IV. DE INTERPRETATIONE

In the preceding chapter I enumerated and discussed what Aristotle calls the Categories. We shall now proceed to the work which stands second in the aggregate called the Organon--the treatise De Interpretatione.

We have already seen that the Aristotelian Ontology distinguishes one group of varieties of Ens (or different meanings of the term Ens) as corresponding to the diversity of the ten Categories; while recognizing also another variety of Ens as Truth, with its antithesis Non-Ens as Falsehood.[1] The former group was dealt with in the preceding chapter; the latter will form the subject of the present chapter. In both, indeed, Ontology is looked at as implicated with Logic; that is, Ens is considered as distributed under significant names, fit to be coupled in propositions. This is the common basis both of the Categoriæ and of the treatise De Interpretatione. The whole classification of the Categories rests on the assumption of the proposition with its constituent parts, and on the different relation borne by each of the nine genera of predicates towards their common Subject. But in the Categoriæ no account was taken of the distinction between truth and falsehood, in the application of these predicates to the Subject. If we say of Sokrates, that he is fair, pug-nosed, brave, wise, &c., we shall predicate truly; if we say that he is black, high-nosed, cowardly, stupid, &c., we shall predicate falsely; but in each case our predicates will belong to the same Category--that of Quale. Whether we describe him as he now is, standing, talking, in the market-place at Athens; or whether we describe him as he is not, sitting down, singing, in Egypt--in both speeches, our predicates rank under the same Categories, Jacere, Agere, Ubi. No account is taken in the Categoriæ of the distinction between true and false application of predicates; we are only informed under what number of general heads all our predicates must be included, whether our propositions be true or false in each particular case.

[Footnote 1: See above in the preceding chapter, p. 60.]

But this distinction between true and false, which remained unnoticed in the Categoriæ, comes into the foreground in the treatise De Interpretatione. The Proposition, or enunciative speech,[2] is distinguished from other varieties of speech (interrogative, precative, imperative) by its communicating what is true or what is false. It is defined to be a complex significant speech, composed of two terms at least, each in itself significant, yet neither of them, separately taken, communicating truth or falsehood. The terms constituting the Proposition are declared to be a Noun in the nominative case, as Subject, and a Verb, as Predicate; this latter essentially connoting time, in order that the synthesis of the two may become the enunciation of a fact or quasi-fact, susceptible of being believed or disbelieved. All this mode of analysing a proposition, different from the analysis thereof given or implied in the Categoriæ, is conducted with a view to bring out prominently its function of imparting true or false information. The treatise called the Categoriæ is a theory of significant names subjicible and predicable, fit to serve as elements of propositions, but not yet looked at as put together into actual propositions; while in the treatise De Interpretatione they are assumed to be put together, and a theory is given of Propositions thus completed.

[Footnote 2: Aristot. De Interpret. p. 17, a. 1: [Greek: lo/gos a)pophantiko/s].]

Words spoken are marks significant of mental impressions associated with them both by speaker and hearer; words written are symbols of those thus uttered. Both speech and writing differ in different nations, having no natural connection with the things signified. But these last, the affections or modifications of the mind, and the facts or objects of which they are representations or likenesses, are the same to all. Words are marks primarily and directly of the first, secondarily and indirectly of the second.[3] Aristotle thus recognizes these two aspects--first, the subjective, next the objective, as belonging, both of them conjointly, to significant language, yet as logically distinguishable; the former looking to the proximate correlatum, the latter to the ultimate.

[Footnote 3: Ibid. p. 16, a. 3, seq. [Greek: ô(\n me/ntoi tau=ta sêmei=a prô/tôs, tau)ta\ pa=si pathê/mata tê=s psuchê=s, kai\ ô(=n tau=ta o(moiô/mata, pra/gmata ê)/dê tau)ta/.]]

For this doctrine, that the mental affections of mankind, and the things or facts which they represent, are the same everywhere, though the marks whereby they are signified differ, Aristotle refers us to his treatise De Animâ, to which he says that it properly belongs.[4] He thus recognizes the legitimate dependence of Logic on Psychology or Mental Philosophy.

[Footnote 4: Aristot. De Interpret. p. 16, a. 8: [Greek: peri\ me\n ou)=n tau/tôn ei)/rêtai e)n toi=s peri\ psuchê=s; a)/llês ga\r pragmatei/as.] It was upon this reference, mainly, that Andronikus the Rhodian rested his opinion, that the treatise De Interpretatione was not the work of Aristotle. Andronikus contended that there was nothing in the De Animâ to justify the reference. But Ammonius in his Scholia (p. 97, Brand.) makes a sufficient reply to the objection of Andronikus. The third book De Animâ (pp. 430, 431) lays down the doctrine here alluded to. Compare Torstrick's Commentary, p. 210.]

That which is signified by words (either single or in combination) is some variety of these mental affections or of the facts which they represent. But the signification of a single Term is distinguished, in an important point, from the signification of that conjunction of terms which we call a Proposition. A noun, or a verb, belonging to the aggregate called a language, is associated with one and the same phantasm[5] or notion, without any conscious act of conjunction or disjunction, in the minds of speakers and hearers: when pronounced, it arrests for a certain time the flow of associated ideas, and determines the mind to dwell upon that particular group which is called its meaning.[6] But neither the noun nor the verb, singly taken, does more than this; neither one of them affirms, or denies, or communicates any information true or false. For this last purpose, we must conjoin the two together in a certain way, and make a Proposition. The signification of the Proposition is thus specifically distinct from that of either of its two component elements. It communicates what purports to be matter of fact, which may be either true or false; in other words, it implies in the speaker, and raises in the hearer, the state of belief or disbelief, which does not attach either to the noun or to the verb separately. Herein the Proposition is discriminated from other significant arrangements of words (precative, interrogative, which convey no truth or falsehood), as well as from its own component parts. Each of these parts, noun and verb, has a significance of its own; but these are the ultimate elements of speech, for the parts of the noun or of the verb have no significance at all. The Verb is distinguished from the Noun by connoting time, and also by always serving as predicate to some noun as subject.[7]

[Footnote 5: Ibid. p. 16, a. 13: [Greek: ta\ me\n ou)=n o)no/mata au)ta\ kai\ ta\ r(ê/mata e)/oike tô=| a)/neu diaire/seôs kai\ sunthe/seôs noê/mati, oi(=on to\ a)/nthrôpos kai\ to\ leuko/n, o(/tan mê\ proste/thê| ti; ou)/te ga\r pseu=dos ou)/te a)lêthe/s pô.]]

[Footnote 6: Ibid. p. 16, b. 19: [Greek: au)ta\ me\n kath' e(auta\ lego/mena ta\ r(ê/mata o)no/mata/ e)sti kai\ sêmai/nei ti (i(/stêsi ga\r o( le/gôn tê\n dia/noian, kai\ o( a)kou/sas ê)re/mêsen) a)ll' ei) e)sti\n ê)\ mê/, ou)/pô sêmai/nei], &c.

Compare Analyt. Poster. II. xix. pp. 99, 100, where the same doctrine occurs: the movement of association is stopped, and the mind is determined to dwell upon a certain idea; one among an aggregate of runaways being arrested in flight, another halts also, and so the rest in succession, until at length the Universal, or the sum total, is detained, or "stands still" as an object of attention. Also Aristot. Problem. p. 956, b. 39.]

[Footnote 7: Aristot. De Interpr. p. 16, b. 2, seq.]

