FOM: RE: Cantor's Diagonal Argument
montez at rollanet.org
Fri Jun 28 16:32:47 EDT 2002
Before 12:28, on 28 June 2002, Richard Arthur wrote:
``This first assumption, that there are infinite sets, whilst obviously
natural for a set theorist, is perhaps not as innocent as it might seem.''
I find this assumption natural, but also, I find speaking English natural.
But English, with its idioms and exceptions to the rules, is far from what I
think you mean by ``innocent''. (I hope I am understanding your intention
in this context.) Acceptance of the existence of an infinite set does
require a bit of an ontological commitment. Similarly, moving to an
English-speaking country and trying to earn a living requires a certain type
of commitment. However, studying the theory of infinite sets takes less of
an ontological commitment than beliving there is a theory of all finite
sets. Here I shall give a reference: ``Models and Ultraproducts: An
Introduction'', by J.L. Bell and A.B. Slomson, page 93, Corollary 3.5.
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