CHAPTER VII.

ANALYTICA POSTERIORA I.

In the two books of Analytica Priora, Aristotle has carried us through the full doctrine of the functions and varieties of the Syllogism; with an intimation that it might be applied to two purposes — Demonstration and Dialectic. We are now introduced to these two distinct applications of the Syllogism: first, in the Analytica Posteriora, to Demonstration; next, in the Topica, to Dialectic. We are indeed distinctly told that, as far as the forms and rules of Syllogism go, these are alike applicable to both;1 but the difference of matter and purpose in the two cases is so considerable as to require a distinct theory and precepts for the one and for the other.

The contrast between Dialectic (along with Rhetoric) on the one hand and Science on the other is one deeply present to the mind of Aristotle. He seems to have proceeded upon the same fundamental antithesis as that which appears in the Platonic dialogues; but to have modified it both in meaning and in terminology, dismissing at the same time various hypotheses with which Plato had connected it.

The antithesis that both thinkers have in view is Opinion or Common Sense versus Science or Special Teaching and Learning; those aptitudes, acquirements, sentiments, antipathies, &c., which a man imbibes and appropriates insensibly, partly by his own doing and suffering, partly by living amidst the drill and example of a given society — as distinguished from those accomplishments which he derives from a teacher already known to possess them, and in which both the time of his apprenticeship and the steps of his progress are alike assignable.

Common Sense is the region of Opinion, in which there is diversity of authorities and contradiction of arguments without any settled truth; all affirmations being particular and relative, true at one time and place, false at another. Science, on the contrary, deals with imperishable Forms and universal truths, 208which Plato regards, in their subjective aspect, as the innate, though buried, furniture of the soul, inherited from an external pre-existence, and revived in it out of the misleading data of sense by a process first of the cross-examining Elenchus, next of scientific Demonstration. Plato depreciates altogether the untaught, unexamined, stock of acquirements which passes under the name of Common Sense, as a mere worthless semblance of knowledge without reality; as requiring to be broken up by the scrutinizing Elenchus, in order to impress a painful but healthy, consciousness of ignorance, and to prepare the mind for that process of teaching whereby alone Science or Cognition can be imparted.2 He admits that Opinion may be right as well as wrong. Yet even when right, it is essentially different from Science, and is essentially transitory; a safe guide to action while it lasts, but not to be trusted for stability or permanence.3 By Plato, Rhetoric is treated as belonging to the province of Opinion, Dialectic to that of Science. The rhetor addresses multitudes in continuous speech, appeals to received common places, and persuades: the dialectician, conversing only with one or a few, receives and imparts the stimulus of short question and answer; thus awakening the dormant capacities of the soul to the reminiscence of those universal Forms or Ideas which are the only true Knowable.

Like Plato, Aristotle distinguishes the region of Common Sense or Opinion from that of Science, and regards Universals as the objects of Science. But his Universals are very different from those of Plato: they are not self-existent realities, known by the mind from a long period of pre-existence, and called up by reminiscence out of the chaos of sensible impressions. To operate such revival is the great function that Plato assigns to Dialectic. But in the philosophy of Aristotle Dialectic is something very different. It is placed alongside of Rhetoric in the region of Opinion. Both the rhetor and the dialectician deal with all subjects, recognizing no limit; they attack or defend any or all conclusions, employing the process of ratiocination which Aristotle has treated under the name of Syllogism; they take up as premisses any one of the various opinions in circulation, for which some plausible authority may be cited; they follow out the consequences of one opinion in its bearing upon others, favourable or unfavourable, and thus become well furnished209 with arguments for and against all. The ultimate foundation here supposed is some sort of recognized presumption or authoritative sanction4 — law, custom, or creed, established among this or that portion of mankind, some maxim enunciated by an eminent poet, some doctrine of the Pythagoreans or other philosophers, current proverb, answer from the Delphian oracle, &c. Any one of these may serve as a dialectical authority. But these authorities, far from being harmonious with each other, are recognized as independent, discordant, and often contradictory. Though not all of equal value,5 each is sufficient to warrant the setting up of a thesis for debate. In Dialectic, one of the disputants undertakes to do this, and to answer all questions that may be put to him respecting the thesis, without implicating himself in inconsistencies or contradiction. The questioner or assailant, on the other hand, shapes his questions with a view to refute the thesis, by eliciting answers which may furnish him with premisses for some syllogism in contradiction thereof. But he is tied down by the laws of debate to syllogize only from such premisses as the respondent has expressly granted; and to put questions in such manner that the respondent is required only to give or withhold assent, according as he thinks right.

