Chapter XVII: Book II: ch. iii. sect 2:--"It must be granted, that in every (2)

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.

[Footnote 60: Alexander intimates that Aristotle enunciated "necessary sequence" as a part of his definition of Syllogism, for the express purpose of distinguishing it from Induction, which is a sequence _not necessary_ (Schol. ad Top. p. 253, a. 19, Br.): [Greek: to\ d' _e)x a)na/gkês_ proskei/menon e)n tô=| o(/rô|, tê=s **e)pagôgê=s chôri/zei to\n sullogismo/n; **e)/sti me\n ga\r kai\ e)pagôgê\ lo/gos e)n ô(=| tethe/ntôn tinô=n e(/tero/n ti tô=n keime/nôn sumbai/nei, a)ll' _ou)k_ e)x a)na/gkês.]]

[Footnote 61: Alexander (in his Scholia on the Metaphysica, E. i. p. 406**, ed. Bonitz) observes truly: [Greek: a)ll' ei) e)k tê=s ai)sthê/seôs kai\ tê=s e)pagôgê=s pi/stis, ou)k e)/stin a)po/deixis, pro\s pa=san ga\r e)pagôgê\n du/natai/ tis e)ni/stasthai kai\ mê\ e)a=|n to\ katho/lou sumperai/nein.]]

[Footnote 62: Analyt. Prior. II. xxiii. p. 68, b. 27: [Greek: dei= de\ noei=n to\ G to\ e)x a(pa/ntôn tô=n kath' e(/kaston sugkei/menon; ê( ga\r e)pagôgê\ dia\ pa/ntôn.] See Professor Bain's 'Inductive Logic,' chap. i. s. 2, where this process is properly criticised.]

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]

[Footnote 63: Ibid. II. xxiii. p. 68, b. 13: [Greek: a(/panta ga\r pisteu/omen ê)\ dia\ sullogismou= ê)\ e)x e)pagôgê=s]. Here Induction includes Example, though in the next stage he puts the two apart. Compare Anal. Poster. I. i. p. 71, a. 9.]

[Footnote 64: See Mr. John Stuart Mill's System of Logic, Bk. II. ch. iii. a. 4, p. 219, 5th ed.]

[Footnote 65: Aldrich (Artis Log. Rudim. ch. iii. 9, 2, p. 175) and Archbishop Whately (Elem. of Logic, ch. i. p. 209) agree in treating the argument of Induction as a defective or informal Syllogism: see also to the same purpose Sir.** W. Hamilton, Lectures on Logic, vol. i. p. 322. Aldrich treats it as a Syllogism in _Barbara_, with the minor suppressed; but Whately rejects this, because the minor necessary to be supplied is false. He maintains that the premiss suppressed is the major, not the minor. I dissent from both. It appears to me that the opinion which Whately pronounces to be a fallacy is the real truth: "Induction is a distinct kind of argument from the Syllogism" (p. 208). It is the essential property of the Syllogism, as defined by Aristotle and by every one after him, that the truth of the conclusion follows _necessarily_ from the truth of its premisses: that you cannot admit the premisses and reject the conclusion without contradicting yourself. Now this is what the best Induction never attains; and I contend that the presence or absence of this important characteristic is quite enough to constitute "two _distinct kinds_ of argument." Whately objects to Aldrich (whom Hamilton defends) for supplying a suppressed _minor_, because it is "manifestly false" (p. 209). I object to Whately's supplied _major_, because it is uncertified, and therefore cannot be used to prove any conclusion. By clothing arguments from Induction in syllogistic form, we invest them with a character of necessity which does not really belong to them. The establishment of general propositions, and the interpretation of them when established (to use the phraseology of Mr. Mill), must always be distinct mental processes; and the forms appropriate to the latter, involving necessary sequence, ought not to be employed to disguise the want of necessity--the varying and graduated probability, inherent in the former. Mr. Mill says (Syst. Log. Bk. III. ch. iii. s. 1, p. 343, 5th ed.:)--"As Whately remarks, every induction is a syllogism with the major premiss suppressed; or (as I prefer expressing it) every induction may be thrown into the form of a syllogism, by supplying a major premiss." Even in this modified phraseology, I cannot admit the propriety of throwing Induction into syllogistic forms of argument. By doing this we efface the special character of Induction, as the jump from particular cases, more or fewer, to an universal proposition comprising them and an indefinite number of others besides. To state this in forms which imply that it is a necessary step, involving nothing more than the interpretation of a higher universal proposition, appears to me unphilosophical. Mr. Mill says with truth (in his admirable chapter explaining the real function of the major premiss in a Syllogism, p. 211), that the individual cases are all the evidence which we possess; the step from them to universal propositions ought not to be expressed in forms which suppose universal propositions to be already attained.

