On Sep 25, 2008, at 11:11 AM, Pat Hayes wrote: (01)
> ... There's nothing inherently "non-continuous" about FOL.
> ... (02)
Well, maybe there is, in a sense. One cannot fully formalize
continuous mathematics in first-order logic. You have to be able to
quantify over 'all subsets' in order to define limits properly, and
that seems to require second-order logic. But, to return to the focus
of this thread, Tarskian semantics applies to second-order as well as
it does to first-order languages. (03)
Pat (04)
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