Editing Term logic (section)

== 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."<ref>{{cite book |author=Robin Smith |title=Aristotle: Prior Analytics |page=9 }}</ref>

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".<ref>{{cite book |title=The Cambridge Companion to Aristotle |page=41 }}</ref>