FOM: RE: Cantor's Diagonal Argument

[Insall]

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.