Chapter VI · ANALYTICA PRIORA II.

The Second Book of the Analytica Priora seems conceived with a view mainly to Dialectic and Sophistic, as the First Book bore more upon Demonstration.1 Aristotle begins the Second Book by shortly recapitulating what he had stated in the First; and then proceeds to touch upon some other properties of the Syllogism. Universal syllogisms (those in which the conclusion is universal) he says, have always more conclusions than one; particular syllogisms sometimes, but not always, have more conclusions than one. If the conclusion be universal, it may always be converted — simply, when it is negative, or per accidens, when it is affirmative; and its converse thus obtained will be proved by the same premisses. If the conclusion be particular, it will be convertible simply when affirmative, and its converse thus obtained will be proved by the same premisses; but it will not be convertible at all when negative, so that the conclusion proved will be only itself singly.2 Moreover, in the universal syllogisms of the First figure (Barbara, Celarent), any of the particulars comprehended under the minor term may be substituted in place of the minor term as subject of the conclusion, and the proof will hold good in regard to them. So, again, all or any of the particulars comprehended in the middle term may be introduced as subject of the conclusion in place of the minor term; and the conclusion will still remain true. In the Second figure, the change is admissible only in regard to those particulars comprehended under the subject of the conclusion or minor term, and not (at least upon the strength of the syllogism) in regard to those comprehended under the middle term. Finally, wherever the conclusion is particular, the change is admissible, though not by reason of the syllogism in regard to particulars comprehended under the middle term; it is not admissible as regards the minor term, which is itself particular.3

Aristotle has hitherto regarded the Syllogism with a view to its formal characteristics: he now makes an important observation which bears upon its matter. Formally speaking, the two premisses are always assumed to be true; but in any real case of syllogism (form and matter combined) it is possible that either one or both may be false. Now, Aristotle remarks that if both the premisses are true (the syllogism being correct in form), the conclusion must of necessity be true; but that if either or both the premisses are false, the conclusion need not necessarily be false likewise. The premisses being false, the conclusion may nevertheless be true; but it will not be true because of or by reason of the premisses.4

First, he would prove that if the premisses be true, the conclusion must be true also; but the proof that he gives does not seem more evident than the probandum itself. Assume that if A exists, B must exist also: it follows from hence (he argues) that if B does not exist, neither can A exist; which he announces as a reductio ad absurdum, seeing that it contradicts the fundamental supposition of the existence of A.5 Here the probans is indeed equally evident with the probandum, but not at all more evident; one who disputes the latter, will dispute the former also. Nothing is gained in the way of proof by making either of them dependent on the other. Both of them are alike self-evident; that is, if a man hesitates to admit either of them, you have no means of removing his scruples except by inviting him to try the general maxim upon as many particular cases as he chooses, and to see whether it does not hold good without a single exception.

In regard to the case here put forward as illustration, Aristotle has an observation which shows his anxiety to maintain the characteristic principles of the Syllogism; one of which principles he had declared to be — That nothing less than three terms and two propositions, could warrant the inferential step from premisses to conclusion. In the present case he assumed, If A exists, then B must exist; giving only one premiss as ground for the inference. This (he adds) does not contravene what has been laid down before; for A in the case before us represents two propositions conceived in conjunction.6 Here he has given the type of hypothetical reasoning; not recognizing it as a variety per se, nor following it out into its different forms (as his successors did after him), but resolving it into the categorical syllogism.7 He however conveys very clearly the cardinal principle of all hypothetical inference — That if the antecedent be true, the consequent must be true also, but not vice versâ; if the consequent be false, the antecedent must be false also, but not vice versâ.

Having laid down the principle, that the conclusion may be true, though one or both the premisses are false, Aristotle proceeds, at great length, to illustrate it in its application to each of the three syllogistic figures.8 No portion of the Analytica is traced out more perspicuously than the exposition of this most important logical doctrine.