We shall see more fully how Aristotle deals with Dialectic, when we come to the Topica: here I put it forward briefly, in order that the reader may better understand, by contrast, its extreme antithesis, viz., Demonstrative Science and Necessary Truth as conceived by Aristotle. First, instead of two debaters, one of whom sets up a thesis which he professes to understand and undertakes to maintain, while the other puts questions upon it, — Demonstrative Science assumes a teacher who knows, and a learner conscious of ignorance but wishing to know. The teacher lays down premisses which the learner is bound to receive; or if they are put in the form of questions, the learner must answer them as the teacher expects, not according to his own knowledge. Secondly, instead of the unbounded miscellany of subjects treated in Dialectic, Demonstrative Science is confined to a few special subjects, in which alone appropriate premisses can be obtained, and definitions framed. Thirdly, instead 210of the several heterogeneous authorities recognized in Dialectic, Demonstrative Science has principia of its own, serving as points of departure; some principia common to all its varieties, others special or confined to one alone. Fourthly, there is no conflict of authorities in Demonstrative Science; its propositions are essential, universal, and true per se, from the commencement to the conclusion; while Dialectic takes in accidental premisses as well as essential. Fifthly, the principia of Demonstrative Science are obtained from Induction only; originating in particulars which are all that the ordinary growing mind can at first apprehend (notiora nobis), but culminating in universals which correspond to the perfection of our cognitive comprehension (notiora naturâ.)6

Amidst all these diversities, Dialectic and Demonstrative Science have in common the process of Syllogism, including such assumptions as the rules of syllogizing postulate. In both, the conclusions are hypothetically true (i.e. granting the premisses to be so). But, in demonstrative syllogism, the conclusions are true universally, absolutely, and necessarily; deriving this character from their premisses, which Aristotle holds up as the cause, reason, or condition of the conclusion. What he means by Demonstrative Science, we may best conceive, by taking it as a small τέμενος or specially cultivated enclosure, subdivided into still smaller separate compartments — the extreme antithesis to the vast common land of Dialectic. Between the two lies a large region, neither essentially determinate like the one, nor essentially indeterminate like the other; an intermediate region in which are comprehended the subjects of the treatises forming the very miscellaneous Encyclopædia of Aristotle. These subjects do not admit of being handled with equal exactness; accordingly, he admonishes us that it is important to know how much exactness is attainable in each, and not to aspire to more.7

211In setting out the process of Demonstration, Aristotle begins from the idea of teaching and learning. In every variety thereof some præcognita must be assumed, which the learner must know before he comes to be taught, and upon which the teacher must found his instruction.8 This is equally true, whether we proceed (as in Syllogism) from the more general to the less general, or (as in Induction) from the particular to the general. He who comes to learn Geometry must know beforehand the figures called circle and triangle, and must have a triangular figure drawn to 212contemplate; he must know what is a unit or monad, and must have, besides, exposed before him what is chosen as the unit for the reasoning on which he is about to enter. These are the præcognita required for Geometry and Arithmetic. Some præcognita are also required preparatory to any and all reasoning: e.g., the maxim of Identity (fixed meaning of terms and propositions), and the maxims of Contradiction and of Excluded Middle (impossibility that a proposition and its contradictory can either be both true or both false.)9 The learner must thus know beforehand certain Definitions and Axioms, as conditions without which the teacher cannot instruct him in any demonstrative science.

Aristotle, here at the beginning, seeks to clear up a difficulty which had been raised in the time of Plato as between knowledge and learning. How is it possible to learn at all? is a question started in the Menon.10 You either know a thing already, and, on this supposition, you do not want to learn it; or you do not know it, and in this case you cannot learn it, because, even when you have learnt, you cannot tell whether the matter learnt is what you were in search of. To this difficulty, the reply made in the Menon is, that you never do learn any thing really new. What you are said to learn, is nothing more than reminiscence of what had once been known in an anterior life, and forgotten at birth into the present life; what is supposed to be learnt is only the recall of that which you once knew, but had forgotten. Such is the Platonic doctrine of Reminiscence. Aristotle will not accept that doctrine as a solution; but he acknowledges the difficulty, and intimates that others had already tried to solve it without success. His own solution is that there are two grades of cognition: (1) the full, complete, absolute; (2) the partial, incomplete, qualified. What you already know by the first of these grades, you cannot be said to learn; but you may learn that which you know only by the second grade, and by such learning you bring your incomplete cognition up to completeness.

