Logical truth

Definition

Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions. In other words, a logical truth is a statement which is not only true, but one which is true under all interpretations of its logical components. Thus, logical truths such as "if p, then p" can be considered tautologies. Logical truths are thought to be the simplest case of statements which are analytically true. All of philosophical logic can be thought of as providing accounts of the nature of logical truth, as well as logical consequence.

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Hilbert system History of logic History of mathematical logic Horseshoe (symbol)IMPLY gate If and only if Image (mathematics)Inaccessible cardinal Independence (mathematical logic)Index of logic articles Indiana Philosophy Ontology Project 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)Inverter (logic gate)Isomorphism Joint denial Knowledge Kolmogorov complexity Kripke's theory of truth Kripke–Platek set theory Lambda calculus Language, Truth, and Logic 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 NAND Logical NOR Logical biconditional Logical conjunction Logical connective Logical consequence Logical constant Logical disjunction Logical equality Logical equivalence Logical form Logical implication Logical positivism Logical positivists Logical truth table Logicism Löwenheim–Skolem theorem Many-valued logic Map (mathematics)Material conditional Material nonimplication Mathematical logic Mathematical object Metalanguage Metalogic Metamathematics Minimal axioms for Boolean algebra Modal logic Model complete theory Model theory Monadic predicate calculus Monadic second-order logic Morse–Kelley set theory NAND gate NIMPLY gate NOR gate NP (complexity)Naive set theory Name Natural deduction Necessity and sufficiency Negation New Foundations Non-Euclidean geometry Non-classical logic Non-logical symbol Non-standard model Non-standard 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