It is possible (he then continues, again at considerable length) to invert the syllogism and to demonstrate in a circle. That is, you may take the conclusion as premiss for a new syllogism, together with one of the old premisses, transposing its terms; and thus you may demonstrate the other premiss. You may do this successively, first with the major, to demonstrate the minor; next, with the minor, to demonstrate the major. Each of the premisses will thus in turn be made a demonstrated conclusion; and the circle will be complete. But this can be done perfectly only in Barbara, and when, besides, all the three terms of the syllogism reciprocate with each other, or are co-extensive in import; so that each of the two premisses admits of being simply converted. In all other cases, the process of circular demonstration, where possible at all, is more or less imperfect.9

Having thus shown under what conditions the conclusion can be employed for the demonstration of the premisses, Aristotle proceeds to state by what transformation it can be employed for the refutation of them. This he calls converting the syllogism; a most inconvenient use of the term convert (ἀντιστρέφειν), since he had already assigned to that same term more than one other meaning, distinct and different, in logical procedure.10 What it here means is reversing the conclusion, so as to exchange it either for its contrary, or for its contradictory; then employing this reversed proposition as a new premiss, along with one of the previous premisses, so as to disprove the other of the previous premisses — i.e. to prove its contrary or contradictory. The result will here be different, according to the manner in which the conclusion is reversed; according as you exchange it for its contrary or its contradictory. Suppose that the syllogism demonstrated is: A belongs to all B, B belongs to all C; Ergo, A belongs to all C (Barbara). Now, if we reverse this conclusion by taking its contrary, A belongs to no C, and if we combine this as a new premiss with the major of the former syllogism, A belongs to all B, we shall obtain as a conclusion B belongs to no C; which is the contrary of the minor, in the form Camestres. If, on the other hand, we reverse the conclusion by taking its contradictory, A does not belong to all C, and combine this with the same major, we shall have as conclusion, B does not belong to all C; which is the contradictory of the minor, and in the form Baroco: though in the one case as in the other the minor is disproved. The major is contradictorily disproved, whether it be the contrary or the contradictory of the conclusion that is taken along with the minor to form the new syllogism; but still the form varies from Felapton to Bocardo. Aristotle shows farther how the same process applies to the other modes of the First, and to the modes of the Second and Third figures.11 The new syllogism, obtained by this process of reversal, is always in a different figure from the syllogism reversed. Thus syllogisms in the First figure are reversed by the Second and Third; those in the second, by the First and Third; those in the Third, by the First and Second.12

Of this reversing process, one variety is what is called the Reductio ad Absurdum; in which the conclusion is reversed by taking its contradictory (never its contrary), and then joining this last with one of the premisses, in order to prove the contradictory or contrary of the other premiss.13 The Reductio ad Absurdum is distinguished from the other modes of reversal by these characteristics: (1) That it takes the contradictory, and not the contrary, of the conclusion; (2) That it is destined to meet the case where an opponent declines to admit the conclusion; whereas the other cases of reversion are only intended as confirmatory evidence towards a person who already admits the conclusion; (3) That it does not appeal to or require any concession on the part of the opponent; for if he declines to admit the conclusion, you presume, as a matter of course, that he must adhere to the contradictory of the conclusion; and you therefore take this contradictory for granted (without asking his concurrence) as one of the bases of a new syllogism; (4) That it presumes as follows:— When, by the contradictory of the conclusion joined with one of the premisses, you have demonstrated the opposite of the other premiss, the original conclusion itself is shown to be beyond all impeachment on the score of form, i.e. beyond impeachment by any one who admits the premisses. You assume to be true, for the occasion, the very proposition which you mean finally to prove false; your purpose in the new syllogism is, not to demonstrate the original conclusion, but to prove it to be true by demonstrating its contradictory to be false.14

By the Reductio ad Absurdum you can in all the three figures demonstrate all the four varieties of conclusion, universal and particular, affirmative and negative; with the single exception, that you cannot by this method demonstrate in the First figure the Universal Affirmative.15 With this exception, every true conclusion admits of being demonstrated by either of the two ways, either directly and ostensively, or by reduction to the impossible.16

