Varieties of Logic

Varieties of Logic
Author: Stewart Shapiro
Publisher:
Total Pages: 235
Release: 2014
Genre: Logic
ISBN: 0199696527

Logical pluralism is the view that different logics are equally appropriate, or equally correct. Logical relativism is a pluralism according to which validity and logical consequence are relative to something. In Varieties of Logic, Stewart Shapiro develops several ways in which one can be a pluralist or relativist about logic. One of these is an extended argument that words and phrases like "valid" and "logical consequence" are polysemous or, perhaps better, are cluster concepts. The notions can be sharpened in various ways. This explains away the "debates" in the literature between inferentialists and advocates of a truth-conditional, model-theoretic approach, and between those who advocate higher-order logic and those who insist that logic is first-order. A significant kind of pluralism flows from an orientation toward mathematics that emerged toward the end of the nineteenth century, and continues to dominate the field today. The theme is that consistency is the only legitimate criterion for a theory. Logical pluralism arises when one considers a number of interesting and important mathematical theories that invoke a non-classical logic, and are rendered inconsistent, and trivial, if classical logic is imposed. So validity is relative to a theory or structure. The perspective raises a host of important questions about meaning. The most significant of these concern the semantic content of logical terminology, words like 'or', 'not', and 'for all', as they occur in rigorous mathematical deduction. Does the intuitionistic 'not', for example, have the same meaning as its classical counterpart? Shapiro examines the major arguments on the issue, on both sides, and finds them all wanting. He then articulates and defends a thesis that the question of meaning-shift is itself context-sensitive and, indeed, interest-relative. He relates the issue to some prominent considerations concerning open texture, vagueness, and verbal disputes. Logic is ubiquitous. Whenever there is deductive reasoning, there is logic. So there are questions about logical pluralism that are analogous to standard questions about global relativism. The most pressing of these concerns foundational studies, wherein one compares theories, sometimes with different logics, and where one figures out what follows from what in a given logic. Shapiro shows that the issues are not problematic, and that is usually easy to keep track of the logic being used and the one mentioned.

Types in Logic Programming

Types in Logic Programming
Author: Frank Pfenning
Publisher: MIT Press
Total Pages: 388
Release: 1992
Genre: Computers
ISBN: 9780262161312

This collection of original research papers assesses and summarizes the impact of types on logic programming. Type theory is a well-established branch of theoretical computer science that has played an important role in the development of imperative and functional programming languages. This collection of original research papers assesses and summarizes the impact of types on logic programming. It covers all of the major themes in this burgeoning field, including simple types, regular tree types, polymorphic types, subtypes, and dependent types. Language design issues as well as semantics, pragmatics, and applications of types are discussed.The benefits that type considerations have to offer logic programming are being increasingly realized: through type checking many errors can be caught before a program is run, resulting in more reliable programs; types form an expressive basis for module systems, since they prescribe a machine-verifiable interface for the code encapsulated within a module; and types may be used to improve performance of code generated by a compiler. The research in this collection describes these benefits as well as important differences in the impact of types in functional and logic programming.

The Logic of Time

The Logic of Time
Author: Johan van Benthem
Publisher: Springer Science & Business Media
Total Pages: 308
Release: 2013-03-09
Genre: Philosophy
ISBN: 9401579474

The subject of Time has a wide intellectual appeal across different dis ciplines. This has shown in the variety of reactions received from readers of the first edition of the present Book. Many have reacted to issues raised in its philosophical discussions, while some have even solved a number of the open technical questions raised in the logical elaboration of the latter. These results will be recorded below, at a more convenient place. In the seven years after the first publication, there have been some noticeable newer developments in the logical study of Time and temporal expressions. As far as Temporal Logic proper is concerned, it seems fair to say that these amount to an increase in coverage and sophistication, rather than further break-through innovation. In fact, perhaps the most significant sources of new activity have been the applied areas of Linguistics and Computer Science (including Artificial Intelligence), where many intriguing new ideas have appeared presenting further challenges to temporal logic. Now, since this Book has a rather tight composition, it would have been difficult to interpolate this new material without endangering intelligibility.

