eBook of George Grote, Aristotle

In the Second and Third figures, though not in the First, it is possible to obtain conclusions even from two premisses which are contradictory or contrary to each other; but the conclusion will, as a matter of course, be a self-contradictory one. Thus if in the Second figure you have the two premisses — All Science is good; No Science is good — you get the conclusion (in Camestres), No Science is Science. In opposed propositions, the same predicate must be affirmed and denied of the same subject in one of the three different forms — All and None, All and Not All, Some and None. This shows why such conclusions cannot be obtained in the First figure; for it is the characteristic of that figure that the middle term must be predicate in one premiss, and subject in the other.17 In dialectic discussion it will hardly be possible to get contrary or contradictory premisses conceded by the adversary immediately after each other, because he will be sure to perceive the contradiction: you must mask your purpose by asking the two questions not in immediate succession, but by introducing other questions between the two, or by other indirect means as suggested in the Topica.18

17 Analyt. Prior. II. xv. p. 63, b. 22-p. 64, a. 32. Aristotle here declares Subcontraries (as they were later called), — Some men are wise, Some men are not wise, — to be opposed only in expression or verbally (κατὰ τὴν λέξιν μόνον).

18 Ibid. II. xv. p. 64, a. 33-37. See Topica, VIII. i. p. 155, a. 26; Julius Pacius, p. 372, note. In the Topica, Aristotle suggests modes of concealing the purpose of the questioner and driving the adversary to contradict himself: ἐν δὲ τῶς Τοπικοῖς παραδίδωσι μεθόδους τῶν κρύψεων δι’ ἃς τοῦτο δοθήσεται (Schol. p. 192, a. 18, Br.). Compare also Analyt. Prior. II. xix. p. 66, a. 33.

Aristotle now passes to certain general heads of Fallacy, or general liabilities to Error, with which the syllogizing process is beset. What the reasoner undertakes is, to demonstrate the conclusion before him, and to demonstrate it in the natural and appropriate way; that is, from premisses both more evident in themselves and logically prior to the conclusion. Whenever he fails thus to demonstrate, there is error of some kind; but he may err in several ways: (1) He may produce a defective or informal syllogism; (2) His premisses may be more unknowable than his conclusion, or equally unknowable; (3) His premisses, instead of being logically prior to the conclusion, may be logically posterior to it.19

19 Ibid. II. xvi. p. 64, b. 30-35: καὶ γὰρ εἰ ὅλως μὴ συλλογίζεται, καὶ εἰ δι’ ἀγνωστοτέρων ἢ ὁμοίως ἀγνώστων, καὶ εἰ διὰ τῶν ὑστέρων τὸ πρότερον· ἡ γὰρ ἀπόδειξις ἐκ πιστοτέρων τε καὶ προτέρων ἐστιν.… τὰ μὲν δι’ αὑτῶν πέφυκε γνωρίζεσθαι, τὰ δὲ δι’ ἄλλων.

Distinct from all these three, however, Aristotle singles out and dwells upon another mode of error, which he calls Petitio Principii. Some truths, the principia, are by nature knowable through or in themselves, others are knowable only through other things. If you confound this distinction, and ask or assume something of the latter class as if it belonged to the former, you commit a Petitio Principii. You may commit it either by assuming at once that which ought to be demonstrated, or by assuming, as if it were a principium, something else among those matters which in natural propriety would be demonstrated by means of a principium. Thus, there is (let us suppose) a natural propriety that C shall be demonstrated through A; but you, overlooking this, demonstrate B through C, and A through B. By thus inverting the legitimate order, you do what is tantamount to demonstrating A through itself; for your demonstration will not hold unless you assume A at the beginning, in order to arrive at C. This is a mistake made not unfrequently, and especially by some who define parallel lines; for they give a definition which cannot be understood unless parallel lines be presupposed.20

20 Analyt. Prior. II. xvi. p. 64, b. 33-p. 65, a. 9. Petere principium is, in the phrase of Aristotle, not τὴν ἀρχὴν αἰτεῖσθαι, but τὸ ἐν ἀρχῇ αἰτεῖσθαι or τὸ ἐξ ἀρχῆς αἰτεῖσθαι (xvi. p. 64, b. 28, 34).

