CHAPTER VIII.

ANALYTICA POSTERIORA II.

Aristotle begins the Second Book of the Analytica Posteriora by an enumeration and classification of Problems or Questions suitable for investigation. The matters knowable by us may be distributed into four classes:—

Under the first head come questions of Fact; under the second head, questions of Cause or Reason; under the third, questions of Existence; under the fourth, questions of Essence. Under the first head we enquire, Whether a fact or event is so or so? Whether a given subject possesses this or that attribute, or is in this or that condition? enumerating in the question the various supposable alternatives. Under the second head, we assume the first question to have been affirmatively answered, and we proceed to enquire, What is the cause or reason for such fact, or such conjunction of subject and attribute? Under the third head, we ask, Does a supposed subject exist? And if the answer be in the affirmative, we proceed to enquire, under the fourth head, What is the essence of the subject?1

We have here two distinct pairs of Quæsita: Obviously the second head presupposes the first, and is consequent thereupon; while the fourth also presupposes the third. But it might seem a more suitable arrangement (as Themistius and other expositors have conceived) that the third and fourth heads should come first in the list, rather than the first and second; since the third and fourth are simpler, and come earlier in the order of philosophical exposition, while the first and second are more complicated, and cannot be expounded philosophically until after 239the philosophical exposition of the others. This is cleared up by adverting to the distinction, so often insisted on by Aristotle, between what is first in order of cognition relatively to us (nobis notiora), and what is first in order of cognition by nature (naturâ notiora). To us (that is to men taken individually and in the course of actual growth) the phenomena of nature2 present themselves as particulars confused and complicated in every way, with attributes essential and accidental implicated together: we gradually learn first to see and compare them as particulars, next to resolve them into generalities, bundles, classes, and partially to explain the Why of some by means of others. Here we start from facts embodied in propositions, that include subjects clothed with their attributes. But in the order of nature (that is, in the order followed by those who know the scibile as a whole, and can expound it scientifically) that which comes first is the Universal or the simple Subject abstracted from its predicates or accompaniments: we have to enquire, first, whether a given subject exists; next, if it does exist, what is its real constituent essence or definition. We thus see the reason for the order in which Aristotle has arranged the two co-ordinate pairs of Quæsita or Problems, conformable to the different processes pursued, on the one hand, by the common intellect, growing and untrained — on the other, by the mature or disciplined intellect, already competent for philosophical exposition and applying itself to new incognita.

Comparing together these four Quæsita, it will appear that in the first and third (Quod and An), we seek to find out whether there is or is not any middle term. In the second and fourth (Cur and Quid), we already know or assume that there is a middle term; and we try to ascertain what that middle term is.3 The enquiry Cur, is in the main analogous to the enquiry Quid; in both cases, we aim at ascertaining what the cause or middle term is. But, in the enquiry Cur, what we discover is perhaps some independent fact or event, which is the cause of the event quæsitum; while, in the enquiry Quid, what we seek is the real 240essence or definition of the substance — the fundamental, generating, immanent cause of its concomitant attributes. Sometimes, however, the Quid and the Cur are only different ways of stating the same thing. E.g., Quid est eclipsis lunæ? Answer: The essence of an eclipse is a privation of light from the moon, through intervention of the earth between her and the sun. Cur locum habet eclipsis lunæ? Answer: Because the light of the sun is prevented from reaching the moon by intervention of the earth. Here it is manifest that the answers to the enquiries Quid and Cur are really and in substance the same fact, only stated in different phrases.4

That the quæsitum in all these researches is a middle term or medium, is plain from those cases wherein the medium is perceivable by sense; for then we neither require nor enter upon research. For example, if we were upon the moon, we should see the earth coming between us and the sun, now and in each particular case of eclipse. Accordingly, after many such observations, we should affirm the universal proposition, that such intervention of the earth was the cause of eclipses; the universal becoming known to us through induction of particular cases.5 The middle term, the Cause, the Quid, and the Cur, are thus all the same enquiry, in substance; though sometimes such quæsitum is the quiddity or essential nature of the thing itself (as the essence of a triangle is the cause or ground of its having its three angles equal to two right angles, as well as of its other properties), sometimes it is an extraneous fact.6

