Deductive Logic Part 31

A whale gives milk.

.'. A whale is not a fish.

FIGURE III.

-- 654.

B is A. B is not A.

B is C. B is C.

.'. Some C is A. .'. Some C is not A.

We produce instances of C being A by showing that C and A meet, at all events partially, in B. Thus if we wish to produce an instance of the compatibility of great learning with original powers of thought, we might say

Sir William Hamilton was an original thinker.

Sir William Hamilton was a man of great learning.

.'. Some men of great learning are original thinkers.

Or we might urge an exception to the supposed rule about Scotchmen being deficient in humour under the same figure, thus--

Sir Walter Scott was not deficient in humour.

Sir Walter Scott was a Scotchman.

.'. Some Scotchmen are not deficient in humour.

FIGURE IV.

-- 655.

All A is B, No A is B.

All B is C. All B is C.

.'. Some C is A .'.Some C is not A.

We show here that A is or is not a species of C by showing that A falls, or does not fall, under the cla.s.s B, which itself falls under C. Thus--

All whales are mammals.

All mammals are warm-blooded.

.'. Some warm-blooded animals are whales.

No whales are fishes.

All fishes are cold-blooded.

.'. Some cold-blooded animals are not whales.

CHAPTER XVII.

_Of the Syllogism with three figures._

-- 656. It will be remembered that in beginning to treat of figure (-- 565) we pointed out that there were either four or three ligures possible according as the conclusion was a.s.sumed to be known or not. For, if the conclusion be not known, we cannot distinguish between the major and the minor term, nor, consequently, between one premiss and another. On this view the first and the fourth figures are the same, being that arrangement of the syllogism in which the middle term occupies a different position in one premiss from what it does in the other. We will now proceed to const.i.tute the legitimate moods and figures of the syllogism irrespective of the conclusion.

-- 657. When the conclusion is set out of sight, the number of possible moods is the same as the number of combinations that can be made of the four things, A, E, I, O, taken two together, without restriction as to repet.i.tion. These are the following 16:--

AA EA IA OA AE -EE- IE -OE- AI EI -II- -OI- AO -EO- -IO- -OO-

of which seven may be neglected as violating the general rules of the syllogism, thus leaving us with nine valid moods--

AA. AE. AI. AO. EA. EI. IA. IE. OA.

-- 658. We will now put these nine moods successively into the three figures. By so doing it will become apparent how far they are valid in each.

-- 659. Let it be premised that

when the extreme in the premiss that stands first is predicate in the conclusion, we are said to have a Direct Mood;

when the extreme in the premiss that stands second is predicate in the conclusion, we are said to have an Indirect Mood.

-- 660. FIGURE 1.

_Mood AA._ All B is A.

All C is B.

.'. All C is A, or Some A is C, (Barbara & Bramantip).

_Mood AE._ All B is A.

No C is B.

.'. Illicit Process, or Some A is not C, (Fesapo).

_Mood AI._ All B is A.

Some C is B.

.'. Some C is A, or Some A is C. (Darii & Disamis).

_Mood AO._ All B is A.

Some C is not B.

.'. Illicit Process, (Ferio).

_Mood EA._ No B is A.

All C is B.

.'. No C is A, or No A is C, (Celarent & Camenes).

_Mood EI._ No B is A.

Some C is B.

.'. Some C is not A, or Illicit Process.

_Mood IA._ Some B is A.

All C is B.

.'. Undistributed Middle.

_Mood IE._ Some B is C. Some B is not A.

No A is B. All C is B.

.'. Illicit Process, or Some C is not A, (Fresison).

_Mood OA._ Some B is not A.