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Quantifier (logic)

Definition

In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier in the first-order formula expresses that everything in the domain satisfies the property denoted by . On the other hand, the existential quantifier in the formula expresses that there exists something in the domain which satisfies that property. A formula where a quantifier takes widest scope is called a quantified formula. A quantified formula must contain a bound variable and a subformula specifying a property of the referent of that variable.

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A Absolute generality Abstract algebra Abstract logic Accident (fallacy)Ackermann set theory Ad hominem Ad nauseam Affirmative conclusion from a negative premise Affirming a disjunct Affirming the consequent Aleph number Alethic modalities Alfred North Whitehead Alfred Tarski Algebraic logic Almost all Alonzo Church Alphabet (formal languages)Alternative semantics Ambiguity Anaphora (linguistics)Andrzej Mostowski Anecdotal evidence Animistic fallacy Antecedent-contained deletion Appeal to accomplishment Appeal to consequences Appeal to emotion Appeal to fear Appeal to flattery Appeal to loyalty Appeal to motive Appeal to nature Appeal to novelty Appeal to pity Appeal to ridicule Appeal to spite Appeal to the law Appeal to the stone Appeal to tradition Argument Argument from analogy Argument from anecdote Argument from authority Argument from fallacy Argument from incredulity Argument from silence Argument to moderation Argumentum ad baculum Argumentum ad crumenam Argumentum ad lazarum Argumentum ad populum Arity Association fallacy Atomic formula Atomic model (mathematical logic)Atomic sentence Augustus De Morgan Automata theory Automated theorem proving Autonomy of syntax Axiom Axiom of choice Axiom schema Axiomatic set theory Axiomatic system Axiomatization of Boolean algebras Banach–Tarski paradox Base rate fallacy Begging the question Begriffsschrift Bertrand Russell Bijection Binary digit Binary operation Binding (linguistics)Boolean algebra Boolean algebras canonically defined Boolean function Bound variable Bounded quantifier Branching quantifier Bulverism Cantor's diagonal argument Cantor's paradox Cantor's theorem Cardinality Cartesian product Cataphora Categorial grammar Categorical theory Category (mathematics)Category of sets Category theory Charles Sanders Peirce Cherry picking Chronological snobbery Church encoding Church–Turing thesis Circular reasoning Class (set theory)Classical logic Cliché Closure operator Codomain Coercion (linguistics)Cognitive semantics Combinatory categorial grammar Commutativity Compactness theorem Complement (set theory)Complete theory Complex question Computability theory Computable function Computable set Computably enumerable set Computational semantics Computer programming Concrete category Conditional quantifier Conditional sentence Conflation Conjunction fallacy Conservative extension Conservativity Consistency Constructible universe Construction of the real numbers Constructive set theory Context set Continuation Continuous function Continuum hypothesis Contraposition Conversational scoreboard Converse accident Correlation does not imply causation Correlative-based fallacies Countable set Counterfactuals Counting quantification Crossover effects Cumulativity (linguistics)Cylindric algebra David Hilbert De dicto and de re De se Decidability (logic)Decision problem Deductive system Definiteness Denotation Denying the antecedent Denying the correlative Deontic modality Diagram (mathematical logic)Discourse relation Discourse representation theory Disjunction Disjunction (logic)Distributional semantics Domain of a function Domain of discourse Donkey anaphora Double-barreled question Double counting (fallacy)Downward entailing Dual (mathematics)Dynamic semantics E E. C. R. Hehner Ecological fallacy Element (mathematics)Elementary diagram Elementary equivalence Elementary function arithmetic Empty set Encyclopedia of Mathematics Enumeration Epistemic modality Equiconsistency Equivalence relation Equivocation Ernst Schröder (mathematician)Etymological fallacy Euclid's Elements Euclidean geometry European Mathematical Society Even number Eventually (mathematics)Evidentiality Exhaustivity Existential closure Existential fallacy Existential graph Existential quantification Existential quantifier Expression (mathematics)Extension (semantics)Extension by definitions Extension by new constant and function names Extensionality Fallacies of illicit transference Fallacy Fallacy of accent Fallacy of composition Fallacy of division Fallacy of exclusive premises Fallacy of four terms Fallacy of relevance Fallacy of the single cause Fallacy of the undistributed middle False attribution False dilemma False equivalence False precision Faultless disagreement Faulty generalization Fermat's Last Theorem Finitary relation Finite-valued logic Finite model theory Finite set First-order formula First-order logic First-order predicate calculus Fixed-point logic Flag-waving Focus (linguistics)Forcing (mathematics)Formal fallacy Formal grammar Formal language Formal proof Formal semantics (logic)Formal semantics (natural language)Formal system Formation rule Foundations of geometry Foundations of mathematics Free choice inference Free logic Free variable Free variables and bound variables Fubini's theorem Function (mathematics)Function application Functional predicate Furtive fallacy Fuzzy set Gambler's fallacy General set theory Generalized quantifier Generative grammar Genetic fallacy Gentzen George Bentham Giuseppe Peano Givenness Glue semantics Gottlob Frege Grothendieck universe Ground expression Ground formula Gödel's completeness theorem Gödel's incompleteness theorem Gödel's incompleteness theorems Gödel numbering Halting problem Hans Reichenbach 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calculus Large cardinal Leading question Lemma (mathematics)Leon Henkin Leopold Loewenheim Lexical semantics Lindström's theorem Lindström quantifier Linguistic entailment Linguistics wars List of Hilbert systems List of axioms List of fallacies List of first-order theories List of formal systems List of mathematical theories List of set identities and relations List of statements independent of ZFC Loaded language Loaded question Logic Logic translation Logical biconditional Logical conjunction Logical connective Logical consequence Logical constant Logical disjunction Logical equality Logical equivalence Logical form (linguistics)Logical graph Logical theory Logical truth Logically equivalent Logicism Logophoricity Loki's Wager Löwenheim–Skolem theorem Many-valued logic Map (mathematics)Map–territory relation Masked-man fallacy Material conditional Mathematical analysis Mathematical fallacy Mathematical logic Mathematical object Mathematical theory Mathematics McNamara fallacy Meaning postulate Measurable Mereology Metalanguage Minimal axioms for Boolean algebra Mirativity Modal scope fallacy Modal subordination Modality (semantics)Model complete theory Model theory Modulo (jargon)Monad (functional programming)Monadic predicate calculus Monadic second-order logic Montague grammar Moral equivalence Moralistic fallacy Morse–Kelley set theory Motte-and-bailey fallacy Moving the goalposts NP (complexity)Naive set theory Natural deduction Natural language Naturalistic fallacy Negation Negative conclusion from affirmative premises New Foundations Nirvana fallacy No true Scotsman Non-Euclidean geometry Non-logical symbol Non-standard model Non-standard model of arithmetic Not invented here Noun phrases Opaque context Open formula Operation (mathematics)Ordinal analysis Ordinal number Oscar Howard Mitchell Overwhelming exception P (complexity)P versus NP problem Parade of horribles Paradoxes of set theory Partition of a set Paul Halmos Peano arithmetic Peano axioms Per Lindström Per Martin-Löf Performative utterance Philosophy of language Philosophy of mathematics Plural quantification Poisoning the well Polarity item Polyadic algebra Possible world Post hoc ergo propter hoc Power set Pragmatics Predicate (logic)Predicate (mathematical logic)Predicate logic Predicate variable Prenex normal form Presupposition Prime model Primitive recursive arithmetic Primitive recursive function Principia Mathematica Principle of compositionality Principles of Mathematical Logic Privative adjective Probability measure Pronoun Proof by assertion Proof by example Proof of impossibility Proof theory Proposition Propositional attitudes Propositional calculus Propositional formula Propositional variable Psychologist's fallacy Quantificational variability effect Quantifier elimination Quantifier raising Quantifier rank Quantifier shift Quantization (linguistics)Question under discussion Questionable cause Quoting out of context Rationalization (psychology)Real number Real numbers Recursion Recursive set Red-baiting Red herring Reductio ad Hitlerum Reference Regression fallacy Reification (fallacy)Relation (mathematics)Relation algebra Responsive predicate Reverse mathematics Rising declarative Robinson arithmetic Rule of inference Russell's paradox Sampling bias Satisfiability Saturated model Scalar implicature Schröder–Bernstein theorem Scope (formal semantics)Scope (logic)Sealioning Second-order arithmetic Second-order logic Section sign Secundum quid Segmented discourse representation theory Self-verifying theories Semantic argument Semantic domain Semantic parsing Semantic theory of truth Semantics (logic)Semantics of logic Sentence (mathematical logic)Sequent calculus Set-builder notation Set (mathematics)Set theory Signature (logic)Singleton (mathematics)Sir William Hamilton, 9th Baronet Situation semantics Skolem arithmetic Slippery slope Sloppy identity Slothful induction Sorites paradox Soundness Special pleading Spectrum of a sentence 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principle Transitive set True arithmetic Truth-conditional semantics Truth predicate Truth table Truth value Tu quoque Turing machine Two wrongs make a right Type (model theory)Type (type theory)Type shifter Type system Type theory Type theory with records Ultrafilter (set theory)Ultraproduct Uncountable set Undecidable problem Uniform continuity Uninterpreted function Union (set theory)Uniqueness quantification Universal grinder Universal quantification Universal quantifier Universal set Universe (mathematics)University of Hawaii at Manoa Urelement Vacuously true Vagueness Validity (logic)Variable (mathematics)Venn diagram Veridicality Von Neumann universe Von Neumann–Bernays–Gödel set theory Well-formed formula Whataboutism Wilhelm Ackermann Willard Van Orman Quine William Ernest Johnson Wisdom of repugnance Wishful thinking ZFC Zermelo–Fraenkel set theory ∀∃

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