More Precisely: The Math You Need to Do Philosophy

From the Preface Anyone doing philosophy today needs to have a sound understanding of a wide range of basic mathematical concepts. Unfortunately, most applied mathematics texts are designed to meet the needs of scientists. And much of the math used in the sciences is not used in philosophy. You're looking at a mathematics book that's designed to meet the needs of philosophers. More Precisely introduces the mathematical concepts you need in order to do philosophy today. As we introduce these concepts, we illustrate them with many classical and recent philosophical examples. This is math for philosophers. It's important to understand what More Precisely is and what it isn't. More Precisely is not a philosophy of mathematics book. It's a mathematics book. We're not going to talk philosophically about mathematics. We are going to teach you the mathematics you need to do philosophy. We won't enter into any of the debates that rage in the current philosophy of math. Do abstract objects exist? How do we have mathematical knowledge? We don't deal with those issues here. More Precisely is not a logic book. We're not introducing you to any logical calculus. We won't prove any theorems. You can do a lot of math with very little logic. If you know some propositional or predicate logic, it won't hurt. But even if you've never heard of them, you'll do just fine here. More Precisely is an introductory book. It is not an advanced text. It aims to cover the basics so that you're prepared to go into the depths on the topics that are of special interest to you. To follow what we're doing here, you don't need anything beyond high school mathematics. We introduce all the technical notations and concepts gently and with many examples. We'll draw our examples from many branches of philosophy - including metaphysics, philosophy of mind, philosophy of language, epistemology, ethics, and philosophy of religion.