But how or by what process is this quæsitum obtained and made clear? Is it by Demonstration or by Definition? What is Definition, and what matters admit of Definition?7 Aristotle begins by treating the question dialectically; by setting out a series of doubts and difficulties. First, Is it possible that the same cognition, and in the same relation, can be obtained both by Definition and by Demonstration? No; it is not possible. It is plain that much that is known by Demonstration cannot be known by Definition; for we have seen that conclusions both particular and negative are established by Demonstration (in 241the Third and Second figures), while every Definition is universal and affirmative. But we may go farther and say, that even where a conclusion universal and affirmative is established (in the First figure) by Demonstration, that same conclusion can never be known by Definition; for if it could be known by Definition, it might have been known without Demonstration. Now we are assured, by an uncontradicted induction, that this is not the fact; for that which we know by Demonstration is either a proprium of the subject per se, or an accident or concomitant; but no Definition ever declares either the one or the other: it declares only the essence.8

Again, let us ask, vice versâ, Can everything that is declared by Definition, or indeed anything that is declared by Definition, be known also by Demonstration? Neither is this possible. One and the same cognitum can be known only by one process of cognition. Definitions are the principia from which Demonstration departs; and we have already shown that in going back upon demonstrations, we must stop somewhere, and must recognize some principia undemonstrable.9 The Definition can never be demonstrated, for it declares only the essence of the subject, and does not predicate anything concerning the subject; whereas Demonstration assumes the essence to be known, and deduces from such assumption an attribute distinct from the essence.10

Prosecuting still farther the dialectical and dubitative treatment,11 Aristotle now proceeds to suggest, that the Essence (that is, the entire Essence or Quiddity), which is declared by Definition, can never be known by Demonstration. To suppose that it could be so known, would be inconsistent with the conditions of the syllogistic proof used in demonstrating. You prove by syllogism, through a middle term, some predicate or attribute; e.g. because A is predicable of all B, and B is predicable of all C, therefore A is predicable of all C. But you cannot prove, through the middle term B, that A is the essence or quiddity 242of C, unless by assuming in the premisses that B is the essence of C, and that A is the essence of B; accordingly, that the three propositions, AB, BC, AC, are all co-extensive and reciprocate with each other. Here, then, you have assumed as your premisses two essential propositions, AB, BC, in order to prove as an essential proposition the conclusion AC. But this is inadmissible; for your premisses require demonstration as much as your conclusion. You have committed a Petitio Principii;12 you have assumed in your minor premiss the very point to be demonstrated.

If you cannot obtain Definition as the conclusion of syllogistic Demonstration, still less can you obtain it through the method of generic and specific Division; which last method (as has been already shown in the Analytica Priora) is not equal even to the Syllogism in respect of usefulness and efficacy.13 You cannot in this method distinguish between propositions both true and essential, and propositions true but not essential; you never obtain, by asking questions according to the method of generic subdivision, any premisses from which the conclusion follows by necessity. Yet this is what you ought to obtain for the purpose of Demonstration; for you are not allowed to enunciate the full actual conclusion among the premisses, and require assent to it. Division of a genus into its species will often give useful information, as Induction also will;14 but neither the one nor the other will be equivalent to a demonstration. A definition obtained only from subdivisions of a genus, may always be challenged, like a syllogism without its middle term.

Again, neither can you arrive at the definition of a given subject, by assuming in general terms what a definition ought to be, and then declaring a given form of words to be conformable to such assumption; because your minor premiss must involve 243Petitio Principii. The same logical fault will be committed, if you take your departure from an hypothesis in which you postulate the definition of a certain subject, and then declare inferentially what the definition of its contrary must be. The definition which you here assume requires proof as much as that which you infer from it.15 Moreover, neither by this process, nor by that of generic subdivision, can you show any reason why the parts of the definition should coalesce into one essential whole. If they do not thus coalesce — if they be nothing better than distinct attributes conjoined in the same subject, like musicus and grammaticus — the real essence is not declared, and the definition is not a good one.16

