Chapter VII: Analytica Posteriora I (1)

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.

[Footnote 1: Analyt. Prior. I. xxx. p. 46, a. 4-10; Analyt. Post. I. ii. p. 71, a. 23.]

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, which 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.

[Footnote 2: Plato, Sophistes, pp. 228-229; Symposion, pp. 203-204; Theætetus, pp. 148, 149, 150. Compare also 'Plato and the Other Companions of Sokrates,' Vol. I. chs. vi.-vii. pp. 245-288; II. ch. xxvi. p. 376, seq.]

[Footnote 3: Plato, Republic, v. pp. 477-478; Menon, pp. 97-98.]

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 furnished with arguments for and against all. The ultimate foundation here supposed is some sort of recognized presumption or authoritative sanction[4]--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.

[Footnote 4: Aristot. Topica, I. x. p. 104, a. 8, xi. p. 104, b. 19. Compare Metaphysica, A. p. 995, a. 1-10.]

[Footnote 5: Analyt. Post. I. xix. p. 81, b. 18: [Greek: kata\ me\n ou)=n do/xan sullogizome/nois kai\ mo/non dialektikô=s dê=lon o(/ti tou=to mo/non skepte/on, ei) e)x ô(=n e)nde/chetai e)ndoxota/tôn gi/netai o( sullogismo/s, ô(/st' ei) kai\ e)/sti ti tê=| a)lêthei/a| tô=n AB me/son, dokei= de\ mê/, o( dia\ tou/tou sullogizo/menos sullelo/gistai dialektikô=s, pro\s d' a)lê/theian e)k tô=n u(parcho/ntôn dei= skopei=n.] Compare Topica, VIII. xii. p. 162, b. 27.]

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 of 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]

[Footnote 6: Aristot. Topica, VI. iv. p. 141, b. 3-14. [Greek: oi( polloi\ ga\r ta\ toiau=ta prognôri/zousin; ta\ me\n ga\r tê=s tuchou/sês, ta\ d' a)kribou=s kai\ perittê=s dianoi/as katamathei=n e)sti/n.] Compare in Analyt. Post. I. xii. pp. 77-78, the contrast between [Greek: ta\ mathê/mata] and [Greek: oi( dia/logoi].]

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 [Greek: te/menos] 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]

[Footnote 7: Aristot. Ethic. Nikom. I. p. 1094, b. 12-25; p. 1098, a. 26-b. 8; Metaphys. A. p. 995, a. 15; Ethic. Eudem. I. p. 1216, b. 30-p. 1217, a. 17; Politic. VII. p. 1328, a. 19; Meteorolog. I. p. 338, a. 35. Compare Analyt. Post. I. xiii. p. 78, b. 32 (with Waitz's note, II. p. 335); and I. xxvii. p. 87, a. 31.

The passages above named in the Nikomachean Ethica are remarkable: [Greek: le/goito d' a)\n i(kanô=s, ei) kata\ tê\n u(pokeime/nên u(/lên diasaphêthei/ê; to\ ga\r a)kribe\s ou)ch o(moi/ôs e)n a(/pasi toi=s lo/gois e)pizêtête/on, ô(/sper ou)d' e)n toi=s dêmiourgoume/nois. tê\n a)kri/beian mê\ o(moi/ôs e)n a(/pasin e)pizêtei=n (chrê/), a)ll' e)n e(ka/stois kata\ tê\n u(pokeime/nên u(/lên, kai\ e)pi\ tosou=ton e)ph' o(/son oi)kei=on tê=| methodô=|.] Compare Metaphys. E. p. 1025, b. 13: [Greek: a)podeiknu/ousin ê)\ a)nagkai/oteron ê)\ malakô/teron.]

