Philosophy Dictionary of ArgumentsHome
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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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P. Simons on Stronger/weaker - Dictionary of Arguments
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. >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. >Indistinguishability, >Stronger/weaker._____________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. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Simons I P. Simons Parts. A Study in Ontology Oxford New York 1987 |
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> Counter arguments against Simons
> Counter arguments in relation to Strength of Theories
Ed. Martin Schulz, access date 2024-04-20