After stating some other additional difficulties which seem to leave the work of Definition inexplicable, Aristotle relinquishes the dubitative treatment, and looks out for some solution of the puzzle: How may it be possible that the Definition shall become known?17 He has already told us that to know the essence of a thing is the same as to know the cause or reason of its existence; but we must first begin by knowing that the definiendum exists; for there can be no definition of a non-entity, except a mere definition of the word, a nominal or verbal definition. Now sometimes we know the existence of the subject by one or other of its accidental attributes; but this gives us no help towards finding the definition.18 Sometimes, however, we obtain a partial knowledge of its essence along with the knowledge of its existence; when we know it along with some constant antecedent, or through some constant, though derivative, consequent. Knowing thus much, we can often discover the cause or fundamental condition thereof, which is the essence or definition of 244the subject.19 Indeed, it may happen that the constant derivative, and the fundamental essence on which it depends, become known both together; or, again, the cause or fundamental condition may perhaps not be the essence of the subject alone, but some fact including other subjects also; and this fact may then be stated as a middle term. Thus, in regard to eclipse of the moon, we know the constant phenomenal fact about it, that, on a certain recurrence of the time of full moon, the moon casts no light and makes no shadow. Hence we proceed to search out the cause. Is it interposition of the earth, or conversion of the moon’s body, or extinction of her light, &c.? The new fact when shown, must appear as a middle term, throwing into syllogistic form (in the First figure) the cause or rational explanation of a lunar eclipse; showing not merely that there is an eclipse, but what an eclipse is, or what is its definition.20

Aristotle has thus shown how the Essence or Quiddity (τί ἐστι) may become known in this class of cases. There is neither syllogism nor demonstration thereof, yet it is declared through syllogism and demonstration: though no demonstration thereof is possible, yet you cannot know it without demonstration, wherever there is an extraneous cause.21

But the above doctrine will hold only in cases where there is a distinct or extraneous cause; it will not hold in cases where there is none. It is only in the former (as has been said) that a middle term can be shown; rendering it possible that Quiddity or Essence should be declared by a valid formal syllogism, though it cannot be demonstrated by syllogism. In the latter, where there is no distinct cause, no such middle term can be enunciated: the Quiddity or Essence must be assumed as an 245immediate or undemonstrable principium, and must be exposed or set out in the best manner practicable as an existent reality, on Induction or on some other authority. The arithmetician makes his first steps by assuming both what a monad is and that there exists such a monad.22

We may distinguish three varieties of Definition. 1. Sometimes it is the mere explanation what a word signifies; in this sense, it has nothing to do with essence or existence; it is a nominal definition and nothing more.23 2. Sometimes it enunciates the Essence, cause, or reason of the definitum; this will happen where the cause is distinct or extraneous, and where there is accordingly an intervening middle term: the definition will then differ from a demonstration only by condensing into one enunciation the two premisses and the conclusion which together constitute the demonstration.24 3. Sometimes it is an immediate proposition, an indemonstrable hypothesis, assuming Essence or Quiddity; the essence itself being cause, and no extraneous cause — no intervening middle term — being obtainable.25

To know or cognize is, to know the Cause; when we know the Cause, we are satisfied with our cognition. Now there are four Causes, or varieties of Cause:—

1. The Essence or Quiddity (Form) — τὸ τί ἦν εἶναι.

2. The necessitating conditions (Matter) — τό τίνων ὄντων ἀνάγκη τοῦτ’ εἶναι.

3. The proximate mover or stimulator of change (Efficient) — ἡ τί πρῶτον ἐκίνησε.

4. That for the sake of which (Final Cause or End) — τὸ τίνος ἕνεκα.

All these four Causes (Formal, Material, Efficient, Final) appear as middle terms in demonstrating. We can proceed through the medium either of Form, or of Matter, or of Efficient, or of End. The first of the four has already been exemplified — the demonstration246 by Form. The second appears in demonstrating that the angle in a semi-circle is always a right angle; where the middle term (or matter of the syllogism, (τὸ ἐξ οὗ) is, that such angle is always the half of two right angles.26 The Efficient is the middle term, when to the question, Why did the Persians invade Athens? it is answered that the Athenians had previously invaded Persia along with the Eretrians. (All are disposed to attack those who have attacked them first; the Athenians attacked the Persians first; ergo, the Persians were disposed to attack the Athenians.) Lastly, the Final Cause serves as middle term, when to the question, Why does a man walk after dinner? the response is, For the purpose of keeping up his health. In another way, the middle term here is digestion: walking after dinner promotes digestion; digestion is the efficient cause of health.27

