JMC : Elements of Logic / by Cardinal Mercier

53. Figures and Modes of the Syllogism. -- The various forms. of the syllogism, according to the relation of the middle term with the extremes, are called by Aristotle figures (schêmata):

1st Figure: The middle term is subject in the major and attribute in the minor.

2nd Figure: The middle term is attribute in both premises.

3d Figure: The middle term is subject in both premises.

The syllogisms possible in these figures, regard being had to the quantity (universal or particular) of the propositions and their form (affirmative or negative) have been called the modes of the syllogism.

Counting all the possible modes of the syllogism, independently of their logical value, we find a total of 256 forms. Of these 24 are conclusive; and 5 of these 24 are useless without being vicious. Hence we have 19 valid and useful modes of the syllogism.

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