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.
Generalized Quantifiers: Beyond ‘All’ and ‘Some’
Generalized quantifiers extend logical and linguistic expression beyond basic 'all' or 'some'. They enable nuanced statements about quantities like 'most', 'many', 'few', and 'no more than three'.
Geach-Kaplan Sentence
A sentence type probing philosophy of language and logic. It highlights issues of context-dependence, referential opacity, and the boundaries of formal semantic analysis, named after Peter Geach and David Kaplan.
Gap – Truth-Value Gap
A truth-value gap occurs when a statement lacks a definite truth value (true or false). This concept is crucial in logic and semantics, particularly for analyzing vague predicates and paradoxes.
Game-Theoretic Semantics
Game-theoretic semantics interprets linguistic meaning via games between verifier and falsifier. It focuses on the interactive process used to establish truth or falsehood, offering a dynamic perspective on meaning.
Gambler’s Fallacy Explained
The gambler's fallacy is the mistaken belief that past random events influence future ones. This cognitive bias often leads to poor decisions, especially in gambling, by misinterpreting statistical independence.
Fuzzy Logic Explained
Fuzzy logic is a many-valued logic that deals with degrees of truth and certainty, moving beyond traditional true/false. It enables systems to handle imprecise information.
Understanding Mathematical Functions
A function is a fundamental mathematical concept establishing a precise relationship between sets. It ensures each input from the first set maps to exactly one output in the second set,…