X-Message-Number: 26704
Date: Wed, 27 Jul 2005 09:28:26 -0700
From: Mike Perry <>
Subject: Identity issue again
References: <>

Thomas Donaldson:

>Sorry, Mike, but your abstract definition once more fails to produce
>a clear notion of identity AS DISTINCT FROM what you call equivalence.
>How do we work out that every member of set A also belongs to set B,
>and presumably vice versa?

The definition I proposed for "identity" in this case was actually, in 
effect, a (syntactic) definition of meaning for the equality symbol. On the 
other hand, in a general mathematical context, equality indicates 
"identity" not just "equivalence"; "X = Y" should mean that X and Y are one 
and the same, unless specially noted. In set theory, we don't generally 
start with equality as primitive, so we have to define "X = Y" in more 
basic notation (set membership, quantification, etc.).

Relevance to cryonics and such: in the real world, we also deal with 
concepts of "identity" as Thomas has pointed out, and it's especially 
important here that we are clear about our intended meanings--there are 
sharp divisions of opinion on these things, as our postings well demonstrate.

Mike Perry

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