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Syllogism

Definition

A syllogism is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.

Related concepts

Abstract logic Accident (philosophy)Ackermann set theory Affirmative conclusion from a negative premise Aleph number Algebraic logic Alpha Alphabet (formal languages)Ancient Greek language Ancient Philosophy (journal)Apodicticity Argument Argumentation theory Aristotle Arity Assertoric Assertoricity Atomic formula Atomic model (mathematical logic)Atomic sentence Austrian Empire Automata theory Automated theorem proving Axiom Axiom of choice Axiom schema Axiomatic system Axiomatization of Boolean algebras Banach–Tarski paradox Baroco Begriffsschrift Bernard Bolzano Beta Bijection Binary operation Boethius Bohemia Boolean algebra Boolean algebras canonically defined Boolean function Buddhist logic Cantor's diagonal argument Cantor's paradox Cantor's theorem Cardinality Cartesian product Categorical proposition Categorical theory Categories (Aristotle)Category (mathematics)Category of sets Category theory Cf.Charles Leonard Hamblin Church encoding Church–Turing thesis Class (set theory)Classical logic Codomain Cognitive Psychology (journal)Compactness theorem Complement (set theory)Complete theory Computability theory Computable function Computable set Computably enumerable set Concrete category Conditional syllogism Congregation for the Doctrine of the Faith Conservative extension Consistency Constructible universe Construction of the real numbers Constructive set theory Continuum hypothesis Copi Copula (linguistics)Countable set De dicto De re Decidability (logic)Decidable sublanguages of set theory Decision problem Deductive reasoning Deductive system Definition Diagram (mathematical logic)Dictum de omni et nullo Differentia Disjunctive syllogism Distribution of terms Domain of a function Edward N. Zalta Element (mathematics)Elementary diagram Elementary equivalence Elementary function arithmetic Empty set Enthymeme Enumeration Epagoge (moth)Epicheireme Equiconsistency Equivalence relation Euclid's Elements Euclidean geometry Existential fallacy Existential quantification Expression (mathematics)Extension by definitions Extension by new constant and function names Extensionality Fallacy of exclusive premises Fallacy of the undistributed middle Finitary relation Finite-valued logic Finite model theory Finite set First-order logic Fixed-point logic Forcing (mathematics)Formal fallacy Formal grammar Formal language Formal proof Formal semantics (logic)Formal system Formation rule Foundations of geometry Foundations of mathematics Francis Bacon Free logic Free variables and bound variables Function (mathematics)Functional predicate Fuzzy set Gamma General set theory Genus (philosophy)George Boole Gottlob Frege Graph (discrete mathematics)Grothendieck universe Ground expression Ground formula Gödel's completeness theorem Gödel's incompleteness theorems Gödel numbering Halting problem Harvard University Press Hereditary set Higher-order logic Hilbert's axioms Hilbert system History of logic History of mathematical logic Hypothetical syllogism Illicit major Illicit minor Image (mathematics)Immanuel Kant Inaccessible cardinal Independence (mathematical logic)Inductive reasoning Inference Infinite-valued logic Infinite set Infix notation Information theory Inhabited set Injective function Interpretation (logic)Interpretation (model theory)Interpretation function Intersection (set theory)Irving Copi Isagoge Isomorphism Jan Łukasiewicz Jean Buridan John Buridan John Corcoran (logician)Journal of Philosophical Logic Journal of Symbolic Logic Kolmogorov complexity Kripke's theory of truth Kripke–Platek set theory Lambda calculus Large cardinal Laws of Thought Legal syllogism Lemma (mathematics)Lindström's theorem List of Hilbert systems List of axioms 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 List of valid argument forms Logic Logica nova Logica vetus Logical biconditional Logical conjunction Logical connective Logical consequence Logical constant Logical disjunction Logical equality Logical equivalence Logical fallacy Logical truth Logicism Löwenheim–Skolem theorem Many-valued logic Map (mathematics)Material conditional Mathematical logic Mathematical object Metalanguage Methuen Publishing Michael Frede Middle Ages Minimal axioms for Boolean algebra Minor Premise (film)Mnemonic Modal logic Model complete theory Model theory Monadic predicate calculus Monadic second-order logic Morse–Kelley set theory NP (complexity)Naive set theory Natural deduction Negation Negative conclusion from affirmative premises New Foundations Non-Euclidean geometry Non-logical symbol Non-standard model Non-standard model of arithmetic On Interpretation Open formula Operation (mathematics)Ordinal analysis Ordinal number Organon P (complexity)P versus NP problem Paradoxes of set theory Particular proposition Partition of a set Peano axioms Peter Abelard Peter Lang (publisher)Philosophia (journal)Philosophy in Review Philosophy of mathematics Polysyllogism Port-Royal Logic Posterior Analytics Power set Predicable Predicate (grammar)Predicate (mathematical logic)Predicate logic Predicate variable Prime model Primitive recursive arithmetic Primitive recursive function Principia Mathematica Prior Analytics Problem of multiple generality Prometheus Books Proof of impossibility Proof theory Property (philosophy)Proposition Propositional calculus Propositional formula Propositional variable Prosleptic syllogism Psychological Bulletin Quantifier (logic)Quantifier rank Quasi-syllogism Rectangle Recursion Recursive set Relation (mathematics)Reverse mathematics Rhombus Robinson arithmetic Roman Rota Rule of inference Russell's paradox Satisfiability Saturated model Scholasticism 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 Signature (logic)Simon Blackburn Singleton (mathematics)Skolem arithmetic Socrates Sophistical Refutations Soundness Spectrum of a sentence Spectrum of a theory Square (geometry)Square of opposition Stanford Encyclopedia of Philosophy Statistical syllogism Stoic logic Strength (mathematical logic)String (formal languages)Structure (mathematical logic)Substitution (logic)Substructure (mathematics)Sum of Logic Supertask Surjective function Susanne Bobzien Syllogistic fallacy Symbol (formal)Syncategorematic term 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 The False Subtlety of the Four Syllogistic Figures The Laws of Thought The Oxford Dictionary of Philosophy Theorem Theories of truth Theory (mathematical logic)Therefore sign Three-valued logic Timeline of mathematical logic Timothy Smiley Topics (Aristotle)Transfer principle Transitive set True arithmetic 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 proposition Universal quantification Universal set Universe (mathematics)Urelement Validity (logic)Variable (mathematics)Venn diagram Von Neumann universe Von Neumann–Bernays–Gödel set theory Well-formed formula Zermelo–Fraenkel set theory

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