## Philosophy Lexicon of Arguments | |||

Author | Item | Excerpt | Meta data |
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Bigelow, John Books on Amazon |
Canonicalness | I 137 Canonical models/Bigelow/Pargetter: deal with maximally consistent sets of sentences to provide completeness proofs. Canonical models were discovered only after Hughes/Cresswell 1968, they were described in the later work (Hughes/Cresswell 1984). 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. Then we prove this by finding an interpretation according to which it is false. Definition canonical model/Bigelow/Pargetter: provides an interpretation which guarantees that every non-theorem is made wrong in at least one possible world. --- 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. 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. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |

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Ed. Martin Schulz, access date 2017-03-30