CHAPTER XI. How General Concepts arise. How Sense-Perception uses the Third Figure of the Syllogism to store up its Experience in General Terms. § 44. THE activity of the second figure gives occasion to that of the first figure. Then the stored-up experience leads through the application of the first figure to a number of anticipations of perception, which are verified or tested. But by what process do classes, species, genera, and all the universals which furnish the major premise of the first figure arise? The answer to this brings us to the consideration of the third figure. Its schema is: M is P; M is S; hence S is P. Man is a biped; man is rational; hence (some) rational being is a biped. Here man is the middle term, and it is the subject in both premises. In the third figure, as used in sense-perception, the middle term is the object perceived, and the two extremes are connected with each other by the fact that they both belong to the same object. Now, since the middle term is subsumed under both extremes, it follows that only particular affirmative conclusions can be made in it-we can only say some S is P and not all S is P. Some rational beings are bipeds. This may be seen by considering that the middle term (which is the object) participates in the predicate (major premise: horse is an animal), and participates also in the subject (the minor: horse is a quadruped). Hence the subject is connected with the predicate through the object (horse), which is in all cases only a part of the logical sphere of the predicate, and likewise only a part of the sphere of the subject. It follows that this conclusion connects a part of the subject with the predicate. There are six valid modes in this figure-three particular affirmative and three particular negative conclusions. These are named, respectively: Darapti-all M is P; all M is S; hence some S is P. is not P. Ferison-no M is P; some M is S; hence some S is not P. These valid modes, useful as they are in deducing necessary conclusions, like the valid modes of the second and first figures, are nevertheless not of much use in senseperception. Certainty in experience comes from repetition and verification, rather than from single necessary conclusions. Explanation of the Artificial Words used to Name the Modes.-Aristotle, and after him nearly all other writers on logic, hold that the first figure gives the purest and simplest form of the syllogism. The other figures are conceived to rest on it in such a way that the mind in using them unconsciously travels through the first in reaching a conclusion. The road travelled is explained by Aristotle and his followers. The mnemonic words indicate not only the quality (positive or negative) and the quantity (universal or particular) of the major, minor, and conclusion, but also the changes necessary to turn the mode into a corresponding one of the first figure. Thus, in Barbara the three a's show three universal affirmative propositions, each expressed by all are; e in Celarent means none are; i in Darii, some are; o in Ferio, some are not. In the first figure the consonants are not significant, except that the first letters, B, C, D, F, are the first four consonants of the alphabet, and are taken only as the distinguishing characteristics of the modes of that figure. When used in the modes of the other figures they indicate that the mode beginning with one of these letters is to be explained or resolved by transforming it into the mode of the first figure to which the letter belongs. Camestres is to be changed into Celarent; Festino into Ferio; Baroco into Barbara, etc. The consonants, s, m, p, used in one of the modes of the second and third figures, indicate the changes necessary to transform it into a mode of first figure. S denotes simple conversion-i. e., the proposition indicated by the previous vowel must be converted or changed, so that its predicate becomes the subject. Cesare, for example, beginning with C, must be changed to Celarent in first figure. The s indicates that the universal negative proposition, symbolized by the vowel e before it, must be converted simply, its subject and predicate changing places. No man is a bird, converted simply would read no bird is a man. Simple conversion can happen in universal negatives and in particular affirmatives; some birds are waders, converted, reads some waders are birds. Universal affirmatives convert into particular affirmatives, as, the conversion of all men are mortal is not all mortals are men, but some mortals are men, because the subject is only a part of the extent of the predicate. Conversion of a universal affirmative into a particular is conversion per accidens, and is indicated by the letter p.after the vowel representing the proposition. Thus, in Darapti the p indicates that the minor premise, a universal affirmative, represented by the second a, should be converted into a particular affirmative. Per accidens-by accident-means that the form of necessity indicated by allness has been lost and the accidental assumed. If some are and some are not, accident determines which. Finally, m in the mnemonic word indicates that the major and minor premises must be exchanged one for the other. Thus, in Disamis not only must the major premise indicated by the first letter i be converted simply, but it must also exchange places with the minor premise (metathesis or transposition). The c in Baroco and Bocardo indicates that the proposition symbolized by the preceding vowel must be changed into its contradictory (all are into some are not; all are not into some are), when an absurd result will show itself, and prove that any other than the first conclusion is absurd. Baroco and Bocardo are the modes not satisfactorily explained by the logicians.* The circuitous method of reduction by the ad absurdum, although Aristotle's method, is perplexing and unsatisfactory. Take as examples the following: BAROCO-Every animal is endowed with feeling; some living beings are not endowed with feeling; hence some living beings are not animals (the plants, for instance). Here it seems perfectly easy for the mind to come to a direct conclusion from the premises without any process of reductio ad absurdum; for there is a middle term, endowed with feeling, which contains or comprehends all animals, but excludes some living beings. It is a simple logical step to conclude that the some living beings not in the middle term are not in the major term, animals, which is in the middle term. This * See Hamilton's Lectures on Logic, pages 312 and 316, where he says that they “have been at once the cruces and the opprobria of logicians. . . . So intricate was Bocardo considered that it was looked upon as a trap, into which, if you once got, it was no easy matter to find an exit." See also, on page 317, his astonishing attempt to analyze Bocardo. is as clear as Ferio: No non-sentient beings are animals; some living beings are non-sentient; hence some living beings are not animals. Take Bocardo: Some animals are not bipeds; all animals are self-moving; some self-moving beings are not bipeds. Here, as in Baroco, the inference is direct, because all the middle is in the subject and yet is partly outside the predicate; hence the subject is partly outside the predicate, and this insight can not be stated in a form any clearer than it is in Bocardo. 45. The third figure follows the second figure, and can not precede its activity because each of its premises presupposes the action of identifying. The object M is S (horses are quadrupeds-S [quadruped] is recognised in the object). The object M is P (horses are shod with hoofs-P [shod] is now recognised). Thus there are two identifications, one for each premise (both using the second figure of the syllogism), before the third figure can begin to function. Now it acts and connects the two phases of the object (S P), making a new predication, which may serve for a new major premise of the first figure (collecting in the definition of horse the ideas of quadruped and hoofs). Hereafter we may say: Such objects as those (M) are S P, and when we see one of this kind we may recognise it in the second figure at once. Let us suppose that our object before had been a black eagle, a well-known object. Now we recognise eagle and white-head by two acts of the second figure; |