The Final Cause or End is prior in the order of nature, but posterior to the terms of the conclusion in the order of time or generation; while the Efficient is prior in the order of time or generation. The Formal and Material are simultaneous with the effect, neither prior nor posterior.28 Sometimes the same fact may proceed both from a Final cause, and from a cause of Material Necessity; thus the light passes through our lantern for the purpose of guiding us in the dark, but also by reason that the particles of light are smaller than the pores in the glass. Nature produces effects of finality, or with a view to some given end; and also effects by necessity, the necessity being either inherent in the substance itself, or imposed by extraneous force. Thus a stone falls to the ground by necessity of the first kind, but ascends by necessity of the second kind. Among products of human intelligence some spring wholly from design without necessity; but others arise by accident or chance and have no final cause.29

That the middle term is the Cause, is equally true in respect to Entia, Fientia, Præterita, and Futura; only that in respect to Entia, the middle term or Cause must be an Ens; in respect to Fientia it must be a Fiens; in respect to Præterita, a Præteritum; and in respect to Futura, a Futurum; that is, in each case, it must be generated at the corresponding time 247with the major and minor terms in the conclusion.30 What is the cause of an eclipse of the moon? The cause is, that the earth intervenes between moon and sun; and this is true alike of eclipses past, present, and future. Such an intervention is the essence or definition of a lunar eclipse: the cause is therefore Formal, and cause and effect are simultaneous, occurring at the same moment of time. But in the other three Causes — Material, Efficient, Final — where phenomena are successive and not simultaneous, can we say that the antecedent is cause and the consequent effect, time being, as seems to us, a continuum? In cases like this, we can syllogize from the consequent backward to the antecedent; but not from the antecedent forward to the consequent. If the house has been built, we can infer that the foundations have been laid; but, if the foundations have been laid, we cannot infer that the house has been built.31 There must always be an interval of time during which inference from the antecedent will be untrue; perhaps, indeed, it may never become true. Cause and causatum in these three last varieties of Cause, do not universally and necessarily reciprocate with each other, as in the case of the Formal cause. Though time is continuous, events or generations are distinct points marked in a continuous line, and are not continuous with each other.32 The number of these points that may be taken is indeed infinite; yet we must assume some of them as ultimate and immediate principia, in order to construct our syllogism, and provide our middle term.33 Where the middle term reciprocates and is co-extensive with the major and the minor, in such cases we have generation of phenomena in a cycle; e.g., after the earth has been made wet, vapour rises of necessity: hence comes a cloud, hence water; which again falls, and the earth again becomes wet.34 Finally, wherever our conclusion is not universally and necessarily true, but true only in most cases, our immediate principia must also be of the same character, true in most cases, but in most cases only.35

How are we to proceed in hunting out those attributes that are predicated in Quid,36 as belonging to the Essence of the subject? The subject being a lowest species, we must look out for such attributes as belong to all individuals thereof, but which belong 248also to individuals of other species under the same genus. We shall thus find one, two, three, or more, attributes, each of which, separately taken, belongs to various individuals lying out of the species; but the assemblage of which, collectively taken, does not belong to any individual lying out of the species. The Assemblage thus found is the Essence; and the enunciation thereof is the Definition of the species. Thus, the triad is included in the genus number; in searching for its definition, therefore, we must not go beyond that genus, nor include any attributes (such as ens, &c.) predicable of other subjects as well as numbers. Keeping within the limits of the genus, we find that every triad agrees in being an odd number. But this oddness belongs to other numbers also (pentad, heptad, &c.). We therefore look out for other attributes, and we find that every triad agrees in being a prime number, in two distinct senses; first, that it is not measured by any other number; secondly, that it is not compounded of any other numbers. This last attribute belongs to no other odd number except the triad. We have now an assemblage of attributes, which belong each of them to every triad, universally and necessarily, and which, taken all together, belong exclusively to the triad, and therefore constitute its essence or definition. The triad is a number, odd, and prime in the two senses.37 The definitum and the definition are here exactly co-extensive.