The different degrees of exactness attainable in different departments of science, and the reasons upon which such difference depends are well explained in the sixth book of Mr. John Stuart Mill's System of Logic, vol. II. chap. iii. pp. 422-425, 5th ed. Aristotle says that there can be no scientific theory or cognition about [Greek: to\ sumbebêko/s] which he defines to be that which belongs to a subject neither necessarily, nor constantly, nor usually, but only on occasion (Metaphys. E. p. 1026, b. 3, 26, 33; K. p. 1065, a. 1, meaning [Greek: to\ sumbebêko\s mê\ kath' au(to/],--Analyt. Post. I. 6, 75, a. 18; for he uses the term in two different senses--Metaph. [Greek: D]. p. 1025, a. 31). In his view, there can be no science except about constant conjunctions; and we find the same doctrine in the following passage of Mr. Mill:--"Any facts are fitted, in themselves, to be a subject of science, which follow one another according to constant laws; although those laws may not have been discovered, nor even be discoverable by our existing resources. Take, for instance, the most familiar class of meteorological phenomena, those of rain and sunshine. Scientific inquiry has not yet succeeded in ascertaining the order of antecedence and consequence among these phenomena, so as to be able, at least in our regions of the earth, to predict them with certainty, or even with any high degree of probability. Yet no one doubts that the phenomena depend on laws. . . . . Meteorology not only has in itself every requisite for being, but actually is, a science; though from the difficulty of observing the facts upon which the phenomena depend (a difficulty inherent in the peculiar nature of those phenomena), the science is extremely imperfect; and were it perfect, might probably be of little avail in practice, since the data requisite for applying its principles to particular instances would rarely be procurable.

"A case may be conceived of an intermediate character between the perfection of science, and this its extreme imperfection. It may happen that the greater causes, those on which the principal part of the phenomena depends, are within the reach of observation and measurement; so that, if no other causes intervened, a complete explanation could be given, not only of the phenomenon in general, but of all the variations and modifications which it admits of. But inasmuch as other, perhaps many other, causes, separately insignificant in their effects, co-operate or conflict in many or in all cases with those greater causes, the effect, accordingly, presents more or less of aberration from what would be produced by the greater causes alone. Now if these minor causes are not so constantly accessible, or not accessible at all, to accurate observation, the principal mass of the effect may still, as before, be accounted for, and even predicted; but there will be variations and modifications which we shall not be competent to explain thoroughly, and our predictions will not be fulfilled accurately, but only approximately.

"It is thus, for example, with the theory of the Tides. . . . . And this is what is or ought to be meant by those who speak of sciences which are not exact sciences. Astronomy was once a science, without being an exact science. It could not become exact until not only the general course of the planetary motions, but the perturbations also, were accounted for and referred to their causes. It has become an exact science because its phenomena have been brought under laws comprehending the whole of the causes by which the phenomena are influenced, whether in a great or only in a trifling degree, whether in all or only in some cases, and assigning to each of those causes the share of effect that really belongs to it. . . . . The science of human nature falls far short of the standard of exactness now realized in Astronomy; but there is no reason that it should not be as much a science as Tidology is, or as Astronomy was when its calculations had only mastered the main phenomena, but not the perturbations."]

In 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 contemplate; 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.

[Footnote 8: Analyt. Post. I. i. pp. 71-72; Metaphys. A. IX. p. 992, b. 30.]

[Footnote 9: Aristot. Analyt. Post. I, i. p. 71, a. 11-17. [Greek: a(/pan ê)\ phê=sai ê)\ a)pophê=sai a)lêthe/s].]

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.

[Footnote 10: Plato, Menon. p. 80.]

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 figure 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]

[Footnote 11: Aristot. Analyt. Post. I. i. p. 71, a. 17-b. 8: [Greek: e)/sti de\ gnôri/zein ta\ me\n pro/teron gnôri/zonta, tô=n de\ kai\ a)/ma lamba/nonta tê\n gnô=sin, oi(=on o(/sa tugcha/nei o)/nta u(po\ to\ katho/lou, ô(=n e)/chei tê\n gnô=sin. o(/ti me\n ga\r pa=n tri/gônon e)/chei dusi\n o)rthai=s i)/sas, proê/|dei; o(/ti de\ to/de to\ e)n tô=| ê(mikukli/ô| tri/gôno/n e)stin, a(/ma e)pago/menos e)gnô/risen.--pri\n d' e)pachthê=nai ê)\ labei=n sullogismo/n, tro/pon me/n tina i)/sôs phate/on e)pi/stasthai, tro/pon d' a)/llon ou)/. o(\ ga\r mê\ ê)/|dei ei) e)/stin a(plô=s, tou=to pô=s ê)/|dei o(/ti du/o o)rtha\s e)/chei a(plô=s? a)lla\ dê=lon ô(s _ô(di\ me\n e)pi/statai, o(/ti katho/lou e)pi/statai, a(plô=s d' ou)k e)pi/statai_.--ou)de\n (oi)=mai) kôlu/ei, o(\ mantha/nei, e)/stin ô(s e)pi/stasthai, e)/sti d' ô(s a)gnoei=n; a)/topon ga\r ou)k ei) oi)=de/ pôs o(\ mantha/nei, a)ll' ei) ô(di/, oi(=on ê(=| mantha/nei kai\ ô(/s.] Compare also Anal. Post. I. xxiv. p. 86, a. 23, and Metaph. A. ii. p. 982, a. 8; Anal. Prior. II. xxi. p. 67, a. 5-b. 10.)

