75Analyt. Prior. II. xxv. p. 69, a. 20-36.
75Analyt. Prior. II. xxv. p. 69, a. 20-36.
76Ibid. II. xxvi. p. 69, a. 37-b. 37.In objecting to Auniversally, you take a term comprehending the original subject; in objectingparticularly, a term comprehended by it. Of the new term in each case you deny the original predicate, and have thus, as a major premiss, E. For a minor premiss, you affirm, in the first case, the new term as predicate of the original subject (less comprehensive); in the second case, the original subject (more comprehensive) as predicate of the new term. This gives you, in the first case, a conclusion inCelarent(Fig. I.), and, in the second, a conclusion inFelapton(Fig. III.); opposed, the one universally or contrarily, the other particularly or contradictorily, to the original proposition.
76Ibid. II. xxvi. p. 69, a. 37-b. 37.
In objecting to Auniversally, you take a term comprehending the original subject; in objectingparticularly, a term comprehended by it. Of the new term in each case you deny the original predicate, and have thus, as a major premiss, E. For a minor premiss, you affirm, in the first case, the new term as predicate of the original subject (less comprehensive); in the second case, the original subject (more comprehensive) as predicate of the new term. This gives you, in the first case, a conclusion inCelarent(Fig. I.), and, in the second, a conclusion inFelapton(Fig. III.); opposed, the one universally or contrarily, the other particularly or contradictorily, to the original proposition.
The Enthymeme is a syllogism from Probabilities or Signs;77the two being not exactly the same.Probabilitiesare propositions commonly accepted, and true in the greater number of cases; such as, Envious men hate those whom they envy, Persons who are beloved look with affection on those who lovethem. We call it aSign, when one fact is the antecedent or consequent of another, and therefore serves as mark or evidence thereof. The conjunction may be either constant, or frequent, or merely occasional: if constant, we obtain for the major premiss of our syllogism a proposition approaching that which is universally or necessarily true; if not constant but only frequent or occasional, the major premiss of our syllogism will at best only be probable. The constant conjunction will furnish us with a Syllogism or Enthymeme in the First figure; the significant mark being here a genuine middle term — subject in the major premiss, and predicate in the minor. We can then get a conclusion both affirmative and universally true. In other cases, we cannot obtain premisses for a syllogism in the First figure, but only for a syllogism in the Second or Third. In the Third figure, since we get by right no universal conclusions at all, but only particular conclusions, the conclusion of the Enthymeme, though it may happen to be true, is open to refutation. Where by the laws of Syllogism no affirmative conclusion whatever is possible, as in the Second figure, the conclusion obtained by Enthymeme is altogether suspicious. In contrast with the Sign in these figures, that which enters as an effective middle term into the First figure, should be distinguished under the name ofProof(τεκμήριον.)78
77Ibid. II. xxvii. p. 70, a. 10: ἐνθύμημα μὲν οὖν ἐστὶ συλλογισμὸς ἐξ εἰκότων ἢ σημείων· λαμβάνεται δὲ τὸ σημεῖον τριχῶς, ὁσαχῶς καὶ τὸ μέσον ἐν τοῖς σχήμασι.
77Ibid. II. xxvii. p. 70, a. 10: ἐνθύμημα μὲν οὖν ἐστὶ συλλογισμὸς ἐξ εἰκότων ἢ σημείων· λαμβάνεται δὲ τὸ σημεῖον τριχῶς, ὁσαχῶς καὶ τὸ μέσον ἐν τοῖς σχήμασι.