Where the matter that we study is the entire genus, we must begin by distributing it into its lowest species; e.g. number into dyad, triad, &c.; in like manner, taking straight line, circle, right angle, &c.38 We must first search out the definitions of each of these lowest species; and these having been ascertained, we must next look above the genus, to the Category in which it is itself comprised, whether Quantum, Quale, &c. Having done thus much we must study the derivative attributes or propria of the lowest species through the common generalities true respecting the larger. We must recollect that these derivative attributes are derived from the essence and definition of the lowest species, the complex flowing from the simple as its principium: they belong per se only to the lowest species thus 249defined; they belong to the higher genera only through those species.39 It is in this way, and not in any other, that the logical Division of genera, according to specific differences, can be made serviceable for investigation of essential attributes; that is, it can only be made to demonstrate what is derivative from the essence. We have shown already that it cannot help in demonstrating essence or Definition itself. We learn to marshal in proper order the two constituent elements of our definition, and to attach each specific difference to the genus to which it properly belongs. Thus we must not attempt to distribute the genus animal according to the difference of having the wing divided or undivided: many animals will fall under neither of the two heads; the difference in question belongs to the lower genus winged animal, and distributes the same into two species. The characteristic or specific difference must be enunciated and postulated by itself, and must be attached to its appropriate genus in order to form the definition. It is only by careful attention to the steps of legitimate logical Division that we can make sure of including all the particulars and leaving out none.40

Some contemporaries of Aristotle, and among them Speusippus, maintained that it was impossible either to define, or to divide logically, unless you knew all particulars without exception. You cannot (they said) know any one thing, except by knowing its differences from all other things; which would imply that you knew also all these other things.41 To these reasoners Aristotle replies: It is not necessary to know all the differences of every thing; you know a thing as soon as you know its essence, with the properties per se which are derivative therefrom. There are many differences not belonging to the essence, but distinguishing from each other two things having the same essence: you may know the thing, without knowing these accidental 250differences.42 When you divide a genus into two species, distinguished by one proximate specific difference, such that there cannot be any thing that does not fall under one or other of these membra condividentia, and when you have traced the subject investigated under one or other of these members, you can always follow this road until no lower specific difference can be found, and you have then the final essence and definition of the subject; even though you may not know how many other subjects each of the two members may include.43 Thus does Aristotle reply to Speusippus, showing that it is not necessary, for the definition of one thing, that you should know all other things. His reply, as in many other cases, is founded on the distinction between the Essential and the Accidental.

To obtain or put together a definition through logical Division, three points are to be attended to.44 Collect the predicates in Quid; range them in the proper order; make sure that there are no more, or that you have collected all. The essential predicates are genera, to be obtained not otherwise than by the method (dialectical) used in concluding accidents. As regards order, you begin with the highest genus, that which is predicable of all the others, while none of these is predicable of it, determining in like fashion the succession of the rest respectively. The collection will be complete, if you divide the highest genus by an exhaustive specific difference, such that every thing must be included in one or other of the two proximate and opposed portions; and then taking the species thus found as your dividendum, subdivide it until no lower specific difference can be found, or you obtain from the elements an exact equivalent to the subject.45

When the investigation must proceed by getting together a group of similar particulars, you compare them, and note what is the same in all; then turn to another group which are the same in genere yet differ in specie from the first group, and have a different point of community among themselves. You next compare the point of community among the members of the first group, and that among the members of the second group. If the two points of community can be brought under one 251rational formula, that will be the definition of the subject; but if at the end of the process, the distinct points of community are not found resolvable into any final one, this proves that the supposed definiendum is not one but two or more.46 For example, suppose you are investigating, What is the essence or definition of magnanimity? You must study various magnanimous individuals, and note what they have in common quâ magnanimous.47 Thus, Achilles, Ajax, Alkibiades were all magnanimous. Now, that which the three had in common was, that they could not endure to be insulted; on that account Alkibiades went to war with his countrymen, Achilles was angry and stood aloof from the Greeks, Ajax slew himself. But, again, you find two other magnanimous men, Sokrates and Lysander. These two had in common the quality, that they maintained an equal and unshaken temper both in prosperity and adversity. Now when you have got thus far, the question to be examined is, What is the point of identity between the temper that will not endure insult, and the temper that remains undisturbed under all diversities of fortune? If an identity can be found, this will be the essence or definition of magnanimity; to which will belong equanimity as one variety, and intolerance of insult as another. If, on the contrary, no identity can be found, you will then have two distinct mental dispositions, without any common definition.48

