Philosophy Dictionary of ArgumentsHome
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| S 4 / S 5, logic, philosophy: S 4 and S 5 are modal logical systems that differ in terms of what is expressible in them. The increase in expressiveness is achieved by adding axioms. S 5 results from S 4 by the added axiom Mp > NMp. "What is possible is necessarily possible". See also axioms, axiom systems, modal logic, modalities, stronger/weaker._____________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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Maxwell J. Cresswell on S 4 / S 5 - Dictionary of Arguments
Hughes I 39 S4/Hughes/Cresswell: T + Np> NNP - (weaker) - S5: T + M> NMP (stronger) - both are stronger than T. >Stronger/weaker, >Strength of theories, >Axiom systems. Hughes I 110 S4/Hughes/Cresswell: = T + (Lp> LLp). (s) What is necessary is necessary for logical reasons. Stronger than T, weaker than S5. S5: T + (Mp> LMp). ((s) what is possible, is necessarily possible.) Hughes I 69 Semantics/semantic models/Hughes/Cresswell: E.g. T, S4, S5 alone are insufficient to characterize the different meanings of necessity and possibility. Semantic graphs/Hughes/Cresswell: consider various worlds. >Accessibility._____________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. |
Cr I M. J. Cresswell Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988 Cr II M. J. Cresswell Structured Meanings Cambridge Mass. 1984 Hughes I G.E. Hughes Maxwell J. Cresswell Einführung in die Modallogik Berlin New York 1978 |
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Ed. Martin Schulz, access date 2024-04-27