[FOM] Primitive and defined symbols for mereology
Andrew Bacon
noizhed at gmail.com
Sat Jan 13 10:00:00 EST 2007
> I am especially concerned to know how the operation of fusion is formally
> represented. With two individuals x and y, the fusion of x and y would
> seem to be representable by a two-place function-term such as f(x,y).
> But what is the convention when the fusion is taken of all the individuals
> in some infinite set? Does mereology have a way of representing this
> operation without recourse to set-theoretic notions? Or does it resort to
> the hybrid notion of the fusion of all the individuals in such-and-such a
> set or family?
I believe that fusion principles are often expressed in FOL with a
schema, for example
Unrestricted Fusion:
[ExF(x) -> EyAz[z o y <-> Ex[F(x) ^ z o x]]]
For any formula F with no free occurrences of y or z.
(I'm using E and A as existential and universal quantifiers, and o as overlap)
I've also seen them expressed using second order logic, or using
plural quantification instead of a schema (e.g. in Lewis's 'Parts of
Classes'). This way is probably better because models of mereology
with unrestricted fusions shouldn't have any countably infinite
models.
Andrew Bacon
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