[FOM] Primitive and defined symbols for mereology
A. Mani
a_mani_sc_gs at yahoo.co.in
Sat Jan 13 12:02:32 EST 2007
On Friday 12 Jan 2007 16:03, Neil Tennant wrote:
> Could anyone on the fom list please do me the kind favo(u)r of listing the
> preferred symbols in use among mereologists nowadays? It would be
> especially helpful if their LaTeX codes could be supplied.
>
afaik there is no unity.
try $\mathbb{F}$ $\mathbb{P}$ $\mathbb{A}$ etc
> Let me illustrate what I am after by using the easier case of set theory:
>
>
> 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?
>
unrestricted fusion can be represented by an axiom schema. In classical
mereology there were references to classes and such. Formulas can be used for
all operations and axioms... as is done in formal set theory. See the
stanford encyclop too for useful info.
http://plato.stanford.edu/entries/mereology/
> What is the best canonical source for a formal axiomatization of
> mereology?
>
There is one due to Lesniewiski. This has been adapted to rough sets too (in
the Transaction in rough sets vol-2). I think that is very expressive. There
are others of course. Casati and Varziś book (parts & places MIT 1999) is
canonical.
A. Mani
Member, Cal. Math. Soc
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