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

Published: 2006

Total Pages: 404

ISBN-13:

DOWNLOAD EBOOK

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

Published: 2019-11-04

Total Pages: 421

ISBN-13: 100073658X

DOWNLOAD EBOOK

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.

Elements of Logical Reasoning
Elements of Logical Reasoning

Author: Jan von Plato

Publisher: Cambridge University Press

Published: 2014-01-23

Total Pages: 275

ISBN-13: 1139867768

DOWNLOAD EBOOK

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.

The Elements of Mathematical Logic
The Elements of Mathematical Logic

Author: Paul C. Rosenbloom

Publisher:

Published: 1950

Total Pages: 234

ISBN-13:

DOWNLOAD EBOOK

"This book is intended for readers who, while mature mathematically, have no knowledge of mathematical logic. We attempt to introduce the reader to the most important approaches to the subject, and, wherever possible within the limitations of space which we have set for ourselves, to give at least a few nontrivial results illustrating each of the important methods for attacking logical problems"--Preface.

Deductive Logic in Natural Language
Deductive Logic in Natural Language

Author: Douglas Cannon

Publisher: Broadview Press

Published: 2002-11-13

Total Pages: 306

ISBN-13: 9781551114453

DOWNLOAD EBOOK

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.