Editing Term logic (section)

== Syllogism in the first figure ==

In the ''Prior Analytics'' translated by A. J. Jenkins as it appears in volume 8 of the Great Books of the Western World, Aristotle says of the First Figure: "... If A is predicated of all B, and B of all C, A must be predicated of all C."<ref>{{cite book |title=Great Books of the Western World |volume=8 |page=40 }}</ref> In the ''Prior Analytics'' translated by Robin Smith, Aristotle says of the first figure: "... For if A is predicated of every B and B of every C, it is necessary for A to be predicated of every C."<ref>{{cite book |author=Robin Smith |title=Aristotle: ''Prior Analytics'' |page=4 }}</ref>

Taking ''a'' = ''is predicated of all'' = ''is predicated of every'', and using the symbolical method used in the Middle Ages, then the first figure is simplified to:<ref>{{cite book|title=The Cambridge Companion to Aristotle|page=41}}</ref>

:If AaB
:
:and BaC
:
:then AaC.

Or what amounts to the same thing:

:AaB, BaC; therefore AaC

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

:AaB, BaC; therefore, AaC

:AeB, BaC; therefore, AeC

:AaB, BiC; therefore, AiC

:BeC, AiC; therefore, AoC

In the Middle Ages, for [[mnemonic]] reasons they were called "Barbara", "Celarent", "Darii" and "Ferio" respectively.<ref>{{cite book |title=The Cambridge Companion to Aristotle |page=41 }}</ref>

The difference between the first figure and the other two figures is that the syllogism of the first figure is complete while that of the second and third is not. This is important in Aristotle's theory of the syllogism for the first figure is axiomatic while the second and third require proof. The proof of the second and third figure always leads back to the first figure.<ref>{{cite book |author=Henrik Legerlund |title=Modal Syllogistics in the Middle Ages |page=6}}</ref>