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cu'u la xorxes
If I understand correctly, you define: hole(a,P): neither a nor any bit of a is P atom(a,P): a is P and for any split of a at most one bit of a is P. substance(a,P): a is P, some bit of a is P and no bit of a is P-atom. group(a,P): anything else. You then conclude: >However, unlike a hole, a group does contain a bit of which P >holds, since it contains an atom. But the definition allows for groups that don't contain atoms. For example, something that is not P but has some bit that is P-substance.
That occurred to me just a few minutes ago. If we join a substance of a to an individual of a, we get a group which does not consist of just an atom. This only holds of properties which take both substances and individuals: not remna (because remna is inherent individual, and its is remna-Goo that is inherent substance), but blanu: the group of two cubes, one blue only on the surface, one blue throughout.
To be more concrete: Take the property "... is a solid cube". Then a solid sphere would be a group: It is not a hole because some bits of it are solid cubes. It is not an atom, clearly. It is not a substance because it is not a solid cube. Therefore it must be a group. Yet it contains no atoms of solid cube. Probably you don't want substances to necessarily be P, just have some bit that is P and no bit that is P-atom. Then the solid sphere would be a substance with respect to "...is a solid cube".
Ouch. Just as I had to relax P(a) for groups, I have to relax it for substances. OK, back to drawing board...
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Dr Nick Nicholas. opoudjis@hidden.email http://www.opoudjis.net
University of Melbourne: nickn@hidden.email
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