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

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

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

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

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

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

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

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

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

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

It is impossible, however, for a man to believe that one contrary is predicable of its contrary, or that one contrary is identical with its contrary, essentially and as an universal proposition; though he may believe that it is so by accident (i.e. in some particular case, by reason of the peculiarities of that case). In various ways this last is possible; but this we reserve for fuller examination.45

Whenever (Aristotle next goes on to say) the extremes of a syllogism reciprocate or are co-extensive with each other (i.e. when the conclusion being affirmative is convertible simply), the middle term must reciprocate or be co-extensive with both.46 If there be four terms (A, B, C, D), such that A reciprocates with B, and C with D, and if either A or C must necessarily be predicable of every subject; then it follows that either B or D must necessarily also be predicable of every subject. Again, if either A or B must necessarily be predicable of every subject, but never both predicable of the same at once; and if, either C or D must be predicable of every subject, but never both predicable of the same at once; then, if A and C reciprocate, B and D will also reciprocate.47 When A is predicable of all B and all C, but of no other subject besides, and when B is predicable of all C, then A and B must reciprocate with each other, or be co-extensive with each other; that is, B may be predicated of every subject of which A can be predicated, though B cannot be predicated of A itself.48 Again, when A and B are predicable of all C, and when C reciprocates with B, then A must also be predicable of all B.49

Lastly, suppose two pairs of opposites, A and B, C and D; let A be more eligible than B, and D more eligible than C. Then, if A C is more eligible than B D, A will also be more eligible than D. For A is as much worthy of pursuit as B is worthy of avoidance, they being two opposites; the like also respecting C and D. If then A and D are equally worthy of pursuit, B and C are equally worthy of avoidance; for each is equal to each. Accordingly the two together, A C, will be equal to the two together, B D. But this would be contrary to the supposition; since we assumed A to be more eligible than B, and D to be more eligible than C. It will be seen that on this supposition A is more worthy of pursuit than D, and that C is less worthy of avoidance than B; the greater good and the lesser evil being more eligible than the lesser good and the greater evil. Now apply this to a particular case of a lover, so far forth as lover. Let A represent his possession of those qualities which inspire reciprocity of love towards him in the person beloved; B, the absence of those qualities; D, the attainment of actual sexual enjoyment; C, the non-attainment thereof. In this state of circumstances, it is evident that A is more eligible or worthy of preference than D. The being loved is a greater object of desire to the lover qua lover than sexual gratification; it is the real end or purpose to which love aspires; and sexual gratification is either not at all the purpose, or at best only subordinate and accessory. The like is the case with our other appetites and pursuits.50

Such is the relation of the terms of a syllogism in regard to reciprocation and antithesis. Let it next be understood that the canons hitherto laid down belong not merely to demonstrative and dialectic syllogisms, but to rhetorical and other syllogisms also; all of which must be constructed in one or other of the three figures. In fact, every case of belief on evidence, whatever be the method followed, must be tested by these same canons. We believe everything either through Syllogism or upon Induction.51

