Classical and Nonclassical Logics (eBook)

An Introduction to the Mathematics of Propositions

Eric Schechter (Autor)

eBook Download: PDF

2020
520 Seiten
Princeton University Press (Verlag)
978-0-691-22014-7 (ISBN)

Infos

So-called classical logic--the logic developed in the early twentieth century by Gottlob Frege, Bertrand Russell, and others--is computationally the simplest of the major logics, and it is adequate for the needs of most mathematicians. But it is just one of the many kinds of reasoning in everyday thought. Consequently, when presented by itself--as in most introductory texts on logic--it seems arbitrary and unnatural to students new to the subject. In Classical and Nonclassical Logics, Eric Schechter introduces classical logic alongside constructive, relevant, comparative, and other nonclassical logics. Such logics have been investigated for decades in research journals and advanced books, but this is the first textbook to make this subject accessible to beginners. While presenting an assortment of logics separately, it also conveys the deeper ideas (such as derivations and soundness) that apply to all logics. The book leads up to proofs of the Disjunction Property of constructive logic and completeness for several logics. The book begins with brief introductions to informal set theory and general topology, and avoids advanced algebra; thus it is self-contained and suitable for readers with little background in mathematics. It is intended primarily for undergraduate students with no previous experience of formal logic, but advanced students as well as researchers will also profit from this book.

Produkt-Details

• Erscheint lt. Verlag: 6.10.2020
• Zusatzinfo: 39 line illus.
• Sprache: englisch
• Themenwelt: Geisteswissenschaften ► Philosophie ► Allgemeines / Lexika
• Themenwelt: Geisteswissenschaften ► Philosophie ► Logik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• Schlagworte: Ackermann constants • Adequacy • Algebra • algorithm • Ambiguity • asymmetry • Axiom • axiomatic system • Axiom of choice • Banach-Tarski paradox • Binary operation • binary operator • Binary Relation • Bounded quantifier • Brouwer • Certification • chain order • Classical Logic • commutative property • comparative logic • consequence • Contradiction • counterexample • Deduction theorem • Deductive Reasoning • Degeneracy (mathematics) • De Morgan's Laws • Deontic Logic • Derivation • detachment • Diagram (category theory) • discrete topology • Disjoint sets • Elementary proof • empty set • Equation • equivalence class • Eubulides paradox • excluded middle • existential quantification • Extremes • Finite model property • First-Order Logic • formal proof • Foundations of mathematics • functional interpretation • Fuzzy Logic • Fuzzy Logics • generated topology • Goldbach's conjecture • Herbrand Principle • Heyting algebra • heyting algebras • Hilbert's program • Homomorphism • idempotency • Identity theorem • implication • inductive reasoning • inference • Infimum and supremum • Informal Logic • Informal Methods (Validation and Verification) • informal set theory • Integer • intermediate logic • intermediate value theorem • Intuitionistic Logic • Jarden's Proof • Law of noncontradiction • Linear Logic • Logic • Logical connective • Logical disjunction • logicism • lower set topology • Material implication (rule of inference) • Mathematical fallacy • Mathematical Induction • Mathematical Logic • mathematician • Mathematics • Metavariable • Modal Logic • Monotone • Monotonic Function • Naive set theory • Natural deduction • Natural number • natural numbers • Negation • Non-Classical Logic • Non-Euclidean geometry • Non-monotonic logic • Norm (mathematics) • Null set • paraconsistent logic • parentheses • Predicate logic • Predicate (mathematical logic) • proof by contradiction • Proof by contrapositive • Propositional Calculus • Pure Mathematics • Pythagorean Theorem • Quantifier • Quantifier (linguistics) • Quantifier (logic) • Quantum Logic • Range (mathematics) • Recursive set • Rule of inference • Russell's paradox • Semantic • Semantics • sequent • Set (mathematics) • set theory • Sign (mathematics) • soundness • Special case • Subset • symbol sharing • tautology • Tautology (logic) • Term logic • Theorem • Three-Valued Logic • Topology • Transitive relation • Triviality (mathematics) • Turing Machine • Uncountable set • Variable (mathematics) • Zorn's lemma
• ISBN-10: 0-691-22014-X / 069122014X
• ISBN-13: 978-0-691-22014-7 / 9780691220147