Thus, you have learnt, and you know, the universal truth, that every triangle has its three angles equal to two right angles; but you do not yet know that A B C, D E F, G H I, &c., have their two angles equal to two right angles; for you have not yet seen any of these figures, and you do not know that they are triangles. The moment that you see A B C, or hear what 213figure it is, you learn at one and the same time two facts: first, that it is a triangle; next, by virtue of your previous cognition, that it possesses the above-mentioned property. You knew this in a certain way or incompletely before, by having followed the demonstration of the universal truth, and by thus knowing that every triangle had its three angles equal to two right angles; but you did not know it absolutely, being ignorant that A B C was a triangle.11

214Aristotle proceeds to tell us what is meant by knowing a thing absolutely or completely (ἁπλῶς). It is when we believe ourselves to know the cause or reason through which the matter known exists, so that it cannot but be as it is. That is what Demonstration, or Scientific Syllogism, teaches us;12 a Syllogism derived from premisses true, immediate, prior to, and more knowable than the conclusion — causes of the conclusion, and specially appropriate thereto. These premisses must be known beforehand without being demonstrated (i.e. known not through a middle term); and must be known not merely in the sense of 215understanding the signification of the terms, but also in that of being able to affirm the truth of the proposition. Prior or more knowable is understood here as prior or more knowable by nature (not relatively to us, according to the antithesis formerly explained); first, most universal, undemonstrable principia are meant. Some of these are Axioms, which the learner must “bring with him from home,” or know before the teacher can instruct him in any special science; some are Definitions of the name and its essential meaning; others, again, are Hypotheses or affirmations of the existence of the thing defined, which the learner must accept upon the authority of the teacher.13 As these are the principia of Demonstration, so it is necessary that the learner should know them, not merely as well as the conclusions demonstrated, but even better; and that among matters contradictory to the principia there should be none that he knows better or trusts more.14

In Aristotle’s time two doctrines had been advanced, in opposition to the preceding theory: (1) Some denied the necessity of any indemonstrable principia, and affirmed the possibility of, demonstrating backwards ad infinitum; (2) Others agreed in denying the necessity of any indemonstrable principia, but contended that demonstration in a circle is valid and legitimate — e.g. that A may be demonstrated by means of B, and B by means of A. Against both these doctrines Aristotle enters his protest. The first of them — the supposition of an interminable regress — he pronounces to be obviously absurd: the second he declares tantamount to proving a thing by itself; the circular demonstration, besides, having been shown to be impossible, except in the First figure, with propositions in which the predicate reciprocates or is co-extensive with the subject — a very small proportion among propositions generally used in demonstrating.15

216Demonstrative Science is attained only by syllogizing from necessary premisses, such as cannot possibly be other than they are. The predicate must be (1) de omni, (2) per se, (3) quatenus ipsum, so that it is a Primum Universale; this third characteristic not being realized without the preceding two. First, the predicate must belong, and belong at all times, to everything called by the name of the subject. Next, it must belong thereunto per se, or essentially; that is, either the predicate must be stated in the definition declaring the essence of the subject, or the subject must be stated in the definition declaring the essence of the predicate. The predicate must not be extra-essential to the subject, nor attached to it as an adjunct from without, simply concomitant or accidental. The like distinction holds in regard to events: some are accidentally concomitant sequences which may or may not be realized (e.g., a flash of lightning occurring when a man is on his journey); in others, the conjunction is necessary or causal (as when an animal dies under the sacrificial knife).16 Both these two characteristics (de omni and per se) are presupposed in the third (quatenus ipsum); but this last implies farther, that the predicate is attached to the subject in the highest universality consistent with truth; i.e., that it is a First Universal, a primary predicate and not a derivative predicate. Thus, the predicate of having its three angles equal to two right angles, is a characteristic not merely de omni and per se, but also a First Universal, applied to a triangle. It is applied to a triangle, quatenus triangle, as a primary predicate. If applied to a subject of higher universality (e.g., to every geometrical figure), it would not be always true. If applied to a subject of lower universality (e.g., to a right-angled triangle or an isosceles triangle), it would be universally true and would be true per se, but it would be a derivative predicate and not a First Universal; it would not be applied to the isosceles quatenus isosceles, for there is a still higher Universal of which it is predicable, being true respecting any triangle you please. Thus, the properties with which Demonstration, or full and absolute 217Science, is conversant, are de omni, per se, and quatenus ipsum, or Universalia Prima;17 all of them necessary, such as cannot but be true.

Aristotle remarks that there is great liability to error about these Universalia Prima. We sometimes demonstrate a predicate to be true, universally and per se, of a lower species, without being aware that it might also be demonstrated to be true, universally and per se, of the higher genus to which that species belongs; perhaps, indeed, that higher genus may not yet have obtained a current name. That proportions hold by permutation, was demonstrated severally for numbers, lines, solids, and intervals of time; but this belongs to each of them, not from any separate property of each, but from what is common to all: that, however, which is common to all had received no name, so that it was not known that one demonstration might comprise all the four.18 In like manner, a man may know that an equilateral and an isosceles triangle have their three angles equal to two right angles, and also that a scalene triangle has its three angles equal to two right angles; yet he may not know (except sophistically and by accident19) that a triangle in genere has its three angles equal to two right angles, though there be no other triangles except equilateral, isosceles, and scalene. He does not know that this may be demonstrated of every triangle quatenus triangle. The only way to obtain a 218certain recognition of Primum Universale, is, to abstract successively from the several conditions of a demonstration respecting the concrete and particular, until the proposition ceases to be true. Thus, you have before you a brazen isosceles triangle, the three angles whereof are equal to two right angles. You may eliminate the condition brazen, and the proposition will still remain true. You may also eliminate the condition isosceles; still the proposition is true. But you cannot eliminate the condition triangle, so as to retain only the higher genus, geometrical figure; for the proposition then ceases to be always true. Triangle is in this case the Primum Universale.20