Every definition must be an universal proposition, applicable, not exclusively to one particular object, but to a class of greater or less extent. The lowest species is easier to define than the higher genus; this is one reason why we must begin with particulars, and ascend to universals. It is in the higher genera that equivocal terms most frequently escape detection.49 When you are demonstrating, what you have first to attend to is, the completeness of the form of syllogizing: when you are defining, 252the main requisite is to be perspicuous and intelligible; i.e. to avoid equivocal or metaphorical terms.50 You will best succeed in avoiding them, if you begin with the individuals, or with examples of the lowest species, and then proceed to consider not their resemblances generally, but their resemblances in certain definite ways, as in colour or figure. These more definite resemblances you will note first; upon each you will found a formula of separate definition; after which you will ascend to the more general formula of less definite resemblance common to both. Thus, in regard to the acute or sharp, you will consider the acute in sound, and in other matters (tastes, pains, weapons, angles, &c.), and you will investigate what is the common point of identity characterizing all. Perhaps there may be no such identity; the transfer of the term from one to the other may be only a metaphor: you will thus learn that no common definition is attainable. This is an important lesson; for as we are forbidden to carry on a dialectical debate in metaphorical terms, much more are we forbidden to introduce metaphorical terms in a definition.51

To obtain and enunciate correctly the problems suitable for discussion in each branch of science, you must have before you tables of dissection and logical division, and take them as guides;52 beginning with the highest genus and proceeding downward253 through the successively descending scale of sub-genera and species. If you are studying animals, you first collect the predicates belonging to all animals; you then take the highest subdivision of the genus animal, such as bird, and you collect the predicates belonging to all birds; and so on to the next in the descending scale. You will be able to show cause why any of these predicates must belong to the man Sokrates, or to the horse Bukephalus; because it belongs to the genus animal, which includes man and horse. Animal will be the middle term in the demonstration.53 This example is taken from the class-terms current in vulgar speech. But you must not confine yourself to these; you must look out for new classes, bound together by the possession of some common attribute, yet not usually talked of as classes, and you must see whether other attributes can be found constantly conjoined therewith. Thus you find that all animals having horns, have also a structure of stomach fit for rumination, and teeth upon one jaw only. You know, therefore, what is the cause that oxen and sheep have a structure of stomach fit for rumination. It is because they have horns. Having-horns is the middle term of the demonstration.54 Cases may also be found in which several objects possess no common nature or attribute to bind them into a class, but are yet linked together, by analogy, in different ways, to one and the same common term.55 Some predicates will be found to accompany constantly this analogy, or to belong to all the objects quâ analogous, just as if they had one and the same class-nature. Demonstration may be applied to these, as to the former cases.

Problems must be considered to be the same, when the middle term of the demonstration is the same for each, or when the middle term in the one is a subordinate or corollary to that in the other. Thus, the cause of echo, the cause of images in a mirror, the cause of the rainbow, all come under the same general head or middle term (refraction), though with a specific difference in each case. Again, when we investigate the problem, Why does the Nile flow with a more powerful current in the last half of the (lunar) month? the reason is that the month is then more wintry. But why is the month then more wintry? Because the light of the moon is then diminishing. Here are 254two middle terms, the one of which depends upon the other. The problem for investigation is therefore the same in both.56

Respecting Causa and Causatum question may be made whether it is necessary that when the causatum exists, the causa must exist also? The answer must be in the affirmative, if you include the cause in the definition of causatum. Thus, if you include in the definition of a lunar eclipse, the cause thereof, viz., intervention of the earth between moon and sun — then, whenever an eclipse occurs, such intervention must occur also. But it must not be supposed that there is here a perfect reciprocation, and that as the causatum is in this case demonstrable from the cause, so there is the like demonstration of the cause from the causatum. Such a demonstration is never a demonstration of διότι; it is only a demonstration of ὅτι. The causatum is not included in the definition of the cause; if you demonstrate that because the moon is eclipsed, therefore the earth is interposed between the moon and the sun, you prove the fact of the interposition, but you learn nothing about the cause thereof. Again, in a syllogism the middle term is the cause of the conclusion (i.e., it is the reason why the major term is predicated of the minor, which predication is the conclusion); and in this sense the cause and causatum may sometimes reciprocate, so that either may be proved by means of the other. But the causatum here reciprocates with the causa only as premiss and conclusion (i.e., we may know either by means of the other), not as cause and effect; the causatum is not cause of the causa as a fact and reality, as the causa is cause of the causatum.57

