I 8
Stronger/weaker/mereology/Bostock/Simons: weaker: to accept a sum instead of a least upper bound is weaker (still relatively strong). This is needed for Bostocks analogy of parts and subsets. SimonsVsStrong classical mereology: there are sums that are too large or too heterogeneous. In the Hasse diagram, the lower parts are not part of the higher. This means, these do not "consist" of them.
I 88
Even stronger: the rest principle is even stronger: if x is not part of a, then the difference x - y exists. The rest is the maximum supplement to the product x. y (y in x, and vice versa).
Strength: strength is shown by the fact that the existence of appropriate binary sums and binary products is assured. SharvyVs: instead quasi-mereology (without the rest-principle), we assume e.g. that all sets of natural numbers that at least contain one even and one odd number, contain the quantity inclusion as part-relations. Then there is, although {1,2]} is a real part of the set {1,2,3,4}, no difference in the area, since {1,2} by any supplement {3,4}, {1,3,4} and { 2,3,4} can be extended to obtain {1,2,3,4}. Each of the three supplements is separated from {1,2}. That means, no average contains an even and an odd number. But because none is a clear maximum, the difference does not exist. Problem: actually {1,2} and {1,2,3,4} have the difference {3,4} (qua sets). Solution: there is no solution here because through the condition that an even and an odd element has to be present, {1,2} and {1,3,4} are separated.
I 101
Problem: the systems of mereology which should avoid paradoxes of the (stronger) set theory were too strong themselves.
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Set theory, >
Mereology, >
Paradoxes.
I 324
Stronger/weaker/Simons: e.g. the equivalence of various formulations collapses when the principles of the theory are weakened.
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Indistinguishability, >
Stronger/weaker.