78Analyt. Prior. II. xxvii. p. 70, a. 31-b. 6.Aristotle throws in the remark (a. 24), that, when one premiss only of the Enthymeme is enunciated, it is a Sign; when the other is added, it becomes a Syllogism. In the examples given to illustrate the description of the Enthymeme, that which belongs to the First figure has its three terms and two propositions specified like a complete and regular Syllogism; but when we come to the Third and Second figures, Aristotle gives two alternate ways of stating each: one way in full, with both premisses enunciated, constituting a normal, though invalid, Syllogism; the other way, with only one of the premisses enunciated, the other being suppressed as well-known and familiar.Among logicians posterior to Aristotle, the definition given of the Enthymeme, and supposed to be derived from Aristotle was, that it was a Syllogism with one of the premisses suppressed — μονολήμματος. Sir W. Hamilton has impugned this doctrine, and has declared the definition to be both absurd in itself, and not countenanced by Aristotle. (Lectures on Logic, Vol. I. Lect. xx. p. 386, seq.) I think Hamilton is mistaken on this point. (See Mr. Cope’s Introd. to Arist. Rhetoric, p. 103, seq.) Even in the present chapter Aristotle distinctly alludes to the monolemmatic enunciation of the Enthymeme as one mode of distinguishing it from a full Syllogism; and in the Rhetorica he brings out this characteristic still more forcibly. The distinction is one which belongs to Rhetoric more than to Logic; the rhetor, in enunciating his premisses, must be careful not to weary his auditors; he must glance at or omit reasons that are familiar to them; logical fulness and accuracy would be inconsistent with his purpose. The writers subsequent to Aristotle, who think much of the rhetorical and little of the logical point of view, bring out the distinction yet more forcibly. But the rhetorical mode of stating premisses is often not so much an omission either of major or minor, as a confused blending or packing up of both into one.
78Analyt. Prior. II. xxvii. p. 70, a. 31-b. 6.
Aristotle throws in the remark (a. 24), that, when one premiss only of the Enthymeme is enunciated, it is a Sign; when the other is added, it becomes a Syllogism. In the examples given to illustrate the description of the Enthymeme, that which belongs to the First figure has its three terms and two propositions specified like a complete and regular Syllogism; but when we come to the Third and Second figures, Aristotle gives two alternate ways of stating each: one way in full, with both premisses enunciated, constituting a normal, though invalid, Syllogism; the other way, with only one of the premisses enunciated, the other being suppressed as well-known and familiar.
Among logicians posterior to Aristotle, the definition given of the Enthymeme, and supposed to be derived from Aristotle was, that it was a Syllogism with one of the premisses suppressed — μονολήμματος. Sir W. Hamilton has impugned this doctrine, and has declared the definition to be both absurd in itself, and not countenanced by Aristotle. (Lectures on Logic, Vol. I. Lect. xx. p. 386, seq.) I think Hamilton is mistaken on this point. (See Mr. Cope’s Introd. to Arist. Rhetoric, p. 103, seq.) Even in the present chapter Aristotle distinctly alludes to the monolemmatic enunciation of the Enthymeme as one mode of distinguishing it from a full Syllogism; and in the Rhetorica he brings out this characteristic still more forcibly. The distinction is one which belongs to Rhetoric more than to Logic; the rhetor, in enunciating his premisses, must be careful not to weary his auditors; he must glance at or omit reasons that are familiar to them; logical fulness and accuracy would be inconsistent with his purpose. The writers subsequent to Aristotle, who think much of the rhetorical and little of the logical point of view, bring out the distinction yet more forcibly. But the rhetorical mode of stating premisses is often not so much an omission either of major or minor, as a confused blending or packing up of both into one.
Aristotle concludes his Analytica Priora by applying this doctrine of Signs to determine the limits within which Physiognomyas a science is practicable. The basis upon which it rests is this general fact or postulate: That in all natural affections of the animal, bodily changes and mental changes accompany each other. The former, therefore, may become signs or proofs of the latter,79if, in each class of animals, we can discriminate the one specific bodily phenomenon which attaches to each mental phenomenon. Thus, the lion is a courageous animal. What is the bodily sign accompanying a courageous disposition? It is (we assume here) the having extremities of great size. This belongs to all lions, as aproprium; in the sense that, though it may or does belong also to some individuals of other races (as men), it does not belong to any other entire race. Physiognomy as a science will, then, be possible, if we can find races of animals which have only one characteristic mental attribute, and if we can discover what is the physical attribute correlating with it.80But the difficulties are greater when the same race has two characteristic mental attributes (e.g.lions are both courageous and generous), each with its correlative physical attribute; for how can we tell which belongs to which? We have then to study individuals of other races possessing one of these attributes without the other; thus, if we find that courageous men, who are not generous, agree in having large extremities, we may infer that this last circumstance is, in the lion, the correlative mark of his courage and not of his generosity. The physiognomonic inference will be expressed by a syllogism in the First figure, in which the major term (A) reciprocates and is convertible with the middle term (B), while B stretches beyond (or is more extensive than) the minor (C); this relation of the terms being necessary, if there is to be a single mark for a particular attribute.81
79Analyt. Prior. II. xxvii. p. 70, b. 7-16: εἴ τις δίδωσιν ἅμα μεταβάλλειν τὸ σῶμα καὶ τὴν ψυχήν, ὅσα φυσικά ἐστι παθήματα· — συμπάσχειν γὰρ ἀλλήλοις ὑποκεῖται. See the Aristotelian treatise entitled Φυσιογνωμονικά, pp. 808-809, Bekk.
