Section 558. Syllogisms may differ in two ways--
Section 559. Mood depends upon the kind of propositions employed. Thus asyllogism consisting of three universal affirmatives, AAA, would besaid to differ in mood from one consisting of such propositions as EIOor any other combination that might be made. The syllogism previouslygiven to prove the fallibility of the Pope belongs to the moodAAA. Had we drawn only a particular conclusion, 'Some Popes arefallible,' it would have fallen into the mood AAI.
Section 560. Figure depends upon the arrangement of the terms in thepropositions. Thus a difference of figure is internal to a differenceof mood, that is to say, the same mood can be in any figure.
Section 561. We will now show how many possible varieties there are of moodand figure, irrespective of their logical validity.
Since every syllogism consists of three propositions, and each ofthese propositions may be either A, E, I, or O, it is clear that therewill be as many possible moods as there can be combinations of fourthings, taken three together, with no restrictions as torepetition. It will be seen that there are just sixty-four of suchcombinations. For A may be followed either by itself or by E, I, orO. Let us suppose it to be followed by itself. Then this pair ofpremisses, AA, may have for its conclusion either A, E, I, or O, thusgiving four combinations which commence with AA. In like manner therewill be four commencing with AE, four with AI, and four with AO,giving a total of sixteen combinations which commence withA. Similarly there will be sixteen commencing with E, sixteen with I,sixteen with O--in all sixty-four. It is very few, however, of thesepossible combinations that will be found legitimate, when tested bythe rules of syllogism.
There are four possible varieties of figure in a syllogism, as may beseen by considering the positions that can be occupied by the middleterm in the premisses. For as there are only two terms in eachpremiss, the position occupied by the middle term necessarilydetermines that of the others. It is clear that the middle term musteither occupy the same position in both premisses or not, that is, itmust either be subject in both or predicate in both, or else subjectin one and predicate in the other. Now, if we are not acquainted withthe conclusion of our syllogism, we do not know which is the major andwhich the minor term, and have therefore no means of distinguishingbetween one premiss and another; consequently we must Stop here, andsay that there are only three different arrangements possible. But, ifthe Conclusion also be assumed as known, then we are able todistinguish one premiss as the major and the other as the minor; andso we can go further, and lay down that, if the middle term does nothold the same position in both premisses, it must either be subject inthe major and predicate in the minor, or else predicate in the majorand subject in the minor.
When the middle term is subject in the major and predicate in theminor, we are said to have the First Figure.
When the middle term is predicate in both premisses, we are said tohave the Second Figure.
When the middle term is subject in both premisses, we are said to havethe Third Figure.
When the middle term is predicate in the major premiss and subject inthe minor, we are said to have the Fourth Figure.
Section 565. Let A be the major term; B the middle. C the minor.
Figure I. Figure II. Figure III. Figure IV. B--A A--B B--A A--B C--B C--B B--C B--C C--A C--A C--A C--A
All these figures are legitimate, though the fourth is comparativelyvalueless.
Section 566. It will be well to explain by an instance the meaning of the
assertion previously made, that a difference of figure is internal toa difference of mood. We will take the mood EIO, and by varying theposition of the terms, construct a syllogism in it in each of the fourfigures.
I. E No wicked man is happy. I Some prosperous men are wicked. O .'. Some prosperous men are not happy.
II. E No happy man is wicked. I Some prosperous men are wicked. O .'. Some prosperous men are not happy.
III. E No wicked man is happy. I Some wicked men are prosperous. O .'. Some prosperous men are not happy.
IV. E No happy man is wicked. I Some wicked men are prosperous. O .'. Some prosperous men are not happy.
Section 567. In the mood we have selected, owing to the peculiar nature ofthe premisses, both of which admit of simple conversion, it happensthat the resulting syllogisms are all valid. But in the great majorityof moods no syllogism would be valid at all, and in many moods asyllogism would be valid in one figure and invalid in another. As yethowever we are only concerned with the conceivable combinations, apartfrom the question of their legitimacy.
Section 568. Now since there are four different figures and sixty-fourdifferent moods, we obtain in all 256 possible ways of arranging threeterms in three propositions, that is, 256 possible forms of syllogism.
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