When the problem is such, that it is uncertain whether A can be predicated either of C or of B, if you then assume that A is predicable of B, you may perhaps not commit Petitio Principii, but you certainly fail in demonstrating the problem; for no demonstration will hold where the premiss is equally uncertain with the conclusion. But if, besides, the case be such, that B is identical with C, that is, either co-extensive and reciprocally convertible with C, or related to C as genus or species, — in either of these cases you commit Petitio Principii by assuming that A may be predicated of B.21 For seeing that B reciprocates with C, you might just as well demonstrate that A is predicable of B, because it is predicable of C; that is, you might demonstrate the major premiss by means of the minor and the conclusion, as well as you can demonstrate the conclusion by means of the major and the minor premiss. If you cannot so demonstrate the major premiss, this is not because the structure of the syllogism forbids it, but because the predicate of the major premiss is more extensive than the subject thereof. If it be co-extensive and convertible with the subject, we shall have a circular proof of three propositions in which each may be alternately premiss and conclusion. The like will be the case, if the Petitio Principii is in the minor premiss and not in the major. In the First syllogistic figure it may be in either of the premisses; in the Second figure it can only be in the minor premiss, and that only in one mode (Camestres) of the figure.22 The essence of Petitio Principii consists in this, that you exhibit as true per se that which is not really true per se.23 You may commit this fault either in Demonstration, when you assume for true what is not really true, or in Dialectic, when you assume as probable and conformable to authoritative opinion what is not really so.24

21 Ibid. p. 65, a. 1-10.

22 Ibid. p. 65, a. 10: εἰ οὖν τις, ἀδήλου ὄντος ὅτι τὸ Ἀ ὑπάρχει τῷ Γ, ὁμοίως δὲ καὶ ὅτι τῷ Β, αἰτοῖτο τῷ Β ὑπάρχειν τὸ Ἀ, οὕπω δῆλον εἰ τὸ ἐν ἀρχῇ αἰτεῖται, ἀλλ’ ὅτι οὐκ ἀποδείκνυσι, δῆλον· οὐ γὰρ ἀρχὴ ἀποδείξεως τὸ ὁμοίως ἄδηλον. εἰ μέντοι τὸ Β πρὸς τὸ Γ οὕτως ἔχει ὥστε ταὐτὸν εἶναι, ἢ δῆλον ὅτι ἀντιστρέφουσιν, ἢ ὑπάρχει θάτερον θατέρῳ, τὸ ἐν ἀρχῇ αἰτεῖται. καὶ γὰρ ἄν, ὅτι τῷ Β τὸ Ἀ ὑπάρχει, δι’ ἐκείνων δεικνύοι, εἰ ἀντιστρέφοι. νῦν δὲ τοῦτο κωλύει, ἀλλ’ οὐχ ὁ τρόπος. εἰ δὲ τοῦτο ποιοῖ, τὸ εἰρημένον ἂν ποιοῖ καὶ ἀντιστρέφοι ὡς διὰ τριῶν.

This chapter, in which Aristotle declares the nature of Petitio Principii, is obscure and difficult to follow. It has been explained at some length, first by Philoponus in the Scholia (p. 192, a. 35, b. 24), afterwards by Julius Pacius (p. 376, whose explanation is followed by M. B. St. Hilaire, p. 288), and by Waitz, (I. p. 514). But the translation and comment given by Mr. Poste appear to me the best: “Assuming the conclusion to be affirmative, let us examine a syllogism in Barbara:—

All B is A.
All C is B.
∴ All C is A.

And let us first suppose that the major premiss is a Petitio Principii; i.e. that the proposition All B is A is identical with the proposition All C is A. This can only be because the terms B and C are identical. Next, let us suppose that the minor premiss is a Petitio Principii: i.e. that the proposition All C is B is identical with the proposition All C is A. This can only be because B and A are identical. The identity of the terms is, their convertibility or their sequence (ὑπάρχει, ἕπεται). This however requires some limitation; for as the major is always predicated (ὑπάρχει, ἕπεται) of the middle, and the middle of the minor, if this were enough to constitute Petitio Principii, every syllogism with a problematical premiss would be a Petitio Principii.” (See the Appendix A, pp. 178-183, attached to Mr. Poste’s edition of Aristotle’s Sophistici Elenchi.)