Aristotle intimates his opinion, distinctly and even repeatedly, upon the main question debated by Plato in the Kratylus. He lays it down that all significant speech is significant by convention only, and not by nature or as a natural instrument.[8] He tells us also that, in this treatise, he does not mean to treat of all significant speech, but only of that variety which is known as enunciative. This last, as declaring truth or falsehood, is the only part belonging to Logic as he conceives it; other modes of speech, the precative, imperative, interrogative, &c., belong more naturally to Rhetoric or Poetic.[9] Enunciative speech may be either simple or complex; it may be one enunciation, declaring one predicate (either in one word or in several words) of one subject; or it may comprise several such.[10] The conjunction of the predicate with the subject constitutes the variety of proposition called Affirmation; the disjunction of the same two is Negation or Denial.[11] But such conjunction or disjunction, operated by the cogitative act, between two mental states, takes place under the condition that, wherever conjunction may be enunciated, there also disjunction may be enunciated, and vice versâ. Whatever may be affirmed, it is possible also to deny; whatever may be denied, it is possible also to affirm.[12]

[Footnote 8: Ibid. p. 16, a. 26; p. 17, a. 2.]

[Footnote 9: Ibid. p. 17, a. 6: [Greek: o( de\ a)pophantiko\s tê=s nu=n theôri/as]. See the **Scholion of Ammonius, pp. 95, 96, 108, a. 27. In the last passage, Ammonius refers to a passage in one of the lost works of Theophrastus, wherein that philosopher distinguished [Greek: to\n a)pophantiko\n lo/gon] from the other varieties of [Greek: lo/gos], by the difference of [Greek: sche/sis]: the [Greek: a)pophantiko\s lo/gos] was [Greek: pro\s ta\ pra/gmata], or objective; the others were [Greek: pro\s tou\s a)kroôme/nous], i.e. varying with the different varieties of hearers, or subjective.]

[Footnote 10: Ibid. p. 17, a. 25.]

[Footnote 11: Ibid. p. 17, a. 25.]

[Footnote 12: Ibid. p. 17, a. 30: [Greek: a(/pan a)\n e)nde/choito kai\ o(\ kate/phêse/ tis a)pophê=sai, kai\ o(\ a)pe/phêse/ tis kataphê=sai.]]

To every affirmative proposition there is thus opposed a contradictory negative proposition; to every negative a contradictory affirmative. This pair of contradictory opposites may be called an Antiphasis; always assuming that the predicate and subject of the two shall be really the same, without equivocation of terms--a proviso necessary to guard against troublesome puzzles started by Sophists.[13] And we must also distinguish these propositions opposite as Contradictories, from propositions opposite as Contraries. For this, it has to be observed that there is a distinction among things ([Greek: pra/gmata]) as universal or singular, according as they are, in their nature, predicable of a number or not: homo is an example of the first, and Kallias is an example of the second. When, now, we affirm a predicate universally, we must attach the mark of universality to the subject and not to the predicate; we must say, Every man is white, No man is white. We cannot attach the mark of universality to the predicate, and say, Every man is every animal; this would be untrue.[14] An affirmation, then, is contradictorily opposed to a negation, when one indicates that the subject is universally taken, and the other, that the subject is taken not universally, e.g. Omnis homo est albus, Non omnis homo est albus; Nullus homo est albus, Est aliquis homo albus. The opposition is contrary, when the affirmation is universal, and the negation is also universal, i.e., when the subject is marked as universally taken in each: for example, Omnis homo est albus, Nullus homo est albus. Of these contrary opposites, both cannot be true, but both may be false. Contradictory opposites, on the other hand, while they cannot both be true, cannot both be false; one must be false and the other true. This holds also where the subject is a singular term, as Sokrates.[15] If, however, an universal term appear as subject in the proposition indefinitely, that is, without any mark of universality whatever, e.g., Est albus homo_, Non est albus homo, then the affirmative and negative are not necessarily either contrary or contradictory, though they may be so sometimes: there is no opposition, properly speaking, between them; both may alike be true. This last observation (says Aristotle) will seem strange, because many persons suppose that Non est homo albus is equivalent to Nullus homo est albus; but the meaning of the two is not the same, nor does the truth of the latter follow from that of the former,[16] since homo in the former may be construed as not universally taken.

[Footnote 13: Ibid. p. 17, a. 33: [Greek: kai\ e)/stô a)nti/phasis tou=to, kata/phasis kai\ a)po/phasis ai( a)ntikei/menai.]

It seems (as Ammonius observes, Schol. p. 112, a. 33) that [Greek: a)nti/phasis] in this sense was a technical term, introduced by Aristotle.]

[Footnote 14: Aristot. De Interpr. p. 17, a. 37-b. 14: [Greek: e)pei\ d' e)sti\ ta\ me\n katho/lou tô=n pragma/tôn, ta\ de\ kath' e(/kaston (le/gô de\ katho/lou me\n o(\ e)pi\ pleio/nôn pe/phuke katêgorei=sthai, kath' e(/kaston de\ o(\ mê\, oi(=on a)/nthrôpos me\n tô=n katho/lou, Kalli/as de\ tô=n kath' e(/kaston);] &c. Ammonius (in Schol. p. 113, a. 38) says that what is predicated, either of many subjects or of one, must be [Greek: mi/a phu/sis].

The warning against quantifying the predicate appears in this logical treatise of Aristotle, and is repeated in the Analytica Priora, I. xxvii. p. 43, b. 17. Here we have: [Greek: ou)demi/a kata/phasis a)lêthê\s e)/stai, e)n ê(=| tou= katêgoroume/nou katho/lou to\ katho/lou katêgorei=tai, oi(=on e)/sti pa=s a)/nthrôpos pa=n zô=|on] (b. 14).]

[Footnote 15: Ibid. b. 16-29.]

[Footnote 16: Ibid. p. 17, b. 29-37. Mr. John Stuart Mill (System of Logic, Bk. I. ch. iv. s. 4) cites and approves Dr. Whately's observation, that the recognition of a class of Propositions called indefinite "is a solecism, of the same nature as that committed by grammarians when in their list of genders they enumerate the doubtful gender. The speaker must mean to assert the proposition either as an universal or as a particular proposition, though he has failed to declare which."

But Aristotle would not have admitted Dr. Whately's doctrine, declaring what the speaker "must mean." Aristotle fears that his class, indefinite, will appear impertinent, because many speakers are not conscious of any distinction or transition between the particular and the general. The looseness of ordinary speech and thought, which Logic is intended to bring to view and to guard against, was more present to his mind than to that of Dr. Whately: moreover, the forms of Greek speech favoured the ambiguity.

Aristotle's observation illustrates the deficiencies of common speaking, as to clearness and limitation of meaning, at the time when he began to theorize on propositions.

I think that Whately's assumption--"the speaker must mean"--is analogous to the assumption on which Sir W. Hamilton founds his proposal for explicit quantification of the predicate, viz., that the speaker must, implicitly or mentally, quantify the predicate; and that his speech ought to be such as to make such quantification explicit. Mr. Mill has shewn elsewhere that this assumption of Sir. W. Hamilton's is incorrect.]

It thus appears that there is always one negation corresponding to one and the same affirmation; making up together the Antiphasis, or pair of contradictory opposites, quite distinct from contrary opposites. By one affirmation we mean, that in which there is one predicate only, and one subject only, whether taken universally or not universally:--

E.g. Omnis homo est albus ... ... Non omnis homo est albus. Est homo albus ... ... ... Non est homo albus. Nullus homo est albus ... ... Aliquis homo est albus.

But this will only hold on the assumption that album signifies one and the same thing. If there be one name signifying two things not capable of being generalized into one nature, or not coming under the same definition, then the affirmation is no longer one.[17] Thus if any one applies the term himation to signify both horse and man, then the proposition, Est himation album, is not one affirmation, but two; it is either equivalent to Est homo albus and Est equus albus--or it means nothing at all; for this or that individual man is not a horse. Accordingly, in this case also, as well as in that mentioned above, it is not indispensable that one of the two propositions constituting the Antiphasis should be true and the other false.[18]

[Footnote 17: Aristot. De Interpr. p. 18, a. 13, seq.: [Greek: mi/a de/ e)sti kata/phasis kai\ a)po/phasis ê( e(\n kath' e(no\s sêmai/nousa, ê)\ katho/lou o)/ntos katho/lou ê)\ mê\ o(moi/ôs, oi(=on pa=s a)/nthrôpos leuko/s e)stin . . . ei) to\ leuko\n e(\n sêmai/nei. ei) de\ duoi=n e(\n o)/noma kei=tai, e)x ô(=n mê/ e)stin e(/n, ou) mi/a kata/phasis], &c., and the Scholion of Ammonius, p. 116, b. 6, seq.]