Aristotle reports the solution given by others, but from which he himself dissented, of the Platonic puzzle. The respondent was asked, Do you know that every Dyad is even?--Yes. Some Dyad was then produced, which the respondent did not know to be a Dyad; accordingly he did not know it to be even. Now the critics alluded to by Aristotle said that the respondent made a wrong answer; instead of saying I know every Dyad is even, he ought to have said. Every Dyad _which I know to be a Dyad_ is even. Aristotle pronounces that this criticism is incorrect. The respondent knows the conclusion which had previously been demonstrated to him; and that conclusion was, Every triangle has its three angles equal to two right angles; it was not, Every thing _which I know_ to be a triangle has its three angles equal to two right angles. This last proposition had never been demonstrated, nor even stated: [Greek: ou)demi/a ga\r pro/tasis lamba/netai toiau/tê, o(/ti _o(\n su\ oi)=das_ a)rithmo/n, _ê)\ o(\ su\ oi)=das_ eu)thu/grammon, a)lla\ _kata\ panto/s_] (b. 3-5).

This discussion, in the commencement of the Analytica Posteriora (combined with Analyt. Priora, II. xxi.), is interesting, because it shows that even then the difficulties were felt, about the major proposition of the Syllogism, which Mr. John Stuart Mill has so ably cleared up, for the first time, in his System of Logic. See Book II. ch. iii. of that work, especially as it stands in the sixth edition, with the note there added, pp. 232-233. You affirm, in the major proposition of the Syllogism, that every triangle has its three angles equal to two right angles; does not this include the triangle A, B, C, and is it not therefore a _petitio principii_? Or, if it be not so, does it not assert more than you know? The Sophists (upon whom both Plato and Aristotle are always severe, but who were valuable contributors to the theory of Logic by fastening upon the weak points) attacked it on this ground, and raised against it the puzzle described by Aristotle (in this chapter), afterwards known as the Sophism entitled [Greek: o( e)gkekalumme/nos] (see Themistius Paraphras. I. i.; also 'Plato and the Other Companions of Sokrates,' Vol. III. ch. xxxviii. p. 489). The critics whom Aristotle here cites and disapproves, virtually admitted the pertinence of this puzzle by modifying their assertion, and by cutting it down to "Everything _which we know to be a triangle_ has its three angles equal to two right angles." Aristotle finds fault with this modification, which, however, is one way of abating the excess of absolute and peremptory pretension contained in the major, and of intimating the want of a minor to be added for interpreting and supplementing the major; while Aristotle himself arrives at the same result by admitting that the knowledge corresponding to the major proposition is not yet absolute, but incomplete and qualified; and that it is only made absolute when supplemented by a minor.

