A syllogism is composed of two statements, from which a third one, the conclusion, is inferred. Categorical syllogisms are syllogisms made up of three categorical propositions. They are a type of deductive argument, that is, the conclusion (provided the argument form is valid) follows with necessity from the premises. Here are two examples:

	(1)	All Greeks are mortal.

		All Athenians are Greeks.

		Therefore all Athenians are mortal.


	(2)	All mammals are animals.

		All humans are mammals.

		Therefore all humans are animals.

Such arguments were formulated by ancient Greek logicians and have been used by logicians ever since. Hence the trite examples. Both of these categorical syllogisms have the same form. Each one has two premises and a conclusion. The first premise in a standard form categorical proposition is the major premise; the second is the minor premise. The two premises share a common term, called the middle term. In the first example, the middle term is "Greeks"; in the second, "mammals". Since each one has the middle term in common, we cannot distinguish between the premises by means of the middle term. What indicates that the first premise is the major premise is the presence of the predicate term of the conclusion: "mortal" in the first example; "animals" in the second. Similarly, the minor premise contains the subject term of the conclusion--"Athenians" and "humans" respectively. The form of these two syllogisms--and of every other Figure 1 (figure will be explained below) standard form categorical syllogism--can be easily displayed:

	Major Premise:		Middle Term		Predicate Term

	Minor Premise:		Subject Term		Middle Term

	Conclusion:		Subject Term		Predicate Term

Moreover, each of the three propositions in each example is an A proposition: All S are P. Thus we can display the form again, calling attention not only to the position of the terms, but also to the kind of propositions used:

		Major Premise:		All M are P.

		Minor Premise:		All S are M.

		Conclusion:		All S are P.

NOTE: Exercise 2 provides you an opportunity to analyze categorical syllogisms.

Every standard form categorical syllogism will have three terms, with each one used twice in the three propositions which make up the syllogism. The predicate term will be used in the major premise and the conclusion, the subject term in the minor premise and conclusion and the middle term in the two premises. The arrangement of the four propositions--A, E, I or O--determines the mood, or ordering of the three propositions which make up the syllogism. A syllogism with all A propositions, such as those above, is one in mood AAA. One with E propositions as the major premise and conclusion and an I proposition as the minor premise would be in mood EIE. Thus the order of propositions determines the mood of a categorical syllogism. Since there are four kinds of categorical propositions and three propositions in each syllogism, there are 64 possible syllogistic moods. Moreover, there are 16 possible arrangements of the four kinds of propositions with each A, E, I or O proposition serving as the major premise:

		AAA		EAA		IAA		OAA
		AAE		EAE		IAE		OAE
		AAI		EAI		IAI		OAI
		AAO		EAO		IAO		OAO

		AEA		EEA		IEA		OEA
		AEE		EEE		IEE		OEE
		AEI		EEI		IEI		OEI
		AEO		EEO		IEO		OEO

		AIA		EIA		IIA		OIA
		AIE		EIE		IIE		OIE
		AII		EII		III		OII
		AIO		EIO		IIO		OIO

		AOA		EOA		IOA		OOA
		AOE		EOE		IOE		OOE
		AOI		EOI		IOI		OOI
		AOO		EOO		IOO		OOO

These 64 moods can be arranged in four figures, with the figure being determined by the position of the middle term. Since the middle term cannot occur in the conclusion, there are only four possible arrangements of the terms: the middle term can be the subject or predicate of the major premise or the subject or predicate of the minor premise. The usual arrangement of these four figures is this:

		M P		P M		M P		P M
	  (1)	S M	  (2)	S M	  (3)	M S	  (4)	M S
		---		---		---		---
		S P		S P		S P		S P

Since there are 64 moods and four figures, there are 256 possible categorical syllogisms. Each of these 256 syllogisms are distinguished from one another by a distinct mood and figure. Examples (1) and (2) above are AAA-1 categorical syllogisms. Their mood is AAA and their figure is the first one.

NOTE: Exercise 3 provides practice in identifying the mood and figure of syllogisms and constructing syllogisms.

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Copyright © 1999, Michael Eldridge