The syllogism & the laws. Valid syllogistic forms and the laws of identity, non-contradiction and excluded middle are foundational and correct — the bedrock of deductive reasoning for 2,000 years.
Term logic only. It reasons about categories ("all men…") but can't express relations ("every number has a successor") or nested quantifiers — a real ceiling, unseen for millennia.
Thought complete — wasn't. Kant called it finished; Frege (1879) proved otherwise with predicate logic. And "Aristotelian authority" in physics actively held science back for centuries.
A syllogism has three terms — a subject S, a predicate P, and a middle M that links them — and three lines: two premises and a conclusion. The trick is that validity depends only on the shape, not the content: get the form right and the conclusion cannot be false if the premises are true. Pick the two premises below and the machine rules on whether the famous chain holds.
Beneath every syllogism sit three rules so basic they feel like nothing — until you try to think without them. Aristotle was the first to state them as laws.
A thing is what it is. Each term must hold its meaning steady through the argument.
Nothing can both be and not be, in the same respect, at the same time. The one he called the firmest of all.
Either a statement holds or its denial does — no third option. (Later logics would dare to question this one.)
"It is the mark of an educated mind to be able to entertain a thought without accepting it." — Aristotle
Aristotle wrote on nearly everything — logic, physics, biology, the soul, ethics, politics, poetry — and largely founded each as a field. His logic was so complete-seeming that Kant, twenty centuries later, declared it finished and perfect. It was neither.
Gate kept on. The syllogism is real and valid — but it is term logic: it speaks only of whole categories. It cannot express a relation ("Alice is taller than Bob") or stack quantifiers ("for every number there is a larger one") — the sentences mathematics actually runs on. That ceiling stood, invisible, until Gottlob Frege's predicate logic in 1879 blew the roof off. And the flip side of his genius: "the Philosopher's" authority in physics — heavier things fall faster, the heavens are perfect circles — became dogma that delayed science until Galileo. Father of logic, yes. Last word on it, no — and the lineage from here runs straight toward the man who finished what he started.