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

On 2007-05-24, in sci.logic, george wrote:
On May 24, 12:48 pm, Aatu Koskensilta
Curiously, most people studying logic are perfectly
capable of appreciating the mathematical theorem

Meta-mathematical theorem.

It is "meta-mathematical" in the sense that it concerns formal theories. It
is neverheless a perfectly ordinary mathematical theorem no more and no less
peculiar than, say, the proof that there exists a non-Archimedean field.

The fact that I am attacking a common linguistic practice
does NOT imply that I don't understand something, except
maybe why anybody as well-educated as AK will call you
stupid (after having talked with you about the subject for
over a decade) for doing it.

I think I once called you an idiot, some years ago. Since then I have
come to regard such insults pointless in news. Perhaps there have been other
incidents, but as a genral rule I don't go about calling people stupid, and
instead simply call their writings 'silly', 'bizarre', 'blathering' and so
on, when that description is apt. Yours fall in the 'bizarre' category, the
habit of liberally peppering your posts with randomly capitalized insults
adding to the amusement.

I already wrote a perhaps too snarky reply to this post of yours. I have no
intention of addressing the quite strange way you talk about mathematics and
logic, seemingly thinking that talk about models and what not is on a
different level than, say, talk about natural numbers, or this or that
arithmetical claim being true or false. Instead, I'll offer some totally
irrelevant reflections, providing you an opportunity to vent on my horrible
abusiveness.

As you say, I've been here for over a decade -- that's not much of an
accomplishment, anyone can do it given enough time, and others have been
around much longer; and as you noted elsewhere, I was once quite confused
about formal theories, models, the meaning of saying that some sentence in
the language of arithmetic is true or false, what have you. This is only to
be expected, if for no other reason than that textbooks do a piss-poor job
of explaining the relation of formal theories, results about logic, and that
sort of stuff, to the practice of mathematics, ordinary mathematical proofs,
ordinary mathematical talk. Reading posts from people like Torkel Franzen,
Keith Ramsay, Tim Chow and God knows who else, played some little part in
curing me of this sorry state.

Years ago I also engaged in debating cranks, loons, idiots, and your most
respected self, in earnest. It is an utterly pointless activity, though it
might entertain those of certain bent, and it might lead people to work
through some details they have previously glossed over. Having come to this
realisation, it seems much more rewarding to attempt to impart /understanding/,
and where confusion lurks in one's own mind, seek to /understand/. This is
only possible, as a matter of brute fact, when the people involved share the
goal of understanding, and are willing to put in some effort to actually
communicate, instead of repeating the tired routine of "It isn't", "It so is",
"It isn't", "You idiot, it so is", "It isn't". Our "debates" here are a
perfect example, what with you calling me a liar for not sharing your point
of view, and my being totally unwilling to examine your boring jumble of a
take on foundations.

Since you know I know that, what power or principality is persuading you
to abuse me by falsely claiming publicly that I do not know it? C O U L D
I T B E .... ............................... SATAN^H^H^H^H^Hthe ghost
of Torkel Franzen??????????????????

Whatever my relation to the ghost of Torkel Franzen, bless his apathetic
atheist soul, I have never claimed anything about your knowledge or lack
thereof of elementary results in logic. Forgiving the occasional technical
gaffe, it is clear from your writings that you know the basic results in
logic. It's no one else's but your own fault you've chosen to build on these
results a queer contraption of a philosophical view on foundations, a view
that leads you to ineffectually bark at people who discuss or explain these
basic results in language that you find offensive, even if, grudgingly, you
are forced to admit it's standard.

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

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

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