50. Nature and Logical Basis of the Syllogism. -- Take for example this syllogism: The triangle which has two equal sides has two equal angles. This triangle has two equal sides. Therefore it has two equal angles.

To reason is to place within the extension of an abstract type some determinate subject, with the result of concluding that a note which belongs to the abstract type as such is attributable to this determinate subject.

The major is a necessary proposition: it asserts that the predicate of the conclusion (the property of having two equal angles) is necessarily associated with an abstract middle term (a triangle which has two equal sides).

Being abstract, this middle term is not actually universal, but it can be universalized; by an ulterior act of reflection it con be attributed to one, or to several, or to all the inferiors of a species or of a genus.

The reasoning faculty, on enunciating the minor, sees that the middle term extends to the subject of the minor -- it sees that this triangle has two equal sides.

Then, provided that the major and the minor are taken in at one glance, it will be seen that the predicate of the conclusion has two angles equal, necessarily belonging to the middle term, triangle with two sides equal, belongs to the subject of the conclusion which is within the extension of the middle term therefore the necessary connection between the subject of the conclusion and its predicate becomes obvious.

The syllogism is essentially a process of universalization. The principle on which it is founded may be thus enunciated: The note which necessarily applies to an abstract subject -- the middle term -- applies to the subjects of the extension of the middle term.

Obviously, the connection established by reasoning between the extremes and the middle term belongs at once to the comprehension and to the extension of the terms.

In the major, one of the extremes -- the predicate of the conclusion -- is, by reference to its comprehension, connected with the middle term: Whatever things are the same as a third thing are the same as one another.

In the minor, the same middle term is considered with reference to its extension and in this point of view is connected with the other extreme, the subject of the conclusion. Whatever is affirmed or denied of a subject taken in the abstract must be affirmed or denied of all its inferiors and each one of them, in one word, affirmed or denied universally.

The syllogism considered above leads to an affirmative conclusion. The same analyses may be applied to syllogisms with negative conclusions.^{1}

{1} See Criteriology, no. 58: Stuart Mill's objections against the value of the syllogism.