What *is* a mereotopological implicature? For one, it is NOT 'merely' (to
use McEvoy's favourite adverb) a topological implicature.
In a message dated 1/26/2016 10:19:25 A.M. Eastern Standard Time,
donalmcevoyuk@xxxxxxxxxxx writes:
the view that "Things are more than the sum of their parts" is better
termed "holism" rather than "emergence".
Note that in the above, McEvoy is NOT subscribing to the truth of the
alleged axiom, "Things are more than the sum of their parts." Therefore, to
support that the alleged extra is a mere implicature I report a dialogue
between Russell and Moore.
Cheers,
Speranza
MOORE (to Russell): Come in. Come in.
RUSSELL: Very well, if that is in fact truly what you wish. Moore, do you
have any eggs in that basket?
MOORE: No.
RUSSELL: Moore, do you, then, have SOME eggs in that basket?
MOORE: No.
RUSSELL: Moore, do you, then, have EGGS in that basket?
MOORE: Yes.
RUSSELL: And how many eggs do you have?
MOORE: Ten.
RUSSELL: That is, five and five.
MOORE: Yes.
RUSSELL: And would you agree that, as McEvoy reports, 'things', i.e. your
ten eggs, "are more than the sum of their parts" -- each egg, I mean -- or,
if you wish, the shell, the white, and the yolk of each of your ten eggs?
MOORE: How do you mean?
RUSSELL: In symbols: do you disagree that 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
+ 1 = 10.
MOORE: Synthetic a priori.
RUSSELL: I was not asking you to ascribe a philosophical status, alla Kant,
of the proposition. Just its truth.
MOORE: Are you implicating that I should NOT keep all my eggs in one
basket?
RUSSELL: Well, that's ONE way of putting it.
MOORE: Look. I have ten eggs in the basket. All I can say is that IF I had
3 more eggs, I would have 13 eggs. And I can further say that IF I were to
have double 13, I'd have 26 eggs. If 4 eggs were removed, 22 eggs would
remain. Ergo, I would have 12 more eggs than I have now.
RUSSELL: Mereological implicatures, you delight in them, don't you?
MOORE: Mereotopological Implicatures, if you MUST.
REFERENCES
Burkhardt, H., and Dufour, C.A., 1991, "Part/Whole I: History" in
Burkhardt, H., and Smith, B., eds., Handbook of Metaphysics and Ontology.
Muenchen:
Philosophia Verlag.
Casati, R., and Varzi, A., 1999. Parts and Places: the structures of
spatial representation. MIT Press.
Eberle, Rolf, 1970. Nominalistic Systems. Kluwer.
Etter, Tom, 1996. Quantum Mechanics as a Branch of Mereology in Toffoli
T., et al., PHYSCOMP96, Proceedings of the Fourth Workshop on Physics and
Computation, New England Complex Systems Institute.
Forrest, Peter, 2002, "Nonclassical mereology and its application to
sets", Notre Dame Journal of Formal Logic 43: 79-94.
Gruszczynski R., and Pietruszczak A., 2008, "Full development of Tarski's
geometry of solids", Bulletin of Symbolic Logic 14: 481-540. A system of
geometry based on Lesniewski's mereology, with basic properties of
mereological structures.
Hovda, Paul, 2008, "What is classical mereology?" Journal of Philosophical
Logic 38(1): 55-82.
Lucas, J. R., 2000. Conceptual Roots of Mathematics. Routledge. Chpts.
9.12 and 10 discuss mereology, mereotopology, and the related theories of A.N.
Whitehead, all strongly influenced by the unpublished writings of David
Bostock.
Pietruszczak A., 1996, "Mereological sets of distributive classes", Logic
and Logical Philosophy 4: 105-22. Constructs, using mereology, mathematical
entities from set theoretical classes.
Pietruszczak A., 2005, "Pieces of mereology", Logic and Logical Philosophy
14: 211-34. Basic mathematical properties of Lesniewski's mereology.
Srzednicki, J. T. J., and Rickey, V. F., eds., 1984. Lesniewski's Systems:
Ontology and Mereology. Kluwer.
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