I will here add that, though Aldrich himself (as I stated at the beginning of this note) treats the argument from Induction as a defective or informal Syllogism, his anonymous Oxonian editor and commentator takes a sounder view. He says (pp. 176, 177, 184, ed. 1823. Oxon.):--

"The principles acquired by human powers may be considered as twofold. Some are _intuitive_, and are commonly called Axioms; the other class of general principles are those acquired by Induction. But it may be doubted whether this distinction is correct. It is highly probable, if not certain, that those primary Axioms generally esteemed _intuitive_, are in fact acquired by an inductive process; although that process is less discernible, because it takes place long before we think of tracing the actings of our own minds. It is often found necessary to facilitate the understanding of those Axioms, when they are first proposed to the judgment, by illustrations drawn from individual cases. But whether it is, as is generally supposed, the mere _enunciation_ of the principle, or the _principle itself_, which requires the illustration, may admit of a doubt. It seems probable, however that, such illustrations are nothing more than a recurrence to the original method by which the knowledge of those principles was acquired. Thus, the repeated trial or observation of the necessary connection between mathematical coincidence and equality, first authorizes the general position or Axiom relative to that subject. If this conjecture is founded in fact, it follows that both _primary_ and _ultimate_ principles have the same nature and are alike acquired by the exercise of the inductive faculty." "Those who acquiesce in the preceding observations will feel a regret to find _Induction_ classed among defective or informal Syllogisms. It is in fact prior in its order to Syllogism; nor can syllogistic reasoning he carried on to any extent without previous Induction" (p. 184).]

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.

[Footnote 66: Analyt. Prior. II. xxiii. p. 68, b. 35: [Greek: phu/sei me\n ou)=n pro/teros kai\ gnôrimô/teros o( dia\ tou= me/sou sullogismo/s, ê(mi=n d' e)narge/steros o( dia\ tê=s e)pagôgê=s.]]

[Footnote 67: Analyt. Post. I. ii. p. 72, a. 2, b. 29; Ethic. Nik. VI. iii**. p. 1139, b. 28: [Greek: ê( me\n dê\ e)pagôgê\ a)rchê/ e)sti kai\ tou= katho/lou=, o( de\ sullogismo\s e)k tô=n katho/lou. ei)si\n a)/ra a)rchai\ e)x ô(=n o( sullogismo/s, ô(=n ou)k e)/sti sullogismo/s; e)pagôgê\ a)/ra.] Compare Topica, I. xii. p. 105, a. 11; VI. iv. pp. 141, 142**; Physica, I. i. p. 184, a. 16; Metaphysic. E. iv. p. 1029, b**. 4-12. Compare also Trendelenburg's explanation of this doctrine, Erläuterungen zu den Elementen der Aristotelischen Logik, sects. 18, 19, 20, p. 33, seq.]

_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.

[Footnote 68: Aristot. Topica, I. xii. p. 105, a. 13-19: [Greek: e)pagôgê\ de\ ê( a)po\ tô=n kath' e(/kaston e)pi\ ta\ katho/lou e)/phodos; oi(=on ei) e)/sti kubernê/tês o( e)pista/menos kra/tistos kai\ ê(ni/ochos, kai\ o(/lôs e)sti\n o( e)pista/menos peri\ e(/kaston a)/ristos. e)/sti d' ê( me\n e)pagôgê\ pithanô/teron kai\ saphe/steron kai\ kata\ tê\n ai)/sthêsin gnôrimô/teron, _kai\ toi=s polloi=s koino/n_; o( de\ sullogismo\s biastikô/teron kai\ pro\s tou\s a)ntilogikou\s e)nerge/steron.] Also the same treatise. VI. iv. p. 141, b. 17.

