some more basic aspects of mathematics given all indications of being universal while other more developed maths do not. — javra

I don't opine on those. Though, of course, certain concepts that are basic to certain areas of mathematics are not even universally known, let alone universally accepted. But, coincidentally, in another thread someone else mentioned stick counting. I don't necessarily say that it is universal, but I do think that if anything is objective, then finitistic reasoning, whether abstract or concretized by algorithmic manipulation of discrete tokens, is objective. Yet, objectivity and universality are not necessarily the same.

What would philosophers such as Descartes, Leibnitz or Avicenna know about maths? — Joshs

Is that a rhetorical question meant to convey that Descartes and Leibniz knew little about mathematics? Or is it meant ironically to say that indeed they knew a lot about mathematics? In any case, of course it is famous that Descartes and Leibniz are among the most important mathematicians in history.

Gödel, the originator of the incompleteness theorems, was guided by his self-declared mathematical Platonism — Joshs

If I recall correctly from my readings about this, Godel did not arrive at realism until long after he proved the incompleteness theorem. In any case, the proof of the incompleteness theorem does not depend on any particular philosophy.

Yet, while everyone has always universally agreed that 1 + 1 = 2, the formal mathematical proof of the book by which this is established is not universally agreed upon without criticism. As one example of this, at least one of the axioms the book uses, its introduced axiom of reducibility, has a significant number of criticism—thereby not being universally apparent in the same way that 1 + 1 = 2 is but, instead, being a best reasoned supposition which was set down as axiomatic. — javra

Was the axiom of reducibility used in the proof?

the Principia Mathematica (written in 1910) is commonly known to take about a thousand pages to in part formally prove that 1 and 1 is in fact equivalent to 2. — javra

Equals, not merely equivalent to.

Was it approximately 1000 pages or closer to about 360?

Also, the proof is mentioned near the end of the book, but that doesn't mean that that many pages are required to complete the proof, since there is a lot of other material between the axioms and that particular proof. It may be that it would take a lot less pages to simply get to the theorem from the axioms.

No such formal proof occurred previously in human history — javra

No proof had been given with constraints such those of PM, but the theorem is easy to prove in Peano's system that was a couple of decades prior to PM.

A smaller infinity can reach any finite number that a larger infinity can by freezing the larger infinity and letting the smaller one catch up. — Mark Nyquist

Define 'reach', 'freezing' and 'letting catch up'. Better yet, tell me your primitives and your sequence of definitions from the primitives.

it can be possible that one model can be inconsistent with another and not be false. — Mark Nyquist

I'd rather say 'theory' than 'model'.

But then we must ask what we mean by a theory being true or false. In a rigorous sense, a theory is true or false in a model for the language for the theory. A theory may be true in some models and false in others. And of course, if a theory T is inconsistent with a theory S, then there may be models in which T is true but other models in which S is true.

I'm really sceptical of the idea that there is any one true math to decide these issues of infinity. — Mark Nyquist

We'd have to look at the arguments of people who have said that there is. Who do you have in mind? Naturally, we would look at realists such as Godel. And there are also cranks who at least present as if their own vague, undeveloped, impressionistic and incoherently suggested concept is the true concept, as meanwhile they do explicitly represent that classical mathematics is false.

1. I don't know what you mean by ""make sense" of".

2. Frege's system was taken to be a derivation of mathematics from logic alone. Russell's paradox showed that Frege's system was inconsistent. But does that mean that there can't be a derivation of mathematics from logic alone? Whitehead and Russell offered a system that was an attempt to derive mathematics from logic alone, but their system was not logic alone. But does that mean that there can't be a derivation of mathematics from logic alone? The Godel-Rosser theorem may discourage us even more from thinking that we can derive mathematics from logic alone. So, can we derive mathematics from logic alone? I think the preponderance of philosophers of mathematics think we cannot, but there are dissenters.

The best introduction to the subject I have found is in the introduction to Church's 'Introduction To Mathematical Logic', as indeed that whole introduction is a quintessential primer for the basics of logic.

The crank will mangle what I wrote, misrepresent it, presume to knock down strawmen of it. Likely, I won't have to time to compose a response, especially to the sheer volume of his confusions.