The very same point, substantially, is raised in the discussion between Mr. John Stuart Mill and an opponent, in the note above referred to. "A writer in the 'British Quarterly Review' endeavours to show that there is no _petitio principii_ in the Syllogism, by denying that the proposition All men are mortal, asserts or assumes that Socrates is mortal. In support of this denial, he argues that we may, and in fact do, admit the general proposition without having particularly examined the case of Socrates, and even without knowing whether the individual so named is a man or something else. But this of course was never denied. That we can and do draw inferences concerning cases specifically unknown to us, is the datum from which all who discuss this subject must set out. The question is, in what terms the evidence or ground on which we draw these conclusions may best be designated--whether it is most correct to say that the unknown case is proved by known cases, or that it is proved by a general proposition including both sets of cases, the known and the unknown? I contend for the former mode of expression. I hold it an abuse of language to say, that the proof that Socrates is mortal, is that all men are mortal. Turn it in what way we will, this seems to me asserting that a thing is the proof of itself. Whoever pronounces the words, All men are mortal, has affirmed that Socrates is mortal, though he may never have heard of Socrates; for since Socrates, whether known to be a man or not, really is a man, he is included in the words, All men, and in every assertion of which they are the subject. . . . . The reviewer acknowledges that the maxim (Dictum de Omni et Nullo) as commonly expressed--'Whatever is true of a class is true of everything included in the class,' is a mere identical proposition, since the class _is_ nothing but the things included in it. But he thinks this defect would be cured by wording the maxim thus: 'Whatever is true of a class is true of everything which can be shown to be a member of the class:' as if a thing could be shown to be a member of the class without being one."

The qualified manner in which the maxim is here enunciated by the reviewer (what _can be shown_ to be a member of the class) corresponds with the qualification introduced by those critics whom Aristotle impugns ([Greek: lu/ousi ga\r ou) pha/skontes ei)de/nai pa=san dua/da a)rti/an ou)=san, a)ll' _ê(\n i)/sasin o(/ti dua/s_]); and the reply of Mr. Mill would have suited for these critics as well as for the reviewer. The puzzle started in the Platonic Menon is, at bottom, founded on the same view as that of Mr. Mill, when he states that the major proposition of the Syllogism includes beforehand the conclusion. "The general principle, (says Mr. Mill, p. 205), instead of being given as evidence of the particular case, cannot itself be taken for true without exception, until every shadow of doubt which could affect any case comprised in it is dispelled by evidence _aliunde_; and then what remains for the syllogism to prove? From a general principle we cannot infer any particulars but those which the principle itself assumes as known."

To enunciate this in the language of the Platonic Menon, we learn nothing by or through the evidence of the Syllogism, except a part of what we have already professed ourselves to know by asserting the major premiss.]

Aristotle proceeds to tell us what is meant by knowing a thing _absolutely_ or completely ([Greek: a(plô=s]). 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 understanding 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]

[Footnote 12: Aristot. Analyt. Post I. ii. p. 71, b. 9-17. Julius Pacius says in a note, ad c. ii. p. 394: "Propositio demonstrativa est prima, immediata, et indemonstrabilis. His tribus verbis significatur una et eadem conditio; nam propositio prima est, quæ, quod medio caret, demonstrari nequit."

So also Zabarella (In lib. I. Post. Anal. Comm., p. 340, Op. ed. Venet. 1617): "Duæ illæ dictiones (_primis_ et _immediatis_) unam tantum significant conditionem ordine secundam, non duas; idem namque est, principia esse medio carentia, ac esse prima."]

[Footnote 13: Aristot. Analyt. Post. I. ii. p. 72, a. 1-24; Themistius, Paraphr. I. ii. p. 10, ed. Spengel; Schol. p. 199, b. 44. Themistius quotes the definition of an Axiom as given by Theophrastus: [Greek: A)xi/ôma/ e)sti _do/xa_ tis], &c. This shows the difficulty of adhering precisely to a scientific terminology. Theophrastus explains an axiom to be a sort of [Greek: do/xa], thus lapsing into the common loose use of the word. Yet still both he and Aristotle declare [Greek: do/xa] to be of inferior intellectual worth as compared with [Greek: e)pistê/mê] (Anal. Post. I. xxiii.), while at the same time they declare the Axiom to be the very maximum of scientific truth. Theophrastus gave, as examples of Axioms, the **maxim of Contradiction, universally applicable, and, "If equals be taken from equals the remainders will be equal," applicable to homogeneous quantities. Even Aristotle himself sometimes falls into the same vague employment of [Greek: do/xa], as including the Axioms. See Metaphys. B. ii. p. 996, b. 28; [Greek: G]. iii. p. 1005, b. 33.]

[Footnote 14: Aristot. Anal. Post. I. ii. p. 72, a. 25, b. 4. I translate these words in conformity with Themistius, pp. 12-13, and with Mr. Poste's translation, p. 43. Julius Pacius and M. Barthélemy St. Hilaire render them somewhat differently. They also read [Greek: a)meta/ptôtos], while Waitz and Firmin Didot read [Greek: a)meta/peistos], which last seems preferable.]