An Introduction to Non-Classical Logic

An Introduction to Non-Classical Logic
Author: Graham Priest
Publisher: Cambridge University Press
Total Pages: 582
Release: 2008-04-10
Genre: Science
ISBN: 1139469673

This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.

Logical Pluralism

Logical Pluralism
Author: JC Beall
Publisher: Oxford University Press
Total Pages: 152
Release: 2006
Genre: Philosophy
ISBN: 0199288402

Consequence is at the heart of logic, and an account of consequence offers a vital tool in the evaluation of arguments. This text presents what the authors term as 'logical pluralism' arguing that the notion of logical consequence doesn't pin down one deductive consequence relation; it allows for many of them.

If A, Then B

If A, Then B
Author: Michael Shenefelt
Publisher: Columbia University Press
Total Pages: 352
Release: 2013-06-11
Genre: Philosophy
ISBN: 0231161050

While logical principles seem timeless, placeless, and eternal, their discovery is a story of personal accidents, political tragedies, and broad social change. If A, Then B begins with logic's emergence twenty-three centuries ago and tracks its expansion as a discipline ever since. It explores where our sense of logic comes from and what it really is a sense of. It also explains what drove human beings to start studying logic in the first place. Logic is more than the work of logicians alone. Its discoveries have survived only because logicians have also been able to find a willing audience, and audiences are a consequence of social forces affecting large numbers of people, quite apart from individual will. This study therefore treats politics, economics, technology, and geography as fundamental factors in generating an audience for logic--grounding the discipline's abstract principles in a compelling material narrative. The authors explain the turbulent times of the enigmatic Aristotle, the ancient Stoic Chrysippus, the medieval theologian Peter Abelard, and the modern thinkers René Descartes, David Hume, Jeremy Bentham, George Boole, Augustus De Morgan, John Stuart Mill, Gottlob Frege, Bertrand Russell, and Alan Turing. Examining a variety of mysteries, such as why so many branches of logic (syllogistic, Stoic, inductive, and symbolic) have arisen only in particular places and periods, If A, Then B is the first book to situate the history of logic within the movements of a larger social world. If A, Then B is the 2013 Gold Medal winner of Foreword Reviews' IndieFab Book of the Year Award for Philosophy.

Varieties of Logic

Varieties of Logic
Author: Stewart Shapiro
Publisher:
Total Pages: 226
Release: 2014
Genre: Logic
ISBN: 9780191784866

Logical pluralism is the view that different logics are equally appropriate, or equally correct. Logical relativism is a pluralism according to which validity and logical consequence are relative to something. Stewart Shapiro explores various such views. He argues that the question of meaning shift is itself context-sensitive and interest-relative.

Primarily Logic

Primarily Logic
Author: Judy Leimbach
Publisher: Routledge
Total Pages: 135
Release: 2021-09-03
Genre: Education
ISBN: 1000495299

It's never too early to start building thinking skills—skills that will spill over into other areas of the curriculum and into real life. Primarily Logic consists of a series of units designed to introduce logical thinking to young students. It is an excellent, easy-to-use starting point for teaching well-established forms of logical thinking. Each skill is introduced with examples, and then worksheets give students an opportunity to practice the skill. Group lessons and worksheets provide practice in: finding relationships, analogies, thinking logically using “all” and “none” statements, syllogisms, and deductive reasoning using logic puzzles. Logical thinking is both enjoyable and challenging for students as they build a sound foundation for further instruction in critical thinking. Suggestions for related activities are included in the Instructions for Teachers section. For easier logic activities for younger students, try Lollipop Logic. Grades 2-4

The Oxford Handbook of Philosophy of Mathematics and Logic

The Oxford Handbook of Philosophy of Mathematics and Logic
Author: Stewart Shapiro
Publisher: OUP USA
Total Pages: 850
Release: 2005-02-10
Genre: Mathematics
ISBN: 0195148770

Covers the state of the art in the philosophy of maths and logic, giving the reader an overview of the major problems, positions, and battle lines. The chapters in this book contain both exposition and criticism as well as substantial development of their own positions. It also includes a bibliography.