It's also fine to have a philosophical stance that there are no abstract objects. But being true to that stance then requires eschewing even everyday locutions about mathematics and everyday thinking about many things. For that matter, at least for me, the use of language in thought and communications is to provide frameworks for dealing with so-called concrete experience, not merely to remark that one observes the so-called concretes.

Mathematics does not pretend to be isomorphic with all the concrete objects and particles of science. Nor that mathematics is a factual report about concretes. Rather, mathematics provides an idealized framework that we can choose to use in different ways, including providing an axiomatization for the formulas we do use for the sciences. Mathematics is an armature for knowledge about concretes; it is not supposed to be itself a report of those concretes. The armature is not itself the things you put in it.

And the way I understand - other mileages may vary - frameworks, whether mathematical, philosophical or conceptual in any field of study, is that they should facilitate fluid thinking and communicating, and to avoid, if possible, having to stretch oneself in contortions such as having to grasp for convoluted expressions to avoid saying the word 'object' in an utterly natural way when talking about things such as numbers, or to have to eschew the economy of conceptualizing numbers as things rather than to commit to imagining that a number is born and dies, off and on and off and on, every time someone thinks of it and then stops thinking of it or that there even is no 'it' they are thinking of but only physical events in a brain, or that, wait, what is the notion of 'event' anyway without abstraction?

On the other hand, if one wants to try to think of mathematics and formulate it and communicate it but without reference to abstractions or abstract objects, I say have at it. But that doesn't make everybody else wrong for thinking of numbers as things and saying such ordinary things as "the sum of two and two is four". And especially classical mathematics is not crippled by the mere wish of a crank, without a concrete proposed alternative, that there is an unannounced, unarticulated physicalist replacement.

I find it a crude notion that each mathematical mention must correspond to represent each, every and any of the concretes and particles that are themselves present to us mentally as constructs in a conceptual framework. A framework is not an assertion, and its value is being able to conceptually and/or practically cope with or predict experience. Such frameworks may be preferred or not in how well they conceptually and/or practically cope with or predict experience, but also in the satisfaction derived from the conceptual order and beauty they provide. When I am confused by too many facts all at once, or about, for example, how things work, I am relieved of that confusion by a framework that allows me to put that experience in order, to process it. I may be confused by the behaviors of other people, for example. But then I may posit such things as traits, goals, etc. I don't posit that those are concrete things. They are abstractions, they are posited as a conceptual armature so that a person's actions don't appear to me as a random jumble but rather my framework allows me to think of those actions in a narrative and to make predictions about them on that basis. When I there are of numbers mentioned, I don't have to think of them as popping in and out of existence each time they are mentioned or not, but rather I have an armature in which numbers don't do that. And when I there are a lot of numbers involving some problem, either conceptual or practical, that I want to solve, I have a system of principles about numbers that allows me to find the answers I want. That system is an abstract armature, not a concrete thing. It's not required that each concept, each abstraction itself corresponds to a particular concrete.

Meanwhile, maybe there is a way, but I don't know of it, to avoid that thought and language themselves presuppose that 'object', 'thing', 'entity', 'is', 'exists', etc. are basic and that explication of them cannot be done without invoking them anyway. When I say "What is that thing in the sink?" I presuppose even the concept, which itself is an abstraction, that there are things, that concretes are things, and even the notion of 'concrete' is an abstraction. And I don't see anyone who can talk about experience ('experience' also an abstraction) without eventually invoking utter abstractions such as 'object' and 'is', whether referring to abstractions or concretes.

It is fine to say that mathematics should be done intensionally. But cranks go wrong when they claim of the classical mathematics they're criticizing that it does do it intensionally, or that it must be done intensionally, or that it is inconsistent for not doing it intensionally.

Indeed it is a fine idea that we may talk about a program that outputs successively longer finite sequences rather than talking about an infinite sequence. But easier handwaved than axiomatized. There have been proposals for intensional mathematics (especially, for example, Church), but it's not an easy thing, the devil is in the details; it's not realized by crank handwaving, confusions and illogic.