The inductive interrogations of Sokrates relating to matters of common life, and the way in which they convinced ordinary hearers, are strikingly illustrated in the Memorabilia of Xenophon, especially IV. vi.: [Greek: polu\ ma/lista ô(=n e)gô\ oi)=da, o(/te le/goi, tou\s a)kou/ontas o(mologou=ntas parei=chen] (15). The same can hardly be said of the Platonic dialogues.]

[Footnote 69: Bacon, Novum Organ. I. Aphor. 13:--"Syllogismus assensum constringit, non res."]

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 ([Greek: e)mpeiri/a]), 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.

[Footnote 70: Heyder (in his learned treatise, Darstellung der Aristotelischen und Hegelschen Dialektik, p. 226), after having considered the unsatisfactory process whereby Aristotle attempts to resolve Induction into a variety of Syllogism, concludes by a remark which I think just:--"Aus alle dem erhellt zur Genüge, dass sich Aristoteles bei dem Versuch die Induction auf eine Schlussform zurückzuführen, selbst sich nicht recht befriedigt fühlte, und derselbe wohl nur aus seinem durchgängigen Bestreben zu erklären ist, alles wissenschaftliche Verfahren in die Form des Schlusses zu bringen; dass dagegen, seiner eigentlichen Meinung und der strengen Consequenz seiner Lehre zu Folge, die Induction zum syllogistischen und beweisenden Verfahren einen in dem Begriff der beiden Verfahrungsweisen liegenden Gegensatz bildete, was sich ihm dann auch auf das Verhältniss der Induction zur Begriffsbestimmung ausdehnen musste."]

[Footnote 71: Aristot. Analyt. Prior. II. xxiii. p. 68, b. 12; xxvi. p. 69, a. 17. Analyt. Post. II. xix. p. 99, b. 30, seq**.; xiii. p. 97, b. 7. Topica, VIII. i. p. 155, b. 35; p. 156, b. 10; p. 157, a. 14-23; p. 160, a. 36. Metaphys. A. i. p. 980, b. 25-p. 981, a. 30. This first chapter of the Metaphysica is one of the most remarkable passages of Aristotle, respecting the analytical philosophy of mind.]

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 Aristotle[72] 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 indulgence[73] 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]

[Footnote 72: See his Discussions on Philosophy, p. 139, seq.; Lectures on Logic, vol. i. p. 27.]

[Footnote 73: See the remarkable paragraph at the close of the Sophistici Elenchi, already quoted (supra, p. 140, note).]

[Footnote 74: Mr. John Stuart Mill says (Bk. II. ch. i. sect. 3): **"Induction is inferring a proposition from premisses _less general_ than itself, and Ratiocination is inferring a proposition from premisses _equally or more general_." Again in another passage: "We have found that all Inference, consequently all Proof, and all discovery of truths not self-evident, consists of inductions, and the interpretation of inductions; that all our knowledge, not intuitive, comes to us exclusively from that source. What Induction is, therefore, and what conditions render it legitimate, cannot but be deemed the main question of logic--the question which includes all others. It is however one which professed writers on logic have almost entirely passed over. The generalities of the subject, indeed, have not been altogether neglected by metaphysicians; but, for want of sufficient acquaintance with the processes by which science has actually succeeded in establishing general truths, their analysis of the inductive operation, even when unexceptionable as to correctness, has not been specific enough to be made the foundation of practical rules, which might be for Induction itself what the rules of the Syllogism are for interpretation of Induction" (Bk. III. ch. i. s. 1. p. 313.)--"The business of Inductive Logic is to provide rules and models (such as the Syllogism and its rules are for ratiocination) to which if inductive arguments conform, those arguments are conclusive, and not otherwise. This is what the Four Methods profess to be, and what I believe they are universally considered to be by experimental philosophers, who had practised all of them long before any one sought to reduce the practice to theory" (Bk. III. ch. ix. s. 5, p. 471, 5th ed.)--See also the same point of view more copiously set forth, in Mr. Mill's later work, 'Examination of Sir W. Hamilton's Philosophy' (ch. xx. pp. 454-462, 3rd ed.): "It is only as a means to material truth that the formal (or to speak more clearly, the conditional) validity of an operation of thought is of any value; and even that value is only negative: we have not made the smallest positive advance towards right thinking, by merely keeping ourselves consistent in what is perhaps systematic error. This by no means implies that Formal Logic, even in its narrowest sense, is not of very great, though purely negative value."--"Not only however is it indispensable that the larger Logic, which embraces all the general conditions of the ascertainment of truth, should be studied in addition to the smaller Logic, which only concerns itself with the conditions of consistency; but the smaller Logic ought to be (at least, finally) studied as part of the greater--as a portion of the means to the same end; and its relation to the other parts--to the other means--should be distinctly displayed."]