Though Aristotle might seem, even here, to have emphatically contrasted Syllogism with Induction as a ground of belief, he proceeds forthwith to indicate a peculiar form of Syllogism which may be constructed out of Induction. Induction, and the Syllogism from or out of Induction (he says) is a process in which we invert the order of the terms. Instead of concluding from the major through the middle to the minor (i.e. concluding that the major is predicable of the minor), we now begin from the minor and conclude from thence through the middle to the major (i.e. we conclude that the major is predicable of the middle).52 In Syllogism as hitherto described, we concluded that A the major was predicable of C the minor, through the middle B; in the Syllogism from Induction we begin by affirming that A the major is predicable of C the minor; next, we affirm that B the middle is also predicable of C the minor. The two premisses, standing thus, correspond to the Third figure of the Syllogism (as explained in the preceding pages) and would not therefore by themselves justify anything more than a particular affirmative conclusion. But we reinforce them by introducing an extraneous assumption:— That the minor C is co-extensive with the middle B, and comprises the entire aggregate of individuals of which B is the universal or class-term. By reason of this assumption the minor proposition becomes convertible simply, and we are enabled to infer (according to the last preceding chapter) an universal affirmative conclusion, that the major term A is predicable of the middle term B. Thus, let A (the major term) mean the class-term, long-lived; let B (the middle term) mean the class-term, bile-less, or the having no bile; let C (the minor term) mean the individual animals — man, horse, mule, &c., coming under the class-term B, bile-less.53 We are supposed to know, or to have ascertained, that A may be predicated of all C; (i.e. that all men, horses, mules, &c., are long-lived); we farther know that B is predicable of all C (i.e. that men, horses, mules, &c., belong to the class bile-less). Here, then, we have two premisses in the Third syllogistic figure, which in themselves would warrant us in drawing the particular affirmative conclusion, that A is predicable of some B, but no more. Accordingly, Aristotle directs us to supplement these premisses54 by the extraneous assumption or postulate, that C the minor comprises all the individual animals that are bile-less, or all those that correspond to the class-term B; in other words, the assumption, that B the middle does not denote any more individuals than those which are covered by C the minor — that B the middle does not stretch beyond or overpass C the minor.55 Having the two premisses, and this postulate besides, we acquire the right to conclude that A is predicable of all B. But we could not draw that conclusion from the premisses alone, or without the postulate which declares B and C to be co-extensive. The conclusion, then, becomes a particular exemplification of the general doctrine laid down in the last chapter, respecting the reciprocation of extremes and the consequences thereof. We thus see that this very peculiar Syllogism from Induction is (as indeed Aristotle himself remarks) the opposite or antithesis of a genuine Syllogism. It has no proper middle term; the conclusion in which it results is the first or major proposition, the characteristic feature of which it is to be immediate, or not to be demonstrated through a middle term. Aristotle adds that the genuine Syllogism, which demonstrates through a middle term, is by nature prior and more effective as to cognition; but that the Syllogism from Induction is to us plainer and clearer.56

From Induction he proceeds to Example. You here take in (besides the three terms, major, middle, and minor, of the Syllogism) a fourth term; that is, a new particular case analogous to the minor. Your purpose here is to show — not, as in the ordinary Syllogism, that the major term is predicable of the minor, but, as in the Inductive Syllogism — that the major term is predicable of the middle term; and you prove this conclusion, not (as in the Inductive Syllogism) through the minor term, but through the new case or fourth term analogous to the minor.57 Let A represent evil or mischievous; B, war against neighbours, generally; C, war of Athens against Thebes, an event to come and under deliberation; D, war of Thebes against Phokis, a past event of which the issue is known to have been signally mischievous. You assume as known, first, that A is predicable of D, i.e. that the war of Thebes against Phokis has been disastrous; next, that B is predicable both of C and of D, i.e. that each of the two wars, of Athens against Thebes, and of Thebes against Phokis, is a war of neighbours against neighbours, or a conterminous war. Now from the premiss that A is predicable of D, along with the premiss that B is predicable of D, you infer that A is predicable of the class B, or of conterminous wars generally; and hence you draw the farther inference, that A is also predicable of C, another particular case under the same class B. The inference here is, in the first instance, from part to whole; and finally, through that whole, from the one part to another part of the same whole. Induction includes in its major premiss all the particulars, declaring all of them to be severally subjects of the major as predicate; hence it infers as conclusion, that the major is also predicable of the middle or class-term comprising all these particulars, but comprising no others. Example includes not all, but only one or a few particulars; inferring from it or them, first, to the entire class, next, to some new analogous particular belonging to the class.58

