Philosophy Dictionary of ArgumentsHome
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| Canonical: canonical is a form of representation, which obeys certain rules of a science, e.g. a part of mathematics. The main focus here is to eliminate ambiguities and to enable unambiguous transformations._____________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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J. Bigelow on Canonicalness - Dictionary of Arguments
I 137 Canonical models/Bigelow/Pargetter: deal with maximally consistent sets of sentences to provide completeness proofs. >Models, >Completeness, >Proofs, >Provability. Canonical models were discovered only after Hughes/Cresswell 1968(1), they were described in the later work (Hughes/Cresswell 1984)(2). Definition completeness theorem/Bigelow/Pargetter: is a theorem that proves that if a proposition in a certain semantics is guaranteed true this proposition can be proved as a theorem. How can we prove this? How can we prove that each such proposition is a theorem? Solution: we prove the contraposition of the theorem: Instead: If a is assuredly true in semantics, a is a theorem We prove If a is not a theorem, it is not assuredly true in semantics. >Semantics. Then we prove this by finding an interpretation according to which it is false. >Interpretation, >Valuation. Def canonical model/Bigelow/Pargetter: provides an interpretation which guarantees that every non-theorem is made wrong in at least one possible world. >Possible worlds. I 138 We begin that there will be a sentence a, for which either a or ~a is a theorem. This can be added to the axioms to give another consistent set of sentences. Maximum consistent set of sentences/Bigelow/Pargetter: it can be proved that for the axiom systems which we deal with, there is always a maximally consistent set of sentences. >Maximum consistent. That is, a consistent set of sentences to which no further sentence can be added without making the set inconsistent. That is, for each sentence g is either γ in the set or ~ γ. W: be the set of all maximally consistent extensions of the axiom system with which we have begun. >Expansion. 1. Hughes, G. E. and Cresswell, M.C. (1968) An introduction to modal logic. London: Methuen. 2. Hughes, G. E. and Cresswell, M.C. (1984) A companion to modal logic. London: Methuen._____________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. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
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> Counter arguments against Bigelow
> Counter arguments in relation to Canonicalness
Ed. Martin Schulz, access date 2024-04-18