# Categorical Syllogism – 4 Figures: Major and Minor Premise, Conclusion

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• Syllogisms can refer to cats, birds, Canadians, green cheese on the moon, whatever; but once one removes the icky layers of emotional or affective content, which can obscure the processes of thought, one sees that there are only a few different types of syllogisms.

• In the first place, there are exactly 4×4×4 = 64 different ways in which we can arrange the letters A, I, E, O as a triple; that is there are precisely 64 different moods. Let us look at one of these moods, say AAA, in which all three statements are universal affirmatives. Consider the major premise. It involves the terms M and P. In how many different ways can you make an A out of these two terms? There are just two ways; you can say All P are M or you can say All M are P. That is, it.

• The same holds for the minor premise; you can say All S are M or you can say All M are S. On the other hand, for the conclusion you don’t have a choice at all. If the conclusion is to be an A statement, it must be All S are P. This gives us a total of 2×2×1 = 4 possible syllogisms in the AAA mood. The same holds for each one of the other 64 possible moods, giving a grand total of 64×4 = 256 possible syllogisms. As we shall see, very few of these possibilities are valid syllogisms, i.e., valid forms of reasoning.

• Using the mood and figure of a syllogism 256 different types of distinct categorical syllogisms exist, resulting from 4 kinds of major premises, 4 kinds of minor premises, 4 kinds of conclusions and 4 positions of the middle term.

• Classically, of all 256 possible syllogisms, only 19 were considered valid. Later, Of the 256, only 24 are valid forms. Of the 24 valid forms, 15 are unconditionally valid, and 9 are conditionally valid. That a Syllogism Is Valid Means That If Both Premises Are True, Then The Conclusion Must Also Be True.