Metalogic

Definition

Metalogic is the metatheory of logic. Whereas logic studies how logical systems can be used to construct valid and sound arguments, metalogic studies the properties of logical systems. Logic concerns the truths that may be derived using a logical system; metalogic concerns the truths that may be derived about the languages and systems that are used to express truths.

Related concepts

Alphabet Argument Aristotle Axiom Cantor's diagonal argument Cantor's theorem Charles Sanders Peirce Church–Turing thesis Completeness (logic)Consistency Cut-elimination theorem David Hilbert Decidability (logic)Deductive system Effective method Emil Leon Post Empty set Encyclopedia of Mathematics Entscheidungsproblem European Mathematical Society First-order logic Formal grammar Formal language Formal proof Formal semantics (logic)Formal system Formation rule Foundations of geometry Foundations of mathematics Geoffrey Hunter (logician)Gerhard Gentzen Gödel's completeness theorem Gödel's incompleteness theorems Independence (mathematical logic)Interpretation (logic)Leopold Löwenheim Logic Logical consequence Logical system Löwenheim–Skolem theorem Mathematical logic Meaning (linguistics)Metalanguage Metalogic programming Metamathematics Metatheorem Metatheory Model theory Monadic predicate calculus Name Natural number Paul Bernays Power set Predicate logic Proof theory Propositional calculus Propositional logic Reference Rudolf Carnap Rule of inference Satisfiability Semantics Semiotics Sense and reference Sequent calculus Set (mathematics)Soundness String (computer science)Structure (mathematical logic)Symbol (formal)Syntax (logic)Tarski's undefinability theorem Theorem Thoralf Skolem Truth value Type–token distinction Uncountability Use–mention distinction Validity (logic)Well-formed formula Wilhelm Ackermann

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