Handbook of the History of Logic: - Fordham University Faculty

326 Henrik Lagerlund
nowadays sort under semantics, linguistics, or philosophy of language.
In Peter’s case the discussion starts with an outline of two rules of class inclusion
called ‘dictum de omni’ and ‘dictum de nullo’.
Dictum de omni: Nothing is subsumed under the subject term which
is not also said of the predicate term.
(In contemporary logical terms: A ⊇ B)
Dictum de nullo: Nothing is subsumed under the subject term which
is not also removed from the predicate term.
(In contemporary logical terms: A ⊆ B)
These rules are taken to be absolutely fundamental in determining the validity of
the first figure moods and they are said to explain the perfection of the first figure
moods. It is only after having clarified them that they go on to define syllogisms.
The two mentioned definitions are:
and:
A part of discourse in which it is the case that from somethings posited
something else necessarily follows,
From two posited premises another necessarily follows, which is the
conclusion.
The two premises, that is, the major and the minor premise, talked about in the
second definition include three terms, which are the logical subjects and predicates
of the two premises. The terms are called middle, major extreme and minor
extreme. The major premise include the middle and the major extreme terms,
while the minor premise include the middle and the minor extreme. The conclusion
contains the two extreme terms.
The syllogisms are divided into three figures based on the organisation of the
terms involved in the premises.
First figure: Middle and major extreme
Minor extreme and Middle
Example: Every animal is a substance
Every human being is an animal
Second figure: Major extreme and middle
Minor extreme and middle
Example: Every human being is an animal
No Stone is an animal
Third figure: Middle and major extreme
Middle and minor extreme
Example: Every human being is an animal
Every human being is rational