|Completeness, philosophy: A) Systems are complete, if all valid statements are provable. B) The question of the completeness of a description is always concerned with specific purposes of this description within the framework of a theory which applies to the described objects. It is a peculiarity in the case of particle physics that the complete description of elementary particles does not allow the differentiation of other particles of the same type. See also incompleteness, determinateness, 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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Completeness/Bigelow/Pargetter: 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.
Definition "extroverted axiomatics"/Terminology/Bigelow/Pargetter: an axiomatics that is developed in an already existing language.
Completeness/correspondence theory/Bigelow/Pargetter: the existence of completeness proofs provides a kind of correspondence theory.
Completeness: for us, we can show that all the propositions that are true to our semantics in all possible worlds can be derived.
Definition 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.
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._____________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.
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990