Prior Analytics - Syllogism in The Third Figure

Syllogism in The Third Figure

Aristotle says in the Prior Analytics, "... If one term belongs to all and another to none of the same thing, or if they both belong to all or none of it, I call such figure the third." Referring to universal terms, "... then when both P and R belongs to every S, it results of necessity that P will belong to some R."

Simplifying:

If PaS

and RaS

then PiR.

When the four syllogistic propositions, a, e, i, o are placed in the third figure, Aristotle develops six more valid forms of deduction:

PaS, RaS; therefore PiR

PeS, RaS; therefore PoR

PiS, RaS; therefore PiR

PaS, RiS; therefore PiR

PoS, RaS; therefore PoR

PeS, RiS; therefore PoR

In the Middle Ages, for mnemonic reasons, these six forms were called respectively: "Darapti", "Felapton", "Disamis", "Datisi", "Bocardo"and "Ferison".