An axiom is a proposition regarded as self-evidently true without proof.
https://mathworld.wolfram.com/Axiom.html — PL Olcott

Isn't it exactly the point Quine disagrees with? Some self-evident knowledge without proof can be also self-deceiving too.

An axiomatic model of the world is the only way that an AI mind can be created that is the functional equivalent to a human mind. It must be told that {cats} <are> {animals}. — PL Olcott

What if {cats} was someone's nick name, or name of a rock band? They are also cats too, no? In that case , the AI would fail to tell the truth, wouldn't it?

Being 'moral' or 'immoral' is a property of something that is good, not vice-versa. The properties of 'being moral' and 'being immoral' are extensions of 'being good' or 'being bad'. — Bob Ross

I wonder if it is simple as that. Who judges what is moral or immoral? If someone with power and authority comes along, and says to you cutting grass in the winter is bad moral, therefore you are morally bad, then is the authority morally good, and are you morally bad?

Goodness and pleasantness are synonymous, so the weather is good today, so it is pleasant. Does it mean that morally good means morally pleasant? Morally bad means morally unpleasant?

I outlined this in the OP: what did you disagree with? Actual perfection isn't 'goodness for someone', it is perfection as it is in-itself. — Bob Ross

I didn't say that I disagreed with the OP. I was wondering if goodness is an absolute concept. I mean is there such a thing as absolute goodness?

Goodness seems to be a relative concept. It is good only from one's point of view. Something can be good for you, but it can be bad for others. Do you recall an old song lyric "One man's ceiling is the other man's floor."? But I am wondering if there is goodness from all the people in the world. If there were, what could they be?

Goodness is also a property of objects, actions, and situations, but it is dependent on a lot of factors and conditions on the objects, actions and situations. You cannot just say there is moral goodness which is perfect and morally good, and no one really knows what the goodness is without the considerations.

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. — TonesInDeepFreeze

I was just telling you about Pinter's book to say that even classic Set theory books admit the historical controversies with the concept of infinity. I wasn't meaning to say the book is denying, accepting or defining on the infinity as per my view.

If you still don't understand what the point is, then you need to read a book called "The Oxford Handbook of Philosophy of Mathematics and Logic" Edited by Shapiro. Again in that book, there are various different articles with different views on the topic. But one that you must read about is "Quine".

You lied about me when you said I started with insults. — TonesInDeepFreeze

If I really lied, then I would have told you that I lied, which is true. But you claim that I lied, which is false, and a lie.

I didn't lie, but you claim that I lied. Clearly and obviously you are telling a lie.
Therefore in whatever the case, you are the one who lied.

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

Hilary Putnam?

How do your views square with indispensability? — TonesInDeepFreeze

Putnam edited a book called Philosophy of Mathematics Selected readings. He put in there various articles by different people. It is not a book solely written by Putnam. You obviously have no idea about the book, or what the Edited book means.

The problem is that both you and Corvus badly misrepresent Wittgenstein in an attempt to subjugate his name to your psycoceramics.

So far neither of you have been able to cite anything like an endorsement of either your eccentric and unsound view of equity nor Corvus' confusing finite and infinite. Nor will you. — Banno

Under your thinking, anyone not thinking the same as you is misattributing everything. That is just nonsense. Under your eyes, people shouldn't be thinking differently from you.

Anyone thinking differently from you are downright wrong, and misattributing. What is the point of your philosophy? Forcing others to think the same as you do? That is not right.

Many would believe that your posts should be under proactive moderation for the low quality posts you have been spewing out with the meaningless quibblings stemming from your misunderstandings, and forcing people to believe and think exactly the same as yourself.

Many mathematicians? — Michael

Not sure on Mathematicians, but if they are logical, I would presume they would.

nfinite sets have a use in mathematics. That's all that matters. Reading more into them is a mistake. — Michael

Maybe. I don't see much practical point apart from filling in and adding more pages of the textbooks making them heavier.

It was controversial when they didn't know better. It's not controversial now because they know better. Those opposed to set theory now are, for the most part, non-mathematicians who don't know better but think they do. — Michael

Many still believe it is controversial, and I do too. No one is saying it is illegal to use it, but just pointing out the existence of the controversy and also reservation on the theory. No one can deny that.

