Retired Cambridge professor Peter Smith has distilled his experience in teaching philosophers and mathematicians about formal logic into a free, frequently updated (last updated: 2017) study guide to logic, constructed to be easily accessible, with quick-start guides for different kinds of learners, written on the assumption of very little education in either maths or philosophy.

It is perhaps worth pausing to ask whether you, as a budding philosopher, really do want or need to pursue your logical studies much further if you have already worked through a book like mine or Paul Teller’s or Nick Smith’s. Far be it from me to put people off doing more logic: perish the thought! But for many philosophical purposes, you might well survive by just reading this:

Eric Steinhart, More Precisely: The Math You Need to Do Philosophy* (Broadview 2009) The author writes: ‘The topics presented . . . 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, uncount- able 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 stu- dents. It is also useful as a reference book for any philosopher working today.’Steinhart’s book is admirable, and will give many philosophers a handle on some technical ideas going well beyond ‘baby logic’ and which they really should know just a little about, without all the hard work of doing a full mathematical logic course. What’s not to like? It could be enough for you. And then, if there indeed turns out to be some particular area (modal logic, for example) that seems especially germane to your particular philosophical interests, you always can go to the relevant section of this Guide for more.

Teach Yourself Logic 2017: A Study Guide [Peter Smith/Logic Matters]

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(*Image: Eric Gaba, CC-BY-SA; Steve Jurvetson, CC-BY*)