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]

[Footnote 15: Aristot. Analyt. Post. I. iii. p. 72, b. 5-p. 73, a. 20: [Greek: ô(/st' e)peidê\ _o)li/ga toiau=ta_ e)n tai=s a)podei/xesin], &c.]

Demonstrative 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 Science, is conversant, are _de omni_, _per se_, and _quatenus ipsum_, or _Universalia Prima_;[17] all of them necessary, such as cannot but be true.]

[Footnote 16: Aristot. Analyt. Post. I. iv. p. 73, a. 21, b. 16.

[Greek: Ta\ a)/ra lego/mena e)pi\ tô=n a(plô=s e)pistêtô=n kath' au(ta\ ou(/tôs ô(s e)nupa/rchein toi=s katêgoroume/nois ê)\ e)nupa/rchesthai di' au(ta/ te/ e)sti kai\ e)x a)na/gkês] (b. 16, seq.). _Line_ must be included in the definition of the opposites _straight_ or _curve_. Also it is essential to every line that it is either straight or curve. _Number_ must be included in the definition of the opposites _odd_ or _even_; and to be either odd or even is essentially predicable of every number. You cannot understand what is meant by _straight_ or _curve_ unless you have the notion of a _line_.

The example given by Aristotle of _causal_ conjunction (the death of an animal under the sacrificial knife) shows that he had in his mind the perfection of Inductive Observation, including full application of the Method of Difference.]

[Footnote 17: Aristot. Analyt. Post. I. iv. p. 73, b. 25-p. 74, a. 3. [Greek: o(\ toi/nun _to\ tucho\n prô=ton_ dei/knutai du/o o)rtha\s e)/chon ê)\ o(tiou=n a)/llo, tou/tô| prô/tô| u(pa/rchei katho/lou, kai\ ê( _a)po/deixis kath' au(to\_ tou/tou katho/lou e)sti\, tô=n d' a)/llôn tro/pon tina\ ou) kath' au(to/; ou)de\ tou= i)soske/lous ou)k e)/sti katho/lou a)ll' e)pi\ ple/on.]

About the precise signification of [Greek: katho/lou] in Aristotle, see a valuable note of Bonitz (ad Metaphys. Z. iii.) p. 299; also Waitz (ad Aristot. De Interpr. c. vii.) I. p. 334. Aristotle gives it here, b. 26: [Greek: katho/lou de\ le/gô o(\ a)\n kata\ panto/s te u(pa/rchê| kai\ kath' au(to\ kai\ ê(=| au)to/.] Compare Themistius, Paraphr. p. 19, Spengel. [Greek: To\ kath' au(to/] is described by Aristotle confusedly. [Greek: To\ katho/lou], is that which is predicable of the subject as a whole or _summum genus_: [Greek: to\ kata\ panto/s], that which is predicable of every individual, either of the _summum genus_ or of any inferior species contained therein. Cf. Analyt. Post. I. xxiv. p. 85, b. 24: [Greek: ô(=| ga\r kath' au(to\ u(pa/rchei ti, tou=to au)to\ au(tô=| ai)/tion]--the subject is itself the cause or _fundamentum_ of the properties _per se_. See the explanation and references in Kampe, Die Erkenntniss-theorie des Aristoteles, ch. v. pp. 160-165.]

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 accident[19]) 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 certain 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]

[Footnote 18: Aristot. Analyt. Post I. v. p. 74, a. 4-23. [Greek: a)lla\ dia\ to\ mê\ ei)=nai ô)nomasme/non ti pa/nta tau=ta e(/n, a)rithmoi/, mê/kê, chro/nos, sterea/, kai\ ei)/dei diaphe/rein a)llê/lôn, chôri\s e)lamba/neto.] What these four have in common is that which he himself expresses by [Greek: Poso/n]--_Quantum_--in the Categoriæ and elsewhere. (Categor. p. 4, b. 20, seq.; Metaph. [Greek: D]. p. 1020, a. 7, seq.)]

