@misc{Lexicon of Arguments, title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 28 Mar 2024}, author = {Bigelow,John}, subject = {Completeness}, note = {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.}, note = { Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 }, file = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=747085} url = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=747085} }