forums. A more proactive moderation might improve the philosophy being done hereabouts. But so many of the better posts are, as and have shown in this thread, responses to ineptitude.

And so it goes.

Way back, I wrote of Corvus:
But you will double down, again.
— Banno
Even I was not expecting such recalcitrance. That was 24 hours and three pages ago. Those three pages are replete with Corvus' squirming and flailing.

There are interesting and controversial ideas in Wittgenstein's anti-platonism, which could make an excellent thread. But an attempt at any such conversation in these fora would quickly be derailed by those who cannot grasp equality and those who misattribute and fabricate willy-nilly.

That's a limitation on @Jamal's otherwise excellent forums. A more proactive moderation might improve the philosophy being done hereabouts. But so many of the better posts are, as ↪TonesInDeepFreeze and ↪Michael have shown in this thread, responses to ineptitude.

And so it goes. — Banno

Your problem is that you make out as if what you and your cliques say are the only truth, and the rest of the world are false. Many would believe that your posts should be under the moderations for the extremely biased and misunderstood posts and Clequism you have been trying to pursue in this forum.

Trace back all your posts and Tone's in this thread, and you will see who started throwing unfounded posts and ad hominem posts before me, and degraded the discussion into a comedy. All your posts have no grounds for your claims. My posts are based on the philosophy of mathematics (Putnam) and set theories (C. C. Pinter), and various published academic articles.

...you make out as if what you and your cliques say are the only truth, and the rest of the world are false. — Corvus

Sad that the "clique" with which you are in disagreement is that of the mathematicians. Hm.

Anyway, time to move on. Long ago.

Sad that the "clique" with which you are in disagreement is that of the mathematicians. Hm.

Anyway, time to move on. Long ago. — Banno

If you trace back Tone's posts, he starts with ad hominem before getting into philosophy. And you blindly take his side condoning his absurd and incorrect points, as if they are the only truths on the earth. How petty and juvenile. That's too visible, even a 10 year old would sense it. That is not Philosophy. That is a blatant clequism.

This article in SEP outlines and supports my point in this thread. I can drag out all my other books on Philosophy of Math, and Set theories, but it would be too cumbersome. If you wanted, I can do that, but it doesn't seem necessary. You would still keep saying I will double down. No. You are wrong. See how your whole focus of your posts are "You" "Me" "Him", leaving out the matter under discussion in the deep freeze?

I agree with Wittgenstein's Philosophy of Math. I disagree with all those who take Infinity as real entity, and the Infinite Set theorists, whether mathematicians or not.

If infinity was real, then Zeno's Achilles would be still chasing the tortoise in the race track at this very moment. But is he? It is a paradox. You know that.

Set theory's infinity is a tongue in cheek theory taking nonexistent infinity as if it does exist, hence a vacuous theory, which only seems to be making sense in the textbooks. Fine so be it. But if you used it for solving real world problems, you would end up in a deep ditch.

If you trace back Tone's posts, he starts with ad hominem before getting into philosophy. — Corvus

You are blatantly lying about me. Again. Stop lying about me.

Moreover, I addressed the issue of ad hominem in detail. Of course, you SKIP that.

First post of mine in this thread:

https://thephilosophyforum.com/discussion/comment/879009

his absurd and incorrect points — Corvus

You keep saying that, but have not shown anything incorrect in what I've said.

That is a blatant clequism. — Corvus

Banno and I have no allegiance or bond or anything like that. We've disagreed at times too. Merely that we happen to agree on a number of points doesn't make us a "clique". And your silly argument could be turned around. I could say that the opposition I've received to my posts comes from a "clique" of cranks. But I don't, because it would be a foolish thing to assert that they form a clique merely because they disagree with me.

This article in SEP outlines and supports my point in this thread. — Corvus

Please quote any passage in that article that you think claims that Wittgenstein said that in mathematics 'infinite' means 'finite'.

my other books on Philosophy of Math, and Set theories — Corvus

Please name one that you think defines 'infinite' as 'finite'.

But if you used [set theory] for solving real world problems, you would end up in a deep ditch. — Corvus

Set theory axiomatizes the infinitistic classical mathematics, such as calculus, that is used for the sciences. All of the technology that you depend on to survive and flourish uses mathematics involving infinite sets. The very computer you are typing on comes from the work of mathematicians who were steeped in the mathematics of infinite sets. Meanwhile, you do dig yourself deeper and deeper into a ditch.

