Math / Building Blocks
The Grammar of Proof
Logic is the grammar underneath every other page here. A proposition is a statement that is true or false; connectives (and, or, not, implies) build larger ones; quantifiers say "for every" and "there exists." Sets collect things, and a function pairs each input with exactly one output. Proof is how a claim earns its place: by showing it follows from what was already accepted.
Logic and Sets Essentials
A free proof textbook
Book of Proof teaches logic, sets, and proof techniques from the ground up.
book of proofThe formal picture
The Stanford Encyclopedia on classical logic.
sep: classical logicSets, plainly
Membership, subsets, unions, and intersections.
wiki: setsParallel and Competing Theories
Formal reasoning was developed in parallel in India and China, with different questions at the center.
Nyāya
The Indian Nyāya school built a theory of valid knowledge and a five-part inference, with an example as a required step, and argued carefully about how we come to know.
wiki: NyāyaMohist logic
The Chinese Mohists studied names, distinctions, and argument by analogy, asking when two things may be called by the same name.
wiki: Mohism