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)."
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 resons they were called respectively "Camestres", "Cesare", "Festino" and "Baroco".
Read more about this topic: Prior Analytics
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