[Footnote 18: Aristot. De Interpr. p. 18, a. 26. The example which Aristotle here gives is one of a subject designated by an equivocal name; when he had begun with the predicate. It would have been more pertinent if he had said at first, [Greek: ei) o( a)/nthrôpos e(\n sêmai/nei].]

With these exceptions Aristotle lays it down, that, in every Antiphasis, one proposition must be true and the other must be false. But (he goes on to say) this is only true in regard to matters past or present; it is not true in regard to events particular and future. To admit it in regard to these latter, would be to affirm that the sequences of events are all necessary, and none of them casual or contingent; whereas we know, by our own personal experience, that many sequences depend upon our deliberation and volition, and are therefore not necessary. If all future sequences are necessary, deliberation on our part must be useless. We must therefore (he continues) recognize one class of sequences which are not uniform--not predetermined by antecedents; events which may happen, but which also may not happen, for they will not happen. Thus, my coat may be cut into two halves, but it never will be so cut; it will wear out without any such bisection occurring.[19]

[Footnote 19: Aristot. De Interpr. p. 18, a. 28-p. 19, b. 4.]

If you affirm the reality of a fact past or present, your affirmation is of necessity determinately true, or it is determinately false, i.e. the contradictory negation is determinately true. But if you affirm the reality of a fact to come, then your affirmation is not by necessity determinately true, nor is the contradictory negation determinately true. Neither the one nor the other separately is true: nothing is true except the disjunctive antithesis as a whole, including both. If you say, To-morrow there will either be a sea-fight, or there will not be a sea-fight, this disjunctive or indeterminate proposition, taken as a whole, will be true. Yet neither of its constituent parts will be determinately true; neither the proposition, To-morrow there will be a sea-fight, nor the proposition, To-morrow there will not be a sea-fight. But if you speak with regard to past or present--if you say, Yesterday either there was a sea-fight or there was not a sea-fight--then not only will the disjunctive as a whole be true, but also one or other of its parts will be determinately true.[20]

[Footnote 20: Ibid. p. 18, b. 29. Ammonius (Scholia ad De Interpret. p. 119, bb. 18, 28, seq.) expresses Aristotle's meaning in terms more distinct than Aristotle himself: [Greek: mê\ pa/ntôs e)/chein to\ e(/teron mo/rion tê=s a)ntipha/seôs a)phôrisme/nôs a)lêtheu=on], &c. (b. 43).]

This remarkable logical distinction is founded on Aristotle's ontological or physical doctrines respecting the sequence and conjunction of events. He held (as we shall see more fully in the Physica and other treatises) that sequences throughout the Kosmos were to a certain extent regular, to a certain extent irregular. The exterior sphere of the Kosmos (the Aplan=es) with the countless number of fixed stars fastened into it, was a type of regularity and uniformity; eternal and ever moving in the same circular orbit, by necessity of its own nature, and without any potentiality of doing otherwise. But the earth and the elemental bodies, organized and unorganized, below the lunar sphere and in the interior of the Kosmos, were of inferior perfection and of very different nature. They were indeed in part governed and pervaded by the movement and influence of the celestial substance within which they were comprehended, and from which they borrowed their Form or constituent essence; but they held this Form implicated with Matter, i.e. the principle of potentiality, change, irregularity, generation, and destruction, &c. There are thus in these sublunary bodies both constant tendencies and variable tendencies. The constant Aristotle calls 'Nature;' which always aspires to Good, or to perpetual renovation of Forms as perfect as may be, though impeded in this work by adverse influences, and therefore never producing any thing but individuals comparatively defective and sure to perish. The variable he calls 'Spontaneity' and 'Chance,' forming an independent agency inseparably accompanying Nature--always modifying, distorting, frustrating, the full purposes of Nature. Moreover, the different natural agencies often interfere with each other, while the irregular tendency interferes with them all. So far as Nature acts, in each of her distinct agencies, the phenomena before us are regular and predictable; all that is uniform, and all that (without being quite uniform) recurs usually or frequently, is her work. But, besides and along with Nature, there is the agency of Chance and Spontaneity, which is essentially irregular and unpredictable. Under this agency there are possibilities both for and against; either of two alternative events may happen.

It is with a view to this doctrine about the variable kosmical agencies or potentialities that Aristotle lays down the logical doctrine now before us, distinguishing propositions affirming particular facts past or present, from propositions affirming particular facts future. In both cases alike, the disjunctive antithesis, as a whole, is necessarily true. Either there was a sea-fight yesterday, or there was not a sea-fight yesterday: Either there will be a sea-fight to-morrow, or there will not be a sea-fight to-morrow--both these disjunctives alike are necessarily true. There is, however, a difference between the one disjunctive couple and the other, when we take the affirmation separately or the negation separately. If we say, There will be a sea-fight to-morrow, that proposition is not necessarily true nor is it necessarily false; to say that it is either the one or the other (Aristotle argues) would imply that every thing in nature happened by necessary agency--that the casual, the potential, the may be or may not be, is stopped out and foreclosed. But this last is really the case, in regard to a past fact. There was a sea-fight yesterday, is a proposition either necessarily true or necessarily false. Here the antecedent agencies have already spent themselves, blended, and become realized in one or other of the two alternative determinate results. There is no potentiality any longer open; all the antecedent potentiality has been foreclosed. The proposition therefore is either necessarily true or necessarily false; though perhaps we may not know whether it is the one or the other.

In defending his position regarding this question, Aristotle denies (what he represents his opponents as maintaining) that all events happen by necessity. He points to the notorious fact that we deliberate and take counsel habitually, and that the event is frequently modified, according as we adopt one mode of conduct or another; which could not be (he contends), if the event could be declared beforehand by a proposition necessarily or determinately true. What Aristotle means by necessity, however, is at bottom nothing else than constant sequence or conjunction, conceived by him as necessary, because the fixed ends which Nature is aiming at can only be attained by certain fixed means. To this he opposes Spontaneity and Chance, disturbing forces essentially inconstant and irregular; admitting, indeed, of being recorded when they have produced effects in the past, yet defying all power of prediction as to those effects which they will produce in the future. Hence arises the radical distinction that he draws in Logic, between the truth of propositions relating to the past (or present) and to the future.

But this logical distinction cannot be sustained, because his metaphysical doctrine (on which it is founded) respecting the essentially irregular or casual, is not defensible. His opponents would refuse to grant that there is any agency essentially or in itself irregular, casual, and unpredictable.[21] The aggregate of Nature consists of a variety of sequences, each of them constant and regular, though intermixed, co-operating, and conflicting with each other, in such manner that the resulting effects are difficult to refer to their respective causes, and are not to be calculated beforehand except by the highest scientific efforts; often, not by any scientific efforts. We must dismiss the hypothesis of Aristotle, assuming agencies essentially irregular and unpredictable, either as to the past or as to the future. The past has been brought about by agencies all regular, however multifarious and conflicting, and the future will be brought about by the like: there is no such distinction of principle as that which Aristotle lays down between propositions respecting the past and propositions respecting the future.

[Footnote 21: The Stoics were opposed to Aristotle on this point. They recognized no logical difference in the character of the Antiphasis, whether applied to past and present, or to future. Nikostratus defended the thesis of Aristotle against them. See the Scholia of Simplikius on the Categoriæ, p. 87, b. 30-p. 88, a. 24. [Greek: ai( ga\r ei)s to\n me/llonta chro/non e)gklino/menai prota/seis ou)/te a)lêthei=s ei)si\n ou)/te pseudei=s dia\ tê\n tou= e)ndechome/nou phu/sin.]

