Re: Platonism

tchow_at_lsa.umich.edu
Date: 12/03/04 

Date: 03 Dec 2004 00:30:25 GMT

In article <41b04e6a.70649348@netnews.att.net>,
Lester Zick <lesterDELzick@worldnet.att.net> wrote:
>Not the same thing at all. Every cardinal is an ordinal, but every
>ordinal is not necessarily a cardinal unless differences between
>successive ordinals is the same. This is why I asked the question.

Not every ordinal is a cardinal, but every *finite* ordinal is a *finite*
cardinal. So the finite cardinals coincide with the finite ordinals.

Having said that, I actually feel that it's something of a mistake to say
that the finite ordinals are the *same* as the finite cardinals, since
ordinality and cardinality are such different concepts. Calling them
the same seems to commit the sin of believing that the set-theoretic
formalization of these concepts captures the concepts fully, when it
doesn't quite. 

-- 
Tim Chow       tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth.  ---Galileo, Dialogues Concerning Two New Sciences

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