- Gödel(as a historical figure in mathematical logic)
- Kurt Gödel was a 20th-century mathematician and logician who proved that any consistent formal system (a set of logical rules) is incomplete—meaning there are true statements it can't prove.
- Incompleteness results(as used in mathematical logic)
- Mathematical theorems proving that in any logical system complex enough to describe math, there will always be true statements that the system cannot prove to be true.
- Procedural account(as what the statement argues is undermined)
- An explanation based on the idea that something is true or valid simply because it follows the correct step-by-step process or rules.
- Syntactic provability(what the claim says is being confused with metaphysical necessity)
- The ability to prove something is true by following the mechanical rules and symbols of a formal system, like solving an equation by the rules of algebra.
- induction(Offered as the mechanism behind empirical universality.)
- The empirical method by which observations are generalized into rules; yields only comparative or assumed universality, not strict universality.
- proposition(Used in the context of a semantic theory sensitive to differences in subject matter.)
- The content expressed by a sentence, individuated at least in part by the subject matter of the sentence and the contents of its subsentential expressions.
- semantic truth(Tarski's conception, adopted by Carnap from Foundations of Logic and Mathematics (1939) onward)
- A conception of truth defined via semantic rules relating expressions to their interpretations, as opposed to purely syntactic derivability.