In every demonstration the principia or premisses must be not only true, but necessarily true; the conclusion also will then be necessarily true, by reason of the premisses, and this constitutes Demonstration. Wherever the premisses are necessarily true, the conclusion will be necessarily true; but you cannot say, vice versâ, that wherever the conclusion is necessarily true, the syllogistic premisses from which it follows must always be necessarily true. They may be true without being necessarily true, or they may even be false: if, then, the conclusion be necessarily true, it is not so by reason of these premisses; and the syllogistic proof is in this case no demonstration. Your syllogism may have true premisses and may lead to a conclusion which is true by reason of them; but still you have not demonstrated, since neither premisses nor conclusion are necessarily true.21 When an opponent contests your demonstration, he succeeds if he can disprove the necessity of your conclusion; if he can show any single case in which it either is or may be false.22 It is not enough to proceed upon a premiss which is either probable or simply true: it may be true, yet not appropriate to the case: you must take your departure from the first or highest universal of the genus about which you attempt to demonstrate.23 Again, unless you can state the why of your conclusion; that is to say, unless the middle term, by reason of which the conclusion is necessarily true, be itself necessarily true, — you have not demonstrated it, nor do you know it absolutely. Your 219middle term not being necessary may vanish, while the conclusion to which it was supposed to lead abides: in truth no conclusion was known through that middle.24 In the complete demonstrative or scientific syllogism, the major term must be predicable essentially or per se of the middle, and the middle term must be predicable essentially or per se of the minor; thus alone can you be sure that the conclusion also is per se or necessary. The demonstration cannot take effect through a middle term which is merely a Sign; the sign, even though it be a constant concomitant, yet being not, or at least not known to be, per se, will not bring out the why of the conclusion, nor make the conclusion necessary. Of non-essential concomitants altogether there is no demonstration; wherefore it might seem to be useless to put questions about such; yet, though the questions cannot yield necessary premisses for a demonstrative conclusion, they may yield premisses from which a conclusion will necessarily follow.25

In every demonstration three things may be distinguished: (1) The demonstrated conclusion, or Attribute essential to a certain genus; (2) The Genus, of which the attributes per se are the matter of demonstration; (3) The Axioms, out of which, or through which, the demonstration is obtained. These Axioms may be and are common to several genera: but the demonstration cannot be transferred from one genus to another; both the extremes as well as the middle term must belong to the same genus. An arithmetical demonstration cannot be transferred to magnitudes and their properties, except in so far as magnitudes are numbers, which is partially true of some among them. The demonstrations in arithmetic may indeed be transferred to harmonics, because harmonics is subordinate to arithmetic; and, for the like reason, demonstrations in geometry may be transferred to mechanics and optics. But we cannot introduce into geometry any property of lines, which does not belong to them quâ lines; such, for example, as that a straight line is the most beautiful of all lines, or is the contrary of a circular line; for these predicates belong to it, not quâ line, but quâ member of a different or more extensive genus.26 There can be no 220complete demonstration about perishable things, or about any individual line, except in regard to its attributes as member of the genus line. Where the conclusion is not eternally true, but true at one time and not true at another, this can only be because one of its premisses is not universal or essential. Where both premisses are universal and essential, the conclusion must be eternal or eternally true. As there is no demonstration, so also there can be no definition, of perishable attributes.27

