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Moods of the Categorical Syllogism

The major premise, minor premise and the conclusion of a categorical syllogism are all categorical statements. As discussed elsewhere, a categorical statement can be one of four types, A, E, I, or O. Since a syllogism uses only three statements at a time and there are four possible types of statements, there are therefore 64 possible arrangements of statement types. Each of these arrangements is call a "mood" of the syllogism. The enumeration of the moods is left as an exercise for the student.

These moods are expressed as a string of three letters corresponding to the types of the major premise, minor premise and the conclusion respectively. For example, the mood "EAO" has an E type major premise, an A type minor premise, and an O type conclusion.

There are certain rules of syllogisms that limit which moods are valid. The valid moods in each of the four possible figures are given in the table below. Just because a syllogism is in a "valid" mood does not mean that the conclusion will be true. Truth and validity as applied to logic are separate concepts. It is possible to have a valid syllogism and the conclusion be false. Generally, this is because one of the premises is false or because the same terms have slight different wordings. It is also possible to accidentally arrive at a true conclusion using an invalid syllogism.

	Figure 1	Figure 2	Figure 3	Figure 4
Major premise	middle / major M/P	major / middle P/M	middle / major M/P	major / middle P/M
Minor premise	minor / middle S/M	minor / middle S/M	middle / minor M/S	middle / minor M/S
Conclusion	minor / major S/P	minor / major S/P	minor / major S/P	minor / major S/P
Valid moods Traditional names	AAA (AAI) Barbara	AOO Baroco	OAO Bocardo	AAI Bamalip
	EAE (EAO) Celarent	AEE (AEO) Camestres	IAI Disamis	AEE Camenes
		EAE Cesare	AII Datisi	IAI Dimatis
	AII Darii		AAI Darapti
			EAO Felapton	EAO Fesapo
	EIO Ferio	EIO Festino	EIO Ferison	EIO Fresison

The moods in parentheses are considered "weak" since the same two premises can also produce a conclusion that is "universal" instead of "particular". These weaker moods are listed beside their stronger counterparts.

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Updated: September 09, 2008 00:46 -0400
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