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]
(via Four Short Links)
(Image: Eric Gaba, CC-BY-SA; Steve Jurvetson, CC-BY)
