FOM: second-order logic is a myth

Charles Silver csilver at
Tue Mar 9 06:29:40 EST 1999

On Mon, 8 Mar 1999, Stephen G Simpson wrote:

> Robert Black 4 Mar 1999 11:18:06 writes:
>  > OR You insist that plural quantification is just a sneaky way of talking
>  > about sets.  (Despite the joky way in which I presented it, this is
>  > actually my own preferred option, and it appears to be Steve's too.

> Yes, that is my preferred option, at least in those cases when plural
> quantification can't be straightforwardly paraphrased in terms of
> singular quantification. 

Robert Black:

>  > ... But then it seems that you will have to concede that set
>  > theoretical reasoning pervades our thought concerning just about
>  > any topic,

> I don't concede that.
> My point is that set theory is not part of logic. 

	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.  Does anyone know of a theory with much of the power of set
theory that doesn't imply the existence of some sort of container? 

Charlie Silver
Smith College

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