Compare, about Petitio Principii, Aristot. Topic. VIII. xiii. p. 162, b. 34, in which passage Aristotle gives to the fallacy called Petitio Principii a still larger sweep than what he assigns to it in the Analytica Priora. Mr. Poste’s remark is perfectly just, that according to the above passage in the Analytica, every syllogism with a problematical (i.e. real as opposed to verbal) premiss would be a Petitio Principii; that is, all real deductive reasoning, in the syllogistic form, would be a Petitio Principii. To this we may add, that, from the passage above referred to in the Topica, all inductive reasoning also (reasoning from parts to whole) would involve Petitio Principii.

Mr. Poste’s explanation of this difficult passage brings into view the original and valuable exposition made by Mr. John Stuart Mill of the Functions and Logical Value of the Syllogism. — System of Logic, Book II. ch. iii. sect 2:— ”It must be granted, that in every syllogism, considered as an argument to prove the conclusion, there is a Petitio Principii,” &c.

Petitio Principii, if ranked among the Fallacies, can hardly be extended beyond the first of the five distinct varieties enumerated in the Topica, VIII. xiii.

23 Analyt. Prior. II. xvi. p. 65, a. 23-27: τὸ γὰρ ἐξ ἀρχῆς τί δύναται, εἴρηται ἡμῖν, ὅτι τὸ δι’ αὑτοῦ δεικνύναι τὸ μὴ δι’ αὑτοῦ δῆλον. — τοῦτο δ’ ἔστι, τὸ μὴ δεικνύναι.

The meaning of some lines in this chapter (p. 65, a. 17-18) is to me very obscure, after all the explanations of commentators.

24 Ibid. p. 65, a. 35; Topic. VIII. xiii. p. 162, b. 31.

We must be careful to note, that when Aristotle speaks of a principium as knowable in itself, or true in itself, he does not mean that it is innate, or that it starts up in the mind ready made without any gradual building up or preparation. What he means is, that it is not demonstrable deductively from anything else prior or more knowable by nature than itself. He declares (as we shall see) that principia are acquired, and mainly by Induction.

Next to Petitio Principii, Aristotle indicates another fallacious or erroneous procedure in dialectic debate; misconception or misstatement of the real grounds on which a conclusion rests — Non per Hoc. You may impugn the thesis (set up by the respondent) directly, by proving syllogistically its contrary or contradictory; or you may also impugn it indirectly by Reductio ad Absurdum; i.e. you prove by syllogism some absurd conclusion, which you contend to be necessarily true, if the thesis is admitted. Suppose you impugn it in the first method, or directly, by a syllogism containing only two premisses and a conclusion: Non per Hoc is inapplicable here, for if either premiss is disallowed, the conclusion is unproved; the respondent cannot meet you except by questioning one or both of the premisses of your impugning syllogism.25 But if you proceed by the second method or indirectly, Non per Hoc may become applicable; for there may then be more than two premisses, and he may, while granting that the absurd conclusion is correctly made out, contend that the truth or falsehood of his thesis is noway implicated in it. He declares (in Aristotle’s phrase) that the absurdity or falsehood just made out does not follow as a consequence from his thesis, but from other premisses independent thereof; that it would stand equally proved, even though his thesis were withdrawn.26 In establishing the falsehood or absurdity you must take care that it shall be one implicated with or dependent upon his thesis. It is this last condition that he (the respondent) affirms to be wanting.27

25 Analyt. Prior. II. xvii. p. 65, b. 4: ὅταν ἀναιρέθῃ τι δεικτικως διὰ τῶν Α, Β, Γ, &c.; xviii. 66, a. 17: ἢ γὰρ ἐκ τῶν δύο προτάσεων ἢ ἐκ πλειόνων πᾶς ἐστὶ συλλογισμός· εἰ μὲν οὖν ἐκ τῶν δύο, τούτων ἀνάγκη τὴν μὲν ἑτέραν ἢ καὶ ἀμφοτέρας εἶναι ψευδεῖς· &c. Whoever would understand this difficult chapter xvii., will do well to study it with the notes of Julius Pacius (p. 360), and also the valuable exposition of Mr. Poste, who has extracted and illustrated it in Appendix B. (p. 190) of the notes to his edition of the Sophistici Elenchi. The six illustrative diagrams given by Julius Pacius afford great help, though the two first of them appear to me incorrectly printed, as to the brackets connecting the different propositions.