And stop lying about me.

even the notion of reals would go against this argument that mathematical objects "cannot be carried out, cannot be completed" — ssu

I'm referring to a notion in which there are only finite "approximations". That is, that the real number is taken to be the algorithm for generating successive partial finite "approximations".

Please quote any passage in that article that you think claims that Wittgenstein said that in mathematics 'infinite' means 'finite'. — TonesInDeepFreeze

It is his metaphor, meaning that even if you claim it is "infinite", it is actually "finite". It is a type of cynicism. He uses aphorism a lot in his writings. Please don't take it literally. Obviously you have not read Wittgenstein at all.

But the point is not about the word games. The critical point is that "infinity" doesn't exist. When you say "infinite", it actually means "finite" in real life. Even if you keep on counting something infinitely, you must stop counting at some point. You cannot keep going on till the eternity. You stopped counting, and what you have is a finite number.

My point was just to point out that if you use the concept for nonexistence as real existence, and use it in your premises, then you will arrive at contradiction misleading yourself and others who believe you are correct.

throwing unfounded posts and ad hominem posts before me — Corvus

Here, very early in this thread, you imparted an insult snidely couched as a rhetorical question:

Have you [ssu] not read a single math book? — Corvus

Here is my first post in response to you:

it seems barmy to talk about different size of the infinite sets
— Corvus

No set has different sizes. But there are infinite sets that have sizes different from one another. That follows from the axioms.

One is free to reject those axioms, but then we may ask, "Then what axioms do you propose instead?"

One is free to reject the axiomatic method itself, but then we may ask, "Then by what means do you propose by which anyone can check with utter objectivity whether a purported mathematical proof is correct?"

One is free to respond that we check by comparing to reality or facts or something like that. But then we may point out, "People may reasonably disagree about such things as what is or is not the case in whatever exactly is meant by 'reality' or in what the facts are, so we cannot be assured utter objectivity that way."

One is free to say that we don't need utter objectivity, but then we may say, "Fair enough. So your desideratum is different from those using the axiomatic method." — TonesInDeepFreeze

There is no ad hominem there.

Then after more posts in which you continued to dogmatically insist that you are right, blithe to the (not ad hominem) substance of the replies to you, I said:

Of course, my point went right past you no matter that I explained it clearly. — TonesInDeepFreeze

Then, as it got even worse and worse with your strawmen, ignorance of the subject, getting things backwards, etc., I made clear that you're a crank:

https://thephilosophyforum.com/discussion/comment/880933

And, still, you SKIP my remarks about ad hominem, most especially that I don't say that my arguments are supported by ad hominem but rather that, in addition to my arguments on the substantive points, you are indeed ignorant, dogmatic, confused and dishonest. At a certain juncture in threads such as this, the perniciousness of the ignorance, dogmatism, confusion and dishonesty of cranks deserves highlighting.

degraded the discussion into a comedy — Corvus

The ridiculousness is courtesy of you. Maybe not comedy, but still risible is the claim that set theory takes 'infinite' to mean 'finite'.

Please quote any passage in that article that you think claims that Wittgenstein said that in mathematics 'infinite' means 'finite'.
— TonesInDeepFreeze
It is his metaphor — Corvus

Asking a second time, what quote in the article do you claim supports your claim that Wittgenstein said that mathematics takes 'infinite' to mean 'finite'?

But the point is not about the word games. — Corvus

Whose word games? The point is that you claimed that mathematics takes 'infinite' to mean 'finite', and you support that by claiming that Wittgenstein said that mathematics regards 'infinite' to mean 'finite', and you support that by quoting Wittgenstein saying that discussions about 'infinity' are finite. And now you've said that the Stanford article supports you in this.

So what specifically in the Stanford article do you claim supports you in any of this?

This is not word games. The Stanford article is not word games. You claim it supports you, so if it does, you could quote where it does.

When you say "infinite", it actually means "finite" in real life. — Corvus

Even if we agreed that there are no infinite sets, it still wouldn't be the case that 'infinite' means 'finite'.

And even if we agreed that the use of the word 'infinite' breaks down because there are no infinite sets, it still wouldn't be the case that the mathematical meaning of 'infinite' is 'finite'.

And your challenge to me to name books in mathematics that define 'infinite' as 'not finite' was specious, gratuitous and ridiculous. As if that it is not the case that indeed books in mathematics define 'infinite' as 'not finite' but instead absurdly as 'finite'!

