Re: A Guide for Cantor Cranks

Article View: sci.logic

Article #796

#796

From: MoeBlee
Date: Tue, 29 Mar 2011 21:04

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To Mar 29, 3:48 pm, Transfer Principle <lwal...@lausd.net> wrote:

"all known proofs in ZF of the existence of
uncountable sets require both Infinity and Powerset"

and

"Without these axioms the interpretation of the diagonal argument of
Cantor is completely different from the common interpretation."

Those are quite different. To BEGIN with, the first is a clear and the
second is, at best, vague.

> In theories other than ZFC, there really can be a different
> interpretation
> of Cantor's diagonal from the common interpretation.

Interpretations aren't per a THEORY; interpretations are per a
LANGUAGE.

The LANGUAGE of ZFC can have all kinds of interpretations,
irrespective of any theories.

No matter WHAT axioms we adopt, we can interepret some sentence in the
language of ZFC in all kinds of ways.

MoeBlee

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From: MoeBlee <jazzmobe@hotmail.com>
Newsgroups: sci.logic,sci.math,comp.theory,sci.physics,aus.science
Subject: Re: A Guide for Cantor Cranks
Date: Tue, 29 Mar 2011 14:04:12 -0700 (PDT)
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