"The number that comes after the number 1" is clearly intensional, — Metaphysician Undercover

That quote could be written only by someone who does not understand what is meant by 'extensional' and 'intensional'. A name is not just one of extensional or intentional. Rather, a sentence has both an extensional aspect (the denotation) and an intensional aspect (the connotation).

/

'1+1' does not stand for an operation. It stands for the result of an operation applied to an argument.

'+' stands for a function ('operation' if you insist).

'1+1' stands for the value of the function applied to the argument <1 1>.

How do your views square with indispensability? — TonesInDeepFreeze

That reminds me, I still am interested in how he thinks Putnam's indispensability view jibes with his own views.

Axiom
Jane is standing between John and Jack, with John on our left and Jack on our right

Inference
The person to the right of John is identical to the person to the left of Jack

The inference is valid even though Jane, John, and Jack are not physical people and are not abstract entities that exist in some Platonic realm. — Michael

Yep.

Also – and correct me if I'm wrong TonesInDeepFreeze – but "1 + 1" doesn't actually mean "add 1 to 1". Rather, it means "the number that comes after the number 1". And "3 - 1" means "the number that comes before the number 3".

The number that comes after the number 1 is identical to the number that comes before the number 3. — Michael

Each of these is true if and only if each of the others is true:

S = T

S equals T

S is identical with T

S is T

the denotation of 'S' = the denotation of 'T'

the denotation of 'S' equals the denotation of 'T'

the denotation of 'S' is identical with the denotation of 'T'

the denotation of 'S' is the denotation of 'T'

/

All of the below are identical with one another. All of the below are equal to one another. All of the below are the same as one another.

1+1

the sum of 1 and 1

1 added to 1

1 plus 1

the successor of 1

3-1

the difference of 3 and 1

1 subtracted from 3

3 minus 1

the predecessor of 3

2

two

the denotation of '1+1' [but not the Godard movie '1+1']

the denotation of 'the sum of 1 and 1'

the denotation of '1 added to 1'

the denotation of '1 plus 1'

the denotation of 'the successor of 1'

the denotation of '3-1'

the denotation of 'the difference of 3 and 1'

the denotation of '1 subtracted from 3'

the denotation of 'the predecessor of 3'

the denotation of '2'

the denotation of 'two'

when I check Tone's arguments, they are very mainstream — Banno

Just to be clear:

I enjoy reading classical mathematics; I find great wisdom in mathematical logic; I admire the rigor of logic and mathematics; I admire the astounding creativity in logic and mathematics; I recognize that classical mathematics is the basic mathematics used for the sciences; I recognize the objectivity in mechanical checking of proofs (and generally that at least in principle, if time were taken to fully formalize then proofs are mechanically checkable); I admire the intellectual honesty of logicians, mathematicians and many philosophers of logic, mathematics and language; I admire the simplicity of the axiomatization of mathematics from the set theory axioms, especially the relative simplicity, as axiomatizing alternative mathematics is often much more complicated; and I enjoy, though I am haunted by, the philosophical problems that arise from classical mathematics.

But I do not claim that classical mathematics is the only "true" mathematics; or that there can't be a better mathematics; or that it is wrong to have philosophical objections to classical mathematics. Indeed, with my limited time and limited talent for mathematics, I do very much enjoy learning about alternative logics and alternative mathematics, and I very much admire and relish the wisdom, creativity, and productivity of the alternatives, and also the great philosophical debates around classical and non-classical mathematics.

Values are not "inherently intensional".

One may reject ideation and communication premised in abstract objects. But the notion of identity is not even limited to abstract objects. Whatever things one does countenance as existing, named by, say, T and S, we have T = S if and only if T is S. That is what '=' means when it is used in contexts of ordinary identity theory, logic, mathematics and other contexts to. If one wishes to use it with another meaning in another context, then, of course, fine. But that doesn't justify saying that in logic and mathematics it is not used just as logic and mathematics says it is used.

'=' doesn't even require a mathematical theory as its context or even the acceptance of abstractions, but rather that in identity theory, for whatever things, abstract, concrete, physical or are being looked at on your desk right now, the statement of identity is that of being the same thing.

Again, more exactly:

If 'T' and 'S' are terms, then

'T = S' is true if and only if T is S.

