Re: geometry of negation

From: george (greeneg_at_cs.unc.edu)
Date: 02/08/05 

Date: 8 Feb 2005 15:43:53 -0800

mitch wrote:
> If you are the kind of person who believes that only Ph.D's and
> professors
> are entitled to opinions,

I don't personally know anybody like that.
Since I do not have a Ph.D., but do have a temper,
people like that (who happen to know me) generally
have better sense than to let ME KNOW that they
are like that.

> then you should read the paper,
>
> http://www.columbia.edu/~av72/papers/JANCL_2003.pdf

That's a matter of opinion. I can't say I found anything
helpful in it, other than the references to other papers.

>
> This paper discusses the geometry of negation and is entitled
> "The Geometry of Negation." For my part, it is a primer

It is most certainly NOT that.
Knowing what that paper bothers to talk about doesn't
help anyone understand anything you were ever trying
to say about the relevance (or lack thereof) of geometry
to logic.

> for village idiots like George Greene on sci.logic

Jeez, mitch. WHICH issue do you want to debate?
Whether geometry is relevant to negation or whether
George Greene is the village idiot? I can moderate
my responses to the former question but obviously
NOT to the latter! PICK A TOPIC and STICK with it!

> What follows is a discussion of geometry in classical
> logic that I had been working on. In contrast to the
> paper above, it is done entirely within the context
> of classical mathematics.

You started with "classical logic". You ended with "classical
mathematics". This is a BAD transition. You should've STAYED
with "classical logic".

> I have been trying to get a decent discussion about the foundations
of
> mathematics for a very long time. There is a problem with assuming
that
> Fregean logic is capable of representing the use of sets in
mathematics.

There are BUNCHES AND BUNCHES of problems with classical
first-order logic. The fact that it can't do sets is arguably
only the last of MANY. EVERYBODY KNOWS that classical first-
order logic can't do these things, and your allegation that "there
is a problem with assuming that" it can flaunts ignorance of two
points. The first is that everybody already knew this (so why
are you belaboring it?). The second, which is like unto it, is
that in light of these well-known problems, NOBODY DOES assume that
classical first-order logic is capable of representing sets in general.

> And, there is a good chance that mathematicians and logicians
> differ with respect to presupposing Borel's conjecture.

Mathematicians and logicians BOTH know that you get ONE theory
when you postulate Borel's conjecture and OTHER theories when you
postulate alternatives. Mathematicians are presumably more tempted
than logicians to believe that the theories on one side of that divide
are somehow blessed, while the others are cursed, or vice versa.

> But, there is too much static from imbeciles like the
> two mentioned above.

Dip***: IF that static ACTUALLY BOTHERED you, you would've TAKEN
PAINS, in your introductory message, NOT to pour gasoline on the
relevant
fire (pardon the mixture of metaphors) by calling us out all over
again.
Statements like this one and the previous one about village idiots are
guaranteed to get you MORE static, not less. IF static BOTHERS you,
then
comport YOURSELF accordingly.

>
> To those who know me and have not behaved like assholes

Well, that's a third episode, now.

>
> In a typical

Not only is nothing EVER typical, it wouldn't MATTER if it was.

> flame of one of my few postings in the last year George
> Greene challenged me to define logicism and intuitionism.

I did no such thing. I asked you to define YOUR terms.
The point of the challenge as *I* phrased it was that You Personally
Didn't Know *** about logicism or intuitionism, and you therefore
ought
to sit down and shut up (about THOSE terms at least) until AFTER you
learned
some basic DEFINITIONS of them.

> What a task!!!

Hardly. You were only being asked what YOU thought they
meant. That is always easy for EVERYbody. HARD would've been
wrapping your brain around what OTHER people meant. It is NOT
much to your credit that you have finally undertaken some of that
hard work. That is ultimately just one more fallacious appeal to
authority.

> Actually, it suffices to recommend Stewart
> Shapiro's works.

The difference between me and you is that I would NEVER have said to
you,
"your ignorant *** won't know JACK about logicism or intuitionism
until
AFTER you've read Stuart Shapiro's Philosophy of Mathematics".
I was PERFECTLY willing to have the discussion proceed from YOUR
definitions of the terms as opposed to Shapiro's. YOUR problem was
that
YOU DIDN'T HAVE any definitions of your own.

> In "Philosophy of Mathematics" he offers specific
> criteria for distinguishing between classical and intuitionistic
> mathematics.

Well, that's his terminology. The rest of us talk about classical
vs. intuitionistic LOGIC, and what anyone wants to do by way of mapping
that to a whole different way of doing MATH is, well, OVERkill.

I could go on, but I would have to forgo teaching you the lesson that
posting anything as long as what you have just posted, as a single
article, Is Just Fucking Stupid.

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