The remarks of Hobbes, upon the question here discussed by Aristotle, well deserve to be transcribed (De Corpore, part II. ch. X. s. 5):--

"But here, perhaps, some man may ask whether those future things, which are called contingents, are necessary. I say, therefore, that generally all contingents have their necessary causes, but are called contingents in respect of other events, upon which they do not depend; as the rain, which shall be to-morrow, shall be necessary, that is, from necessary causes; but we think and say, it happens by chance, because we do not yet perceive the causes thereof, though they exist now. For men commonly call that casual or contingent, whereof they do not perceive the necessary cause; and in the same manner they use to speak of things past, when not knowing whether a thing be done or no, they say, it is possible it never was done.

"Wherefore, all propositions concerning future things, contingent or not contingent--as this, It will rain to-morrow, or this, To-morrow the sun will rise--are either necessarily true, or necessarily false; but we call them contingent, because we do not yet know whether they be true or false; whereas their verity depends not upon our knowledge, but upon the foregoing of their causes. But there are some, who, though they confess this whole proposition, To-morrow it will either rain or not rain, to be true, yet they will not acknowledge the parts of it, as To-morrow it will rain, or To-morrow it will not rain, to be either of them true by itself; because they say neither this nor that is true determinately. But what is this determinately true, but true upon our knowledge, or evidently true? And therefore they say no more, but that it is not yet known whether it be true or no; but they say it more obscurely, and darken the evidence of the truth with the same words with which they endeavour to hide their own ignorance."

Compare also the fuller elucidation of the subject given by Mr. John Stuart Mill, in his System of Logic, Bk. III. ch. xvii. s. 2:--"An event occurring by chance may be better described as a coincidence from which we have no ground to infer an uniformity; the occurrence of an event in certain circumstances, without our having reason on that account to infer that it will happen again in those circumstances. This, however, when looked closely into, implies that the enumeration of the circumstances is not complete. Whatever the fact was, since it has occurred once, we may be sure that if all the circumstances were repeated, it would occur again; and not only if all, but there is some particular portion of those circumstances, on which the phenomenon is invariably consequent. With most of them, however, it is not connected in any permanent manner: its conjunction with those is said to be the effect of chance, to be merely casual. Facts casually conjoined are separately the effect of causes, and therefore of laws; but of different causes, and causes not connected by any law. It is incorrect then to say that any phenomenon is produced by chance; but we may say that two or more phenomena are conjoined by chance, that they co-exist or succeed one another only by chance."]

There is, indeed, one distinction between inferences as to the past and inferences as to the future, which may have contributed to suggest, though it will not justify, the position here laid down by Aristotle. In regard to the disjunctive--To-morrow there will be a sea-fight, or there will not be a sea-fight--nothing more trustworthy than inference or anticipation is practicable: the anticipation of a sagacious man with full knowledge is more likely to prove correct than that of a stupid man with little knowledge; yet both are alike anticipations, unverifiable at the present moment. But if we turn to the other disjunctive--Yesterday there was a sea-fight, or there was not a sea-fight--we are no longer in the same position. The two disputants, supposed to declare thus, may have been far off, and may have no other means of deciding the doubt than inference. But the inference here is not unverifiable: there exist, or may exist, witnesses or spectators of the two fleets, who can give direct attestation of the reality, and can either confirm or refute the inference, negative or affirmative, made by an absentee. Thus the proposition, Yesterday there was a sea-fight, or the other, Yesterday there was not a sea-fight, will be verifiable or determinably true. There are indeed many inferences as to the past, in regard to which no direct evidence is attainable. Still this is an accident; for such direct evidence may always be supposed or imagined as capable of being brought into court. But, in respect to the future, verification is out of the question; we are confined to the region of inference, well or ill-supported. Here, then, we have a material distinction between the past and the future. It was probably present to the mind of Aristotle, though he misconceives its real extent of operation, and makes it subservient to his still more comprehensive classification of the different contemporaneous agencies (regular and irregular) which he supposes to pervade the Kosmos.

In the treatise before us, he next proceeds to state what collocation of the negative particle constitutes the special or legitimate negation to any given affirmation, or what are the real forms of proposition, standing in contradictory opposition to certain other forms, so as to make up one Antiphasis.[22] The simplest proposition must include a noun and a verb, either definite or indefinite: non homo is a specimen of an indefinite noun--non currit, of an indefinite verb. There must be, in any one proposition, one subject and one predicate; even the indefinite noun or verb signifies, in a certain sense, one thing. Each affirmation comprises a noun, or an indefinite noun, with a verb; the special corresponding or contradictory negation (making up the Antiphasis along with the former) comprises a noun (or an indefinite noun) with an indefinite verb. The simplest proposition is--

Affirmative. Contradictory Negative.

Est homo ... ... ... ... Non est homo. Est non homo ... ... ... ... Non est non homo.

Here are only two pairs of antithetic propositions, or one quaternion. The above is an indefinite proposition (which may be either universal or not). When we universalize it, or turn it an universal proposition, we have--

Affirmative. Contradictory Negative.

Est omnis homo ... ... ... Non est omnis homo. Est omnis non homo ... ... Non est omnis non homo.

[Footnote 22: Aristot. De Interpr. p. 19, b. 5, seq.]

The above are specimens of the smallest proposition; but when we regard larger propositions, such as those (called tertii adjacentis) where there are two terms besides est, the collocation of the negative particle becomes more complicated, and requires fuller illustration. Take, as an example, the affirmative Est justus homo, the true negation of this is, Non est justus homo. In these two propositions, homo is the subject; but we may join the negative with it, and we may consider non homo, not less than homo, as a distinct subject for predication, affirmative or negative. Farther, we may attach est and non est either to justus or to non justus as the predicate of the proposition, with either homo, or non homo, as subject. We shall thus obtain a double mode of antithesis, or two distinct quaternions, each containing two pairs of contradictory propositions. The second pair of the first quaternion will not be in the same relation as the second pair of the second quaternion, to the proposition just mentioned, viz.--(A) Est justus homo; with its negative, (B) Non est justice homo.[23]

[Footnote 23: Aristot. De Interpr. p. 19, b. 19. [Greek: o(/tan de\ to\ e)/sti tri/ton proskatêgorê=tai, ê)/dê dichô=s le/gontai ai( a)ntithe/seis; le/gô de\ oi(=on e)/sti di/kaios a)/nthrôpos; to\ e)/sti tri/ton phêmi\ sugkei=sthai o)/noma ê)\ r(ê=ma e)n tê=| katapha/sei. ô(/ste dia\ tou=to te/ttara e)/stai tau=ta, ô(=n ta\ me\n du/o pro\s tê\n kata/phasin kai\ a)po/phasin e(/xei kata\ to\ stoichou=n ô(s ai( sterê/seis, ta\ de\ du/o, ou)/. [le/gô de\ o(/ti to\ e)/stin ê)\ tô=| dikai/ô| proskei/setai ê)\ tô=| ou) dikai/ô|], ô(/ste kai\ ê( a)po/phasis. te/ttara ou)=n e)/stai. noou=men de\ to\ lego/menon e)k tô=n u(pogegramme/nôn.] In this passage the words which I have enclosed between brackets are altered by Waitz: I shall state presently what I think of his alteration. Following upon these words there ought to be, and it seems from Ammonius (Schol. p. 121, a. 20) that there once was, a scheme or table arranging the four propositions in the order and disposition which we read in the Analytica Priora, I. xlvi. p. 51, b. 37, and which I shall here follow. But no such table now appears in our text; we have only an enumeration of the four propositions, in a different order, and then a reference to the Analytica.]

First, let us assume homo as subject. We have then

(QUATERNION I.)

