[FOM] Primitive and defined symbols for mereology
Marcus Rossberg
mr30 at st-andrews.ac.uk
Mon Jan 15 12:18:25 EST 2007
Neil,
Le\'sniewski's mereology is formulated in his term logic. The locus
classicus for a mereology formulated in FOL is:
Henry S. Leonard and Nelson Goodman: "The calculus of individuals and
its uses", Journal of Symbolic Logic 5 (1940), pp. 45--55
and later with slight changes in the formulation in:
Nelson Goodman: The Structure of Appearance. 3rd ed. Dordrecht:
Riedel, 1977
For German readers an excellent survey covering a plethora of
different systems since (and including) Le\'sniewski (including a ton
of theorems and equivalence proofs for e.g. the systems of Le
\'snieski and Leonard/Goodman) is:
Lothar Ridder: Mereologie. Frankfurt/Main: Kosterman, 2002
Peter Simon's superb book investigates weaker mereological systems:
Peter Simons: Parts: A study in ontology, (Oxford: Oxford University
Press: 1987)
Much awaited and long overdue:
Hans Burkhardt et al. (eds.): Handbook of Mereology.
http://www.philosophiaverlag.com/philosophia.php?la=us&content=7&id=76
Hope all is well!
Best wishes,
Marcus
On 13 Jan 2007, at 15:00, Andrew Bacon wrote:
>> 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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