Deductive Logic Part 29

Here it is evident from the statement that six cases arise--

(1) Total inclusion of the same term in two others (Darapti).

[Ill.u.s.tration]

All B is A.

All B is C.

.'. some C is A.

(2) Total inclusion in the first and partial inclusion in the second (Datisi).

[Ill.u.s.tration]

All B is A.

Some B is C.

.'. some C is A.

(3) Partial inclusion in the first and total inclusion in the second (Disamis).

[Ill.u.s.tration]

Some B is A.

All B is C.

.'. some C is A.

(4) Total exclusion of the first from a term which is wholly included in the second (Felapton).

[Ill.u.s.tration]

No B is A.

All B is C.

.'. some C is not A.

(5) Total exclusion of the first from a term which is partly included in the second (Ferison).

[Ill.u.s.tration]

No B is A.

Some B is C.

.'. some C is not A.

(6) Exclusion of the first from part of a term which is wholly included in the second (Bokardo).

[Ill.u.s.tration]

Some B is not A.

All B is C.

.'. Some C is not A.

FIGURE IV.

-- 637. CANON. If one term is wholly or partly included in another which is wholly included in or excluded from a third, the third term wholly or partly includes the first, or, in the case of total inclusion, is wholly excluded from it; and if a term is excluded from another which is wholly or partly included in a third, the third is partly excluded from the first.

Here we have five cases--

(1) Of the inclusion of a whole term (Bramsntip).

[Ill.u.s.tration]

All A is B.

All B is C.

.'. Some C is (all) A.

(2) Of the inclusion of part of a term (DIMARIS).

[Ill.u.s.tration]

Some A is B.

All B is C.

.'. Some C is (some) A,

(3) Of the exclusion of a whole term (Camenes).

[Ill.u.s.tration]

All A is B.

No B is C.

.'. No C is A.

(4) Partial exclusion on the ground of including the whole of an excluded term (Fesapo).

[Ill.u.s.tration]

No A is B.

All B is C.

.'. Some C is not A.

(5) Partial exclusion on the ground of including part of an excluded term (Fresison).

[Ill.u.s.tration]

No A is B.

Some B is C.

.'. Some C is not A.

-- 638. It is evident from the diagrams that in the subaltern moods the conclusion is not drawn directly from the premisses, but is an immediate inference from the natural conclusion. Take for instance AAI in the first figure. The natural conclusion from these premisses is that the minor term C is wholly contained in the major term A. But instead of drawing this conclusion we go on to infer that something which is contained in C, namely some C, is contained in A.

[Ill.u.s.tration]

All B is A.