For complete demonstration, it is not sufficient that the premisses be true, immediate, and undemonstrable; they must, furthermore, be essential and appropriate to the class in hand. Unless they be such, you cannot be said to know the conclusion absolutely; you know it only by accident. You can only know a conclusion when demonstrated from its own appropriate premisses; and you know it best when it is demonstrated from its highest premisses. It is sometimes difficult to determine whether we really know or not; for we fancy that we know, when we demonstrate from true and universal principia, without being aware whether they are, or are not, the principia appropriate to the case.28 But these principia must always be assumed without demonstration — the class whose essential constituent properties are in question, the universal Axioms, and the Definition or meaning of the attributes to be demonstrated. If these definitions and axioms are not always formally enunciated, it is because we tacitly presume them to be already known and admitted by the learner.29 He may indeed always refuse to grant them in express words, but they are such that he cannot help granting them by internal assent in his mind, to which every syllogism must address itself. When you assume a premiss without demonstrating it, though it be really demonstrable, this, if the learner is favourable and willing to grant it, is an assumption or Hypothesis, valid relatively to him alone, but not valid absolutely: if he is reluctant or adverse, it is a Postulate, which 221you claim whether he is satisfied or not.30 The Definition by itself is not an hypothesis; for it neither affirms nor denies the existence of anything. The pupil must indeed understand the terms of it; but this alone is not an hypothesis, unless you call the fact that the pupil comes to learn, an hypothesis.31 The Hypothesis or assumption is contained in the premisses, being that by which the reason of the conclusion comes to be true. Some object that the geometer makes a false hypothesis or assumption, when he declares a given line drawn to be straight, or to be a foot long, though it is neither one nor the other. But this objection has no pertinence, since the geometer does not derive his conclusions from what is true of the visible lines drawn before his eyes, but from what is true of the lines conceived in his own mind, and signified or illustrated by the visible diagrams.32

The process of Demonstration neither requires, nor countenances, the Platonic theory of Ideas — universal substances beyond and apart from particulars. But it does require that we should admit universal predications; that is, one and the same predicate truly applicable in the same sense to many different particulars. Unless this be so, there can be no universal major premiss, nor appropriate middle term, nor valid demonstrative syllogism.33

The Maxim or Axiom of Contradiction, in its most general enunciation, is never formally enunciated by any special science; but each of them assumes the Maxim so far as applicable to its own purpose, whenever the Reductio ad Absurdum is introduced.34 It is in this and the other common principles or Axioms that all the sciences find their point of contact and communion; and that Dialectic also comes into communion with all of them, as also the science (First Philosophy) that scrutinizes the validity or demonstrability of the Axioms.35 The dialectician is not confined222 to any one science, or to any definite subject-matter. His liberty of interrogation is unlimited; but his procedure is essentially interrogatory, and he is bound to accept the answer of the respondent — whatever it be, affirmative or negative — as premiss for any syllogism that he may construct. In this way he can never be sure of demonstrating any thing; for the affirmative and the negative will not be equally serviceable for that purpose. There is indeed also, in discussions on the separate sciences, a legitimate practice of scientific interrogation. Here the questions proper to be put are limited in number, and the answers proper to be made are determined beforehand by the truths of the science — say Geometry; still, an answer thus correctly made will serve to the interrogator as premiss for syllogistic demonstration.36 The respondent must submit to have such answer tested by appeal to geometrical principia and to other geometrical propositions already proved as legitimate conclusions from the principia; if he finds himself involved in contradictions, he is confuted quâ geometer, and must correct or modify his answer. But he is not bound, quâ geometer, to undergo scrutiny as to the geometrical principia themselves; this would carry the dialogue out of the province of Geometry into that of First Philosophy and Dialectic. Care, indeed, must be taken to keep both questions and answers within the limits of the science. Now there can be no security for this restriction, except in the scientific competence of the auditors. Refrain, accordingly, from all geometrical discussions among men ignorant of geometry and confine yourself to geometrical auditors, who alone can distinguish what questions and answers are really appropriate. And what is here said about geometry, is equally true about the other special sciences.37 Answers may be improper either as foreign to the science under debate, or as appertaining to the science, yet false as to the matter, or as equivocal in middle term; though this last is less likely to occur in Geometry, since the demonstrations are accompanied by diagrams, which help 223to render conspicuous any such ambiguity.38 To an inductive proposition, bringing forward a single case as contributory to an ultimate generalization, no general objection should be offered; the objection should be reserved until the generalization itself is tendered.39 Sometimes the mistake is made of drawing an affirmative conclusion from premisses in the Second figure; this is formally wrong, but the conclusion may in some cases be true, if the major premiss happens to be a reciprocating proposition, having its predicate co-extensive with its subject. This, however, cannot be presumed; nor can a conclusion be made to yield up its principles by necessary reciprocation; for we have already observed that, though the truth of the premisses certifies the truth of the conclusion, we cannot say vice versâ that the truth of the conclusion certifies the truth of the premisses. Yet propositions are more frequently found to reciprocate in scientific discussion than in Dialectic; because, in the former, we take no account of accidental properties, but only of definitions and what follows from them.40

