Lexicon 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.