Learn formal logic in three months
Three months of focused work — 30 minutes a day — takes a curious adult through propositional and first-order predicate logic, including natural deduction proofs and basic metatheory. About 50 hours total. Enough to read a logic-heavy philosophy paper or open a discrete math textbook without the symbols feeling alien.
3 months · ~50 hours · construct and verify proofs in propositional and predicate logic
1.Logic: A Very Short Introduction — Graham Priest
A 150-page paperback that gives you the lay of the land — what logic is, why classical logic isn't the only one, where the field has gone since Frege. Read it before anything technical. Priest is a working logician and writes with the dry precision of someone who has watched undergraduates struggle with this material for thirty years.
~$12 paperback
Logic: A Very Short Introduction →2.forall x — open-source logic textbook
The free textbook that has quietly become the standard intro logic text at North American universities. P.D. Magnus's original and the Calgary remix are both excellent; pick the Calgary edition for the wider exercise set. Work through every problem. The natural-deduction system is the same one used in Carnap.io, the free online proof checker — pair the two and you have a real course.
Free
forall x: Calgary →3.How to Prove It — Daniel Velleman
Velleman's book is technically about mathematical proof, but its first three chapters are the cleanest introduction to predicate logic and proof technique anyone has written. Once you finish forall x's propositional logic chapters, switch to Velleman for the predicate-logic and proof-construction material. This is where logic becomes a tool you can use rather than a notation you can read.
~$35 paperback
How to Prove It →If this doesn't fit you
If your interest is informal logic — argument analysis, fallacies, rhetoric — skip the formal path entirely. Read Walton's Informal Logic and Govier's A Practical Study of Argument. You'll be able to dissect newspaper editorials and won't be able to do a single natural-deduction proof. For most lawyers, journalists, and managers, that's the right trade.
Why this path
Logic is the rare subject where free resources beat paid ones outright — forall x is genuinely better than the textbooks it replaces, and Carnap.io grades proofs faster than any tutor. Priest gives you the intellectual context first so the symbols mean something. Velleman extends the formal machinery into the proofs working mathematicians actually write. Skipping the exercises is the only way to fail this; logic is a craft, and reading proofs is not the same as constructing them.