FOM: second-order logic is a myth

Charles Silver csilver at sophia.smith.edu
Wed Mar 10 12:40:23 EST 1999

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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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