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?