Handbook of the History of Logic: - Fordham University Faculty

The Development of Supposition Theory in the Later 12 th through 14 th Centuries 165
‘Every A is B’ converts per accidens to ‘Some B is A’
‘NoAisB’ converts per accidens to ‘Some B is not A’. 8
Since the universal changes to a particular, this form of conversion is sometimes
called “conversion by limitation”. 9
1.6 Syllogisms
Syllogisms form the heart of what is commonly called Aristotelian logic. A syllogism
is a special form of argument containing two premises and a conclusion, each
of which is a standard form categorical proposition. There are three terms; one of
them, the “middle” term, occurs once in each premise. Each of the other terms
occurs once in a premise and once in the conclusion. An example of a syllogism is
any argument having the following pattern:
Every M is P
SomeMisS
∴ Some S is P
The first premise is called the major premise and the second is called the minor.
These individual patterns are called “moods”, and they are classified into three
“figures”. (The first figure includes moods in which the middle term occurs as
subject in one premise and predicate in the other; in the second figure the middle
term is predicate in both, and in the third figure it is the subject in both.) Aristotle
discusses some of the first figure moods as well as all of the second and third figure
moods in chapters 4-6 of Prior Analytics I, and he discusses the remaining first
figure moods in chapter 7, for a total of 19 good moods. There are five additional
valid moods that neither he nor medieval authors mention; these are moods which
conclude with a particular proposition when its super-alternate universal version
is also provable from the same premises. 10 An example of such a mood is:
Every A is B
Every C is A
∴ Some C is B
All 24 valid moods are included in the following table. 11
8Cf. Peter of Spain, T I.15, (8). Many authors (including Aristotle) did not mention converting
the Universal Negative in this way. This conversion is a consequence of other logical relations
assumed in the square.
9An additional mode of conversion — conversion by contraposition — is discussed in section
2.5.
10Arnauld & Nicole [1662, 142]: “. . . people have been satisfied with classifying syllogisms
only in terms of the nobler conclusion, which is the general. Accordingly they have not counted
as a separate type of syllogism the one in which only a particular conclusion is drawn when a
general conclusion is warranted.”
11Some authors say that Aristotle has only 14 valid moods; these are the ones he discussed
explicitly in chapters 4-6 of the Prior Analytics. Five more are sketched in chapter 7. Medieval
authors included all 19. Aristotle also provides counterexamples for all invalid moods, for a
complete case by case coverage of all possible syllogisms.