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

On 2007-05-24, in sci.logic, george wrote:
On May 24, 9:50 am, Aatu Koskensilta <aatu.koskensi...@xxxxxxxxx>
wrote:
It is also important to note that that a consistent theory might prove false
statements is a mathematical observation no more problematic than, say, the
existence of non-Archimedean fields or non-Abelian groups.

That is completely incoherent.

I'm sure it is to you. Curiously, most people studying logic are perfectly
capable of appreciating the mathematical theorem that consistent theories
can prove false statements, in the sense that while they might initially
find it puzzling, after explanations and examples they understand the
mathematical content of the assertion, and can follow the proof.

AK is about to get very abusive regarding what the community
does, and I am about to get equally contemptuous reactively
about how the community could stand to do a FEW things
DIFFERENTLY.

I liked your characterisation of my style as "arrant pedantry" better, but
perhaps it's true the community could use more tedious insulting in capitals,
with a few bizarre rants thrown in for good measure.

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.

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