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Aristotle's logic and the syllogism
c. 350 BC· Idea or argument· Knowledge, logic & science
Well documentedSolid records, texts or physical evidence.
The first formal system of logic: Aristotle's method of testing arguments by their form, built around the three-line syllogism.
See it on the Philosophy map →The idea
The idea: an argument's validity depends on its form, not its subject. 'All humans are mortal; all Greeks are human; so all Greeks are mortal' works for the same reason as any 'All A are B; all C are A; so all C are B.' In the Prior Analytics Aristotle sorted which patterns of 'all', 'some' and 'no' guarantee a conclusion. The main limitation: it cannot handle relations with nested quantifiers, such as 'every tenant pays some landlord.'
Why it matters
It was the standard of rigorous reasoning for over two thousand years; Kant thought logic was complete. It also pioneered using letters as variables.
Where it comes from
His six logical works, later grouped as the Organon ('tool'), survive; the Prior Analytics sets out the syllogism. Arabic and Latin commentaries spread them.
Still debated
How his system related to the rival Stoic logic of whole propositions, and whether he meant it as a method of discovery or only of proof.
Connections (2)
▸Aristotle founded Aristotle's logic and the syllogismWell documented
The connection
Aristotle claimed, with some justice, that no one before him had systematized reasoning. He introduced letters to stand for terms, defined the syllogism, and worked out which combinations of 'all', 'some' and 'no' premises guarantee a conclusion, creating the first formal logic.
When and how
Athens, around 350 BC, possibly while he was still teaching at Plato's Academy; set out in the Prior Analytics.
How we know
At the end of his Sophistical Refutations he says he found nothing earlier on reasoning to build on; the texts themselves survive.
Debates and open questions
Exactly when he developed the system is unknown, and whether Plato's method of division or Greek geometry gave him the idea is debated.
▸Aristotle's logic and the syllogism was superseded by the logic of Gottlob Frege and modern logicWell documented
The connection
For two thousand years Aristotle's syllogism ('all men are mortal; Socrates is a man...') was treated as complete; Kant said logic had not advanced a step. Frege's quantifiers handled relations and nested statements, like 'everyone loves someone,' that syllogisms could not, making the old logic a small special case of the new.
When and how
Jena, Germany, 1879, in Frege's 88-page booklet Begriffsschrift ('concept-script'), which almost no one understood at the time.
How we know
The Begriffsschrift itself; historians of logic such as William and Martha Kneale date modern logic from it, and logic textbooks now teach its methods.
Debates and open questions
Credit is shared with Boole's algebra of logic (1847) and Peirce's quantifiers (1885); and 'superseded' may overstate it, since valid syllogisms remain valid.