Editing Term logic (section)

== Syllogism in the second figure ==

This is what Robin Smith says in English that Aristotle said in Ancient Greek: "... If M belongs to every N but to no X, then neither will N belong to any X. For if M belongs to no X, neither does X belong to any M; but M belonged to every N; therefore, X will belong to no N (for the first figure has again come about)."<ref>{{cite book |author=Robin Smith |title=Aristotle: Prior Analytics |page=7}}</ref>

The above statement can be simplified by using the symbolical method used in the Middle Ages:

:If MaN
:
:but MeX
:
:then NeX.
:
:For if MeX
:
:then XeM
:
:but MaN
:
:therefore XeN.

When the four syllogistic propositions, a, e, i, o are placed in the second figure, Aristotle comes up with the following valid forms of deduction for the second figure:

:MaN, MeX; therefore NeX

:MeN, MaX; therefore NeX

:MeN, MiX; therefore NoX

:MaN, MoX; therefore NoX

In the Middle Ages, for mnemonic reasons they were called respectively "Camestres", "Cesare", "Festino" and "Baroco".<ref>{{cite book |title=The Cambridge Companion to Aristotle |page=41}}</ref>