26 Ibid. II. xvii. p. 65, b. 38, b. 14, p. 66, a. 2, 7: τὸ μὴ παρὰ τοῦτο συμβαίνειν τὸ ψεῦδος — τοῦ μὴ παρὰ τὴν θέσιν εἶναι τὸ ψεῦδος — οὐ παρὰ τὴν θέσιν συμβαίνει τὸ ψεῦδος — οὐκ ἂν εἴη παρὰ τὴν θέσιν.

Instead of the preposition παρά, Aristotle on two occasions employs διά — οὕτω γὰρ ἔσται διὰ τὴν ὑπόθεσιν — p. 65, b. 33, p. 66, a. 3.

The preposition παρά, with acc. case, means on account of, owing to, &c. See Matthiæ and Kühner’s Grammars, and the passage of Thucydides i. 141; καὶ ἕκαστος οὐ παρὰ τὴν ἑαυτοῦ ἀμέλειαν οἰεται βλάψειν, μέλειν δέ τινι καὶ ἄλλῳ ὑπὲρ ἑαυτοῦ τι προϊδεῖν, &c., which I transcribe partly on account of Dr. Arnold’s note, who says about παρὰ here:— “This is exactly expressed in vulgar English, all along of his own neglect, i. e. owing to his own neglect.”

27 Ibid. II. xvii. p. 65, b. 33: δεῖ πρὸς τοὺς ἐξ ἀρχῆς ὅρους συνάπτειν τὸ ἀδύνατον· οὕτω γὰρ ἔσται διὰ τὴν ὑπόθεσιν.

Aristotle tells us that this was a precaution which the defender of a thesis was obliged often to employ in dialectic debate, in order to guard against abuse or misapplication of Reductio ad Absurdum on the part of opponents, who (it appears) sometimes took credit for success, when they had introduced and demonstrated some absurd conclusion that had little or no connection with the thesis.28 But even when the absurd conclusion is connected with the thesis continuously, by a series of propositions each having a common term with the preceding, in either the ascending or the descending scale, we have here more than three propositions, and the absurd conclusion may perhaps be proved by the other premisses, without involving the thesis. In this case the respondent will meet you with Non per Hoc:29 he will point out that his thesis is not one of the premisses requisite for demonstrating your conclusion, and is therefore not overthrown by the absurdity thereof. Perhaps the thesis may be false, but you have not shown it to be so, since it is not among the premisses necessary for proving your absurdum. An absurdum may sometimes admit of being demonstrated by several lines of premisses,30 each involving distinct falsehood. Every false conclusion implies falsity in one or more syllogistic or prosyllogistic premisses that have preceded it, and is owing to or occasioned by this first falsehood.31

28 Analyt. Prior. II. xvii. p. 65, a. 38: ὃ πολλάκις ἐν τοῖς λόγοις εἰώθαμεν λέγειν, &c. That the Reductio ad Absurdum was sometimes made to turn upon matters wholly irrelevant, we may see from the illustration cited by Aristotle, p. 65, b. 17.

29 In this chapter of the Analytica, Aristotle designates the present fallacy by the title, Non per Hoc, οὐ παρὰ τοῦτο — οὐ παρὰ τὴν θέσιν συμβαίνει τὸ ψεῦδος. He makes express reference to the Topica (i.e. to the fifth chapter of Sophist. Elenchi, which he regards as part of the Topica), where the same fallacy is designated by a different title, Non Causa pro Causâ, τὸ ἀναίτιον ὡς αἴτιον τιθέναι. We see plainly that this chapter of the Anal. Priora was composed later than the fifth chapter of Soph. El.; whether this is true of the two treatises as wholes is not so certain. I think it probable that the change of designation for the same fallacy was deliberately adopted. It is an improvement to dismiss the vague term Cause.

30 Ibid. II. xvii. p. 66, a. 11: ἐπεὶ ταὐτό γε ψεῦδος συμβαίνειν διὰ πλειόνων ὑποθέσεων οὐδὲν ἴσως ἄτοπον, οἷον τὰς παραλλήλους συμπίπτειν, &c.

