|Systems, philosophy of science: systems are compilations of rules for the formation of statements on a previously defined subject domain. Apart from the - usually recursive - rules for the combination of expressions or signs, the specification of the vocabulary or sign set of the system is also required. See also axioms, axiom systems, theories, strength of theories, expressiveness, rules, order, recursion, models, structure, system theory._____________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. |
Maxwell J. Cresswell on Systems - Dictionary of Arguments
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" - MMp simply results in p - p. ~ p.
Hughes I 243
>"Non-normal worlds"/Kripke: (here also assessed with 0) - Definition regular (I 258) is a system in which the modal status is maintained.
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._____________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 [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
M. J. Cresswell
Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988
M. J. Cresswell
Structured Meanings Cambridge Mass. 1984
Maxwell J. Cresswell
Einführung in die Modallogik Berlin New York 1978