Aristotle's syllogism dominated logic for many centuries until Frege came along
All men are mortal; Socrates is a man; so Socrates is mortal. Aristotle set out this pattern of reasoning around 350 BC, and it proved so durable that Immanuel Kant declared logic essentially finished. Then in 1879 Gottlob Frege introduced quantifiers and variables, and the old system finally had a rival.
A syllogism links two premises to a conclusion. In the classic categorical form each statement says all, some, none or some-not of two categories. The premises share a middle term that drops out of the conclusion: in all humans are mortal, all Greeks are humans, therefore all Greeks are mortal, humans is the bridge that disappears.
Medieval Europe knew only part of Aristotle until the Prior Analytics resurfaced around the mid-12th century and launched what was called the New Logic. Scholars treated it as a closed, complete doctrine. Boethius had earlier kept the tradition alive through clear textbooks, Peter Abelard sharpened thinking about statements involving necessity and possibility, and Jean Buridan, perhaps the leading late medieval logician, folded syllogisms into a broader logic of consequence. After him, little happened for about two centuries.
Critics pointed to a blind spot. A syllogism guarantees that conclusions follow from assumptions but says nothing about whether the assumptions are true. Francis Bacon, in the 17th century, urged that premises about nature be tested by experiment and argued for a more inductive approach. George Boole, far from rejecting Aristotle, aimed to go beyond him by recasting logic as equations and handling statements with many terms, not just two.
Frege's Begriffsschrift made syllogistic logic a special case of a more powerful calculus, and in some academic settings first-order predicate logic replaced it. The old form survives in surprising places, though. Advocates arguing before the Roman Rota, the Catholic Church's appeals tribunal, are still required to present their arguments as syllogisms.
Source: Syllogism