The question then arises, Can there be more than one cause of the same causatum? Is it necessary that the same effect should be produced in all cases by the same cause? In other words, 255when the same predicate is demonstrated to be true of two distinct minors, may it not be demonstrated in one case by one middle term, and in the other case by a different middle term?58 Answer: In genuine and proper scientific problems the middle term is the rational account (definition, interpretation) of the major extreme; this middle term therefore, or the cause, must in all cases be one and the same. The demonstration in these cases is derived from the same essence; it is per se, not per accidens. But there are other problems, not strictly and properly scientific, in which cause and causatum are connected merely per accidens; the demonstration being operated by a middle term which is not of the essence of the major, but is only a sign or concomitant.59 According as the terms of the conclusion are related to each other, so also will the middle term be related to both. If the conclusion be equivocal, the middle term will be equivocal also; if the predicate in the conclusion be in generic relation to the subject, the major also will be in generic relation to the middle. Thus, if you are demonstrating that one triangle is similar to another, and that one colour is similar to another, the word similar in these two cases is not univocal, but equivocal; accordingly, the middle term in the demonstration will also be equivocal. Again, if you are demonstrating that four proportionals will also be proportionals alternately, there will be one cause or middle term, if the subject of the conclusion be lines; another, if the subject be numbers. Yet the middle term or cause in both is the same, in as far as both involve a certain fact of increment.60

The major term of the syllogism will in point of extension be larger than any particular minor, but equal or co-extensive with the sum total of the particulars. Thus the predicate deciduous, affirmable of all plants with broad leaves, is greater in extension than the subject vines, also than the subject fig-trees; but it is equal in extension to the sum total of vines and fig-trees (the other particular broad-leaved plant). The middle also, in an universal demonstration, reciprocates with the major, being its definition. Here the true middle or cause of the effect that vines and fig-trees shed their leaves, is not that they are broad-leaved plants, but rather a coagulation of sap or some such fact.61

The last chapter of the present treatise is announced by 256Aristotle as the appendix and completion of his entire theory of Demonstrative Science, contained in the Analytica Priora, which treats of Syllogism, and the Analytica Posteriora, which treats of Demonstration. After formally winding up the whole enquiry, he proceeds to ask regarding the principia of Demonstrative Science: What are they? How do they become known? What is the mental habit or condition that is cognizant of them?62

Aristotle has already laid down that there can be no Demonstration without certain præcognita to start from; and that these præcognita must, in the last resort, be principia undemonstrable, immediately known, and known even more accurately than the conclusions deduced from them. Are they then cognitions, or cognizant habits and possessions, born along with us, and complete from the first? This is impossible (Aristotle declares); we cannot have such valuable and accurate cognitions from the first moments of childhood, and yet not be at all aware of them. They must therefore be acquired; yet how is it possible for us to acquire them?63 The fact is, that, though we do not from the first possess any such complete and accurate cognitions as these, we have from the first an inborn capacity or potentiality of arriving at them. And something of the same kind belongs to all animals.64 All of them possess an apprehending and discriminating power born with them, called Sensible Perception; but, though all possess such power, there is this difference, that with some the act of perception dwells for a longer or shorter time in the mind; with others it does not. In animals with whom it does not dwell, there can be no knowledge beyond perception, at least as to all those matters wherein perception is evanescent; but with those that both perceive and retain perceptions257 in their minds, ulterior knowledge grows up.65 There are many such retentive animals, and they differ among themselves: with some of them reason or rational notions arise out of the perceptions retained; with others, it is not so. First, out of perception arises memory; next, out of memory of the same often repeated, arises experience, since many remembrances numerically distinct are summed up into one experience. Lastly, out of experience, or out of the universal notion, the unum et idem which pervades and characterizes a multitude of particulars, when it has taken rest and root in the mind, there arises the principium of art and science: of science, in respect to objects existent; of art, in respect to things generable.66 And thus these mental habits or acquirements neither exist in our minds determined from the beginning, nor do they spring from 258other acquirements of greater cognitive efficacy. They spring from sensible perception; and we may illustrate their growth by what happens in the panic of a terrified host, where first one runaway stops in his flight, then a second, then a third, until at last a number docile to command is collected. One characteristic feature of the mind is to be capable of this process.67