Knowledge of Fact and knowledge of the Cause must be distinguished, and even within the same Science.41 In some syllogisms the conclusion only brings out τὸ ὅτι — the reality of certain facts; in others, it ends in τὸ διότι — the affirmation of a cause, or of the Why. The syllogism of the Why is, where the middle term is not merely the cause, but the proximate cause, of the conclusion. Often, however, the effect is more notorious, so that we employ it as middle term, and conclude from it to its reciprocating cause; in which case our syllogism is only of the ὅτι; and so it is also when we employ as middle term a cause not proximate but remote, concluding from that to the effect.42 Sometimes224 the syllogisms of the ὅτι may fall under one science, those of the διότι under another, namely, in the case where one science is subordinate to another, as optics to geometry, and harmonics to arithmetic; the facts of optics and harmonics belonging to sense and observation, the causes thereof to mathematical reasoning. It may happen, then, that a man knows τὸ διότι well, but is comparatively ignorant τοῦ ὅτι: the geometer may have paid little attention to optical facts.43 Cognition of the διότι is the maximum, the perfection, of all cognition; and this, comprising arithmetical and geometrical theorems, is almost always attained by syllogisms in the First figure. This figure is the most truly scientific of the three; the other two figures depend upon it for expansion and condensation. It is, besides, the only one in which universal affirmative conclusions can be obtained; for in the Second figure we get only negative conclusions; in the Third, only particular. Accordingly, propositions declaring Essence or Definition, obtained only through universal affirmative conclusions, are yielded in none but the First figure.44

As there are some affirmative propositions that are indivisible, i.e., having affirmative predicates which belong to a subject at once, directly, immediately, indivisibly, — so there are also some indivisible negative propositions, i.e., with predicates that belong negatively to a subject at once, directly, &c. In all such there is no intermediate step to justify either the affirmation of the predicate, or the negation of the predicate, respecting the given subject. This will be the case where neither the predicate nor the subject is contained in any higher genus.45

225In regard both to these propositions immediate and indivisible, and to propositions mediate and deducible, there are two varieties of error.46 You may err simply, from ignorance, not knowing better, and not supposing yourself to know at all; or your error may be a false conclusion, deduced by syllogism through a middle term, and accompanied by a belief on your part that you do know. This may happen in different ways. Suppose the negative proposition, No B is A, to be true immediately or indivisibly. Then, if you conclude the contrary of this47 (All B is A) to be true, by syllogism through the middle term C, your syllogism must be in the First figure; it must have the minor premiss false (since B is brought under C, when it is not contained in any higher genus), and it may have both premisses false. Again, suppose the affirmative proposition, All B is A, to be true immediately or indivisibly. Then if you conclude the contrary of this (No B is A) to be true, by syllogism through the middle term C, your syllogism may be in the First figure, but it may also be in the Second figure, your false conclusion being negative. If it be in the First figure, both its premisses may be false, or one of them only may be false, either indifferently.48 If it be in the Second figure, either premiss singly may be wholly false, or both may be partly false.49

Let us next assume the affirmative proposition, All B is A, to be true, but mediate and deducible through the middle term C. If you conclude the contrary of this (No B is A) through the same middle term C, in the First figure, your error cannot arise from falsity in the minor premiss, because your minor (by the laws of the figure) must be affirmative; your error must arise from a false major, because a negative major is not inconsistent with the laws of the First figure. On the other hand, if you conclude the contrary in the First figure through a different 226middle term, D, either both your premisses will be false, or your minor premiss will be false.50 If you employ the Second figure to conclude your contrary, both your premisses cannot be false, though either one of them singly may be false.51

Such will be the case when the deducible proposition assumed to be true is affirmative, and when therefore the contrary conclusion which you profess to have proved is negative. But if the deducible proposition assumed to be true is negative, and if consequently the contrary conclusion must be affirmative, — then, if you try to prove this contrary through the same middle term, your premisses cannot both be false, but your major premiss must always be false.52 If, however, you try to prove the contrary through a different and inappropriate middle term, you cannot convert the minor premiss to its contrary (because the minor premiss must continue affirmative, in order that you may arrive at any conclusion at all), but the major can be so converted. Should the major premiss thus converted be true, the minor will be false; should the major premiss thus converted be false, the minor may be either true or false. Either one of the premisses, or both the premisses, may thus be false.53

Errors of simple ignorance (not concluded from false syllogism) may proceed from defect or failure of sensible perception, in one or other of its branches. For without sensation there can be no induction; and it is from induction only that the premisses for demonstration by syllogism are obtained. We cannot arrive at universal propositions, even in what are called abstract sciences, except through induction of particulars; nor can we demonstrate except from universals. Induction and Demonstration are the only two ways of learning; and the particulars composing our inductions can only be known through sense.54

Aristotle next proceeds to show (what in previous passages he 227had assumed)55 that, if Demonstration or the syllogistic process be possible — if there be any truths supposed demonstrable, this implies that there must be primary or ultimate truths. It has been explained that the constituent elements assumed in the Syllogism are three terms and two propositions or premisses; in the major premiss, A is affirmed (or denied) of all B; in the minor, B is affirmed of all C; in the conclusion, A is affirmed (or denied) of all C.56 Now it is possible that there may be some one or more predicates higher than A, but it is impossible that there can be an infinite series of such higher predicates. So also there may be one or more subjects lower than C, and of which C will be the predicate; but it is impossible that there can be an infinite series of such lower subjects. In like manner there may perhaps be one or more middle terms between A and B, and between B and C; but it is impossible that there can be an infinite series of such intervening middle terms. There must be a limit to the series ascending, descending, or intervening.57 These remarks have no application to reciprocating propositions, in which the predicate is co-extensive with the subject.58 But they apply alike to demonstrations negative and affirmative, and alike to all the three figures of Syllogism.59