[Footnote 19: Aristot. Analyt. Post. I. v. p. 74, a. 27: [Greek: ou)/pô oi)=de to\ tri/gônon o(/ti du/o o)rthai=s, ei) mê\ _to\n sophistiko\n tro/pon_ ou)de\ katho/lou tri/gônon, ou)/d' ei) mêde/n e)sti para\ tau=ta tri/gônon e(/teron.] The phrase [Greek: to\n sophistiko\n tro/pon] is equivalent to [Greek: to\n sophistiko\n **tro/pon to\n kata\ sumbebêko/s], p. 71, b. 10. I see nothing in it connected with Aristotle's characteristic of a Sophist (special professional life purpose--[Greek: tou= bi/ou tê=| proaire/sei], Metaphys. [Greek: G]. p. 1004, b. 24): the phrase means nothing more than _unscientific_.]

[Footnote 20: Aristot. Analyt Post I. v. p. 74, a. 32-b. 4.]

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 middle 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]

[Footnote 21: Ibid. vi. p. 74, b. 5-18. [Greek: e)x a)lêthô=n me\n ga\r e)/sti kai\ mê\ a)podeiknu/nta sullogi/sthai, e)x a)nagkai/ôn d' ou)k e)/stin a)ll' ê)\ a)podeiknu/nta; tou=to ga\r ê)/dê a)podei/xeô/s e)stin.] Compare Analyt. Prior. I. ii. p. 53, b. 7-25.]

[Footnote 22: Aristot. Analyt. Post. I. vi. p. 74, b. 18: [Greek: sêmei=on d' o(/ti ê( a)po/deixis e)x a)nagkai/ôn, o(/ti kai\ ta\s e)nsta/seis ou(/tô phe/romen pro\s tou\s oi)ome/nous a)podeiknu/nai, o(/ti ou)k a)na/gkê], &c.]

[Footnote 23: Ibid. vi. p. 74, b. 21-26: [Greek: dê=lon d' e)k tou/tôn kai\ o(/ti eu)ê/theis oi( lamba/nein oi)o/menoi kalô=s ta\s a)rcha/s, e)a\n e)/ndoxos ê)=| ê( pro/tasis kai\ a)lêthê/s, oi(=on oi( sophistai\ o(/ti to\ e)pi/stasthai to\ e)pistê/mên e)/chein;], &c.]

[Footnote 24: Aristot. Analyt. Post. I. vi. p. 74, b. 26-p. 75, a. 17.]

[Footnote 25: Ibid. vi. p. 75, a. 8-37.

On the point last mentioned, M. Barthélemy St. Hilaire observes in his note, p. 41: "Dans les questions de dialectique, la conclusion est nécessaire en ce sens, qu'elle suit nécessairement des prémisses; elle n'est pas du tout nécessaire en ce sens, que la chose qu'elle exprime soit nécessaire. Ainsi il faut distinguer la nécessité de la forme et la nécessité de la matière: ou comme disent les scholastiques, _necessitas illationis et necessitas materiæ_. La dialectique se contente de la première, mais la demonstration a essentiellement besoin des deux."]

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 complete 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]

[Footnote 26: Ibid. vii. p. 75, a. 38-b. 20. Mr. Poste, in his translation, here cites (p. 50) a good illustrative passage from Dr. Whewell's Philosophy of the Inductive Sciences, Book II. ii.:--"But, in order that we may make any real advance in the discovery of truth, our ideas must not only be clear; they must also be _appropriate_. Each science has for its basis a different class of ideas; and the steps which constitute the progress of one science can never be made by employing the ideas of another kind of science. No genuine advance could ever be obtained in Mechanics by applying to the subject the ideas of space and time merely; no advance in Chemistry by the use of mere mechanical conceptions; no discovery in Physiology by referring facts to mere chemical and mechanical principles." &c.]

[Footnote 27: Aristot. Analyt. Post. I. viii. p. 75, b. 21-36. Compare Metaphys. Z. p. 1040, a. 1: [Greek: dê=lon o(/ti ou)k a)\n ei)/ê au)tô=n (tô=n phthartô=n) ou)/th' o(rismo\s ou)/t' a)po/deixis]. Also Biese, Die Philosophie des Aristoteles, ch. iv. p. 249.]

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 you 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]

[Footnote 28: Ibid. ix. p. 75, b. 37-p. 76, a. 30.]