79Analyt. Prior. II. xxvii. p. 70, b. 7-16: εἴ τις δίδωσιν ἅμα μεταβάλλειν τὸ σῶμα καὶ τὴν ψυχήν, ὅσα φυσικά ἐστι παθήματα· — συμπάσχειν γὰρ ἀλλήλοις ὑποκεῖται. See the Aristotelian treatise entitled Φυσιογνωμονικά, pp. 808-809, Bekk.
80Ibid. II. xxvii. p. 70, b. 22. About the characteristics of the lion see Aristot. Physiognom. p. 809, b. 14-36: τὰ περὶ τὴν ψυχὴν δοτικὸν καὶ ἐλεύθερον, μεγαλόψυχον καὶ φιλόνικον, καὶ πραῢ καὶ δίκαιον καὶ φιλόστοργον πρὸς ἃ ἂν ὁμιλήσῃ.
80Ibid. II. xxvii. p. 70, b. 22. About the characteristics of the lion see Aristot. Physiognom. p. 809, b. 14-36: τὰ περὶ τὴν ψυχὴν δοτικὸν καὶ ἐλεύθερον, μεγαλόψυχον καὶ φιλόνικον, καὶ πραῢ καὶ δίκαιον καὶ φιλόστοργον πρὸς ἃ ἂν ὁμιλήσῃ.
81Ibid. II. xxvii. p. 70, b. 31-36.
81Ibid. II. xxvii. p. 70, b. 31-36.
Here the treatise ends; but the reader will remember that, in describing the canons laid down by Aristotle for the Syllogism with its three Figures and the Modes contained therein, I confined myself to the simple Assertory syllogism, postponing for the moment the long expositions added by him about Modal syllogisms, involving the Possible and the Necessary. What is proper to be said about this complicated and useless portion of the Analytica Priora, may well come in here; for, in truth,the doctrines just laid down about Probabilities, Signs, and Proofs, bring us back to the Modals under a different set of phrases. The Possible or Problematical is that, of the occurrence or reality of which we doubt, neither believing nor disbelieving it, not being prepared to assert either that it is, or that it is not;that which may be or may not be. It is our manner of speaking, when we have only signs or probabilities to guide us, and not certain proofs. The feeling of doubt is, as a psychological phenomenon, essentially distinct from the feeling of belief which, in its objective aspect, correlates with certainty or matter of fact; as well as from the feeling of disbelief, the correlate of which can only be described negatively. Every man knows these feelings by his own mental experience. But in describing the feeling of doubt, as to its matter or in its objective aspect, we must take care to use phrases which declare plainly both sides of its disjunctive or alternative character. The Possible is,That which either may be or may not be. AsThat which may be, it stands opposed to the Impossible; asThat which may not be, it stands opposed to the Necessary. It thus carries with it negation both of impossibility and of necessity; but, in common parlance, the first half of this meaning stands out prominently, and is mistaken for the whole. Aristotle, as we saw previously, speaks equivocally on this point, recognizing a double signification of the term: he sometimes uses it in the sense opposed only to impossible, maintaining that what is necessary must also be possible; sometimes in the truer sense, opposed both to necessity and to impossibility.82
82Aristot. De Interpret. xiii. p. 22. Analyt. Prior. I. xiii. p. 32, a. 21, 29, 36, xiv. p. 33, b. 22; xix. p. 38, a. 35.
82Aristot. De Interpret. xiii. p. 22. Analyt. Prior. I. xiii. p. 32, a. 21, 29, 36, xiv. p. 33, b. 22; xix. p. 38, a. 35.