31 Ibid. II. xviii. p. 66, a. 16-24: ὁ δὲ ψευδὴς λόγος γίνεται παρὰ τὸ πρῶτον ψεῦδος, &c.

In impugning the thesis and in extracting from your opponent the proper concessions to enable you to do so, you will take care to put the interrogations in such form and order as will best disguise the final conclusion which you aim at establishing. If you intend to arrive at it through preliminary syllogisms (prosyllogisms), you will ask assent to the necessary premisses in a confused or inverted order, and will refrain from enunciating at once the conclusion from any of them. Suppose that you wish to end by showing that A may be predicated of F, and suppose that there must be intervening steps through B, C, D, E. You will not put the questions in this regular order, but will first ask him to grant that A may be predicated of B; next, that D may be predicated of E; afterwards, that B may be predicated of C, &c. You will thus try to obtain all the concessions requisite for your final conclusion, before he perceives your drift. If you can carry your point by only one syllogism, and have only one middle term to get conceded, you will do well to put the middle term first in your questions. This is the best way to conceal your purpose from the respondent.32

32 Analyt. Prior. II. xix. p. 66, a. 33-b. 3: χρὴ δ’ ὅπερ φιλάττεσθαι παραγγέλλομεν ἀποκρινομένους, αὐτοὺς ἐπιχειροῦντας πειρᾶσθαι λανθάνειν. — κἂν δι’ ἑνὸς μέσου γίνηται ὁ συλλογισμός, ἀπὸ τοῦ μέσου ἄρχεσθαι· μάλιστα γὰρ ἂν οὕτω λάνθανοι τὸν ἀποκρινόμενον. See the explanation of Pacius, p. 385. Since the middle term does not appear in the conclusion, the respondent is less likely to be prepared for the conclusion that you want to establish. To put the middle term first, in enunciating the Syllogism, is regarded by Aristotle as a perverted and embarrassing order, yet it is the received practice among modern logicians.

It will be his business to see that he is not thus tripped up in the syllogistic process.33 If you ask the questions in the order above indicated, without enunciating your preliminary conclusions, he must take care not to concede the same term twice, either as predicate, or as subject, or as both; for you can arrive at no conclusion unless he grants you a middle term; and no term can be employed as middle, unless it be repeated twice. Knowing the conditions of a conclusion in each of the three figures, he will avoid making such concessions as will empower you to conclude in any one of them.34 If the thesis which he defends is affirmative, the elenchus by which you impugn it must be a negative; so that he will be careful not to concede the premisses for a negative conclusion. If his thesis be negative, your purpose will require you to meet him by an affirmative; accordingly he must avoid granting you any sufficient premisses for an affirmative conclusion. He may thus make it impossible for you to prove syllogistically the contrary or contradictory of his thesis; and it is in proving this that the elenchus or refutation consists. If he will not grant you any affirmative proposition, nor any universal proposition, you know, by the rules previously laid down, that no valid syllogism can be constructed; since nothing can be inferred either from two premisses both negative, or from two premisses both particular.35

33 Analyt Prior. II. xix. p. 66, a. 25-32: πρὸς δὲ τὸ μὴ κατασυλλογίζεσθαι παρατηρητέον, ὅταν ἄνευ τῶν συμπερασμάτων ἐρωτᾷ τὸν λόγον, &c.

Waitz (p. 520) explains κατασυλλογίζεσθαι, “disputationum et interrogationum laqueis aliquem irretire.” This is, I think, more correct than the distinction which M. Barthélemy St. Hilaire seeks to draw, “entre le Catasyllogisme et la Réfutation,” in the valuable notes to his translation of the Analytica Priora, p. 303.

34 Ibid. II. xix. p. 66, a. 25-32.

35 Ibid. xx. p. 66, b. 4-17. The reader will observe how completely this advice given by Aristotle is shaped for the purpose of obtaining victory in the argument and how he leaves out of consideration both the truth of what the opponent asks to be conceded, and the belief entertained by the defendant. This is exactly the procedure which he himself makes a ground of contemptuous reproach against the Sophists.

