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Logic and Structure
New corrected printing of a well-established text on logic at the introductory level.
Logic and Structure
Dirk van Dalen’s popular textbook Logic and Structure, now in its fifth edition, provides a comprehensive introduction to the basics of classical and intuitionistic logic, model theory and Gödel’s famous incompleteness theorem. Propositional and predicate logic are presented in an easy-to-read style using Gentzen’s natural deduction. The book proceeds with some basic concepts and facts of model theory: a discussion on compactness, Skolem-Löwenheim, non-standard models and quantifier elimination. The discussion of classical logic is concluded with a concise exposition of second-order logic. In view of the growing recognition of constructive methods and principles, intuitionistic logic and Kripke semantics is carefully explored. A number of specific constructive features, such as apartness and equality, the Gödel translation, the disjunction and existence property are also included. The last chapter on Gödel's first incompleteness theorem is self-contained and provides a systematic exposition of the necessary recursion theory. This new edition has been properly revised and contains a new section on ultra-products.
L.E.J. Brouwer – Topologist, Intuitionist, Philosopher
Dirk van Dalen’s biography studies the fascinating life of the famous Dutch mathematician and philosopher Luitzen Egbertus Jan Brouwer. Brouwer belonged to a special class of genius; complex and often controversial and gifted with a deep intuition, he had an unparalleled access to the secrets and intricacies of mathematics. Most mathematicians remember L.E.J. Brouwer from his scientific breakthroughs in the young subject of topology and for the famous Brouwer fixed point theorem. Brouwer’s main interest, however, was in the foundation of mathematics which led him to introduce, and then consolidate, constructive methods under the name ‘intuitionism’. This made him one of the main prot...
Phenomenology, Logic, and the Philosophy of Mathematics
In this 2005 book, logic, mathematical knowledge and objects are explored alongside reason and intuition in the exact sciences.
Handbook of Philosophical Logic
The ninth volume of the Second Edition contains major contributions on Rewriting Logic as a Logical and Semantic Framework, Logical Frameworks, Proof Theory and Meaning, Goal Directed Deductions, Negations, Completeness and Consistency as well as Logic as General Rationality. Audience: Students and researchers whose work or interests involve philosophical logic and its applications.
Mystic, Geometer, and Intuitionist: The dawning revolution
Luitzen Egbertus Jan Brouwer is a remarkable figure, both in the development of mathematics and in wider Dutch history. A mathematical genius with strong mystical and philosophical leanings, he advocated a constructivistic, more human view of mathematics and science. A sophisticated analysis of a crucial era of mathematical research, this book is an important insight into the life of one of its most fascinating characters.
Axiomatic Method and Category Theory
This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in ma...
The Princeton Companion to Mathematics
The ultimate mathematics reference book This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries—written especially for this book by some of the world's leading mathematicians—that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music—and much, much more. Unparalleled in its depth of ...
Brouwer meets Husserl
Can a line be analysed mathematically such a way that it does not fall apart into a set of discrete points? Are there objects of pure mathematics that can change through time? L. E. J. Brouwer argued that the two questions are related and that the answer to both is "yes", introducing the concept of choice sequences. This book subjects Brouwer's choice sequences to a phenomenological critique in the style of Husserl.
