Deductive Logic Part 28

An A conclusion necessitates both premisses being A propositions (by Rule 7). But the minor term is distributed in the conclusion, as being the subject of an A proposition, and must therefore be distributed in the minor premiss, in order to which it must be the subject. Therefore the middle term must be the predicate and is consequently undistributed. In order therefore that the middle term may be distributed, it must be subject in the major premiss, since that also is an A proposition. But when the middle term is subject in the major and predicate in the minor premiss, we have what is called the first figure.

CHAPTER XV.

_Of the Special Canons of the Four Figures._

-- 633. So far we have given only a negative test of legitimacy, having shown what moods are not invalidated by running counter to any of the special rules of the four figures. We will now lay down special canons for the four figures, conformity to which will serve as a positive test of the validity of a given mood in a given figure. The special canon of the first figure--will of course be practically equivalent to the Dictum de Omni et Nullo. All of them will be expressed in terms of extension, for the sake of perspicuity.

_Special Canons of the Four Figures._

FIGURE 1.

-- 634. CANON. If one term wholly includes or excludes another, which wholly or partly includes a third, the first term wholly or partly includes or excludes the third.

Here four cases arise--

[Ill.u.s.tration]

(1) Total inclusion (Barbara).

All B is A.

All C is B.

.'. All C is A.

[Ill.u.s.tration]

(2) Partial inclusion (Darii).

All B is A.

Some C is B.

.'. Some C is A.

[Ill.u.s.tration]

(3) Total exclusion (Celarent).

No B is A.

All C is B.

.'. No C is A.

[Ill.u.s.tration]

(4) Partial exclusion (Ferio).

No B is A.

Some C is B.

.'. Some C is not A.

FIGURE II.

-- 635. CANON. If one term is excluded from another, which wholly or partly includes a third, or is included in another from which a third is wholly or partly excluded, the first is excluded from the whole or part of the third.

Here we have four cases, all of exclusion--

(1) Total exclusion on the ground of inclusion in an excluded term (Cesare).

[Ill.u.s.tration]

No A is B.

All C is B.

.'. No C is A.

(2) Partial exclusion on the ground of a similar partial inclusion (Festino).

[Ill.u.s.tration]

No A is B.

Some C is B.

.'. Some C is not A.

(3) Total exclusion on the ground of exclusion from an including term (Camestres).

[Ill.u.s.tration]

All A is B.

No C is B.

.'. No C is A.

(4) Partial exclusion on the ground of a similar partial exclusion (Baroko).

[Ill.u.s.tration]

All A is B.

Some C is not B.

.'. Some C is not A.

FIGURE III.

-- 636. CANON. If two terms include another term in common, or if the first includes the whole and the second a part of the same term, or vice versa, the first of these two terms partly includes the second; and if the first is excluded from the whole of a term which is wholly or in part included in the second, or is excluded from part of a term which is wholly included in the second, the first is excluded from part of the second.