Re: Godel proved maths inconsistent not incompleteness theorem

Newberry <newberryxy@xxxxxxxxx> writes:

On Apr 18, 2:47 pm, stevendaryl3...@xxxxxxxxx (Daryl McCullough)
wrote:

You are confused about what it means to "use Euclid's
axioms". Euclid's axioms are all *provable* using ZF alone
(once the terms in Euclid have been properly translated
into the corresponding concepts in ZF).

1) I rather doubt that ZFC can prove the parallel postulate.

Of course it can. It just depends on how you interpret the geometric
terms.

2) I question whether the translation can possibly be legitimate.
Geometry is synthetic; it is about the properties of the physical
space. The rest of mathematics is analytic. You cannot derive geometry
from logic/set theory any more than you can derive physics from logic/
set theory. (Needles to say you can reason about physics and geometry
using logic and mathematics proper, but that goes without saying.)

Er, yeah, good point. Aside from the fact that you claim the rest of
math is analytic without proof and the odd assumption that a synthetic
theory can't "legitimately" be interpreted in an analytic theory.
Those two details seem to come out of thin air, but the rest is
air-tight.

You *do* realize that no one is talking about "deriv[ing] geometry
from logic/set theory", don't you?

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