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

"R. Srinivasan" <sradhakr@xxxxxxxxxx> wrote in message
news:1178611917.763611.280950@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
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.

Axiom sets are created by the very real work of formulating a concensus, or
general agreement, that resolves the contradictions in the previous state of
affairs.

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.

In the sense that agreements can change when revolutions occur, yes they are
temporary.

In the present case Phil is presupposing an infinite set of natural numbers
by "definition" or fiat, and then picking and choosing a subset of axioms to
proceed with.

karl m


.

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