The Possible or Problematical, however, in this latter complete sense —What may or may not be— exhibits various modifications or gradations. 1. The chances on either side may be conceived as perfectly equal, so that there is no probability, and we have no more reason for expecting one side of the alternative than the other; the sequence or conjunction is indeterminate. Aristotle construes this indeterminateness in many cases (not assubjective, or as depending upon our want of complete knowledge and calculating power, but) asobjective, insuperable, and inherent in many phenomenal agencies; characterizing it, under the names of Spontaneity and Chance, as the essentially unpredictable. 2. The chances on both sides may be conceived as unequal and the ratio between them as varying infinitely: the usual and ordinary tendency of phenomena — what Aristotle callsNature — prevails in the majority of cases, but not in all; being liable to occasional counteraction from Chance and other forces. Thus, between Necessity and perfect constancy at one extreme (such as the rotation of the sidereal sphere), and Chance at the other, there may be every shade of gradation; from natural agency next below the constant, down to the lowest degree of probability.83
83Analyt. Prior. I. xiii. p. 32, b. 5-19. τὸ δ’ ἀόριστον τῷ μηδὲν μᾶλλον οὕτως ἢ ἐκείνως. Compare Metaphys.K. p. 1064, b. 32.
83Analyt. Prior. I. xiii. p. 32, b. 5-19. τὸ δ’ ἀόριστον τῷ μηδὲν μᾶλλον οὕτως ἢ ἐκείνως. Compare Metaphys.K. p. 1064, b. 32.
Now, within the range of these limits lie what Aristotle describes as Signs and Probabilities; in fact, all the marks which we shall presently come to as distinguishing thedialecticalsyllogism from thedemonstrative. But here is involved rather the matter of the Syllogism than its form. The form indeed is so far implicated, that (as Aristotle justly remarks at the end of the Analytica Priora84), the First figure is the only one that will prove both conjunctions and disjunctions, as well constant as occasional; the Third figure proves only occasional conjunctions and occasional disjunctions, not constant; the Second figure will prove no conjunctions at all, but only disjunctions, constant as well as occasional. Here a difference of form is properly pointed out as coupled with and founded on a difference of matter. But the special rules given by Aristotle, early in the present treatise, for the conversion of Modal Propositions, and the distinctions that he draws as to the modal character of the conclusion according as one or other of the premisses belongs to one or other of the different modes, — are both prolix and of little practical value.85
84Analyt. Prior. II. xxvii. p. 70, a. 2-38. Compare what is said here about εἰκός, σημεῖον, τεκμήριον, with the first chapter of the Topica, and the dialectic syllogism as there described: ὁ ἐξ ἐνδόξων συλλογιζόμενος.
84Analyt. Prior. II. xxvii. p. 70, a. 2-38. Compare what is said here about εἰκός, σημεῖον, τεκμήριον, with the first chapter of the Topica, and the dialectic syllogism as there described: ὁ ἐξ ἐνδόξων συλλογιζόμενος.
85Ibid. I. viii.-xxii. p. 29, b. 29-p. 40, b. 16.
85Ibid. I. viii.-xxii. p. 29, b. 29-p. 40, b. 16.
What he calls the Necessary might indeed, from the point of view now reached, cease to be recognized as a separate mode at all. The Certain and the Problematical are real modes of the Proposition; objective correlates to the subjective phases called Belief and Doubt. But no proposition can be more than certain: the wordnecessary, in strictness, implies only a peculiarity of the evidence on which our belief is grounded. Granting certain given premisses to be true, a given conclusion must be true also, if we would avoid inconsistency and contradiction.
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;1but 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.
1Analyt. Prior. I. xxx. p. 46, a. 4-10; Analyt. Post. I. ii. p. 71, a. 23.
1Analyt. 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 SenseversusScience 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-examiningElenchus, 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 scrutinizingElenchus, 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.2He 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.3By 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.
2Plato, 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.
2Plato, 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.
3Plato, Republic, v. pp. 477-478; Menon, pp. 97-98.
3Plato, 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 furnishedwith 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,5each 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.
4Aristot. Topica, I. x. p. 104, a. 8, xi. p. 104, b. 19. Compare Metaphysica,A.p. 995, a. 1-10.
4Aristot. Topica, I. x. p. 104, a. 8, xi. p. 104, b. 19. Compare Metaphysica,A.p. 995, a. 1-10.
