Philosophy Dictionary of ArgumentsHome
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| Completeness: Completeness typically refers to the property of a system where all necessary elements or operations exist, ensuring that every statement is either provable or disprovable within that system. See also Incompleteness, Definiteness, Determination, Distinction, Indistinguishability._____________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 Completeness - Dictionary of Arguments
I 134 Completeness/Bigelow/Pargetter: completeness occurs when our explicit semantics guarantees all and only the extroverted asserted theorems. That is, our semantics does not read anything into our language, which is not already there. >Semantics/Bigelow. Def "extroverted axiomatics"/Terminology/Bigelow/Pargetter: an axiomatics that is developed in an already existing language. >Axioms, >Axiom systems. I 135 Completeness/correspondence theory/Bigelow/Pargetter: the existence of completeness proofs provides a kind of correspondence theory. >Correspondence theory, >Proofs, >Provability. Completeness: for us, we can show that all the propositions that are true to our semantics in all possible worlds can be derived. >Derivation, >Derivability, >Possible worlds. I 137 Def completeness theorem/Bigelow/Pargetter: is a theorem that proves that if a proposition in a certain semantics is assuredly 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. We prove this by finding an interpretation according to which it is false. >Falsification, >Verification, >Verifiability._____________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 Completeness
Ed. Martin Schulz, access date 2024-04-16