File spoon-archives/marxism2.archive/marxism2_1996/96-07-10.220, message 115


Date: Wed, 19 Jun 1996 17:17:07 -0500
From: rahul-AT-peaches.ph.utexas.edu (Rahul Mahajan)
Subject: Re: ..cat


>     The intuitiionist argument (see Brouwer) is that
>just writing 1, 2, 3, ... or an 8 on its side is not a
>complete description.  These are labels, or indicators,
>but not complete descriptions.  In fact they argue that
>finite mentalities cannot "fully describe" infinity by
>any means.  Of course intuitionism is a minority view
>among mathematicians.
>Barkley Rosser

I didn't recognize the name earlier. Brouwer was the guy who rejected the
axiom of the excluded middle and wanted to rebuild mathematics using only
constructive proofs (funny, I don't think there's a constructive proof of
his famous fixed-point theorem.). It always seemed totally bizarre to me.
Fortunately, other mathematicians didn't agree, or we'd only have 10% of
the mathematics that we  actually have.

Anyway, the definition of infinity is a lot further along than 1,2,3,... or
an 8 on its side. The simplest definition I know is that an infinite set is
one that is equipollent with at least one proper subset of itself (i.e.,
there exists a bijection between them). Describes infinity well enough for
me, but then reductio ad absurdum was always good enough for me too.

Rahul




     --- from list marxism2-AT-lists.village.virginia.edu ---


   

Driftline Main Page

 

Display software: ArchTracker © Malgosia Askanas, 2000-2005