MATHEMATICAL LOGIC OTIL PAPER

by Ian Chiswell, Wilfrid Hodges

Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can't be calculated; for example the correctness of a derivation proving a given sequent can be tested mechanically, but there is no general mechanical test for the existence of a derivation proving the given sequent. The undecidability results are proved rigorously in an optional final chapter, assuming Matiyasevich's theorem characterising the computably enumerable relations. Rigorous proofs of the adequacy and completeness proofs of the relevant logics are provided, with careful attention to the languages involved.
Optional sections discuss the classification of mathematical structures by first-order theories; the required theory of cardinality is developed from scratch. Throughout the book there are notes on historical aspects of the material, and connections with linguistics and computer science, and the discussion of syntax and semantics is influenced by modern linguistic approaches. Two basic themes in recent cognitive science studies of actual human reasoning are also introduced. Including extensive exercises and selected solutions, this text is ideal for students in logic, mathematics, philosophy, and computer science.

Genres: Logic, Mathematics, Philosophy, Science, Nonfiction

250 pages, Paperback

First published May 17, 2007

Reviews

[Cain S. · Rating 5 out of 5]

Possibly, the simplest introduction to the subject.

[Edvin Illes · Rating 4 out of 5]

Paradigm-shifting book for me. Understanding that our natural language is following the same formally defined mathematical logical framework is wild.

“The more I think about language, the more it amazes me that people ever understand each other at all.” - Kurt Gödel

[Why_de_WHU · Rating 3 out of 5]

Not enough and too simple for a math undergraduate student

[Lulu]

Logic