Re: Cantor's circular "proof" that evens = integers

On May 8, 12:26 am, george <gree...@xxxxxxxxxx> wrote:
On May 6, 5:04 am, Phil <toob-head...@xxxxxxxxxxxxx> wrote:

Well, I am pointing out that that is true ONLY when that
infinite set is combined with the proper axioms.

It is NOT POSSIBLE for it NOT to be so combined.
"that infinite set" DOES NOT HAVE *ANY* EXISTENCE
apart from these axioms! THAT infinite set was PRODUCED BY
*the axiom of infinity*!

That position brings you perilously close to that of NAFL, which
basically asserts that truth for formal propositions is always with
respect to axioms, i.e., with respect to axiomatic theories. The next
step you need to take is to ask what brings axioms (theories) into
"existence"? NAFL takes the stand that it is the human mind. So
infinite sets (temporarily) exist for a particular human mind if and
only if that human (temporarily) has a theory in mind that proves the
existence of infinite sets. But what if the theory in question neither
proves nor disproves the existence of infinite sets? Then infinite
sets can neither exist nor not-exist for that mind. Examining this
angle further leads to the conclusion that NAFL will not permit
theories that prove the existence of infinite sets, i.e., the theory
of hereditarily finite sets must disprove the existence of infinite
sets.

Classically the position you take may not be tenable. Existence of
infinite sets will have to be "prior" to axioms. I doubt if your
colleagues in this NG will agree with your stand.

I have been very busy with both professional and personal stuff for
the last 2-3 weeks. I will respond to your FOL vs NAFL comments (as
well as those of Jan Burse) when I can free up some time. I have not
been following this thread or others in sci.logic for a while now,
just butted in upon seeing that comment of yours.

Regards, RS

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