And whether 'T' and 'S' stand for abstract things, abstract objects, values that are abstract things, values that are abstract objects, concrete things, physical things, or whatever things you are looking at right now on your desk.

And how can anyone, even a crank, not understand:

1+1 = 2

'1' refers to the number one. And since '1' and '1' are the same numeral, it would be redundant, though obviously true, to say that both '1' and '1' refer to the number one.

Then, '1+1' refers the SUM of the number one with the number one. And that SUM is the number two. Or in more formulated mathematics, '1+1' refers to the successor of the number one; and the successor of the number one is the number two.

The denotation of '1+1' is not two of the number one, but rather it is the SUM of the number one with the number one.

'2' refers to the number two, and '1+1' refers to the sum of the number one and the number one, which is the number two. So '2' and '1+1' both refer to the number two, so '2' and '1+1' refer to the same number. That is, 1+1 is 2, which is expressed as:

1+1 = 2.

It is difficult to reason with someone about mathematics who doesn't understand that 1+1 is 2.

(Yes, I can hear sane and rational people saying, "Really, Tones? You spent your precious time tonight explaining to a grown person that 1+1 is 2?")

/

Taking Chat GPT as an authority, or even remotely reliable, as does the crank is pathetic.

Anyway, I couldn't resist. Chat GPT told me that:


1+1 equals 2.

1+1 is 2.

/

In mathematics and logic 'equality' and 'identity' mean the same.

/

The reason I say that '=' stands for the identity relation is not that "it would make it consistent with the theory I support". Rather, in mathematics, not just in set theory, ordinarily '=' stands for equality, which is identity.

But the crank is now arguing that in mathematics it's equality, which is not identity, which is untrue.

/

In ordinary mathematics, bijection is not a "procedure". Rather a bijection is a certain kind of function.

And we do prove the existence of certain bijections.

And one does not "perform" a bijection.

Here's a bijection:

{<1 1>}

One does not "perform" it.

Here's a bijection:

{<k j> | k in N & j = 2*k}

One does not "perform" it.

(But maybe there's no point in explaining this to someone who does not understand 1+1 = 2.)

/

The crank misrepresents again by claiming I mentioned intensionality regarding a person's name to support a mathematical claim. I explained exactly the role of mentioning the example of intensionality and that it was not an argument that such an example applies mathematically. But the crank skipped that so that he could misrepresent my point.

If you are asking in which article he said it, I recall it was from a book I don't own. But I saw it in the internet somewhere. — Corvus

I searched 'Wittgenstein mathematics infinite means finite'. Of course, there are hits with all those terms, but the one I saw come up with a preview close to your claim is this thread itself.

And, again, the levels:

You claimed that mathematics regards 'infinite' to mean 'finite'. You claimed falsely.

Then you claimed that Wittgenstein said it. But the quote you adduced did not say that mathematics regards 'infinite' to mean 'finite'.

Then you said that Wittgenstein meant it as metaphor. But, at least without context, it is not clear what the metaphor would be there. And even if the claim that mathematics regards 'infinite' to mean 'finite' is
metaphor, it doesn't relieve that you did not present as metaphor yourself.

Then you claimed that the Stanford article supports that Wittgenstein said that mathematics regards 'infinite' to mean 'finite'. But there you cannot give a quote in which the article says that or even implies it.

Then you claim that your original claim that mathematics regards 'infinite' to mean 'finite' was merely metaphorical. But since it doesn't read as metaphor, when you were first told that mathematics does not regard 'infinite' to mean 'finite', you could at that time just say that indeed you do not claim that mathematics regards 'infinite' to mean 'finite'.

Meanwhile, you challenged me to cite a book that defines 'infinite' as 'not finite', while your own favorite book itself gives that definition.

Meanwhile, you lie about the very record of posts in this thread.

And you hypocritically decry ad hominem, while you use ad hominem. And you ignore the detailed remarks I said about ad hominem.

And all of that is in your pursuit to take down set theory, while you know virtually nothing about it, are confused about it, misrepresent it, and ignore explanations given you about it.

/

So someone might say, "Oh, but Tones, why are you going on, prosecuting this one little item?"