Anyway, still would like to read the quotes that you think say that mathematics regards 'infinite' to mean 'finite'.

Even if you keep on counting something infinitely, you must stop counting at some point. You cannot keep going on till the eternity. You stopped counting, and what you have is a finite number. — Corvus

No one counts infinitely. To say "counting infinitely and stopping", in this context, is a contradiction.

The theory of infinite sets is not premised on the supposition that a person can count infinitely.

This has been gone over and over and over already...

use the concept for nonexistence as real existence — Corvus

I'm glad I don't do that.

A more proactive moderation — Banno

I don't know what that would be, but I disfavor censoring cranks or admins using "chilling effects". On the other hand, it is indeed disheartening when admins censor or use chilling effects against posters who are calling out cranks and saying forthrightly that they are ignorant, confused, dogmatic and dishonest. And highly irrational for admins to use chilling effects to slow discussion about mathematics on the basis that it is not philosophy, when cranks are posting confusions and falsehoods about the mathematics as part of their criticisms of it. Moreover, we do not find that sentiment of clamping down against other subjects that are not philosophical or even being discussed from a philosophical point of view.

My posts are based on the philosophy of mathematics (Putnam) — Corvus

Hilary Putnam?

How do your views square with indispensability?

Yes. The dynamic is complex, yet remarkably the site remains fairly stable. It seems to me that amongst recent recruits there is little background in philosophy, logic, maths or even physics, but perhaps it always seems so.

The blatant misrepresentation seen here is a very different thing to the psycoceramics. The latter on occasion does force one to explain or re think.

All by way of repeating that the bad posts do elicit good replies.

But I wonder if the general reader is able to tell the one from the other.

Hilary Putnam? — TonesInDeepFreeze

To some extent the misunderstanding of various authors may be the result of our friends being autodidactic. The supposition that somehow the SEP article on Wittgenstein's philosophy of mathematics supports psycoceramic views might be a result of shallow reading of such tertiary sources. These topics are vast, needing careers, rather than degrees, to understand the topic, let alone make a significant contribution.

Anyway, respect to the mods for what they do. While it might be a little bit better, it could easily be a whole lot worse.

My posts are based on the philosophy of mathematics (Putnam) and set theories (C. C. Pinter), and various published academic articles. — Corvus

And Chat GPT.

It is bewildering why challenged me to show a book that defines 'infinite' as 'not finite' when you could have looked yourself at the book by C.C. Pinter in which he writes:

"A set A is said to be finite if A is in one-to-one correspondence with a natural number n; otherwise, A is said to be infinite."

Exactly the definition I gave, and exactly the definition found in many many books on set theory and fields of mathematics!

And the book is, as any ordinary textbook in set theory, chock full of use of infinite sets and infinite sets of different cardinalities from one another.

A poster who starts out in a thread by declaring "end of story" does not bode well.

I am getting a good laugh though at that poster challenging me to show a book that gives the very definition that is in the book he says he "bases" his posting on!

A poster who starts out in a thread by declaring "end of story" does not bode well. — TonesInDeepFreeze

That paragraph kinda set up for the gross oversimplification that was to come though.

And the book is, as any ordinary textbook in set theory, chock full of use of infinite sets and infinite sets of different cardinalities from one another. — TonesInDeepFreeze

Of course it is a book of Set Theory. However, it explains the historical background of the concept of infinity how controversial the concept was in detail. You only picked out the usage of the infinity in the book for insisting your point in this thread. I read it from the start to the end.

A poster who starts out in a thread by declaring "end of story" does not bode well.

I am getting a good laugh though at that poster challenging me to show a book that gives the very definition that is in the book he says he "bases" his posting on! — TonesInDeepFreeze

You obviously have problem understanding metaphors and ordinary use of English language. You seem to bite into a little words in the expressions, and as if one has to stick to the every word and comma in the sentence in the legal contract. I tend to write with metaphorical and simile expressions and idioms a lot just like other ordinary English users. You can't seem to understand that.

degraded the discussion into a comedy
— Corvus

The ridiculousness is courtesy of you. Maybe not comedy, but still risible is the claim that set theory takes 'infinite' to mean 'finite'. — TonesInDeepFreeze

You start your post with throwing insults to others before even going into the points under discussion. What courtesy are you talking about?