Thursday, September 09, 2010

Concerning plurals

A guest post from Tom McKay, who writes:

Concerning plurals, there is no problem about expressing the things you
mention within the system for plurals that I developed. (That by itself doesn't
answer the metaphysical question initially posed. But it provides some
linguistic resources for discussing it. Also note that van Inwagen himself uses
plural language when he asks when some things compose a single thing. The
relation ‘These compose that’ is non-distributively plural in its first argument
place. There is no representation of that in standard (singular) first-order
logic, without the help of set theory or mereological summing or something like
that as a means to introduce a singular representative of some things.)

Naïve set theory ordinarily allows the building of a hierarchy of sets
(some sets are members of other sets), and the plural language does not in
itself introduce anything like that.

Russell spoke of ‘a set as many’ (as well as another conception of ‘a set
as one’). But by calling it ‘a set’ he is already undermining the idea of there
being many. I think that Russell just didn’t follow this idea out in a coherent

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