Because every time I catch this crank in his intellectual dishonesty (even to the extent of lying about the record of posts) he comes back with even more intellectual dishonesty. It is worth making that clear as yet another object lesson about the perniciousness of Internet crankery.

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? — Corvus

You lied about me when you said I started with insults. I gave you the links that prove that you're lying about that. And even showed that you first made an insult against another poster.

The record of posts shows that I posted without personal remarks, and for a while, until it became clear that you are posting in bad faith - from ignorance, confusion, strawman, evasion of refutations.

For the second time, you are lying when you claim that I started posts in this thread (for that matter, any thread) with insults. Meanwhile look in the mirror for a change - there's a huge steel beam across your eye.

And the courtesy I'm talking about, Mr. Metaphor who can't discern irony, is just what I said it is: that you provide comedic relief when you go through all the ridiculous contortions you do just to avoid simply recognizing that set theory does not define 'infinite' as 'finite'.

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. — Corvus

I understand metaphor.

I didn't demand perfection in what you said.

You said that mathematics regards 'infinite' to mean 'finite'. That's not a metaphor. If you meant that it was a metaphor or that you didn't actually mean to say that mathematics regards 'infinite' to mean 'finite', then you could have conveyed that the first time I told you that mathematics does not regard 'infinite' to mean 'finite'.

Then you deflected to say that it's something that Wittgenstein said. So, that deflects from you making the claim to you claiming that Wittgenstein made the claim. But the Wittgenstein quote, whiles perhaps ironic and acerbic, does not as presented without more context, say that mathematics regards 'infinite' to mean 'finite.

So then you deflected again to say that the Stanford article supports your claim about Wittgenstein. But you fail to give any quote from the Stanford article.

It might be that Wittgenstein meant that mathematics regards 'infinite' to mean 'finite', but you have not shown that he did, and even if he did, merely that he did would not show that mathematics regards 'infinite' to mean 'finite'.

So now you deflect to a claim that is false (that I don't understand metaphor) and one that is both false and a strawman (that the reason I don't agree with you is that I demand perfection of expression). And, this is while you've been complaining about ad hominem, as your quote above is itself ad hominem. And while you've completely skipped my detailed points about ad hominem in posting.

What about our interest in crackpots like Tones? — Metaphysician Undercover

That's a beam calling the mote a beam.

You only picked out the usage of the infinity in the book for insisting your point in this thread. — Corvus

I read the chapter about the history of set theory and philosophy about it. I haven't posted anything to dispute of it nor, in certain parts, anything to affirm it.

Included in that chapter, the author explains the importance of formalization, very much along the lines I did earlier in this thread, on which point you disputed.

I read much of the rest of the book, as it interests me in the particular way that it develops a class theory.

Anyway, the bulk of the book is an intro to set theory, covering material I have studied in similar textbooks, though, as mentioned, I'm tempted to go back over that material with this book, as I am interested in the authors particular way it develops a class theory.

I read it from the start to the end. — Corvus

But you missed the definition of 'infinite' that completely agrees with the one I mentioned but that you challenged me to cite a textbook that uses that definition. So, I am still baffled why you challenged me to cite a textbook when your own favorite book on set theory, which you claim to have read, is one of many many textbooks that give the definition you challenged me to show that it is in a textbook.

And I highly recommend that you reread that chapter on the history of set theory and philosophy about it, so you will see how the author and I are aligned on the subject of formalization, as you instead displayed that you don't understand it and as you objected to my remarks about it in your usual style of confusion, strawman and non sequitur.

There is no 'Godel's paradox'.

Anyway, as best I understand your question, the answer is 'no'.

You can hold in your hands and read every volume of the 'Journal of Symbolic Logic' in its original printing, as at the start of the rows of them is Vol. 1 No. 1 from March 1936 with Church's 'A Note on the Entscheidungsproblem' itself. It's a pretty great feeling.

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!

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.

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

Hilary Putnam?

How do your views square with indispensability?

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.

use the concept for nonexistence as real existence — Corvus

I'm glad I don't do that.

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...

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'.

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.

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'?

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'.

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.

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".

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.

A library is a candy store, temple, sanctuary, and sparkling pool under a waterfall, all in one.