The Halting Problem
The halting problem asks if it's possible to determine if any given program will halt or run forever. Alan Turing proved this fundamental problem to be undecidable.
Grelling Paradox
The Grelling paradox explores self-reference in language. It questions whether the word 'heterological' (not describing itself) applies to itself, leading to a logical contradiction.
Gödel’s Slingshot Argument
Gödel's slingshot argument challenges theories distinguishing facts from true propositions. It questions the coherence of fine-grained semantic distinctions, impacting truth and reference theories.
Gödel’s Second Incompleteness Theorem
Gödel's second incompleteness theorem states that no consistent formal system strong enough to include basic arithmetic can prove its own consistency. This profound result builds upon his first incompleteness theorem.
Gödel’s First Incompleteness Theorem
Gödel's First Incompleteness Theorem states that any consistent formal system capable of basic arithmetic contains true statements that are unprovable within the system itself. This reveals inherent limitations of formal…
Gödel-Dummett Logic
A distinct intuitionistic logic, Gödel-Dummett logic incorporates a principle of maximal elements. This allows it to articulate specific intermediate truth values situated between absolute true and false.
Gödel Sentence
A self-referential sentence in formal systems, a Gödel sentence demonstrates incompleteness theorems by asserting its own unprovability within that system. It's a cornerstone of mathematical logic.
Gödel Numbering
Gödel numbering assigns unique natural numbers to symbols, formulas, and proofs in formal systems. This allows mathematical statements to be represented as numbers, forming the basis of Gödel's incompleteness theorems.
Truth-Value Glut
A truth-value glut arises in formal semantics when a theory assigns multiple truth values to a single sentence, often due to paradoxes or underspecification. This challenges classical logic.
Glivenko’s Theorem
Glivenko's theorem in logic connects classical and intuitionistic systems. It states that any formula provable in classical logic is also provable via its double negation in intuitionistic logic.