5Analyt. Post. I. xix. p. 81, b. 18: κατὰ μὲν οὖν δόξαν συλλογιζομένοις καὶ μόνον διαλεκτικῶς δῆλον ὅτι τοῦτο μόνον σκεπτέον, εἰ ἐξ ὧν ἐνδέχεται ἐνδοξοτάτων γίνεται ὁ συλλογισμός, ὥστ’ εἰ καὶ ἔστι τι τῇ ἀληθείᾳ τῶνΑΒμέσον, δοκεῖ δὲ μή, ὁ διὰ τούτου συλλογιζόμενος συλλελόγισται διαλεκτικῶς, πρὸς δ’ ἀλήθειαν ἐκ τῶν ὑπαρχόντων δεῖ σκοπεῖν. Compare Topica, VIII. xii. p. 162, b. 27.
5Analyt. Post. I. xix. p. 81, b. 18: κατὰ μὲν οὖν δόξαν συλλογιζομένοις καὶ μόνον διαλεκτικῶς δῆλον ὅτι τοῦτο μόνον σκεπτέον, εἰ ἐξ ὧν ἐνδέχεται ἐνδοξοτάτων γίνεται ὁ συλλογισμός, ὥστ’ εἰ καὶ ἔστι τι τῇ ἀληθείᾳ τῶνΑΒμέσον, δοκεῖ δὲ μή, ὁ διὰ τούτου συλλογιζόμενος συλλελόγισται διαλεκτικῶς, πρὸς δ’ ἀλήθειαν ἐκ τῶν ὑπαρχόντων δεῖ σκοπεῖν. 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, insteadof the several heterogeneous authorities recognized in Dialectic, Demonstrative Science hasprincipiaof its own, serving as points of departure; someprincipiacommon 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 trueper se, from the commencement to the conclusion; while Dialectic takes in accidental premisses as well as essential. Fifthly, theprincipiaof 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
6Aristot. Topica, VI. iv. p. 141, b. 3-14. οἱ πολλοὶ γὰρ τὰ τοιαῦτα προγνωρίζουσιν· τὰ μὲν γὰρ τῆς τυχούσης, τὰ δ’ ἀκριβοῦς καὶ περιττῆς διανοίας καταμαθεῖν ἐστίν. Compare in Analyt. Post. I. xii. pp. 77-78, the contrast between τὰ μαθήματα and οἱ διάλογοι.
6Aristot. Topica, VI. iv. p. 141, b. 3-14. οἱ πολλοὶ γὰρ τὰ τοιαῦτα προγνωρίζουσιν· τὰ μὲν γὰρ τῆς τυχούσης, τὰ δ’ ἀκριβοῦς καὶ περιττῆς διανοίας καταμαθεῖν ἐστίν. Compare in Analyt. Post. I. xii. pp. 77-78, the contrast between τὰ μαθήματα and οἱ διάλογοι.
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
7Aristot. 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: λέγοιτο δ’ ἂν ἱκανῶς, εἰ κατὰ τὴν ὑποκειμένην ὕλην διασαφηθείη· τὸ γὰρ ἀκριβὲς οὐχ ὁμοίως ἐν ἅπασι τοῖς λόγοις ἐπιζητητέον, ὥσπερ οὐδ’ ἐν τοῖς δημιουργουμένοις. τὴν ἀκρίβειαν μὴ ὁμοίως ἐν ἅπασιν ἐπιζητεῖν (χρή), ἀλλ’ ἐν ἑκάστοις κατὰ τὴν ὑποκειμένην ὕλην, καὶ ἐπὶ τοσοῦτον ἐφ’ ὅσον οἰκεῖον τῇ μεθοδῷ. Compare Metaphys.E.p. 1025, b. 13: ἀποδεικνύουσιν ἢ ἀναγκαίοτερον ἢ μαλακώτερον.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 τὸ συμβεβηκός 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 τὸ συμβεβηκὸς μὴ καθ’ αὑτό, — Analyt. Post. I. 6, 75, a. 18; for he uses the term in two different senses — Metaph.Δ. 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.â€�
7Aristot. 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: λέγοιτο δ’ ἂν ἱκανῶς, εἰ κατὰ τὴν ὑποκειμένην ὕλην διασαφηθείη· τὸ γὰρ ἀκριβὲς οὐχ ὁμοίως ἐν ἅπασι τοῖς λόγοις ἐπιζητητέον, ὥσπερ οὐδ’ ἐν τοῖς δημιουργουμένοις. τὴν ἀκρίβειαν μὴ ὁμοίως ἐν ἅπασιν ἐπιζητεῖν (χρή), ἀλλ’ ἐν ἑκάστοις κατὰ τὴν ὑποκειμένην ὕλην, καὶ ἐπὶ τοσοῦτον ἐφ’ ὅσον οἰκεῖον τῇ μεθοδῷ. Compare Metaphys.E.p. 1025, b. 13: ἀποδεικνύουσιν ἢ ἀναγκαίοτερον ἢ μαλακώτερον.