These chapters respecting Induction and Example are among the most obscure and perplexing in the Aristotelian Analytica. The attempt to throw both Induction and Example into the syllogistic form is alike complicated and unfortunate; moreover, the unsatisfactory reading and diversities in the text, among commentators and translators, show that the reasoning of Aristotle has hitherto been imperfectly apprehended.59 From some of his phrases, we see that he was aware of the essential antithesis between Induction and Syllogism; yet the syllogistic forms appear to have exercised such fascination over his mind, that he could not be satisfied without trying to find some abnormal form of Syllogism to represent and give validity to Induction. In explaining generally what the Syllogism is, and what Induction is, he informs us that the Syllogism presupposes and rests upon the process of Induction as its postulate. For there can be no valid Syllogism without an universal proposition in one (at least) of the premisses; and he declares, unequivocally, that universal propositions are obtained only through Induction. How Induction operates through the particular facts of sense, remembered, compared, and coalescing into clusters held together by associating similarity, he has also told us; it is thus that Experience, with its universal notions and conjunctions, is obtained. But this important process is radically distinct from that of syllogizing, though it furnishes the basis upon which all syllogizing is built.

The central idea of the Syllogism, as defined by Aristotle, is that of a conclusion following from given premisses by necessary sequence;60 meaning by the term necessary thus much and no more — that you cannot grant the premisses, and deny the conclusion, without being inconsistent with yourself, or falling into contradiction. In all the various combinations of propositions, set forth by Aristotle as the different figures and modes of Syllogism, this property of necessary sequence is found. But it is a property which no Induction can ever possess.61 When Aristotle professes to point out a particular mode of Syllogism to which Induction conforms, he can only do so by falsifying the process of Induction, and by not accurately distinguishing between what is observed and what is inferred. In the case which he takes to illustrate the Inductive Syllogism — the inference from all particular bile-less animals to the whole class bile-less — he assumes that we have ascertained the attribute to belong to all the particulars, and that the inductive inference consists in passing from all of them to the class-term; the passage from premisses to conclusion being here necessary, and thus falling under the definition of Syllogism; since, to grant the premisses, and yet to deny the conclusion, involves a contradiction. But this doctrine misconceives what the inductive inference really is. We never can observe all the particulars of a class, which is indefinite as to number of particulars, and definite only in respect of the attributes connoted by the class-term. We can only observe some of the particulars, a greater or smaller proportion. Now it is in the transition from these to the totality of particulars, that the real inductive inference consists; not in the transition from the totality to the class-term which denotes that totality and connotes its determining common attribute. In fact, the distinction between the totality of particulars and the meaning of the class-term, is one not commonly attended to; though it is worthy of note in an analysis of the intellectual process, and is therefore brought to view by Aristotle. But he employs it incorrectly as an intermediate step to slur over the radical distinction between Induction and Syllogism. He subjoins:62— “You must conceive the minor term C (in the Inductive Syllogism) as composed of all the particulars; for Induction is through all of them.” You may say that Induction is through all the particulars, if you distinguish this totality from the class-term, and if you treat the class-term as the ultimate terminus ad quem. But the Induction must first travel to all the particulars; being forced to take start from a part only, and then to jump onward far enough to cover the indefinite unobserved remainder. This jump is the real Induction; and this can never be brought under the definition of Syllogism; for in the best and most certain Induction the sequence is never a necessary one: you may grant the premisses and deny the conclusion without contradicting yourself.

Aristotle states very clearly:— “We believe everything either through Syllogism, or from Induction.”63 Here, as well as in several other passages, he notes the two processes as essentially distinct. The Syllogism requires in its premisses at least one general proposition; nor does Aristotle conceive the “generalities as the original data:”64 he derives them from antecedent Induction. The two processes are (as he says) opposite in a certain way; that is, they are complementary halves of the same whole; Induction being the establishment of those universals which are essential for the deductive march of the Syllogism; while the two together make up the entire process of scientific reasoning. But he forgets or relinquishes this antithesis, when he presents to us the Inductive process as a given variety of Syllogism. And the objection to such a doctrine becomes the more manifest, since in constructing his Inductive Syllogism, he is compelled to admit either that there is no middle term, or that the middle term is subject of the conclusion, in violation of the syllogistic canons.65

