Aristotelian Syllogisms

Syllogism is the word in Aristotle's Greek that is translated "deduction." In English, the term has come to refer specifically to deductive arguments with two premises. Aristotle went through all possible combinations of two premises and a conclusion that could be made with propositions of the form “All/Some A are/aren’t B” to figure out which ones were valid deductions. He identified 14 valid forms, all of which could be restated in four forms which he called "perfect."

Later logicians identified 10 more forms, which could also be restated in terms of Aristotle's four perfect forms. All 24 forms were later given names by Medieval logicians. We can call these the Aristotelian Syllogisms.

Why, in each of these cases, do the premises necessitate the conclusion? It is because one premise is a universal proposition saying something about everything of a certain sort and the other premise tells us that something else is that sort of thing. The conclusion then applies the universal premise about all things of the sort to the thing that the other premise tells us is a member of that sort. If the universal premise is really true, and the thing in question really belongs to the relevant sort, then the universal premise will, of course, have to apply to that thing.

The Perfect (or First-Figure) Syllogisms

Barbara

Celarent

Darii

Ferio

Second Figure Syllogisms

Cesare

Camestres

Festino

Baroco

Third Figure Syllogisms

Darapti

Felapton

Disamis

Datisi

Bocardo

Ferison