Classical and Nonclassical Logics : : An Introduction to the Mathematics of Propositions /

Classical and Nonclassical Logics : : An Introduction to the Mathematics of Propositions / / Eric Schechter.

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 th...

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Superior document:Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013
VerfasserIn:
Schechter, Eric,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2021]
©2005
Year of Publication:2021
Language:English
Online Access:
Physical Description:1 online resource (520 p.) :; 39 line illus.
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100 1 |a Schechter, Eric,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Classical and Nonclassical Logics :  |b An Introduction to the Mathematics of Propositions /  |c Eric Schechter. 
264 1 |a Princeton, NJ :   |b Princeton University Press,   |c [2021] 
264 4 |c ©2005 
300 |a 1 online resource (520 p.) :  |b 39 line illus. 
336 |a text  |b txt  |2 rdacontent 
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505 0 0 |t Frontmatter --   |t Contents --   |t Part A Preliminaries --   |t Chapter 1 Introduction for teachers --   |t Chapter 2 Introduction for students --   |t Chapter 3 Informal set theory --   |t Chapter 4 Topologies and interiors (postponable) --   |t Chapter 5 English and informal classical logic --   |t Chapter 6 Definition of a formal language --   |t Part B Semantics --   |t Chapter 7 Definitions for semantics --   |t Chapter 8 Numerically valued interpretations --   |t Chapter 9 Set-valued interpretations --   |t Chapter 10 Topological semantics (postponable) --   |t Chapter 11 More advanced topics in semantics --   |t Part C Basic syntactics --   |t Chapter 12 Inference systems --   |t Chapter 13 Basic implication --   |t Chapter 14 Basic logic --   |t Part D One-formula extensions --   |t Chapter 15 Contraction --   |t Chapter 16 Expansion and positive paradox --   |t Chapter 17 Explosion --   |t Chapter 18 Fusion --   |t Chapter 19 Not-elimination --   |t Chapter 20 Relativity --   |t Part E Soundness and major logics --   |t Chapter 21 Soundness --   |t Chapter 22 Constructive axioms: avoiding not-elimination --   |t Chapter 23 Relevant axioms: avoiding expansion --   |t Chapter 24 Fuzzy axioms: avoiding contraction --   |t Chapter 25 Classical logic --   |t Chapter 26 Abelian logic --   |t Part F Advanced results --   |t Chapter 27 Harrop's principle for constructive logic --   |t Chapter 28 Multiple worlds for implications --   |t Chapter 29 Completeness via maximality --   |t References --   |t Symbol list --   |t Index 
506 0 |a restricted access  |u http://purl.org/coar/access_right/c_16ec  |f online access with authorization  |2 star 
520 |a 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. 
538 |a Mode of access: Internet via World Wide Web. 
546 |a In English. 
588 0 |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) 
650 0 |a Mathematics  |x Philosophy. 
650 0 |a Proposition (Logic). 
650 7 |a MATHEMATICS / Logic.  |2 bisacsh 
653 |a Ackermann constants. 
653 |a Banach-Tarski paradox. 
653 |a Brouwer. 
653 |a Eubulides paradox. 
653 |a Herbrand Principle. 
653 |a Heyting algebras. 
653 |a Jarden's Proof. 
653 |a adequacy. 
653 |a algorithm. 
653 |a ambiguity. 
653 |a binary operator. 
653 |a certification. 
653 |a chain order. 
653 |a comparative logic. 
653 |a consequence. 
653 |a derivation. 
653 |a detachment. 
653 |a discrete topology. 
653 |a equivalence class. 
653 |a excluded middle. 
653 |a extremes. 
653 |a functional interpretation. 
653 |a fuzzy logics. 
653 |a generated topology. 
653 |a homomorphism. 
653 |a idempotency. 
653 |a implication. 
653 |a informal set theory. 
653 |a lower set topology. 
653 |a monotone. 
653 |a natural numbers. 
653 |a parentheses. 
653 |a quantifier. 
653 |a semantic. 
653 |a symbol sharing. 
653 |a tautology. 
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856 4 0 |u https://doi.org/10.1515/9780691220147?locatt=mode:legacy 
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