[Footnote 29: Ibid. x. p. 76, a. 31-b. 22.]

[Footnote 30: Aristot. Analyt. Post. I. x. p. 76, b. 29-34: [Greek: e)a\n me\n dokou=nta lamba/nê| tô=| mantha/nonti, u(poti/thetai, kai\ e)/stin ou)/ch a(plô=s u(po/thesis, a)lla\ pro\s e)kei=non mo/non, a)\n de\ ê)\ mêdemi/a=s e)nou/sês do/xês ê)\ kai\ e)nanti/as e)nou/sês lamba/nê| to\ au)to/, ai)tei=tai. kai\ tou/tô| diaphe/rei _u(po/thesis_ kai\ _ai)/têma_], &c. Themistius, Paraphras. p. 37, Spengel.]

[Footnote 31: Ibid. p. 76, b. 36: [Greek: tou=to d' ou)ch u(po/thesis, ei) mê\ kai\ _to\ a)kou/ein_ u(po/thesi/n tis ei)=nai phê/sei]. For the meaning of [Greek: _to\ a)kou/ein_], compare [Greek: o( a)kou/ôn], infra, Analyt. Post. I. xxiv. p. 85, b. 22.]

[Footnote 32: Ibid. p. 77, a. 1: [Greek: o( de\ geôme/três ou)de\n sumperai/netai tô=| tê/nde ei)=nai tê\n grammê\n ê(\n au)to\s e)/phthegktai, a)lla\ ta\ dia\ tou/tôn dêlou/mena.]

Themistius, Paraphr. p. 37: [Greek: ô(/sper ou)d' oi( geôme/trai ke/chrêntai tai=s grammai=s u(pe\r ô(=n diale/gontai kai\ deiknu/ousin, a)ll' a(\s e)/chousin e)n tê=| psuchê=|, ô(=n ei)si\ su/mbola ai( grapho/menai.]

A similar doctrine is asserted, Analyt. Prior. I. xli. p. 49, b. 35, and still more clearly in De Memoria et Reminiscentia, p. 450, a. 2-12.]

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]

[Footnote 33: Aristot. Analyt. Post. I. xi. p. 77, a. 5-9.]

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 confined 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 to 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]

[Footnote 34: Ibid. a. 10, seq.]

[Footnote 35: Ibid. a. 26-30: [Greek: kai\ ei)/ tis katho/lou peirô=|to deiknu/nai ta\ koina/, oi(=on o(/ti a(/pan pha/nai ê)\ a)popha/nai, ê)\ o(/ti i)/sa a)po\ i)/sôn, ê)\ tô=n toiou/tôn a)/tta.] Compare Metaph. K. p. 1061**, b. 18.]

[Footnote 36: Aristot. Analyt. Post. I. xii, p. 77, a. 36-40; Themistius, p. 40.

The text is here very obscure. He proceeds to distinguish Geometry especially (also other sciences, though less emphatically) from [Greek: ta\ e)n toi=s dialo/gois] (I. xii. p. 78, a. 12).

Julius Pacius, ad Analyt. Post. I. viii. (he divides the chapters differently), p. 417, says:--"Differentia interrogationis dialecticæ et demonstrativæ hæc est. Dialecticus ita interrogat, ut optionem det adversario, utrum malit affirmare an negare. Demonstrator vero interrogat ut rem evidentiorem faciat; id est, ut doceat ex principiis auditori notis."]

[Footnote 37: Ibid. I. xii. p. 77, b. 1-15; Themistius, p. 41: [Greek: ou) ga\r ô(/sper tô=n e)ndo/xôn oi( polloi\ kritai/, ou(/tô kai\ tô=n kat' e)pistê/mên oi( a)nepistê/mones].]

[Footnote 38: Analyt. Post. I. xii. p. 77, b. 16-33. Propositions within the limits of the science, but false as to matter, are styled by Aristotle [Greek: pseudographê/mata]. See Aristot. Sophist. Elench. xi. p. 171, b. 14; p. 172, a. 1.

"L'interrogation syllogistique se confondant avec la proposition, il s'ensuit que l'interrogation doit être, comme la proposition, propre à la science dont il s'agit." (Barthélemy St Hilaire, note, p. 70). Interrogation here has a different meaning from that which it bears in Dialectic.]