Definition
A syllogism is a two-premise argument built from quantified statements about classes of things — claims of the form "all", "some", or "no". From a major premise and a minor premise it draws a single conclusion, as in the textbook example: all humans are mortal; all Greeks are humans; therefore all Greeks are mortal.
The syllogism was Aristotle's great achievement and the foundation of Western logic for more than two thousand years. It was the first systematic attempt to classify valid argument patterns and to explain why they are valid.
Why it matters
How it works
A syllogism links three terms across two premises. One term, the middle term, appears in both premises and connects them, while the other two terms reappear in the conclusion. Whether the argument is valid depends entirely on how the quantifiers and terms are arranged — that is, on its logical form.
Priest uses syllogistic logic to show both the power and the limits of Aristotle's framework. It handles arguments about classes elegantly, but it cannot capture inferences involving relations or nested quantifiers. Closing that gap took the modern quantificational logic of the nineteenth century, which subsumes the syllogism as a small special case.