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More Precisely: The Math You Need to Do Philosophy

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Strangely, Amazon can't seem to post the product description for More Precisely. So, as the author, I'll do it myself.

More Precisely is a mathematics book that's designed to meet the needs of philosophers. It's not a philosophy of math book and it's not a logic book - it's a math book for philosophers. More Precisely shows how to apply mathematical tools in various branches of philosophy. It gives you the foundations you need to read and write philosophical texts that use mathematical concepts and notations. The mathematical notations and concepts are introduced gradually. They are illustrated with examples taken from ethics, epistemology, metaphysics, philosophy of mind, philosophy of religion, and other branches of philosophy. The topics presented by More Precisely include: basic set theory; relations and functions; machines; probability; formal semantics; utilitarianism; and infinity. The chapters on sets, relations, and functions provide you with all you need to know to apply set theory in any branch of philosophy. The chapter of machines includes finite state machines, networks of machines, the game of life, and Turing machines. The chapter on formal semantics includes both extensional semantics, Kripkean possible worlds semantics, and Lewisian counterpart theory. The chapter on probability covers basic probability, conditional probability, Bayes theorem, and various applications of Bayes theorem in philosophy. The chapter on utilitarianism covers act utilitarianism, applications involving utility and probability (expected utility), and applications involving possible worlds and utility. The chapters on infinity cover recursive definitions, limits, countable infinity, Cantor's diagonal and power set arguments, uncountable infinities, the aleph and beth numbers, and definitions by transfinite recursion. More Precisely is designed both as a text book and reference book to meet the needs of upper level undergraduates and graduate students. It is also useful as a reference book for any philosopher working today.

I love this book. As someone who is preparing for grad school, I really wanted to be sure that I was up to date on all of the logic and mathematics that are needed to do contemporary analytic philosophy. More Precisely is an excellent tool for reaching this goal. It is incredibly informative with great examples and is very easy to read. It painlessly teaches many essential concepts, such as set theory, Bayesian inference, and modal semantics. This book should be required for all serious philosophy students.