Author: Thomas FowlerPublisher: Oxford : Clarendon Press
ISBN:
Category : Logic
Languages : en
Pages : 216
Book Description
The Elements of Deductive Logic
Author: Thomas FowlerPublisher: Oxford : Clarendon Press
ISBN:
Category : Logic
Languages : en
Pages : 216
Book Description
Philosophy of Mathematics and Deductive Structure in Euclid's Elements
Author: Ian MuellerPublisher: Courier Dover Publications
ISBN:
Category : Mathematics
Languages : en
Pages : 404
Book Description
A survey of Euclid's Elements, this text provides an understanding of the classical Greek conception of mathematics and its similarities to modern views as well as its differences. It focuses on philosophical, foundational, and logical questions -- rather than focusing strictly on historical and mathematical issues -- and features several helpful appendixes.
The Elements of Formal Logic
Author: G. E. HughesPublisher: Routledge
ISBN: 1000737047
Category : Philosophy
Languages : en
Pages : 354
Book Description
Originally published in 1965. This is a textbook of modern deductive logic, designed for beginners but leading further into the heart of the subject than most other books of the kind. The fields covered are the Propositional Calculus, the more elementary parts of the Predicate Calculus, and Syllogistic Logic treated from a modern point of view. In each of the systems discussed the main emphases are on Decision Procedures and Axiomatisation, and the material is presented with as much formal rigour as is compatible with clarity of exposition. The techniques used are not only described but given a theoretical justification. Proofs of Consistency, Completeness and Independence are set out in detail. The fundamental characteristics of the various systems studies, and their relations to each other are established by meta-logical proofs, which are used freely in all sections of the book. Exercises are appended to most of the chapters, and answers are provided.
Logic, Deductive and Inductive
Author: Carveth ReadDeductive Logic in Natural Language
Author: Douglas CannonPublisher: Broadview Press
ISBN: 1460400836
Category : Philosophy
Languages : en
Pages : 306
Book Description
This text offers an innovative approach to the teaching of logic, which is rigorous but entirely non-symbolic. By introducing students to deductive inferences in natural language, the book breaks new ground pedagogically. Cannon focuses on such topics as using a tableaux technique to assess inconsistency; using generative grammar; employing logical analyses of sentences; and dealing with quantifier expressions and syllogisms. An appendix covers truth-functional logic.
Elements of Logical Reasoning
Author: Jan von PlatoPublisher: Cambridge University Press
ISBN: 1139867768
Category : Mathematics
Languages : en
Pages : 275
Book Description
Some of our earliest experiences of the conclusive force of an argument come from school mathematics: faced with a mathematical proof, we cannot deny the conclusion once the premises have been accepted. Behind such arguments lies a more general pattern of 'demonstrative arguments' that is studied in the science of logic. Logical reasoning is applied at all levels, from everyday life to advanced sciences, and a remarkable level of complexity is achieved in everyday logical reasoning, even if the principles behind it remain intuitive. Jan von Plato provides an accessible but rigorous introduction to an important aspect of contemporary logic: its deductive machinery. He shows that when the forms of logical reasoning are analysed, it turns out that a limited set of first principles can represent any logical argument. His book will be valuable for students of logic, mathematics and computer science.
Introduction to Logic
Author: Alfred TarskiPublisher: Courier Corporation
ISBN: 0486318893
Category : Mathematics
Languages : en
Pages : 271
Book Description
This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. Exercises appear throughout.
Elements of Deductive Logic
Author: Noah Knowles DavisPublisher:
ISBN:
Category : Philosophy
Languages : en
Pages : 238
Book Description
Putting Logic in Its Place
Author: David ChristensenPublisher: Oxford University Press
ISBN: 0199263256
Category : Mathematics
Languages : en
Pages : 200
Book Description
What role, if any, does formal logic play in characterizing epistemically rational belief? Traditionally, belief is seen in a binary way - either one believes a proposition, or one doesn't. Given this picture, it is attractive to impose certain deductive constraints on rational belief: that one's beliefs be logically consistent, and that one believe the logical consequences of one's beliefs. A less popular picture sees belief as a graded phenomenon. This picture (explored more bydecision-theorists and philosophers of science thatn by mainstream epistemologists) invites the use of probabilistic coherence to constrain rational belief. But this latter project has often involved defining graded beliefs in terms of preferences, which may seem to change the subject away fromepistemic rationality.Putting Logic in its Place explores the relations between these two ways of seeing beliefs. It argues that the binary conception, although it fits nicely with much of our commonsense thought and talk about belief, cannot in the end support the traditional deductive constraints on rational belief. Binary beliefs that obeyed these constraints could not answer to anything like our intuitive notion of epistemic rationality, and would end up having to be divorced from central aspects of ourcognitive, practical, and emotional lives.But this does not mean that logic plays no role in rationality. Probabilistic coherence should be viewed as using standard logic to constrain rational graded belief. This probabilistic constraint helps explain the appeal of the traditional deductive constraints, and even underlies the force of rationally persuasive deductive arguments. Graded belief cannot be defined in terms of preferences. But probabilistic coherence may be defended without positing definitional connections between beliefsand preferences. Like the traditional deductive constraints, coherence is a logical ideal that humans cannot fully attain. Nevertheless, it furnishes a compelling way of understanding a key dimension of epistemic rationality.
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