(A) Est justus homo ... ... ... ... (B) Non est justus homo. (D) Non est non justus homo ... ... ... (C) Est non justus homo.

Examining the relation borne by the last two among these four propositions (C and D), to the first two (A and B), the simple affirmative and negative, we see that B is the legitimate negative of A, and D that of C. We farther see that B is a consequence of C, and D a consequence of A, but not vice versâ: that is, if C is true, B must certainly be true; but we cannot infer, because B is true, that C must also be true: while, if A is true, D must also be true; but D may perhaps be true, though A be not true. In other words, the relation of D to A and of C to B, is the same as it would be if the privative term injustus were substituted in place of non justus; i.e. if the proposition C (Est injustus homo) be true, the other proposition B (Non est justus homo) must certainly be true, but the inference will not hold conversely; while if the proposition A (Est justus homo) be true, it must also be true to say D (Non est injustus homo), but not vice versâ.[24]

[Footnote 24: Referring to the words cited in the preceding note, I construe [Greek: ta\ de\ du/o, ou)/] as Boethius does (II. pp. 384-385), and not in agreement with Ammonius (Schol. p. 122, a. 26, Br.), who, however, is followed both by Julius Pacius and Waitz (p. 344). I think it impossible that these words, [Greek: ta\ de\ du/o, ou)/], can mean (as Ammonius thinks) the [Greek: kata/phasis] and [Greek: a)po/phasis] themselves, since the very point which Aristotle is affirming is the relation of these words, [Greek: pro\s tê\n kata/phasin kai\ a)po/phasin], i.e. to the affirmative and negative started from--

(A) Est justus homo ... ... ... ... (B) Non est justus homo.

As the words [Greek: ta\ me\n du/o] refer to the second contradictory pair (that is, C and D) in the first Quaternion, so the words [Greek: ta\ de\ du/o, ou)/] designate the second contradictory pair (G and H) in the second Quaternion. Though G and H are included in the second Quaternion, they are here designated by the negative relation ([Greek: ta\ de\ du/o, ou)/]) which they bear to A and B, the first contradictory pair of the first Quaternion. [Greek: dichô=s le/gontai ai( a)ntithe/seis] (line 20) is explained and illustrated by line 37--[Greek: au(=tai me\n ou)=n du/o a)nti/keintai, a)/llai de\ du/o pro\s to\ ou)k a)/nthrôpos ô(s u(pokei/meno/n ti prostethe/n]. Lastly, Aristotle expressly states that the second Quaternion will stand independently and by itself (p. 20, a. 1), having noticed it in the beginning only in relation to the first.]

Such is the result obtained when we take homo as the subject of the proposition; we get four propositions, of which the two last (C and D) stand to the two first (B and A) in the same relation as if they (C and D) were privative propositions. But if, instead of homo, we take non homo as Subject of the proposition (justus or non justus being predicates as before), we shall then obtain two other pairs of contradictory propositions; and the second pair of this new quaternion will not stand in that same relation to these same propositions B and A. We shall then find that, instead of B and A, we have a different negative and a different affirmative, as the appropriate correlates to the third and fourth propositions. The new quaternion of propositions, with non homo as subject, will stand thus--

(QUATERNION II.)

(E) Est justus non homo ... ... ... (F) Non est justus non homo. (H) Non est non justus non homo ... (G) Est non justus non homo.[25]

Here we see that propositions G and H do not stand to B and A in the same relations as C and D stand to B and A; but that they stand in that same relation to two perfectly different propositions, F and E. That is, if in place of non **justus, in propositions G and H, we substitute the privative term injustus (thus turning G into Est injustus non homo, and turning H into Non est injustus non homo), the relation of G, when thus altered, to F, and the relation of H, when thus altered, to E, will be the same as it was before. Or, in other words, if G be true, F will certainly be true, but not vice versâ; and if E be true, H will certainly be true, but not vice versâ.

[Footnote 25: Aristot. De Interpr. p. 19, b. 36. [Greek: au(=tai me\n ou)=n du/o a)nti/keintai] (the two pairs--A B and C D--of the first quaternion), [Greek: a)/llai de\ du/o pro\s to\ ou)k a)/nthrôpos ô(s u(pokei/meno/n ti prostethe/n;]

(E) [Greek: e)/sti di/kaios ou)k a)/nthrôpos] ... ... ... (F) [Greek: ou)k e)/sti di/kaios ou)k a)/nthrôpos.] (H) [Greek: ou)k e)/stin ou) di/kaios ou)k a)/nthrôpos] ... (G) [Greek: e)/stin ou) di/kaios ou)k a)/nthrôpos.]

[Greek: plei/ous de\ tou/tôn ou)k e)/sontai a)ntithe/seis. au(=tai de\ chôri\s e)kei/nôn au)tai\ kath' e(auta\s e)/sontai, ô(s o)no/mati tô=| ou)k a)/nthrôpos chrô/menai.] The second [Greek: au(=tai] alludes to this last quaternion, [Greek: e)kei/nôn] to the first. I have, as in the former case, transposed propositions three and four of this second quaternion, in order that the relation of G to F and of H to E may be more easily discerned.

There are few chapters in Aristotle more obscure and puzzling than the tenth chapter of the De Interpretatione. It was found so by Alexander, Herminus, Porphyry, Ammonius, and all the Scholiasts. Ammonius (Schol. pp. 121, 122, Br.) reports these doubts, and complains of it as a riddle almost insolvable. The difficulties remain, even after the long note of Waitz, and the literal translation of M. Barthélemy St. Hilaire.]

The propositions which we have hitherto studied have been indefinite; that is, they might be universal or not. But if we attach to them the sign of universality, and construe them as universals, all that we have said about them would still continue to be true, except that the propositions which are diametrically (or diagonally) opposed would not be both true in so many instances. Thus, let us take the first quaternion of propositions, in which est is attached to homo, and let us construe these propositions as universal. They will stand thus--

(A) Omnis est homo justus ... ... (B) Non omnis est homo justus. (D) Non omnis est homo non justus (C) Omnis est homo non justus.

In these propositions, as in the others before noticed, the same relation prevails between C and B, and between A and D; if C be true, B also is true, but not vice versâ; if A be true, D also will be true, but not vice versâ. But the propositions diagonally opposed will not be so often alike true:[26] thus, if A be true (Omnis est homo justus), C cannot be true (Omnis est homo non justus); whereas in the former quaternion of propositions (indefinite, and therefore capable of being construed as not universal) A and C might both be alike true.[27]

[Footnote 26: Aristot. De Interpret. p. 19, b. 35. [Greek: plê\n ou)ch o(moi/ôs ta\s kata\ dia/metron e)nde/chetai sunalêtheu/ein; e)nde/chetai de\ pote/.] The "diameter" or "diagonal" is to be understood with reference to the scheme or square mentioned p. 119, note, the related propositions standing at the angles, as above.]

[Footnote 27: The Scholion of Ammonius, p. 123, a. 17, Br., explains this very obscure passage: [Greek: a)ll' e)pi\ me\n tô=n a)prosdiori/stôn] (indefinite propositions, such as may be construed either as universal or as particular), [Greek: kata\ tê\n e)ndechome/nên u(/lên ta/s te katapha/seis] (of the propositions diagonally opposite), [Greek: sunalêtheu/ein a)llê/lais sumbai/nei kai\ ta\s a)popha/seis, a(/te tai=s merikai=s i)sodunamou/sas. e)pi\ de\ tô=n prosdiôrisme/nôn] (those propositions where the mark of universality is tacked to the Subject), [Greek: peri\ ô(=n nuni\ au)tô=| o( lo/gos, tê=s katho/lou katapha/seôs kai\ tê=s e)pi\ me/rous a)popha/seôs, ta\s me\n katapha/seis a)du/naton sunalêtheu=sai kath' oi(andê/pote u(/lên, ta\s me/ntoi a)popha/seis sumbai/nei sunalêtheu/ein kata\ mo/nên tê\n e)ndechome/nên;] &c.]

