TonesInDeepFreeze

What passages from Frege, Russell or Hilbert do you have in mind? Frege proposed a system to derive mathematics from logic alone. That system was not ...

I bet if you put the cyber equivalent of a ravenous rat in its face like in '1984' then you could break it. Would say anything, begging like HAL 9000.

No, don't call it that. It's, at best, confusing notation. The set of all sets is: {x | x is a set} If you want, call it z: z = {x | x is a set} But w...

Meanwhile, still this: https://thephilosophyforum.com/discussion/comment/879811 You have been confused about the same thing you were confused about th...

I think you can understand this if, for a few moments, you clear your mind of the voice in it that keeps saying "I am right. I know I am right. I must...

It is exactly the point that it is not a mathematical expression, so mathematics is not called on to account for its intensionality. More generally th...

I like cities as grim and forbidding as can be, thus without palm trees.

Let S be any set other than the set of all sets. Let T be the set of all sets that are not S. T is not the set of all sets, and the set of all sets is...

Going back to your first post: No, we do not. Suppose, toward a contradiction, that there is an x such that for all y, we have that y is a member of x...

Wrong. You cannot produce a valid demonstration that There is an x and y such that x is a member of x and x is a member of y implies There is an x suc...

Got it. One can get Chat GPT to claim just about anything you want it to claim. I've gotten it to make all kinds of ridiculously false claims. I've ev...

Oh puhleeze! The point is not about the definition of 'lie' but rather that there would not be any point in you saying that it doesn't lie if you didn...

After catching Chat GPT in what seems to be a conflation of equivalence with equality (indeed equivalence and identity are not the same, while equalit...

Chat GPT got it wrong. As is common. In mathematics, equality and identity are the same. Are you serious?

We don't say what 'is a member of' means. Rather, 'member of' is the primitive relation of set theory. What happens then with that primitive is determ...

You're confused. What you skipped is my refutation (posted twice) of your claim that a set can't be both a member of itself and a member of another se...

My knowledge in mathematics is quite meager compared with people more dedicated to the study. That might be true. Also, the fact that formal logic is ...

What's worse, a population of palm trees in a city, or a city in a population of palm trees?

Members of what? Of course, every set is the set of all and only its members. And in ordinary set theory, every set is a member of another set. If by ...

That is confused. A set of all sets has as members all the sets. Let that sink in. ALL sets are members of the set of all sets. So whether a set x is ...

Virtually any student is subjected to certain instruction whether they like it or not. It would be fair to say that New Math is not good only if one a...

What is the "whole confusion"? Yes, there are people who don't know about set theory and are confused about it so that they make false and/or confused...

I don't think so. And it's clear to me. There are infinite sets that have sizes different from one another. More formally: There exist x and y such th...

There are areas of great puzzlement and disagreement in the philosophy of mathematics. But I don't know what specific confusions you refer to, specifi...

Of course. And I have many times explicitly said that no one is obligated to accept, like, or work with any given set of axioms and inference rules. B...

What I said was that it is objective to mechanically check that a purported formal proof is indeed a proof from the stated axioms and rules of inferen...

I don't say that. I say that 'infinity', applied to set theory, is not advisable, because in set theory there is no object called 'infinity', especial...

So he spent $85,000 for just a fancy noun. I told him it was not a wise purchase.

My cousin spent $85,000 on an infinity pool because he thinks that if he swims in it he will live forever.

That seems to me to be a trenchant observation.

That is one thing you say that makes sense and is correct.

For me, as a kid, New Math was wonderful. It opened my imagination to different ways of looking at mathematics, not just learning by rote how to do lo...

Of course, but I'm saying that in context of sets in mathematics, 'infinity' as a noun invites misunderstanding, especially as it suggests there is an...

It’s the reverse. In recent threads, the notion infinity has been raised with reference to mathematics - in the original posts and in replies. And I h...

Hear hear.

One can do whatever one wants with numbers. That doesn't vitiate that it is reasonable that I and others have commented on the mathematics.

I didn't say anything about 'equating to math'. Rather, the context includes mathematics, as also other posters have taken it.

Actually, in that instance I responded to the poster who has written: That is a mathematical context.

Ordinarily, one would take that to be referencing mathematics, as have posters in this thread, not just me.

'infinity pool' for example. But I'm talking about the context here.

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 rejec...

'infinity' is not an adjective.

Do you mean: If S is a subset of some set T and x is member of S, then x cannot be a member of T ? That's incorrect. By the definition of 'subset', if...

I have never argued against the point that there are different sizes (cardinalities). And I have never said that other people may not also point out t...

That is silly. Mathematicians don't claim that the mathematical sense of incompleteness trumps all other senses of that rubric in other fields. Just a...

Again, the intellectual dishonesty of the crank in action. In this case, blatant strawman by misrepresentation of what his interlocutors have said. An...

Of course. Except incompleteness (in the sense of the incompleteness theorem). I never said such a thing. Maybe other people have.

It could not be more clear. You wrote: "if we are considering the set of all natural numbers, then we thereby know that this set is infinite because t...

Yes, he is prominent, therefore natural to refer to him.

Works both ways. It would be better if I had said that. The philosophy of mathematics needs for there to be mathematics to philosophize about and deve...