Gödel's second incompleteness theorem states that no consistent formal system strong enough to include basic arithmetic can prove its own…
Gödel's First Incompleteness Theorem states that any consistent formal system capable of basic arithmetic contains true statements that are unprovable…
A distinct intuitionistic logic, Gödel-Dummett logic incorporates a principle of maximal elements. This allows it to articulate specific intermediate truth…
Gödel numbering assigns unique natural numbers to symbols, formulas, and proofs in formal systems. This allows mathematical statements to be…
A truth-value glut arises in formal semantics when a theory assigns multiple truth values to a single sentence, often due…
Glivenko's theorem in logic connects classical and intuitionistic systems. It states that any formula provable in classical logic is also…
Generalized quantifiers extend logical and linguistic expression beyond basic 'all' or 'some'. They enable nuanced statements about quantities like 'most',…
A sentence type probing philosophy of language and logic. It highlights issues of context-dependence, referential opacity, and the boundaries of…
A truth-value gap occurs when a statement lacks a definite truth value (true or false). This concept is crucial in…
Frege's theorem establishes that arithmetic is reducible to logic. It demonstrates how basic arithmetic principles can be derived from logical…