It is thus that Aristotle explains the distinctions of meaning in propositions, arising out of the altered collocation of the negative particle; the distinction between (1) Non est justus, (2) Est non justus, (3) Est injustus. The first of the three is the only true negative, corresponding to the affirmative Est Justus. The second is not a negative at all, but an affirmative ([Greek: e)k metathe/seôs], or by transposition, as Theophrastus afterwards called it). The third is an affirmative, but privative. Both the second and the third stand related in the same manner to the first; that is, the truth of the first is a necessary consequence either of the second or of the third, but neither of these can be certainly inferred from the first. This is explained still more clearly in the Prior Analytics; to which Aristotle here makes express reference.[28]

[Footnote 28: Aristot. De Interpr. p. 19, b. 31. [Greek: tau=ta me\n ou)=n, ô(/sper e)n toi=s A)nalutikoi=s le/getai, ou(/tô te/taktai.]

Waitz in his note suggests that instead of [Greek: te/taktai] we ought to read [Greek: teta/chthô]. But if we suppose that the formal table once existed in the text, in an order of arrangement agreeing with the Analytica, this conjectural change would be unnecessary.

Waitz has made some changes in the text of this chapter, which appear to me partly for the better, partly not for the better. Both Bekker and Bussemaker (Firmin Didot) retain the old text; but this old text was a puzzle to the ancient commentators, even anterior to Alexander of Aphrodisias. I will here give first the text of Bekker, next the changes made by Waitz: my own opinion does not wholly coincide with either. I shall cite the text from p. 19, b. 19, leaving out the portion between lines 30 and 36, which does not bear upon the matter here discussed, while it obscures the legitimate sequence of Aristotle's reasoning.

(Bekker.)--[Greek: O(/tan de\ to\ e)/sti tri/ton proskatêgorê=tai, ê)/dê dichô=s le/gontai ai( a)ntithe/seis. le/gô de\ oi(=on e)/sti di/kaios a)/nthrôpos; to\ e)/sti tri/ton phêmi\ sugkei=sthai o)/noma ê)\ r(ê=ma e)n tê=| katapha/sei. ô(/ste dia\ tou=to te/ttara e)/stai tau=ta, ô(=n ta\ me\n du/o pro\s tê\n kata/phasin kai\ a)po/phasin e(/xei kata\ to\ stoichou=n ô(s ai( sterê/seis, ta\ de\ du/o, ou)/. le/gô d' o(/ti to\ e)/stin ê)\ tô=| dikai/ô| proskei/setai ê)\ tô=| ou) dikai/ô|] (25), [Greek: ô(/ste kai\ ê( a)po/phasis. te/ttara ou)=n e)/stai.] (Here follow the first pairs of Antitheses, or the first Quaternion of propositions in the order as given)--

(A) [Greek: e)/sti di/kios a)/nthrôpos] ... ... (B) [Greek: ou)k e)/sti di/kios a)/nthrôpos.]y (C) [Greek: e)/stin ou) di/kaios a)/nthrôpos] ... (D) [Greek: ou)k e)/stin ou) di/kaios a)/nthrôpos.]

[Greek: to\ ga\r e)/stin e)ntau=tha kai\ to\ ou)k e)/sti tô=| dikai/ô| proskei/setai kai\ tô=| ou) dikai/ô|] (30).--[Greek: Au(=tai me\n ou)=n du/o a)nti/keintai, a)/llai de\ du/o pro\s to\ ou)k a)/nthrôpos ô(s u(pokei/meno/n ti] (38) [Greek: prostethe/n.] (Here follow the second pairs of Antitheses, or the second Quaternion of propositions, again in the order from which I have departed above)--

(E) [Greek: e)/sti di/kaios ou)k a)/nthrôpos] ... ... (F) [Greek: Ou)k e)/sti di/kaios ou)k a)/nthrôpos.] (G) [Greek: e)/stin ou) di/kaios ou)k a)/nthrôpos] ... (H) [Greek: Ou)k e)/stin ou) di/kaios ou)k a)/nthrôpos.]

[Greek: plei/ous de\ tou/tôn ou)k e)/sontai a)ntithe/seis. au(=tai de\] (the second Quaternion) [Greek: chôri\s e)kei/nôn] (first Quaternion) [Greek: au)tai\ kath' e(auta\s e)/sontai, ô(s o)no/mati tô=| ou)k a)/nthrôpos chrô/menai.]

In line 38, instead of [Greek: prostethe/n], he reads [Greek: prostethe/ntos].

Of these three alterations the first appears to me good, but insufficient; the second not good, though the passage as it stands in Bekker requires amendment; and the third, a change for the worse.

The purpose of Aristotle is here two-fold. First, to give the reason why, when the propositions were tertii adjacentis, there were two Quaternions or four couples of antithetical propositions; whereas in propositions secundi adjacentis, there was only one Quaternion or two couples of antithetical propositions. Next, to assign the distinction between the first and the second Quaternion in propositions tertii adjacentis.

Now the first of these two purposes is marked out in line 25, which I think we ought to read not by substituting the words of Waitz in place of the words of Bekker, but by retaining the words of Bekker and inserting the words of Waitz as an addition to them. The passage after such addition will stand thus--[Greek: le/gô d' o(/ti to\ e)/stin ê)\ tô=| dikai/ô| proskei/setai ê)\ tô=| ou) dikai/ô|, kai\ ê)\ tô=| a)nthrô/pô| ê)\ tô=| ou)k a)nthrô/pô|, ô(/ste kai\ ê( a)po/phasis. te/ttara ou)=n e)/stai.] Here Aristotle declares the reason why ([Greek: ou)=n]) there come to be four couples of propositions; that reason is, because [Greek: e)/sti] and [Greek: ou)k e)/sti] may be joined either with [Greek: di/kaios] or [Greek: ou) di/kaios] and either with [Greek: a)/nthrôpos] or with [Greek: ou)k a)/nthrôpos]. Both these alternatives must be specified in order to make out a reason why there are two Quaternions or four couples of antithetical propositions. But the passage, as read by Bekker, gives only one of these alternatives, while the passage, as read by Waitz, gives only the other. Accordingly, neither of them separately is sufficient; but both of them taken together furnish the reason required, and thus answer Aristotle's purpose.

Aristotle now proceeds to enunciate the first of the two Quaternions, and then proceeds to line 30, where the reading of Bekker is irrelevant and unmeaning; but the amendment of Waitz appears to me still worse, being positively incorrect in statement of fact. Waitz reads [Greek: to\ ga\r e)/stin e)ntau=tha] (in the first Quaternion, which has just been enunciated) [Greek: kai\ to\ ou)k e)/stin tô=| a)nthrô/pô| proskei/setai kai\ tô=| ou)k a)nthrô/pô|]. These last words are incorrect in fact, for [Greek: ou)k a)/nthrôpos] does not appear in the first Quaternion, but is reserved for the second. While the reading of Waitz is thus evidently wrong, that of Bekker asserts nothing to the purpose. It is useless to tell us merely that [Greek: e)/sti] and [Greek: ou)k e)/stin] attach both to [Greek: di/kaios] and to [Greek: ou) di/kaios] in this first Quaternion ([Greek: e)ntau=tha]), because that characteristic is equally true of the second Quaternion (presently to follow), and therefore constitutes no distinction between the two. To bring out the meaning intended by Aristotle I think we ought here also to retain the words of Bekker, and to add after them some, though not all, of the words of Waitz. The passage would then stand thus--[Greek: to\ ga\r e)/stin e)ntau=tha kai\ to\ ou)k e)/sti tô=| dikai/ô| proskei/setai kai\ tô=| ou) dikai/ô|, kai\ tô=| a)nthrô/pô|, a)ll' ou) tô=| ou)k a)nthrô/pô|.] Or perhaps [Greek: kai\ ou) tô=| ou)k a)nthrô/pô|] might suffice in the last clause (being a smaller change), though [Greek: a)ll' ou)] seem the proper terms to declare the meaning. In the reading which I propose, the sequence intended by Aristotle is clear and intelligible. Having first told us that [Greek: e)/stin] and [Greek: ou)k e)/sti] being joined alternately with [Greek: di/kaios] and with [Greek: ou) di/kaios] and also with [Greek: a)/nthrôpos] and [Greek: ou)k a)/nthrôpos], make up two Quaternions, he proceeds to enunciate the distinctive character belonging to the first Quaternion of the two, viz., that in it [Greek: e)/sti] and [Greek: ou)k e)/stin] are joined both with [Greek: di/kaios] and [Greek: ou) di/kaios], and also with [Greek: a)/nthrôpos] but not with [Greek: ou)k a)/nthrôpos], This is exactly the truth.

