From: Steve (steve@multisell.com)
Date: Mon Jun 17 2002 - 08:00:32 MDT
> Date: Sun, 16 Jun 2002 06:36:43 -0700
> From: "Lee Corbin" <lcorbin@tsoft.com>
> Subject: As Many As (was Changing One's Mind)
>
> Scerir writes
>
> > In example (adapted from a recent discussion on FOM) ...
> >
> > The theorem that the set of all natural numbers {0,1,...} is
> > equinumerous with the set of all even numbers (0,2,...}, is
> > true if it is meant that every number has a double, and every
> > double is the double of one, and no more than one number.
> >
> > But if every number has a double, and every double is the
> > double of just one number, does it follow that there are "as many"
> > doubles (even numbers) as singles (integers), given the meaning
> > of "as many"? Is it correct to define "as many" or
> > "equinumerous" using the idea of 1-1 correspondence?
>
> The way that I understand it, Cantor really got somewhere with
> his definitions. Some people even called it a paradise ;-)
>
Mathematics is a fictional system and at best approximates the
world. "1" cannot possibly be another "1" (the identity statement on which
it
all rests) because the two "1"'s are in a different location/ sides of the
"=" symbol. Maths is tautologous & empty if it boils down to 1 "is" itself.
Maths is a subset of logic, which is similarly fictitious, and only
tells us about the E-2 brain/ mind, not about the external world. At
least since maths is a fiction we have the option to periodically invent new
versions. Russell & Whitehead showed that language similarly boils down to
logic, logos ... the way that the mind operates.
Steve Nichols
www.multi.co.uk/identity.htm
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