Philosophy Lexicon of Arguments

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Strength of theories, philosophy: theories and systems can be compared in terms of their strength. With increasing expressiveness of a system, e.g. the possibility that statements refer to themselves, however, grows the risk of paradoxes. Strength and expressiveness do not always go hand in hand. Thus, e.g. the modal logical system S5, which is stronger than the system S4, is unable to establish a unique temporal order. Aspects of strength and weakness are inter alia the set of derivable sentences, or the size of the subject area of a theory or system. See also theories, systems, modal logic, axioms, axiom systems, expansion, mitigation, areas.

Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.

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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.
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.
I 101
Problem: the systems of mereology which should avoid paradoxes of the (stronger) set theory were too strong themselves.
I 324
Stronger/weaker/Simons: E.g. equivalence of various formulations collapses when the principles of the theory are weakened. - (> Indistinguishability).

Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.

Si I
P. Simons
Parts Oxford New York 1987

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Ed. Martin Schulz, access date 2017-11-24