Aristotle next proceeds to the second Quaternion, where he points out, as the characteristic distinction, that [Greek: ou)k a)/nthrôpos] comes in and [Greek: a)/nthrôpos] disappears, while [Greek: di/kaios] and [Greek: ou) di/kaios] remain included, as in the first. This is declared plainly by Aristotle in line 37:--[Greek: au(=tai me\n ou)=n du/o a)nti/keintai] (referring to the two pairs of antithetical propositions in the first Quaternion), [Greek: a)/llai de\ pro\s to\ ou)k a)/nthrôpos ô(s u(pokei/meno/n ti prostethe/n; e)/sti di/kaios ou)k a)/nthrôpos, e)/stin ou) di/kaios ou)k a)/nthrôpos-ou)k e)/sti di/kaios ou)k a)/nthrôpos, e)/stin ou) di/kaios ou)k a)/nthrôpos-ou)k e)/stin ou) di/kaios ou)k a)/nthrôpos.] When we read these words, [Greek: a)/llai de\ du/o pro\s to\ ou)k a)/nthrôpos ô(s u(pokei/meno/n ti prostethe/n], as applied to the second Quaternion, we see that there must have been some words preceding which excluded [Greek: ou)k a)/nthrôpos] from the first Quaternion. Waitz contends for the necessity of changing [Greek: prostethe/n] into [Greek: prostethe/ntos]. I do not concur with his reasons for the change; the words that follow, p. 20, line 2, [Greek: ô(s o)no/mati tô=| ou)k a)/nthrôpos chrô/menai (proschrô/menai)], are a reasonable justification of [Greek: prostethe/n--ou)k a)/nthrôpos ô(s u(pokei/meno/n ti prostethe/n] being very analogous to [Greek: ou)k a)/nthrôpos ô(s o)/noma].

This long note, for the purpose of restoring clearness to an obscure text, will appear amply justified if the reader will turn to the perplexities and complaints of the ancient Scholiasts, revealed by Ammonius and Boethius. Even earlier than the time of Alexander (Schol. p. 122**, b. 47) there was divergence in the MSS. of Aristotle; several read [Greek: tô=| dikai/ô|] (p. 19, b. 25), several others read [Greek: tô=| a)nthrô/pô|]. I think that all of them were right in what they retained, and wrong by omission only or mainly.]

After this very subtle and obscure distinction between propositions secundi adjacentis, and those tertii adjacentis, in respect to the application of the negative, Aristotle touches on the relation of contrariety between propositions. The universal affirmation Omne est animal justum has for its contrary Nullum est animal justum. It is plain that both these propositions will never be true at once. But the negatives or contradictories of both may well be true at once: thus, Non omne animal est justum (the contradictory of the first) and Est aliquid animal justum (the contradictory of the second) may be and are both alike true. If the affirmative proposition Omnis homo est non justus be true, the negative Nullus est homo justus must also be true; if the affirmative Est aliquis homo justus be true, the negative Non omnis homo est non justus must also be true. In singular propositions, wherever the negative or denial is true, the indefinite affirmative ([Greek: e)k metathe/seôs], in the language of Theophrastus) corresponding to it will also be true; in universal propositions, the same will not always hold. Thus, if you ask, Is Sokrates wise? and receive for answer No, you are warranted in affirming, Sokrates is not wise (the indefinite affirmation). But if you ask, Are all men wise? and the answer is No, you are not warranted in affirming, All men are not wise. This last is the contrary of the proposition, All men are wise; and two contraries may both be false. You are warranted in declaring only the contradictory negative, Not all men are wise.[29]

[Footnote 29: Aristot. De Interpret. p. 20, a. 16-30.]

Neither the indefinite noun ([Greek: ou)k a)/nthrôpos]) nor the indefinite verb ([Greek: ou) tre/chei--ou) di/kaios]) is a real and true negation, though it appears to be such. For every negation ought to be either true or false; but non homo, if nothing be appended to it, is not more true or false (indeed less so) than homo.[30]

[Footnote 30: Ibid. a. 31, seq.]

The transposition of substantive and adjective makes no difference in the meaning of the phrase; Est albus homo is equivalent to Est homo albus. If it were not equivalent, there would be two negations corresponding to the same affirmation; but we have shown that there can be only one negation corresponding to one affirmation, so as to make up an Antiphasis.[31]

[Footnote 31: Ibid. b. 1-12. That [Greek: e)sti\ leuko\s a)/nthrôpos], and [Greek: e)sti\n a)/nthrôpos leuko/s], mean exactly the same, neither more nor less--we might have supposed that Aristotle would have asserted without any proof; that he would have been content [Greek: a)po\ tô=n pragma/tôn pistou=sthai] (to use the phrase of Ammonius in a portion of the Scholia, p. 121, a. 27). But he prefers to deduce it as a corollary from a general doctrine much less evident than the statement itself; and after all, his deduction is not conclusive, as Waitz has already remarked (ad Organ. I. p. 351).]

In one and the same proposition, it is indispensable that the subject be one and the predicate one; if not, the proposition will not be one, but two or more. Both the subject and the predicate indeed may consist of several words; but in each case the several words must coalesce to make one total unity; otherwise the proposition will not be one. Thus, we may predicate of man--animal, bipes, mansuetum; but these three coalesce into one, so that the proposition will be a single one. On the other hand the three terms homo, albus, ambulans, do not coalesce into one; and therefore, if we predicate all respecting the same subject, or if we affirm the same predicate respecting all three, expressing them all by one word, the proposition will not be one, but several.[32]

[Footnote 32: Aristot. De Interpr. p. 20, b. 13-22.]

Aristotle follows this up by a remark interesting to note, because we see how much his generalities were intended to bear upon the actual practice of his day, in regard to dialectical disputation. In dialectic exercise, the respondent undertook to defend a thesis, so as to avoid inconsistency between one answer and another, against any questions which might be put by the opponent. Both the form of the questions, and the form of the answers, were determined beforehand. No question was admissible which tended to elicit information or a positive declaration from the respondent. A proposition was tendered to him, and he was required to announce whether he affirmed or denied it. The question might be put in either one of two ways: either by the affirmative alone, or by putting both the affirmative and the negative; either in the form, Is Rhetoric estimable? or in the form, Is Rhetoric estimable or not? To the first form the respondent answered Yes or No: to the second form, he replied by repeating either the affirmative or the negative, as he preferred. But it was not allowable to ask him, What is Rhetoric? so as to put him under the necessity of enunciating an explanation of his own.[33]

[Footnote 33: See the Scholia of Ammonius, p. 127, Br.]