We must presume Syllogisms without a middle term, when we read:— “The Syllogism through a middle term is by nature prior, and of greater cognitive efficacy; but to us the Syllogism through Induction is plainer and clearer.”66 Nor, indeed, is the saying, when literally taken, at all well-founded; for the pretended Syllogisms from Induction and Example, far from being clear and plain, are more involved and difficult to follow than Barbara and Celarent. Yet the substance of Aristotle’s thought is true and important, when considered as declaring the antithesis (not between varieties of Syllogisms, but) between Induction and Example on the one part, and Syllogism (Deduction) on the other. It is thus that he sets out the same antithesis elsewhere, both in the Analytica Posteriora and the Topica.67 Prior and more cognizable by nature or absolutely, prior and more cognizable to us or in relation to us — these two are not merely distinct, but the one is the correlate and antithesis of the other.

To us the particulars of sense stand first, and are the earliest objects of knowledge. To us, means to the large variety of individual minds, which grow up imperceptibly from the simple capacities of infancy to the mature accomplishments of adult years; each acquiring its own stock of sensible impressions, remembered, compared, associated; and each learning a language, which both embodies in general terms and propositions the received classification of objects, and communicates the current emotional beliefs. We all begin by being learners; and we ascend by different paths to those universal notions and beliefs which constitute the common fund of the advanced intellect; developed in some minds into principia of philosophy with their consequences. By nature, or absolutely, these principia are considered as prior, and as forming the point of departure: the advanced position is regarded as gained, and the march taken is not that of the novice, but that of the trained adult, who having already learnt much, is doubly equipped either for learning more or for teaching others; who thus stands on a summit from whence he surveys nature as a classified and coherent whole, manifesting herself in details which he can interpret and sometimes predict. The path of knowledge, seen relatively to us, is one through particulars, by way of example to fresh particulars, or by way of induction to universals. The path of knowledge, by nature or absolutely, is from universals by way of deduction either to new universals or to new particulars. By the cognitive nature of man, Aristotle means the full equipment, of and for cognition, which our mature age exhibits; notiora naturâ are the acquisitions, points of view, and processes, familiar in greater or less perfection to such mature individuals and societies. Notiora nobis are the facts and processes with which all of us begin, and which belong to the intellect in its highest as well as its lowest stage; though, in the higher stages, they are employed, directed, and modified, by an acquired intellectual capital, and by the permanent machinery of universal significant terms in which that capital is invested.

Such is the antithesis between notiora naturâ (or simpliciter) and notiora nobis (or quoad nos), which Aristotle recognizes as a capital point in his philosophy, and insists upon in many of his writings. The antithesis is represented by Example and Induction, in the point of view — quoad nos — last mentioned; by Syllogism or Deduction, in the other point of view — naturâ. Induction (he says),68 or the rising from particulars to universals, is plainer, more persuasive, more within the cognizance of sensible perception, more within the apprehension of mankind generally, than Syllogism; but Syllogism is more cogent and of greater efficacy against controversial opponents. What he affirms here about Induction is equally true about the inference from Example, that is, the inference from one or some particulars, to other analogous particulars; the rudimentary intellectual process, common to all human and to many animal minds, of which Induction is an improvement and an exaltation. While Induction will be more impressive, and will carry assent more easily with an ordinary uncultivated mind, an acute disputant may always deny the ultimate inference, for the denial involves no contradiction. But the rightly constructed Syllogism constrains assent;69 the disputant cannot grant the premisses and deny the conclusion without contradicting himself. The constraining force, however, does not come into accurate and regulated working until the principles and conditions of deductive reasoning have been set forth — until the Syllogism has been analysed, and the characteristics of its validity, as distinguished from its invalidity, have been marked out. This is what Aristotle teaches in the Analytica and Topica. It admits of being set out in regular figure and mode — forms of premisses with the conclusion appropriate to each; and the lesson must be learnt before we can know how far the force of deductive reasoning, which begins with the notiora naturâ, is legitimately binding and trustworthy.

