Re: Epistemology 201: The Science of Science

From: Albert Wagner (albertwagner_at_cox.net)
Date: 03/22/05 

Date: Tue, 22 Mar 2005 09:19:50 -0600

robert j. kolker wrote:
>
> Albert Wagner wrote:
>
>> Mathematical terms, yes. But not mathematiker terms.
>
> You are truly a putz. Really. You are. You have been given correct
> definitions (barring few typographical errors be me, sorry about that)
> all along. You simply will not accept that the theory of infinite sets,
> as established by Cantor in 1870 and cleaned up of its paradoxes

I consider infinity to be undefined and undefinable. Cantor
treats it as a number.

> subsequently is a good working theory.

I'll grant that mathematics deals with abstractions by building
on axioms; and the nature of mathematical axioms is that they are
only coincidentally related to reality, i.e. they are fictitious.
So, Cantor's set theory is 'a good working theory' only for
mathematicians unconcerned with reality.

> Set theory is the pillar of just
> about every branch of mathematics developed or invented since its
> inception. Most of Analysis restest on Point Set Topology which rests
> squarely on set theory.

OK. No argument. My objections would only become relevant when
your 'good working theory' is applied to reality, where there are
no infinities. 

-- 
"I know that most men, including those at ease with
problems of the greatest complexity, can seldom
accept even the simplest and most obvious truth
if it be such as would oblige them to admit the falsity
of conclusions which they have delighted in explaining
to colleagues, which they have proudly taught to others,
and which they have woven, thread by thread,
into the fabric of their lives." -
	-- Tolstoy

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