@misc{Lexicon of Arguments, title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 28 Mar 2024}, author = {Cresswell,Maxwell J.}, subject = {Systems}, note = {Hughes I 65 System/Part/Hughes/Cresswell(s):parts of formulas are not themselves parts of the system already to which the formulas belong to. - ((s) "p" can never be an axiom, otherwise all sentences would be true.) Hughes I 237 Non-regular systems/Modal Logic/Hughes/Cresswell: can include formulas of the form p. ~ p where the eradication of the modal operator simply results in p, E.g. systems with e.g. C 13 MMp - "no statement is necessarily necessary" >Modal operators, >Deletion. MMp simply results in p - p. ~ p. Hughes I 243 >"Non-normal worlds"/Kripke: (here also assessed with 0). I 258 Def regular: is a system in which the modal status is maintained. >Modalities Hughes I 238 Non-regular systems/modal logics/Hughes/Cresswell: Problem: in S1 - S3, neither a nor b are themselves a thesis - they also have no common variable either. - Problem in the case of (a v b): could be valid while neither a nor b would be valid. Solution/Halldén: "normal interpretation": here either a or b is valid, but neither I-a nor I-b is valid. So there are valid formulas that are not theorems. >Theorems, >Logic, >Formulas.}, note = { 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 }, file = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=272854} url = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=272854} }