abductive reasoning abraham fraenkel abstract algebra al-farabi al-ghazali al-kindi alan turing alfred north whitehead alfred tarski algebra algebra of sets alonzo church antinomy argument argumentation theory aristotle arithmetic atomic formula averroes avicenna axiom axiom of choice axiom of determinacy axiom of power set axiom schema of replacement axiomatic system bernard bolzano bertrand russell binary operation binary relation boolean-valued model boolean function boolean satisfiability problem borel equivalence relation borel hierarchy cardinal number cardinality cartesian product category theory charles peirce classical logic cogency combinatorics completeness computability logic consistency constructible universe constructive set theory continuum hypothesis crispin wright critical thinking david hilbert deductive reasoning deductive system deontic logic descriptive set theory determinacy dharmakirti dialetheism discrete mathematics doxastic logic dynamical systems theory effective descriptive set theory elementary algebra epistemic logic equivalence class equivalence relation errett bishop fakhr al-din al-razi fallacy fictionalism finite set finitism first-order logic formal grammar formal interpretation formal language formal proof formal semantics formal system foundations of mathematics fuzzy logic game theory general set theory general topology geometry georg cantor george boole gerhard gentzen giuseppe peano god gottlob frege group theory henri lebesgue hilary putnam history of logic hyperarithmetical theory ibn hazm ibn taymiyyah ibn al-nafis inaccessible cardinal indian logic inductive reasoning inference infinitary combinatorics infinite set infinity informal logic information theory inner model theory intuitionism intuitionistic logic kanada karl weierstrass keith devlin large cardinal property leopold kronecker linear algebra linear logic list of basic topics in logic list of fallacies list of logicians list of mathematical logic topics list of paradoxes list of rules of inference list of set theory topics logic logic in china logic in islamic philosophy logic in computer science logical atomism logical connective logical consequence logicism lotfi asker zadeh ludwig wittgenstein mathematical analysis mathematical logic mathematical physics mathematics matthew foreman meagre set measurable cardinal metalogic metamath modal logic model theory monadic predicate calculus mozi nagarjuna naive set theory natural number new foundations nominalism non-monotonic logic number number theory ontology ordered pair organon paraconsistent logic paradox paul bernays paul cohen peano axioms philosophical logic philosophical realism philosophy of logic platonic realism pointclass polish space power set predicate logic principia mathematica probability theory projective hierarchy proof theory proposition propositional calculus quantification real analysis real line real number reason reasoning recursion theory relevance logic richard dedekind rough set rudolf carnap rule of inference saul kripke second-order logic set set-theoretic topology shahab al-din suhrawardi soundness statistics subset syllogism symmetric difference table of logic symbols temporal logic term logic theorem theory of computation thoralf skolem topology trigonometry truth table type theory universal set urelement validity vector space venn diagram von neumann universe wadge hierarchy well-formed formula wikibooks willard van orman quine zeno of elea zermelo set theory