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 τὸ συμβεβηκός 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 τὸ συμβεβηκὸς μὴ καθ’ αὑτό, — Analyt. Post. I. 6, 75, a. 18; for he uses the term in two different senses — Metaph.Δ. 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 somepræcognitamust be assumed, which the learner must know before he comes to be taught, and upon which the teacher must found his instruction.8This 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 tocontemplate; 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 thepræcognitarequired for Geometry and Arithmetic. Somepræcognitaare 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.)9The learner must thus know beforehand certain Definitions and Axioms, as conditions without which the teacher cannot instruct him in any demonstrative science.
8Analyt. Post. I. i. pp. 71-72; Metaphys.A.IX. p. 992, b. 30.
8Analyt. Post. I. i. pp. 71-72; Metaphys.A.IX. p. 992, b. 30.
9Aristot. Analyt. Post. I, i. p. 71, a. 11-17. ἅπαν ἢ φῆσαι ἢ ἀποφῆσαι ἀληθές.
9Aristot. Analyt. Post. I, i. p. 71, a. 11-17. ἅπαν ἢ φῆσαι ἢ ἀποφῆσαι ἀληθές.
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 tolearnat all? is a question started in the Menon.10You 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 neverdolearn 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.
10Plato, Menon. p. 80.
10Plato, 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 theyaretriangles. The moment that you see A B C, or hear whatfigure 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 thisin a certain wayor incompletely before, by having followed the demonstration of the universal truth, and by thus knowing thateverytriangle 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
11Aristot. Analyt. Post. I. i. p. 71, a. 17-b. 8: ἔστι δὲ γνωρίζειν τὰ μὲν πρότερον γνωρίζοντα, τῶν δὲ καὶ ἄμα λαμβάνοντα τὴν γνῶσιν, οἷον ὅσα τυγχάνει ὄντα ὑπὸ τὸ καθόλου, ὧν ἔχει τὴν γνῶσιν. ὅτι μὲν γὰρ πᾶν τρίγωνον ἔχει δυσὶν ὀρθαῖς ἴσας, προῄδει· ὅτι δὲ τόδε τὸ ἐν τῷ ἡμικυκλίῳ τρίγωνόν ἐστιν, ἅμα ἐπαγόμενος ἐγνώρισεν. — πρὶν δ’ ἐπαχθῆναι ἢ λαβεῖν συλλογισμόν, τρόπον μέν τινα ἴσως φατέον ἐπίστασθαι, τρόπον δ’ ἄλλον οὔ. ὃ γὰρ μὴ ᾔδει εἰ ἔστιν ἁπλῶς, τοῦτο πῶς ᾔδει ὅτι δύο ὀρθὰς ἔχει ἁπλῶς; ἀλλὰ δῆλον ὡςὡδὶ μὲν ἐπίσταται.,ὅτι καθόλου ἐπίσταται, ἁπλῶς δ’ οὐκ ἐπίσταται. — οὐδὲν (οἶμαι) κωλύει, ὃ μανθάνει, ἔστιν ὡς ἐπίστασθαι, ἔστι δ’ ὡς ἀγνοεῖν· ἄτοπον γὰρ οὐκ εἰ οἶδέ πως ὃ μανθάνει, ἀλλ’ εἰ ὡδί, οἷον ᾗ μανθάνει καὶ ὥς. 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 Dyadwhich I know to be a Dyadis 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 thingwhich I knowto be a triangle has its three angles equal to two right angles. This last proposition had never been demonstrated, nor even stated: οὐδεμία γὰρ πρότασις λαμβάνεται τοιαύτη, ὅτιὃν σὺ οἶδαςἀριθμόν,ἢ ὃ σὺ οἶδαςεὐθύγραμμον, ἀλλὰκατὰ παντός(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 apetitio 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 ὁ ἐγκεκαλυμμένος (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 “Everythingwhich we know to be a trianglehas its three angles equal to two right angles.â€� 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 nopetitio principiiin 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 classisnothing 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.â€�The qualified manner in which the maxim is here enunciated by the reviewer (whatcan be shownto be a member of the class) corresponds with the qualification introduced by those critics whom Aristotle impugns (λύουσι γὰρ οὐ φάσκοντες εἰδέναι πᾶσαν δυάδα ἀρτίαν οὖσαν, ἀλλ’ἣν ἴσασιν ὅτι δυάς); 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 evidencealiunde; 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.â€�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.