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]

[Footnote 75: Analyt. Prior. II. xxv. p. 69, a. 20-36.]

[Footnote 76: Ibid. II. xxvi. p. 69, a. 37-b. 37.

In objecting to A _universally_, you take a term comprehending the original subject; in objecting _particularly_, a term comprehended by it. Of the new term in each case you deny the original predicate, and have thus, as a major premiss, E. For a minor premiss, you affirm, in the first case, the new term as predicate of the original subject (less comprehensive); in the second case, the original subject (more comprehensive) as predicate of the new term. This gives you, in the first case, a conclusion in _Celarent_ (Fig. I.), and, in the second, a conclusion in _Felapton_ (Fig. III.); opposed, the one universally or contrarily, the other particularly or contradictorily, to the original proposition.]

The Enthymeme is a syllogism from Probabilities or Signs;[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_ ([Greek: tekmê/rion].)[78]

[Footnote 77: Ibid. II. xxvii. p. 70, a. 10: [Greek: e)nthu/mêma me\n ou)=n e)sti\ sullogismo\s e)x ei)ko/tôn ê)\ sêmei/ôn; lamba/netai de\ to\ sêmei=on trichô=s, o(sachô=s kai\ to\ me/son e)n toi=s schê/masi.]]

[Footnote 78: Analyt. Prior. II. xxvii. p. 70, a. 31-b. 6.

Aristotle throws in the remark (a. 24), that, when one premiss only of the Enthymeme is enunciated, it is a Sign; when the other is added, it becomes a Syllogism. In the examples given to illustrate the description of the Enthymeme, that which belongs to the First figure has its three terms and two propositions specified like a complete and regular Syllogism; but when we come to the Third and Second figures, Aristotle gives two alternate ways of stating each: one way in full, with both premisses enunciated, constituting a normal, though invalid, Syllogism; the other way, with only one of the premisses enunciated, the other being suppressed as well-known and familiar.

Among logicians posterior to Aristotle, the definition given of the Enthymeme, and supposed to be derived from Aristotle was, that it was a Syllogism with one of the premisses suppressed--[Greek: monolê/mmatos]. Sir W. Hamilton has impugned this doctrine, and has declared the definition to be both absurd in itself, and not countenanced by Aristotle. (Lectures on Logic, Vol. I. Lect. xx. p. 386, seq.) I think Hamilton is mistaken on this point. (See Mr. Cope's Introd. to Arist. Rhetoric, p. 103, seq.) Even in the present chapter Aristotle distinctly alludes to the monolemmatic enunciation of the Enthymeme as one mode of distinguishing it from a full Syllogism; and in the Rhetorica he brings out this characteristic still more forcibly. The distinction is one which belongs to Rhetoric more than to Logic; the rhetor, in enunciating his premisses, must be careful not to weary his auditors; he must glance at or omit reasons that are familiar to them; logical fulness and accuracy would be inconsistent with his purpose. The writers subsequent to Aristotle, who think much of the rhetorical and little of the logical point of view, bring out the distinction yet more forcibly. But the rhetorical mode of stating premisses is often not so much an omission either of major or minor, as a confused blending or packing up of both into one.]

