|Description: "Barbara", one
of the fundamental syllogisms of Aristotelian logic. All
is , and all is , therefore all is
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
mortal beings, and S is Socrates, these word phrases can be represented
(all men are mortal) and
(Socrates is a man) therefore
(Socrates is mortal). Russell and
Whitehead note that the "syllogism in Barbara is derived..."
syl 14. (quote after Theorem *2.06 of [WhiteheadRussell] p. 101). Most
of the proof is in alsyl 1523. There are a legion of sources for Barbara,
(Contributed by David A.