Aristotle proceeds to repeat the illustration in clearer terms — at least in terms which he thinks clearer.68 We perceive the particular individual; yet sensible perception is of the universal in the particular (as, for example, when Kallias is before us, we perceive man, not the man Kallias). Now, when one of a set of particulars dwells some time in the mind, first an universal notion arises; next, more particulars are perceived and detained, and universal notions arise upon them more and more comprehensive, until at last we reach the highest stage — the most universal and simple. From Kallias we rise to man; from such and such an animal, to animal in genere; from animal in genere, still higher, until we reach the highest or indivisible genus.69 Hence it is plain that the first and highest principia can become known to us only by Induction; for it is by this process that sensible perception builds up in us the Universal.70 Now among 259those intellective habits or acquirements, whereby we come to apprehend truth, there are some (Science and Noûs) that are uniformly and unerringly true, while others (Opinion and Ratiocination) admit an alternative of falsehood.71 Comparing Science with Noûs, the latter, and the latter only, is more accurate and unerring than Science. But all Science implies demonstration, and all that we know by Science is conclusions deduced by demonstration. We have already said that the principia of these demonstrations cannot be themselves demonstrated, and therefore cannot be known by Science; we have also said that they must be known more accurately than the conclusions. How then can these principia themselves be known? They can be known only by Noûs, and from particulars. It is from the principia known by Noûs, with the maximum of accuracy, that Science demonstrates her conclusions. Noûs is the great principium of Science.72

The manner in which Aristotle here describes how the principia of Syllogism become known to the mind deserves particular attention. The march up to principia is not only different from, but the reverse of, the march down from principia; like the athlete who runs first to the end of the stadium, and then back.73 Generalizing or universalizing is an acquired intellectual habit or permanent endowment; growing out of numerous particular acts or judgments of sense, remembered, compared, and coalescing into one mental group through associating resemblance. As the ethical, moral, practical habits, are acquirements growing out of a repetition of particular acts, so also the intellectual, 260theorizing habits are mental results generated by a multitude of particular judgments of sense, retained and compared, so as to imprint upon the mind a lasting stamp of some identity common to all. The Universal (notius naturâ) is thus generated in the mind by a process of Induction out of particulars which are notiora nobis; the potentiality of this process, together with sense and memory, is all that is innate or connatural.

The principia, from which the conclusions of Syllogism are deduced, being thus obtained by Induction, are, in Aristotle's view, appreciated by, or correlated with, the infallible and unerring Noûs or Intellect.74 He conceives repeated and uncontradicted Induction as carrying with it the maximum of certainty and necessity: the syllogistic deductions constituting Science he regards as also certain; but their certainty is only derivative, and the principia from which they flow he ranks still higher, as being still more certain.75 Both the one and the other he pointedly contrasts with Opinion and Calculation, which he declares to be liable to error.

Aristotle had inherited from Plato this doctrine of an infallible Noûs or Intellect, enjoying complete immunity from error. But, instead of connecting it (as Plato had done) with reminiscences of an anterior life among the Ideas, he assigned to it a position as terminus and correlate to the process of Induction.76 The like postulate and pretension passed afterwards to the Stoics, and 261various other philosophical sects: they could not be satisfied without finding infallibility somewhere. It was against this pretension that the Academics and Sceptics entered their protest; contending, on grounds sometimes sophistical but often very forcible, that it was impossible to escape from the region of fallibility, and that no criterion of truth, at once universal and imperative, could be set up.

It is to be regretted that Aristotle should have contented himself with proclaiming this Inductive process as an ideal, culminating in the infallible Noûs; and that he should only have superficially noticed those conditions under which it must be conducted in reality, in order to avoid erroneous or uncertified results. This is a deficiency however which has remained unsupplied until the present century.77

[END OF CHAPTER VIII]

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