We have already seen that error may arise by wrong enunciation or arrangement of the terms of a syllogism, that is, defects in its form; but sometimes also, even when the form is correct, error may arise from wrong belief as to the matters affirmed or denied.36 Thus the same predicate may belong, immediately and essentially, alike to several distinct subjects; but you may believe (what is the truth) that it belongs to one of them, and you may at the same time believe (erroneously) that it does not belong to another. Suppose that A is predicable essentially both of B and C, and that A, B, and C, are all predicable essentially of D. You may know that A is predicable of all B, and that B is predicable of all D; but you may at the same time believe (erroneously) that A is not predicable of any C, and that C is predicable of all D. Under this state of knowledge and belief, you may construct two valid syllogisms; the first (in Barbara, with B for its middle term) proving that A belongs to all D; the second (in Celarent, with C for its middle term) proving that A belongs to no D. The case will be the same, even if all the terms taken belong to the same ascending or descending logical series. Here, then, you know one proposition; yet you believe the proposition contrary to it.37 How can such a mental condition be explained? It would, indeed, be an impossibility, if the middle term of the two syllogisms were the same, and if the premisses of the one syllogism thus contradicted directly and in terms, the premisses of the other: should that happen, you cannot know one side of the alternative and believe the other. But if the middle term be different, so that the contradiction between the premisses of the one syllogism and those of the other, is not direct, there is no impossibility. Thus, you know that A is predicable of all B, and B of all D; while you believe at the same time that A is predicable of no C, and C of all D; the middle term being in one syllogism B, in the other, C.38 This last form of error is analogous to what often occurs in respect to our knowledge of particulars. You know that A belongs to all B, and B to all C; you know, therefore, that A belongs to all C. Yet you may perhaps be ignorant of the existence of C. Suppose A to denote equal to two right angles; B, to be the triangle generally; C, a particular visible triangle. You know A B the universal proposition; yet you may at the same time believe that C does not exist; and thus it may happen that you know, and do not know, the same thing at the same time. For, in truth, the knowledge, that every triangle has its three angles equal to two right angles, is not (as a mental fact) simple and absolute, but has two distinct aspects; one as concerns the universal, the other as concerns the several particulars. Now, assuming the case above imagined, you possess the knowledge in the first of these two aspects, but not in the second; so that the apparent contrariety between knowledge and no knowledge is not real.39 And in this sense the doctrine of Plato in the Menon is partially true — that learning is reminiscence. We can never know beforehand particular cases per se; but in proportion as we extend our induction to each case successively, we, as it were, recognize that, which we knew beforehand as a general truth, to be realized in each. Thus when we ascertain the given figure before us to be a triangle, we know immediately that its three angles are equal to two right angles.40

36 Analyt. Prior. II. xxi. p. 66, b. 18: συμβαίνει δ’ ἐνίοτε, καθάπερ ἐν τῇ θέσει τῶν ὅρων ἀπατώμεθα, καὶ κατὰ τὴν ὑπόληψιν γίνεσθαι τὴν ἀπάτην.

The vague and general way in which Aristotle uses the term ὑπόληψις, seems to be best rendered by our word belief. See Trendelenburg ad Aristot. De Animâ, p. 469; Biese, Philos. des Aristot. i. p. 211.

37 Ibid. II. xxi. p. 66, b. 33: ὥστε ὅ πως ἐπίσταται, τοῦτο ὅλως ἀξιοῖ μὴ ὑπολαμβάνειν· ὅπερ ἀδύνατον.

38 Ibid. II. xxi. p. 67, a. 5-8.

39 Analyt. Prior. II. xxi. p. 67, a. 19: οὕτω μὲν οὖν ὡς τῇ καθόλου οὖδε το Γ ὅτι δύο ὀρθαί, ὡς δὲ τῇ καθ’ ἕκαστον οὐκ οἶδεν, ὥστ’ οὐχ ἕξει τὰς ἐναντίας (sc. ἐπιστήμος).

40 Ibid. a. 22: οὐδαμοῦ γὰρ συμβαίνει προεπίστασθαι τὸ καθ’ ἕκαστον, ἀλλ’ ἅμα τῇ ἐπαγωγῇ λαμβάνειν τὴν τῶν κατὰ μέρος ἐπιστήμην ὥσπερ ἀναγνωρίζοντας, &c. Cf. Anal. Post. I. ii. p. 71, b. 9, seq.; Plato, Menon, pp. 81-82.