Both the two main points of Aristotle’s doctrine — the antithesis between Induction and Deduction, and the dependence of the latter process upon premisses furnished by the former, so that the two together form the two halves of complete ratiocination and authoritative proof — both these two are confused and darkened by his attempt to present the Inductive inference and the Analogical or Paradeigmatic inference as two special forms of Syllogistic deduction.70 But when we put aside this attempt, and adhere to Aristotle’s main doctrine — of Induction as a process antithetical to and separate from Deduction, yet as an essential preliminary thereto, — we see that it forms the basis of that complete and comprehensive System of Logic, recently elaborated in the work of Mr. John Stuart Mill. The inference from Example (i.e. from some particulars to other similar particulars) is distinguished by Aristotle from Induction, and is recognized by him as the primitive intellectual energy, common to all men, through which Induction is reached; its results he calls Experience (ἐμπειρία), and he describes it as the real guide, more essential than philosophical generalities, to exactness of performance in detail.71 Mr. John Mill has been the first to assign to Experience, thus understood, its full value and true position in the theory of Ratiocination; and to show that the Paradeigmatic process exhibits the prime and ultimate reality of all Inference, the real premisses and the real conclusion which Inference connects together. Between these two is interposed the double process of which Induction forms the first half and Deduction the second; neither the one nor the other being indispensable to Inference, but both of them being required as securities for Scientific inference, if we desire to have its correctness tested and its sufficiency certified; the real evidence, whereby the conclusion of a Syllogism is proved, being the minor premiss, together with (not the major premiss itself, but) the assemblage of particular facts from which by Induction the major premiss is drawn. Now Aristotle had present to his mind the conception of Inference as an entire process, enabling us from some particular truths to discover and prove other particular truths: he considers it as an unscientific process, of which to a limited extent other animals besides man are capable, and which, as operative under the title of Experience in mature practical men, is a safer guide than Science amidst the doubts and difficulties of action. Upon this foundation he erects the superstructure of Science; the universal propositions acquired through Induction, and applied again to particulars or to lower generalities, through the rules of the deductive Syllogism. He signalizes, with just emphasis, the universalizing point of view called Science or Theory; but he regards it as emerging from particular facts, and as travelling again downwards towards particular facts. The misfortune is, that he contents himself with barely recognizing, though he distinctly proclaims the necessity of, the inductive part of this complex operation; while he bestows elaborate care upon the analysis of the deductive part, and of the rules for conducting it. From this disproportionate treatment, one half of Logic is made to look like the whole; Science is disjoined from Experience, and is presented as consisting in Deduction alone; every thing which is not Deduction, is degraded into unscientific Experience; the major premiss of the Syllogism being considered as part of the proof of the conclusion, and the conclusion being necessarily connected therewith, we appear to have acquired a locus standi and a binding cogency such as Experience could never supply; lastly, when Aristotle resolves Induction into a peculiar variety of the Syllogism, he appears finally to abolish all its separate dignity and jurisdiction. This one-sided view of Logic has been embraced and perpetuated by the Aristotelian expositors, who have carefully illustrated, and to a certain extent even amplified, the part which was already in comparative excess, while they have added nothing to the part that was in defect, and have scarcely even preserved Aristotle’s recognition of it as being not merely legitimate but essential. The vast body of Inductive Science, accumulated during the last three centuries, has thus, until recently, been allowed to grow up, as if its proofs and processes had nothing to do with Logic.

