Philosophy Lexicon of Arguments

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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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HC I 39
S4/Hughes/Cresswell: T + Np> NNP - (weaker) - S5: T + M> NMP (stronger) - both are stronger than T -
HC 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.)
HC 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.

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.

Cr I
M. J. Cresswell
Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988

M. J. Cresswell
Structured Meanings Cambridge Mass. 1984

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Ed. Martin Schulz, access date 2018-04-21