We thus, by help of the universal, acquire a theoretical knowledge of particulars, but we do not know them by the special observation properly belonging to each particular case: so that we may err in respect to them without any positive contrariety between our cognition and our error; since what we know is the universal, while what we err in is the particular. We may even know that A is predicable of all B, and that B is predicable of all C; and yet we may believe that A is not predicable of C. We may know that every mule is barren, and that the animal before us is a mule, yet still we may believe her to be in foal; for perhaps we may never have combined in our minds the particular case along with the universal proposition.41 A fortiori, therefore, we may make the like mistake, if we know the universal only, and do not know the particular. And this is perfectly possible. For take any one of the visible particular instances, even one which we have already inspected, so soon as it is out of sight we do not know it by actual and present cognition; we only know it, partly from the remembrance of past special inspection, partly from the universal under which it falls.42 We may know in one, or other, or all, of these three distinct ways: either by the universal; or specially (as remembered): or by combination of both — actual and present cognition, that is, by the application of a foreknown generality to a case submitted to our senses. And as we may know in each of these three ways, so we may also err or be deceived in each of the same three ways.43 It is therefore quite possible that we may know, and that we may err or be deceived about the same thing, and that, too, without any contrariety. This is what happens when we know both the two premisses of the syllogism, but have never reflected on them before, nor brought them into conjunction in our minds. When we believe that the mule before us is in foal, we are destitute of the actual knowledge; yet our erroneous belief is not for that reason contrary to knowledge; for an erroneous belief, contrary to the universal proposition, must be represented by a counter-syllogism.44

41 Ibid. II. xxi. p. 67, a. 36: οὐ γὰρ ἐπίσταται ὅτι τὸ Α τῷ Γ, μὴ συνθεωρῶν τὸ καθ’ ἑκάτερον.

42 Analyt. Prior. II. xxi. p. 67, a. 39: οὐδὲν γὰρ τῶν αἰσθητῶν ἔξω τῆς αἰσθήσεως γενόμενον ἴσμεν, οὔδ’ ἂν ᾐσθημένοι τυγχάνωμεν, εἰ μὴ ὡς τῷ καθόλου καὶ τῷ ἔχειν τὴν οἰκείαν ἐπιστήμην, ἀλλ’ οὐχ ὡς τῷ ἐνεργεῖν.

Complete cognition (τὸ ἐνεργεῖν, according to the view here set forth) consists of one mental act corresponding to the major premiss; another corresponding to the minor; and a third including both the two in conscious juxta-position. The third implies both the first and the second; but the first and the second do not necessarily imply the third, nor does either of them imply the other; though a person cognizant of the first is in a certain way, and to a certain extent, cognizant of all the particulars to which the second applies. Thus the person who knows Ontology (the most universal of all sciences, τοῦ ὄντος ᾗ ὄν), knows in a certain way all scibilia. Metaphys. A., p. 982, a. 21: τούτων δὲ τὸ μὲν πάντα ἐπίστασθαι τῷ μάλιστα ἔχοντι τὴν καθόλου ἐπιστήμην ἀναγκαῖον ὑπάρχειν· οὕτος γὰρ οἶδέ πως πάντα τὰ ὑποκείμενα. Ib. a. 8: ὑπολαμβάνομεν δὴ πρῶτον μὲν ἐπίστασθαι πάντα τὸν σοφὸν ὡς ἐνδέχεται, μὴ καθ’ ἕκαστον ἔχοντα ἐπιστήμην αὐτῶν. See the Scholia of Alexander on these passages, pp. 525, 526, Brandis; also Aristot. Analyt. Post. I. xxiv. p. 86, a. 25; Physica, VII. p. 247, a. 5. Bonitz observes justly (Comm. ad Metaphys. p. 41) as to the doctrine of Aristotle: “Scientia et ars versatur in notionibus universalibus, solutis ac liberis à conceptu singularum rerum; ideoque, etsi orta est à principio et experientiâ, tradi tamen etiam iis potest qui careant experientiâ.”