Description: "Barbara", one of the fundamental syllogisms of Aristotelian logic. All
ph is ps , and all ch is ph , therefore all ch is
ps . In Aristotelian notation, AAA-1: MaP and SaM therefore SaP.
For example, given "All men are mortal" and "Socrates is a man", we can
prove "Socrates is mortal". If H is the set of men, M is the set of
mortal beings, and S is Socrates, these word phrases can be represented
as A. x ( x e. H -> x e. M ) (all men are mortal) and
A. x ( x = S -> x e. H ) (Socrates is a man) therefore
A. x ( x = S -> x e. M ) (Socrates is mortal). Russell and
Whitehead note that "the syllogism in Barbara is derived from
[[ syl ]" (quote after Theorem *2.06 of WhiteheadRussell p. 101).
Most of the proof is in alsyl . There are a legion of sources for
Barbara, including http://www.friesian.com/aristotl.htm ,
http://plato.stanford.edu/entries/aristotle-logic/ , and
https://en.wikipedia.org/wiki/Syllogism . (Contributed by David A.
Wheeler, 24-Aug-2016)