Elements of Logical Reasoning
1st Edition
Published on 31. January 2014
978-1-139-69900-6 (ISBN)
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.
Reviews / Votes
'Elements of Logical Reasoning fills a gap by providing some much needed explanation and motivation to an otherwise dry literature.' Henry Towsner, The Mathematical IntelligencerMore details
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
College/higher education
Professional and scholarly
File size
3,50 MB
ISBN-13
978-1-139-69900-6 (9781139699006)
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Schweitzer Classification
Other editions
Additional editions
Jan von Plato
Elements of Logical Reasoning
Book
01/2014
Cambridge University Press
€104.90
Shipment within 15-20 days
Person
Jan von Plato is Professor of Philosophy at the University of Helsinki. He is the author of Creating Modern Probability (Cambridge University Press, 1994) and, with Sara Negri, Structural Proof Theory (Cambridge University Press, 2001) and Proof Analysis (Cambridge University Press, 2011).
Content
Part I. First Steps in Logical Reasoning: 1. Starting points; 2. Rules of proof; 3. Natural deduction; 4. Proof search; 5. Classical natural deduction; 6. Proof search in classical logic; 7. The semantics of propositional logic; Part II. Logical Reasoning with the Quantifiers: 8. The quantifiers; 9. Derivations in predicate logic; 10. The semantics of predicate logic; Part III. Beyond Pure Logic: 11. Equality and axiomatic theories; 12. Elements of the proof theory of arithmetic; Part IV. Complementary Topics: 13. Normalization and cut elimination; 14. Deductive machinery from Aristotle to Heyting.
