Philosophy Lexicon of Arguments

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Simons, Peter
 
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Stronger/weaker I 8
Stronger/weaker/mereology/Bostock/Simons: weaker: to accept a sum instead of least upper bound. - (Still relatively strong). - This is needed for Bostocks analogy of parts and subsets. - SimonsVs - strong classical mereology: there are sums that are too large or too heterogeneous. - In Hasse diagram, the lower parts are not part of the higher. - That means, these do not "consist" of them.
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I 88
even stronger: rest principle: if x is not part of a, then the difference exists x - y - The rest is the maximum supplement to the product x. y (y in x, and vice versa). - Strength: shown by the fact that the existence of appropriate binary sums and binary products is assured. - SharvyVs: instead quasi-mereology - (without rest-principle) - Assuming E.g. all sets of natural numbers that at least contain one even and one odd number, contain as part-relations the quantity inclusion - 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: not here because through the condition that an even and an odd element has to be present, {1,2} and {1,3,4} are separated.
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I 101
Problem: the systems of mereology which should avoid paradoxes of the (stronger) set theory were too strong themselves.
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I 324
Stronger/weaker/Simons: E.g. equivalence of various formulations collapses when the principles of the theory are weakened. - (> Indistinguishability).

Si I
P. Simons
Parts Oxford New York 1987


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Ed. Martin Schulz, access date 2017-03-28