In Dialectical Syllogism it is enough if the premisses be admitted or reputed as propositions immediately true, whether they are so in reality or not; but in Scientific or Demonstrative Syllogism they must be so in reality: the demonstration is not complete unless it can be traced up to premisses that are thus immediately or directly true (without any intervening middle term).60 That there are and must be such primary or immediate premisses, Aristotle now undertakes to prove, by some dialectical reasons, and other analytical or scientific reasons.61 He himself 228thus distinguishes them; but the distinction is faintly marked, and amounts, at most, to this, that the analytical reasons advert only to essential predication, and to the conditions of scientific demonstration, while the dialectical reasons dwell upon these, but include something else besides, viz., accidental predication. The proof consists mainly in the declaration that, unless we assume some propositions to be true immediately, indivisibly, undemonstrably, — Definition, Demonstration, and Science would be alike impossible. If the ascending series of predicates is endless, so that we never arrive at a highest generic predicate; if the descending series of subjects is endless, so that we never reach a lowest subject, — no definition can ever be attained. The essential properties included in the definition, must be finite in number; and the accidental predicates must also be finite in number, since they have no existence except as attached to some essential subject, and since they must come under one or other of the nine later Categories.62 If, then, the two extremes are thus fixed and finite — the highest predicate and the lowest subject — it is impossible that there can be an infinite series of terms between the two. The intervening terms must be finite in number. The Aristotelian theory therefore is, that there are certain propositions directly and immediately true, and others derived from them by demonstration through middle terms.63 It is alike an error to assert that every thing can be demonstrated, and that nothing can be demonstrated.

It is plain from Aristotle’s own words64 that he intended these four chapters (xix.-xxii.) as a confirmation of what he had already asserted in chapter iii. of the present treatise, and as farther refutation of the two distinct classes of opponents there indicated: (1) those who said that everything was demonstrable, demonstration in a circle being admissible; (2) those who said that nothing was demonstrable, inasmuch as the train of predication229 upwards, downwards, and intermediate, was infinite. Both these two classes of opponents agreed in saying, that there were no truths immediate and indemonstrable; and it is upon this point that Aristotle here takes issue with them, seeking to prove that there are and must be such truths. But I cannot think the proof satisfactory; nor has it appeared so to able commentators either of ancient or modern times — from Alexander of Aphrodisias down to Mr. Poste.65 The elaborate amplification 230added in these last chapters adds no force to the statement already given at the earlier stage; and it is in one respect a change for the worse, inasmuch as it does not advert to the important distinction announced in chapter iii., between universal truths known by Induction (from sense and particulars), and universal truths known by Deduction from these. The truths immediate and indemonstrable (not known through a middle term) are the inductive truths, as Aristotle declares in many places, and most emphatically at the close of the Analytica Posteriora. But in these chapters, he hardly alludes to Induction. Moreover, while trying to prove that there must be immediate universal truths, he neither gives any complete list of them, nor assigns any positive characteristic whereby to identify them. Opponents might ask him whether these immediate universal truths were not ready-made inspirations of the mind; and if so, what better authority they had than the Platonic Ideas, which are contemptuously dismissed.

We have thus recognized that there exist immediate (ultimate or primary) propositions, wherein the conjunction between predicate and subject is such that no intermediate term can be assigned between them. When A is predicated both of B and C, this may perhaps be in consequence of some common property possessed by B and C, and such common property will form a middle term. For example, equality of angles to two right angles belongs both to an isosceles and to a scalene triangle, and it belongs to them by reason of their common property — triangular figure; which last is thus the middle term. But this need not be always the case.66 It is possible that the two propositions — A predicated of B, A predicated of C — may both of them be immediate propositions; and that there may be no community of nature between B and C. Whenever a middle term can be found, demonstration is possible; but where no middle term can be found, demonstration is impossible. The proposition, whether affirmative or negative, is then an immediate or indivisible one. Such propositions, and the terms of which they are composed, are the ultimate elements or principia of Demonstration. Predicate and subject are brought constantly into closer and closer conjunction, until at last they become one and indivisible.67 Here we reach the unit or element 231of the syllogizing process. In all scientific calculations there is assumed an unit to start from, though in each branch of science it is a different unit; e.g. in barology, the pound-weight; in harmonics, the quarter-tone; in other branches of science, other units.68 Analytical research teaches us that the corresponding unit in Syllogism is the affirmative or negative proposition which is primary, immediate, indivisible. In Demonstration and Science it is the Noûs or Intellect.69

