*More Precisely* is a rigorous and engaging introduction to the mathematics necessary to do philosophy. Eric Steinhart provides lucid explanations of many basic mathematical concepts and sets out the most commonly used notational conventions. He also demonstrates how mathematics applies to fundamental issues in various branches of philosophy, including metaphysics, philosophy of language, epistemology, and ethics. This second edition adds a substantial section on decision and game theory, as well as a chapter on information theory and the efficient coding of information.

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“*More Precisely* is a very useful tool for philosophers with a limited formal background who nevertheless aim to leave a lasting mark on the discipline.” — Nathan Salmon, Distinguished Professor of Philosophy, University of California, Santa Barbara

“Back in the day, philosophy graduate students might have been expected to complete a course in metalogic. It would be far better to complete a course that covers the topics presented here. This is excellent coverage of a wide range of mathematical ideas and techniques that are at the heart of many contemporary issues in metaphysics and epistemology.” — F. Thomas Burke, University of South Carolina

COMMENTS ON FIRST EDITION

“[*More Precisely*] addresses a need by giving an elementary presentation of a number of technical concepts used in philosophy, which previously were not collected together. It should be especially useful for students preparing for graduate work whose undergraduate training is likely to have skipped over at least some of the concepts that the book covers. The material in each chapter is presented in a very clear and engaging way, without presupposing any background beyond basic high school mathematics.” — Susan Vineberg, Wayne State University

“This is the book I wish I had when I was learning philosophy. It does an excellent job introducing students to the formal tools that philosophers use in an accessible yet rigorous way. From set theory to possible words semantics to probability theory to the mathematics of infinity, all the key concepts are taught in a way that will provide students the foundation for being solid philosophers. Moreover, the concepts are taught in an engaging way, and frequent examples are given to explain why these formal notions are philosophically relevant. I’m going to ask all my incoming graduate students to read this book. And there’s enough material in here that most philosophy professors could learn something from the book as well.” — Bradley Monton, University of Colorado, Boulder

“This is a splendid and innovative book. It explains accurately and accessibly a wide range of technical topics frequently drawn upon in philosophy. Wonderfully informative and clear, this book is a lifeline for students at undergraduate or graduate level.” — Chris Daly, University of Manchester

“This is a great resource! Philosophers have always used the tools of mathematics to make their claims clearer and more precise, even more so since the end of the nineteenth century. Until now we haven’t had a systematic way to acquire those tools. Steinhart’s book remedies the situation, presenting the fundamental ideas thoroughly and comprehensively. Highly recommended for anyone getting into the serious study of philosophy.” — Anthony Dardis, Hofstra University