Philosophy of Mathematics and Deductive Structure in Euclid's Elements

Philosophy of Mathematics and Deductive Structure in Euclid's Elements
Author: Ian Mueller
Publisher: Courier Dover Publications
Total Pages: 404
Release: 2006
Genre: Mathematics
ISBN:

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

The Elements of Formal Logic
Author: G. E. Hughes
Publisher: Routledge
Total Pages: 354
Release: 2019-11-04
Genre: Philosophy
ISBN: 1000737047

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.

Deductive Logic in Natural Language

Deductive Logic in Natural Language
Author: Douglas Cannon
Publisher: Broadview Press
Total Pages: 306
Release: 2002-11-13
Genre: Philosophy
ISBN: 1460400836

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.

Introduction to Logic

Introduction to Logic
Author: Alfred Tarski
Publisher: Courier Corporation
Total Pages: 271
Release: 2013-07-04
Genre: Mathematics
ISBN: 0486318893

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 Logical Reasoning

Elements of Logical Reasoning
Author: Jan von Plato
Publisher: Cambridge University Press
Total Pages: 275
Release: 2014-01-23
Genre: Mathematics
ISBN: 1139867768

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.

Logic, Deductive and Inductive

Logic, Deductive and Inductive
Author: Carveth Read
Publisher: Franklin Classics Trade Press
Total Pages: 408
Release: 2018-11-08
Genre:
ISBN: 9780344885792

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.