Aristotle concludes his Analytica Priora by applying this doctrine of Signs to determine the limits within which 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]

[Footnote 79: Analyt. Prior. II. xxvii. p. 70, b. 7-16: [Greek: ei)/ tis di/dôsin a(/ma metaba/llein to\ sô=ma kai\ tê\n psuchê/n, o(/sa phusika/ e)sti pathê/mata;--sumpa/schein ga\r a)llê/lois u(pokei=tai.] See the Aristotelian treatise entitled [Greek: Phusiognômonika/], pp. 808-809, Bekk.]

[Footnote 80: Ibid. II. xxvii. p. 70, b. 22. About the characteristics of the lion see Aristot. Physiognom. p. 809, b. 14-36: [Greek: ta\ peri\ tê\n psuchê\n dotiko\n kai\ e)leu/theron, megalo/psuchon kai\ philo/nikon, kai\ prau+\ kai\ di/kaion kai\ philo/storgon pro\s a(\ a)\n o(milê/sê|.]]

[Footnote 81: Ibid. II. xxvii. p. 70, b. 31-36.]

Here the treatise ends; but the reader will remember that, in describing the canons laid down by Aristotle for the Syllogism with its three Figures and the Modes contained therein, I confined myself to the simple Assertory syllogism, postponing for the moment the long expositions added by him about Modal syllogisms, involving the Possible and the Necessary. What is proper to be said about this complicated and useless portion of the Analytica Priora, may well come in here; for, in truth, the doctrines just laid down about Probabilities, Signs, and Proofs, bring us back to the Modals under a different set of phrases. The Possible or Problematical is that, of the occurrence or reality of which we doubt, neither believing nor disbelieving it, not being prepared to assert either that it is, or that it is not; _that which may be or may not be_. It is our manner of speaking, when we have only signs or probabilities to guide us, and not certain proofs. The feeling of doubt is, as a psychological phenomenon, essentially distinct from the feeling of belief which, in its objective aspect, correlates with certainty or matter of fact; as well as from the feeling of disbelief, the correlate of which can only be described negatively. Every man knows these feelings by his own mental experience. But in describing the feeling of doubt, as to its matter or in its objective aspect, we must take care to use phrases which declare plainly both sides of its disjunctive or alternative character. The Possible is, _That which either may be or may not be_. 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]

[Footnote 82: Aristot. De Interpret. xiii. p. 22. Analyt. Prior. I. xiii. p. 32, a. 21, 29, 36, xiv. p. 33, b. 22; xix. p. 38, a. 35.]

The Possible or Problematical, however, in this latter complete sense--_What may or may not be_--exhibits various modifications or gradations. 1. The chances on either side may be conceived as perfectly equal, so that there is no probability, and we have no more reason for expecting one side of the alternative than the other; the sequence or conjunction is indeterminate. Aristotle construes this indeterminateness in many cases (not 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]

[Footnote 83: Analyt. Prior. I. xiii. p. 32, b. 5-19. [Greek: to\ d' a)o/riston tô=| mêde\n ma=llon ou(/tôs ê)\ e)kei/nôs]. Compare Metaphys. K. p. 1064, b. 32.]

Now, within the range of these limits lie what Aristotle describes as Signs and Probabilities; in fact, all the marks which we shall presently come to as distinguishing 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 Priora[84]), 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]

[Footnote 84: Analyt. Prior. II. xxvii. p. 70, a. 2-38. Compare what is said here about [Greek: ei)ko/s, sêmei=on, tekmê/rion], with the first chapter of the Topica, and the dialectic syllogism as there described: [Greek: o( e)x e)ndo/xôn sullogizo/menos].]

[Footnote 85: Ibid. I. viii.-xxii. p. 29, b. 29-p. 40, b. 16.]

What he calls the Necessary might indeed, from the point of view now reached, cease to be recognized as a separate mode at all. The Certain and the Problematical are real modes of the Proposition; objective correlates to the subjective phases called Belief and Doubt. But no proposition can be more than certain: the 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.