Re: Why? [was Re: Cantor`s powerset theorem is false?]

Newberry wrote:
I am talking about strings of symbols that carry infinite amount of
information. They do not and cannot exist. I think it summarizes the
whole controversy. Either you believe in them or you don't. Cantor's
diagonal argument implies that they exist.

What strings of symbols? If you're talking about strings of symbols in
a formal language, then well formed formulas (certain strings of
symbols) are always finite. That should not be confused with
denumerable sequences of objects of the theory.

If they don't then there is
a bijection from N to P(N) and you need to modify your axioms.

You're just posting conclusions from your own horrible misunderstanding
of the theory. Such conclusions have nothing to do with the actual
mathematics of set theory.

There is an analogy with the non-standard models of PA, where there are
infinite numbers and there exist infinitely long proofs (i.e. strings.)

By definition, proofs are finite.

Among other thing there is a proof of Goedel's formula only it is
infinitely long.

Then it is not a proof.

Or you're referring to some kind of system than those that are referred
to by the incompleteness theorem.

In regular working mathematical logic, formulas and proofs are finite.

MoeBlee

.

Relevant Pages

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