In real life infinite set doesn't exist. I start putting something in a box forming a set, soon the box gets full or the object runs out. It doesn't go on filling the box forever.

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'? — TonesInDeepFreeze

It is a metaphor from my point of view. It is obvious, and I have kindly explained it to you above.
It a way of expression saying, when something is so bad, one could say "Well it's f***ing great." Anyone can see and use it to describe the situation with cynicism. If you have problem understanding it, I cannot help you.

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. I will try to find it, and update on the book title and page. I don't have the information off hand. I couldn't have made the quote from my own imagination. To me, it sounded a genius in the expression at the time of reading it.

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?

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.

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.

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.

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.

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 argue by mere assertion. — TonesInDeepFreeze

Ok whatever. Have a good day. cheers.

You've not shown that I've distorted any fact. Meanwhile, you've been distorting all over the place, as I have shown. — TonesInDeepFreeze

Most of your own posts are filled with distortions. See that's what I meant. You don't recall you have been writing in your own posts.

and now trying to speak for me
— Corvus

I haven't presumed to speak for you. — TonesInDeepFreeze

I am only replying to your posts, the way they are. But you two Laurel and Hardy are not worth the time. All the best.

You're lying again. I committed no action that constitutes speaking for Banno. — TonesInDeepFreeze

Stop distorting the facts, and be your own man and honest to yourself.

I haven't presumed to speak for Banno.

You're lying again. — TonesInDeepFreeze

It sounds like you are a little string controlled doll in Banno's pocket.

I explicitly said I do not speak for Banno. — TonesInDeepFreeze

Your sayings and actions are totally different. You don't even know what you have been saying, but denying it. That is truly incorrigible.

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 — TonesInDeepFreeze

You do. But of course you won't admit it.
The concept of infinity is for description of motions, actions and operations.
The use of infinity in the set theory is ambiguity.

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.

"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.

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?

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.

↪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.

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.

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?

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.

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.

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.

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.

(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.

The first point here is that you misrepresented Wittgenstein. The second point here is that you refuse to acknowledge your error. The third point is that this is an approach you have repeated in this thread and elsewhere. And not only you, but various others, many of them having contributed to this thread, adopt a similar lack of accountability. — Banno

Not only your reading on Wittgenstein is wrong, but also you seem to be misunderstanding many things in philosophy. It is not just this thread, but also in many other threads you seem to be claiming things from your misunderstandings and misrepresentation of the facts. Therefore you seem to be going around the circles on the points not getting clear to the point with no depth and no accuracy in many occasions.

Plus you seem to be tending to take sides of the posters regardless of right or wrong of the points, but who you think your cliques are. It is visible many times, and hard to miss it.

I would be disappointed with Wittgenstein if what he meant in the quote was truly "mathematician's discussions are finite, and they all end." to mean the discussions as per se, as you keep on insisting.

But I know your insistence comes from your misunderstanding of Wittgenstein, and what he meant was the concept of infinite in mathematics is actually "finite", henceforth his usual aphoristic claim, "their discussion will end."

Ok, you can interpret him whatever way you want. But it doesn't make sense. That is the point. 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. It was a contentious topic at the time. He didn't agree with it. That is the way I understood him on the point. It was just reflecting my point very nicely for the definition of infinity. I am not trying to change your views or ideas. Just telling you about it because you wanted the argument.

With the possible exception of attempting to have you admit an error. — Banno

How can anyone admit error when the other party is pushing his wrong ideas with the misinterpretation of Wittgenstein, and inability to explain fully what the world "infinity" means, when asked?
How can one admit error when he is not in error but the other party is?

I have showen that you misattributed a remark to Wittgenstein. Cheers. — Banno

You haven't even explained what "infinity" means. W. would have said, there is no meaning on which things that cannot be described in words.

You are descending into incoherence. No discussion is not finite. A double negative that you deserve. Yes, no discussion goes on forever.

With the possible exception of attempting to have you admit an error. — Banno

So it is evident your interpretation on W. was wrong.