FOM: second-order logic is a myth
Charles Silver
csilver at sophia.smith.edu
Wed Mar 10 12:40:23 EST 1999
On Wed, 10 Mar 1999, Pat Hayes wrote:
> Charlie Silver writes:
>
> > To me, the major point that separates (intuitive) quantification
> >from set theory is that you can say "for all x..." without implying that
> >the x's must be *in* something. For example, take: "All Canada geese fly
> >south for the winter." I don't think anything in this statement implies
> >that in addition to there being some number of geese there is also a *set*
> >of geese.
>
> Surely it isn't proper to think of a set as a container.
I'm sorry if my terminology obscured my point. Robert Black also
called attention to the fact that 'container' is not a good term. Perhaps
I can state it better this way: There's a difference between quantifying
over some number of objects and quantifying over a *set* of objects. My
example concerned Canada geese and the notion that they could be
quantified over. Ask yourself whether the geese must be in a *set* prior
to being quantified over. I think they don't. They don't have to be "in"
anything. They don't even have to be "lassoed," to use a notion
attributed to Kripke. Set theory is concerned with whether certain sets
exist. For example, a choice set. I asked whether there's a theory that
has much of the strength of set theory but doesn't require that the
objects be *in* something. Robert Black suggested mereology may be one
such theory. I haven't looked into this yet.
Charlie
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