Having thus, in the long preceding reasoning, sought to prove that all demonstration must take its departure from primary undemonstrable principia — from some premisses, affirmative and negative, which are directly true in themselves, and not demonstrable through any middle term or intervening propositions, Aristotle now passes to a different enquiry. We have some demonstrations in which the conclusion is Particular, others in which it is Universal: again, some Affirmative, some Negative, Which of the two, in each of these alternatives, is the best? We have also demonstrations Direct or Ostensive, and demonstrations Indirect or by way of Reductio ad Absurdum. Which of these two is the best? Both questions appear to have been subjected to debate by contemporary philosophers.70

Aristotle discusses these points dialectically (as indeed he points out in the Topica that the comparison of two things generally, as to better and worse, falls under the varieties of dialectical enquiry71), first stating and next refuting the arguments on the weaker side. Some persons may think (he says) that demonstration of the Particular is better than demonstration of the Universal: first, because it conducts to fuller cognition of that which the thing is in itself, and not merely that which it is quatenus member of a class; secondly, because demonstrations of the Universal are apt to generate an illusory belief, that the Universal is a distinct reality apart from and independent of all its particulars (i.e., that figure in general has a real existence apart from all particular figures, and number in general apart from all particular numbers, &c.), while demonstrations of the Particular do not lead to any such illusion.72

232To these arguments Aristotle replies:— 1. It is not correct to say that cognition of the Particular is more complete, or bears more upon real existence, than cognition of the Universal. The reverse would be nearer to the truth. To know that the isosceles, quatenus triangle, has its three angles equal to two right angles, is more complete cognition than knowing simply that the isosceles has its three angles equal to two right angles. 2. If the Universal be not an equivocal term — if it represents one property and one definition common to many particulars, it then has a real existence as much or more than any one or any number of the particulars. For all these particulars are perishable, but the class is imperishable. 3. He who believes that the universal term has one meaning in all the particulars, need not necessarily believe that it has any meaning apart from all particulars; he need not believe this about Quiddity, any more than he believes it about Quality or Quantity. Or if he does believe so, it is his own individual mistake, not imputable to the demonstration. 4. We have shown that a complete demonstration is one in which the middle term is the cause or reason of the conclusion. Now the Universal is most of the nature of Cause; for it represents the First Essence or the Per Se, and is therefore its own cause, or has no other cause behind it. The demonstration of the Universal has thus more of the Cause or the Why, and is therefore better than the demonstration of the Particular. 5. In the Final Cause or End of action, there is always some ultimate end for the sake of which the intermediate ends are pursued, and which, as it is better than they, yields, when it is known, the only complete explanation of the action. So it is also with the Formal Cause: there is one highest form which contains the Why of the subordinate forms, and the knowledge of which is therefore better; as when, for example, the exterior angles of a given isosceles triangle are seen to be equal to four right angles, not because it is isosceles or triangle, but because it is a rectilineal figure. 6. Particulars, as such, fall into infinity of number, and are thus unknowable; the Universal tends towards oneness and simplicity, and is thus essentially knowable, more fully demonstrable than the infinity of particulars. The demonstration thereof is therefore better. 7. It is also better, on another ground; for he that knows the Universal does in a certain sense know also the Particular;73 but he that knows the Particular cannot be said in any sense to 233know the Universal. 8. The principium or perfection of cognition is to be found in the immediate proposition, true per se. When we demonstrate, and thus employ a middle term, the nearer the middle term approaches to that principium, the better the demonstration is. The demonstration of the Universal is thus better and more accurate than that of the Particular.74

Such are the several reasons enumerated by Aristotle in refutation of the previous opinion stated in favour of the Particular. Evidently he does not account them all of equal value: he intimates that some are purely dialectical (λογικά); and he insists most upon the two following:— 1. He that knows the Universal knows in a certain sense the Particular; if he knows that every triangle has its three angles equal to two right angles, he knows potentially that the isosceles has its three angles equal to the same, though he may not know as yet that the isosceles is a triangle. But he that knows the Particular does not in any way know the Universal, either actually or potentially.75 2. The Universal is apprehended by Intellect or Noûs, the highest of all cognitive powers; the Particular terminates in sensation. Here, I presume, he means, that, in demonstration of the Particular, the conclusion teaches you nothing more than you might have learnt from a direct observation of sense; whereas in that of the Universal the conclusion teaches you more than you could have learnt from direct sensation, and comes into correlation with the highest form of our intellectual nature.76

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 234inferior 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

235There 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 236It 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 237fluctuating, 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

[END OF CHAPTER VII]

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