11Aristot. Analyt. Post. I. i. p. 71, a. 17-b. 8: ἔστι δὲ γνωρίζειν τὰ μὲν πρότερον γνωρίζοντα, τῶν δὲ καὶ ἄμα λαμβάνοντα τὴν γνῶσιν, οἷον ὅσα τυγχάνει ὄντα ὑπὸ τὸ καθόλου, ὧν ἔχει τὴν γνῶσιν. ὅτι μὲν γὰρ πᾶν τρίγωνον ἔχει δυσὶν ὀρθαῖς ἴσας, προῄδει· ὅτι δὲ τόδε τὸ ἐν τῷ ἡμικυκλίῳ τρίγωνόν ἐστιν, ἅμα ἐπαγόμενος ἐγνώρισεν. — πρὶν δ’ ἐπαχθῆναι ἢ λαβεῖν συλλογισμόν, τρόπον μέν τινα ἴσως φατέον ἐπίστασθαι, τρόπον δ’ ἄλλον οὔ. ὃ γὰρ μὴ ᾔδει εἰ ἔστιν ἁπλῶς, τοῦτο πῶς ᾔδει ὅτι δύο ὀρθὰς ἔχει ἁπλῶς; ἀλλὰ δῆλον ὡςὡδὶ μὲν ἐπίσταται.,ὅτι καθόλου ἐπίσταται, ἁπλῶς δ’ οὐκ ἐπίσταται. — οὐδὲν (οἶμαι) κωλύει, ὃ μανθάνει, ἔστιν ὡς ἐπίστασθαι, ἔστι δ’ ὡς ἀγνοεῖν· ἄτοπον γὰρ οὐκ εἰ οἶδέ πως ὃ μανθάνει, ἀλλ’ εἰ ὡδί, οἷον ᾗ μανθάνει καὶ ὥς. 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 Dyadwhich I know to be a Dyadis 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 thingwhich I knowto be a triangle has its three angles equal to two right angles. This last proposition had never been demonstrated, nor even stated: οὐδεμία γὰρ πρότασις λαμβάνεται τοιαύτη, ὅτιὃν σὺ οἶδαςἀριθμόν,ἢ ὃ σὺ οἶδαςεὐθύγραμμον, ἀλλὰκατὰ παντός(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 apetitio 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 ὁ ἐγκεκαλυμμένος (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 “Everythingwhich we know to be a trianglehas its three angles equal to two right angles.â€� 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 nopetitio principiiin 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 classisnothing 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 (whatcan be shownto be a member of the class) corresponds with the qualification introduced by those critics whom Aristotle impugns (λύουσι γὰρ οὐ φάσκοντες εἰδέναι πᾶσαν δυάδα ἀρτίαν οὖσαν, ἀλλ’ἣν ἴσασιν ὅτι δυάς); 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 evidencealiunde; 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.â€�
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 thingabsolutelyor 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;12a 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 ofunderstanding the signification of the terms, but also in that of being able to affirm the truth of the proposition.Priorormore knowableis understood here as prior or more knowableby nature(notrelatively to us, according to the antithesis formerly explained); first, most universal, undemonstrableprincipiaare meant. Some of these are Axioms, which the learner must “bring with him from home,â€� 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.13As these are theprincipiaof 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 theprincipiathere should be none that he knows better or trusts more.14