Validity (logic)

Definition

In logic, specifically in deductive reasoning, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. It is not required for a valid argument to have premises that are actually true, but to have premises that, if they were true, would guarantee the truth of the argument's conclusion. Valid arguments must be clearly expressed by means of sentences called well-formed formulas.

Related concepts

Abductive reasoning Abstract logic Ackermann set theory Aleph number Algebraic logic Alphabet (formal languages)Analytic–synthetic distinction Antecedent (logic)Antinomy Argument Argumentation theory Arity Atomic formula Atomic model (mathematical logic)Atomic sentence Automata theory Automated theorem proving Axiom Axiom of choice Axiom schema Axiomatic system Axiomatization of Boolean algebras Banach–Tarski paradox Bijection Binary operation Boolean algebra Boolean algebras canonically defined Boolean function Cantor's diagonal argument Cantor's paradox Cantor's theorem Cardinality Cartesian product Categorical theory Category (mathematics)Category of sets Category theory Church encoding Church–Turing thesis Class (set theory)Classical logic Codomain Compactness theorem Complement (set theory)Complete theory Computability theory Computable function Computable set Computably enumerable set Concrete category Consequent Conservative extension Consistency Constructible universe Construction of the real numbers Constructive set theory Continuum hypothesis Contradiction Converse implication Converse nonimplication Corresponding conditional Countable set Critical thinking Decidability (logic)Decision problem Deductive closure Deductive reasoning Deductive system Definition Description Diagram (mathematical logic)Dichotomy Domain of a function Element (mathematics)Elementary diagram Elementary equivalence Elementary function arithmetic Empty set Enumeration Equiconsistency Equivalence relation Euclid's Elements Euclidean geometry Exclusive or Existential quantification Expression (mathematics)Extension by definitions Extension by new constant and function names Extensionality False (logic)Finitary relation Finite-valued logic Finite model theory Finite set First-order logic Fixed-point logic Forcing (mathematics)Formal grammar Formal language Formal proof Formal semantics (logic)Formal semantics (natural language)Formal system Formation rule Foundations of geometry Foundations of mathematics Free logic Free variables and bound variables Function (mathematics)Functional predicate Fuzzy set General set theory Grothendieck universe Ground expression Ground formula Gödel's completeness theorem Gödel's incompleteness theorems Gödel numbering Halting problem Hereditary set Higher-order logic Hilbert's axioms Hilbert system History of logic History of mathematical logic If and only if Image (mathematics)Inaccessible cardinal Independence (mathematical logic)Index of logic articles Inductive reasoning Inference Infinite-valued logic Infinite set Informal logic Information theory Inhabited set Injective function Interpretation (logic)Interpretation (model theory)Interpretation function Intersection (set theory)Isomorphism John Etchemendy Jon Barwise Kolmogorov complexity Kripke's theory of truth Kripke–Platek set theory L. T. F. Gamut Lambda calculus Large cardinal Lemma (mathematics)Lindström's theorem Linguistic entailment List of Boolean algebra topics List of Hilbert systems List of axioms List of fallacies List of first-order theories List of formal systems List of logic symbols List of logicians List of mathematical logic topics List of mathematical theories List of paradoxes List of rules of inference List of set identities and relations List of set theory topics List of statements independent of ZFC Logic Logic in computer science Logical NOR Logical biconditional Logical conjunction Logical connective Logical consequence Logical constant Logical disjunction Logical equality Logical equivalence Logical form Logical truth Logicism Löwenheim–Skolem theorem Many-valued logic Map (mathematics)Material conditional Material nonimplication Mathematical fallacy Mathematical logic Mathematical object Metalanguage Metalogic Metamathematics Minimal axioms for Boolean algebra Model complete theory Model theory Monadic predicate calculus Monadic second-order logic Morse–Kelley set theory NP (complexity)Naive set theory Name Natural deduction Necessary consequence Necessity and sufficiency Negation New Foundations Non-Euclidean geometry Non-classical logic Non-logical symbol Non-standard model Non-standard model of arithmetic Open formula Operation (mathematics)Ordinal analysis Ordinal number Outline of logic P (complexity)P versus NP problem Paradox Paradoxes of set theory Partition of a set Peano axioms Philosophical logic Philosophy of logic Philosophy of mathematics Power set Predicate (mathematical logic)Predicate logic Predicate variable Premise Prime model Primitive recursive arithmetic Primitive recursive function Principia Mathematica Probability Proof of impossibility Proof theory Proposition Propositional calculus Propositional formula Propositional variable Quantifier (logic)Quantifier rank Reason Recursion Recursive set Reductio ad absurdum Reference Relation (mathematics)Reverse mathematics Robinson arithmetic Rule of inference Russell's paradox Satisfiability Saturated model Schröder–Bernstein theorem Second-order arithmetic Second-order logic Self-verifying theories Semantic theory of truth Semantics of logic Sentence (mathematical logic)Sequent calculus Set (mathematics)Set theory Sheffer stroke Signature (logic)Singleton (mathematics)Skolem arithmetic Soundness Spectrum of a sentence Spectrum of a theory Square of opposition Statement (logic)Strength (mathematical logic)String (formal languages)Structure (mathematical logic)Substitution (logic)Substructure (mathematics)Supertask Surjective function Syllogism Symbol (formal)Syntax (logic)T-schema Tarski's axiomatization of the reals Tarski's axioms Tarski's theory of truth Tarski's undefinability theorem Tarski–Grothendieck set theory Tautology (logic)Term (logic)Term logic Theorem Theories of truth Theory (mathematical logic)Three-valued logic Timeline of mathematical logic Transfer principle Transitive set True arithmetic Truth Truth predicate Truth table Truth value Turing machine Type (model theory)Type theory Ultrafilter (set theory)Ultraproduct Uncountable set Undecidable problem Uninterpreted function Union (set theory)Uniqueness quantification Universal quantification Universal set Universe (mathematics)Urelement Variable (mathematics)Venn diagram Von Neumann universe Von Neumann–Bernays–Gödel set theory Well-formed formula Zermelo–Fraenkel set theory Ω-logic

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