But though this restricted conception of Logic or the theory of Reasoning has arisen naturally from Aristotle’s treatment, I maintain that it does not adequately represent his view of that theory. In his numerous treatises on other subjects, scarcely any allusion is made to the Syllogism; nor is appeal made to the rules for it laid down in the Analytica. His conviction that the formalities of Deduction were only one part of the process of general reasoning, and that the value of the final conclusion depended not merely upon their being correctly performed, but also upon the correctness of that initial part whereby they are supplied with matter for premisses — is manifested as well by his industry (unrivalled among his contemporaries) in collecting multifarious facts, as by his specific declarations respecting Induction. Indeed, a recent most erudite logician, Sir William Hamilton, who insists upon the construction of Logic in its strictest sense as purely formal, blames Aristotle72 for having transgressed this boundary, and for introducing other considerations bearing on diversities of matter and of material evidence. The charge so made, to whatever extent it is well-founded, does rather partake of the nature of praise; inasmuch as it evinces Aristotle’s larger views of the theory of Inference, and confirms his own statement that the Deductive process was only the last half of it, presupposing a prior Induction. It is only this last half that Aristotle has here analysed, setting forth its formal conditions with precepts founded thereupon; while he claims to have accomplished the work by long and patient investigation, having found not the smallest foundation laid by others, and bespeaks indulgence73 as for a first attempt requiring to be brought to completion by others. He made this first step for himself; and if any one would make a second step, so as to apply the same analysis to the other half, and to bring out in like manner the formal conditions and principles of Induction, we may fairly believe that Aristotle would have welcomed the act, as filling up what he himself recognized to be a gap in the entire compass of Reasoning. As to his own achievement, it is certain that he could not have composed the Analytica and Topica, if he had not had before him many specimens of the deductive process to study and compare. Neither could the inductive process have been analysed, until after the examples of successful advance in inductive science which recent years have furnished. Upon these examples, mainly, has been based the profound System of Mr. John Stuart Mill, analysing and discriminating the formalities of Induction in the same way as those of Deduction had before been handled by Aristotle; also fusing the two together as co-operative towards one comprehensive scheme of Logic — the Logic of Evidence generally, or of Truth as discoverable and proveable. In this scheme the Syllogistic Theory, or Logic of Consistency between one proposition and others, is recognized as an essential part, but is no longer tolerated as an independent whole.74

After adverting to another variety of ratiocinative procedure, which he calls Apagoge or Abduction (where the minor is hardly more evident than the conclusion, and might sometimes conveniently become a conclusion first to be proved),75 Aristotle goes on to treat of Objection generally — the function of the dialectical respondent. The Enstasis or Objection is a proposition opposed not to a conclusion, but to the proposition set up by the defendant. When the proposition set up by him is universal, as it must be if he seeks to establish an universal conclusion, your objection may be either universal or particular: you may deny either the whole of his proposition, or only one portion of the particulars contained under it; the denial of one single particular, when substantiated, being enough to overthrow his universal. Accordingly, your objection, being thus variously opposed to the proposition, will lie in the syllogistic figures which admit opposite conclusions; that is, either in the First or Third; for the Second figure admits only negative conclusions not opposed to each other. If the defendant has set up an Universal Affirmative, you may deny the whole and establish a contrary negative, in the First figure; or you may deny a part only, and establish a contradictory negative, in the Third figure. The like, if he has set up an Universal Negative: you may impugn it either by an universal contrary affirmative, in the First figure; or by a particular contradictory affirmative, in the Third figure.76

The Enthymeme is a syllogism from Probabilities or Signs;77 the two being not exactly the same. Probabilities are 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 love them. We call it a Sign, 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 of Proof (τεκμήριον.)78

Aristotle concludes his Analytica Priora by applying this doctrine of Signs to determine the limits within which Physiognomy as 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,79 if, 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 a proprium; 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.80 But 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

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. As That which may be, it stands opposed to the Impossible; as That 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

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 as subjective, or as depending upon our want of complete knowledge and calculating power, but) as objective, 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 calls Nature — 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

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 the dialectical syllogism from the demonstrative. 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

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 word necessary, 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.