Aristotle

Next, Aristotle compares the Affirmative with the Negative demonstration, and shows that the Affirmative is the better. Of two demonstrations (he lays it down) that one which proceeds upon a smaller number of postulates, assumptions, or propositions, is better than the other; for, to say nothing of other reasons, it conducts you more speedily to knowledge than the other, and that is an advantage. Now, both in the affirmative and in the negative syllogism, you must have three terms and two propositions; but in the affirmative you assume only that something is; while in the negative you assume both that something is, and that something is not. Here is a double assumption instead of a single; therefore the negative is the worse or inferior of the two.77 Moreover, for the demonstration of a negative conclusion, you require one affirmative premiss (since from two negative premisses nothing whatever can be concluded); while for the demonstration of an affirmative conclusion, you must have two affirmative premisses, and you cannot admit a negative. This, again, shows that the affirmative is logically prior, more trustworthy, and better than the negative.78 The negative is only intelligible and knowable through the affirmative, just as Non-Ens is knowable only through Ens. The affirmative demonstration therefore, as involving better principles, is, on this ground also, better than the negative.79 A fortiori, it is also better than the demonstration by way of Reductio ad Absurdum, which was the last case to be considered. This, as concluding only indirectly and from impossibility of the contradictory, is worse even than the negative; much more therefore is it worse than the direct affirmative.80

If we next compare one Science with another, the prior and more accurate of the two is, (1) That which combines at once the ὅτι and the διότι; (2) That which is abstracted from material conditions, as compared with that which is immersed therein — for example, arithmetic is more accurate than harmonics; (3) The more simple as compared with the more complex: thus, arithmetic is more accurate than geometry, a monad or unit is a substance without position, whereas a point (more concrete) is a substance with position.81 One and the same science is that which belongs to one and the same generic subject-matter. The premisses of a demonstration must be included in the same genus with the conclusion; and where the ultimate premisses are heterogeneous, the cognition derived from them must be considered as not one but a compound of several.82 You may find two or more distinct middle terms for demonstrating the same conclusion; sometimes out of the same logical series or table, sometimes out of different tables.83

There cannot be demonstrative cognition of fortuitous events,84 for all demonstration is either of the necessary or of the customary. Nor can there be demonstrative cognition through sensible perception. For though by sense we perceive a thing as such and such (through its sensible qualities), yet we perceive it inevitably as hoc aliquid, hic, et nunc. But the Universal cannot be perceived by sense; for it is neither hic nor nunc, but semper et ubique.85 Now demonstrations are all accomplished by means of the Universal, and demonstrative cognition cannot therefore be had through sensible perception. If the equality of the three angles of a triangle to two right angles were a fact directly perceivable by sense, we should still have looked out for a demonstration thereof: we should have no proper scientific cognition of it (though some persons contend for this): for sensible perception gives us only particular cases, and Cognition or Science proper comes only through knowing the Universal.86 If, being on the surface of the moon, we had on any one occasion seen the earth between us and the sun, we could not have known from that single observation that such interposition is the cause universally of eclipses. We cannot directly by sense perceive the Universal, though sense is the principium of the Universal. By multiplied observation of sensible particulars, we can hunt out and elicit the Universal, enunciate it clearly and separately, and make it serve for demonstration.87 The Universal is precious, because it reveals the Cause or διότι, and is therefore more precious, not merely than sensible observation, but also than intellectual conception of the ὅτι only, where the Cause or διότι lies apart, and is derived from a higher genus. Respecting First Principles or Summa Genera, we must speak elsewhere.88 It is clear, therefore, that no demonstrable matter can be known, properly speaking, from direct perception of sense; though there are cases in which nothing but the impossibility of direct observation drives us upon seeking for demonstration. Whenever we can get an adequate number of sensible observations, we can generalize the fact; and in some instances we may perhaps not seek for any demonstrative knowledge (i.e. to explain it by any higher principle). If we could see the pores in glass and the light passing through them, we should learn through many such observations why combustion arises on the farther side of the glass; each of our observations would have been separate and individual, but we should by intellect generalize the result that all the cases fall under the same law.89

Aristotle next proceeds to refute, at some length, the supposition, that the principia of all syllogisms are the same. We see at once that this cannot be so, because some syllogisms are true, others false. But, besides, though there are indeed a few Axioms essential to the process of demonstration, and the same in all syllogisms, yet these are not sufficient of themselves for demonstration. There must farther be other premisses or matters of evidence — propositions immediately true (or established by prior demonstrations) belonging to each branch of Science specially, as distinguished from the others. Our demonstration relates to these special matters or premisses, though it is accomplished out of or by means of the common Axioms.90

Science or scientific Cognition differs from true Opinion, and the cognitum from the opinatum, herein, that Science is of the Universal, and through necessary premisses which cannot be otherwise; while Opinion relates to matters true, yet which at the same time may possibly be false. The belief in a proposition which is immediate (i. e., undemonstrable) yet not necessary, is Opinion; it is not Science, nor is it Noûs or Intellect — the principium of Science or scientific Cognition. Such beliefs are fluctuating, as we see every day; we all distinguish them from other beliefs, which we cannot conceive not to be true and which we call cognitions.91 But may there not be Opinion and Cognition respecting the same matters? There may be (says Aristotle) in different men, or in the same man at different times; but not in the same man at the same time. There may also be, respecting the same matter, true opinion in one man’s mind, and false opinion in the mind of another.92

With some remarks upon Sagacity, or the power of divining a middle term in a time too short for reflection (as when the friendship of two men is on the instant referred to the fact of their having a common enemy), the present book is brought to a close.93

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 the 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 essence 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 the 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 of 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 Petitio 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