GrandMinnow

No, that set is a member of the power set of the power set of the set of real numbers. And I don't understand the rest of your post, starting with "an...

No, your argument is nothing like Cantor's argument. Cantor proved that there does not exist a surjection from the one set onto the other, peforce tha...

What is the name and author of the text? The axiom of infinity is not a mathematical object named 'infinity'. Moreover, the axiom of infinity itself i...

This post got out of sequence. I put the text in my next post.

I wrote "isomorphism" in scare quotes because I don't mean an actual function. I mean that tuples and sequences are "isomorphic" in that you can recov...

If you like I can recommend a few textbooks in first order predicate logic and then set theory that would provide you with a self-course in this subje...

That's not how we say it. Rather, we say the cardinality of N equals the cardinality of E. card(N) = card(E) The even numbers in N are just the member...

This post by TheMadFool was supposed to rolled into this thread: This is a question from an elementary math book: u = u + 1. (i) Find the value of u (...

I wouldn't state it that way. If we mean first order Peano arithmetic (PA), then there are not in PA definitions of 'set', 'class', and 'proper class'...

There are two different domains of discussion: (1) mathematics itself and (2) philosophy of mathematics. (1) MATHEMATICS ITSELF (There are forms of ma...

Did Brouwer describe Hilbert's formal theories as a 'game'? Maybe he did, but I think it was Weyl's mention of a 'game' that Hilbert was most salientl...

Without unique readability we wouldn't even have true in one reading and not in another. Without unique readability we wouldn't even have the recursiv...

Unique readability affords definition by recursion, and definition by recursion affords the method of models, which provides that every statement has ...

Proving unique readability is necessary for proving the definition by recursion theorems. Each formal system will have its own proofs of unique readab...

There are different variants of formalism. Only a quite extreme variant holds that mathematics is meaningless, let alone that it is useless.

Right, standard analysis does not admit infinitesimals. However, calculus can be formulated in non-standard analysis or in internal set theory, as tho...

Yes, it is not a problem in itself to refer to 'games'. If is fair enough to say that Hilbert took mathematics, in a certain regard, as concerned with...

I did not claim to address, let alone undermine, your thesis. I set straight certain of the mathematical subjects you mentioned. That is not pedantic....

That was not Hilbert's view. It seems you are confusing Hilbert with Russell. That is terribly incorrect. Godel's result is that, for any S that is a ...