Date: Mar 25, 2013 4:42 PM
Author: fom
Subject: Re: Mathematics and the Roots of Postmodern Thought

On 3/25/2013 11:59 AM, david petry wrote:

> The intuition, which has been articulated by many first rate
> mathematicians at least since Poincare', is that we should not
> try to talk about things that we can't actually talk about.

Frege once characterized the empty set as a "forest without trees".

Modern mereology follows Lesniewski in denying the existence of
an empty set.

Shall these be accepted as arguments to ban speaking of zero?

> Cantorian set theory, which purports to prove that there exist
> uncountable sets
> (and hence sets containing more things than we can actually
> talk about) is then seen as nonsense on an intuitive level.

Cantor's diagonal argument exposes a difficulty in
treating the continuum as being the same as the
sequence of natural numbers -- that is, as treating
infinity ambiguously.

To disentangle this issue mathematically requires a
theory of transfinite arithmetic.

Even if Cantor viewed his own conception in terms of
realism, why do you presume that this is required of
everyone else?