Under these canons of dialectic debate, each question was required to be really and truly one, so as to admit of a definite answer in one word. The questioner was either unfair or unskilful, if he wrapped up two questions really distinct in the same word, and thus compelled the respondent either to admit them both, or to deny them both, at once. Against this inconvenience Aristotle seeks to guard, by explaining what are the conditions under which one and the same word does in fact include more than one question. He had before brought to view the case of an equivocal term, which involves such duplication: if himation means both horse and man, it will often happen that questions respecting himation cannot be truly answered either by Yes or No. He now brings to view a different case in which the like ambiguity is involved. To constitute one proposition, it is essential both that the subject should be one, and that the predicate should be one; either of them indeed may be called by two or three names, but these names must coalesce into one. Thus, animal, bipes, mansuetum, coalesce into homo, and may be employed either as one subject or as one predicate; but homo, albus, ambulans, do not coalesce into one; so that if we say, Kallias est homo, albus, ambulans, the proposition is not one but three.[34] Accordingly, the respondent cannot make one answer to a question thus complicated. We thus find Aristotle laying down principles--and probably no one had ever attempted to do so before him--for the correct management of that dialectical debate which he analyses so copiously in the Topica.

[Footnote 34: Aristot. De Interpret. p. 20, b. 2. seq.; Ammonius, Schol. pp. 127-128, a. 21, Br. Compare De Sophist. Elench. p. 169, a. 6-15.]

There are cases (he proceeds to state) in which two predicates may be truly affirmed, taken separately, respecting a given subject, but in which they cannot be truly affirmed, taken together.[35] Kallias is a currier, Kallias is good--both these propositions may be true; yet the proposition, Kallias is a good currier, may not be true. The two predicates are both of them accidental co-inhering in the same individual; but do not fuse themselves into one. So, too, we may truly say, Homer is a poet; but we cannot truly say, Homer is.[36] We see by this last remark,[37] how distinctly Aristotle assigned a double meaning to est: first, per se, as meaning existence; next, relatively, as performing the function of copula in predication. He tells us, in reply either to Plato or to some other contemporaries, that though we may truly say, Non-Ens est opinabile, we cannot truly say Non-Ens est, because the real meaning of the first of these propositions is, **Non-Ens est opinabile non esse.[38]

[Footnote 35: Aristot. De Interpr. p. 21, a. 7, seq.]

[Footnote 36: Ibid. a. 27.]

[Footnote 37: Compare Schol. (ad Anal. Prior. I.) p. 146, a. 19-27; also Eudemi Fragment. cxiv. p. 167, ed. Spengel.

Eudemus considered [Greek: e)/stin] as one term in the proposition. Alexander dissented from this, and regarded it as being only a copula between the terms, [Greek: sunthe/seôs mênutiko\n mo/rion tô=n e)n tê=| prota/sei o(/rôn.]]

[Footnote 38: Aristot. De Interpr. p. 21, a. 32; compare Rhetorica, ii. p. 1402, a. 5. The remark of Aristotle seems to bear upon the doctrine laid down by Plato in the Sophistes, p. 258--the close of the long discussion which begins, p. 237, about [Greek: to\ mê\ o)/n], as Ammonius tells us in the Scholia, p. 112, b. 5, p. 129, b. 20, Br. Ammonius also alludes to the Republic; as if Plato had delivered the same doctrine in both; which is not the fact. See 'Plato and the Other Companions of Sokrates,' vol. II. ch. xxvii. pp. 447-458, seq.]

Aristotle now discusses the so-called Modal Propositions--the Possible and the Necessary. What is the appropriate form of Antiphasis in the case of such propositions, where possible to be, or necessary to be, is joined to the simple is. After a chapter of some length, he declares that the form of Antiphasis suitable for the Simple proposition will not suit for a Modal proposition; and that in the latter the sign of negation must be annexed to the modal adjective--possible, not possible, &c. His reasoning here is not merely involved, but substantially incorrect; for, in truth, both in one and in the other, the sign of contradictory negation ought to be annexed to the copula.[39] From the Antiphasis in Modals Aristotle proceeds to legitimate sequences admissible in such propositions, how far any one of them can be inferred from any other.[40] He sets out four tables, each containing four modal determinations interchangeable with each other.

1. Possible (physically) to be. 2. Possible (logically) to be. 3. Not impossible to be. 4. Not necessary to be.

1. Possible (physically) not to be. 2. Possible (logically) not to be. 3. Not impossible not to be. 4. Not necessary not to be.

1. Not possible (physically) to be. 2. Not possible (logically) to be. 3. Impossible to be. 4. Necessary not to be.

1. Not possible (physically) not to be. 2. Not possible (logically) not to be. 3. Impossible not to be. 4. Necessary to be.

Aristotle canvasses these tables at some length, and amends them partly by making the fourth case of the second table change place with the fourth of the first.[41] He then discusses whether we can correctly say that the necessary to be is also possible to be. If not, then we might say correctly that the necessary to be is not possible to be; for one side or other of a legitimate Antiphasis may always be truly affirmed. Yet this would be absurd: accordingly we must admit that the necessary to be is also possible to be. Here, however, we fall seemingly into a different absurdity; for the possible to be is also possible not to be; and how can we allow that what is necessary to be is at the same time possible not to be? To escape from such absurdities on both sides, we must distinguish two modes of the Possible: one, in which the affirmative and negative are alike possible; the other in which the affirmative alone is possible, because it is always and constantly realized. If a man is actually walking, we know that it is possible for him to walk; and even when he is not walking, we say the same, because we believe that he may walk if he chooses. He is not always walking; and in his case, as in all other intermittent realities, the affirmative and the negative are alike possible. But this is not true in the case of necessary, constant, and sempiternal realities. With them there is no alternative possibility, but only the possibility of their doing or continuing to do. The celestial bodies revolve, sempiternally and necessarily; it is therefore possible for them to revolve; but there is no alternative possibility; it is not possible for them not to revolve. Perpetual reality thus includes the unilateral, but not the bilateral, possibility.[42]

[Footnote 39: Aristot. De Interpret. p. 21, a. 34-p. 22, a. 13. See the note of Waitz, ad Organ. I. p. 359, who points out the error of Aristotle, partly indicated by Ammonius in the Scholia.

The rule does not hold in propositions with the sign of universality attached to the subject; but it is at least the same for Modals and Non-modals.]

[Footnote 40: Aristot. De Interpr. p. 22, a. 14-b. 28.]

[Footnote 41: Aristot. De Interpr. p. 22, b. 22, [Greek: lei/petai toi/nun] &c.; Ammonius, Schol. p. 133, b. 5-27-36.

Aristotle also intimates (p. 23, a. 18) that it would be better to reverse the order of the propositions in the tables, and to place the Necessary before the Possible. M. Barthélemy St. Hilaire has inserted (in the note to his Translation, p. 197) tables with this reversed order.]

[Footnote 42: Aristot. De Interpret. p. 22, b. 29-p. 23, a. 15.]

Having thus stated that possible to be, in this unilateral and equivocal sense but in no other, is a legitimate consequence of necessary to be, Aristotle proceeds to lay down a tripartite distinction which surprises us in this place. "It is plain from what has been said that that which is by Necessity, is in Act or Actuality; so that if things sempiternal are prior, Actuality is prior to Possibility. Some things, like the first (or celestial) substances, are Actualities without Possibility; others (the generated and perishable substances) which are prior in nature but posterior in generation, are Actualities along with Possibility; while a third class are Possibilities only, and never come into Actuality" (such as the largest number, or the least magnitude).[43]

[Footnote 43: Ibid. p. 23, a. 21-26.]

Now the sentence just translated (enunciating a doctrine of Aristotle's First Philosophy rather than of Logic) appears decidedly to contradict what he had said three lines before, viz., that in one certain sense, the necessary to be included and implied the possible to be; that is, a possibility or potentiality unilateral only, not bilateral; for we are here told that the celestial substance is Actuality without Possibility (or Potentiality), so that the unilateral sense of this last term is disallowed. On the other hand, a third sense of the same term is recognized and distinguished; a sense neither bilateral nor unilateral, but the negation of both. This third sense is hardly intelligible, giving as it does an impossible Possible; it seems a self-contradictory description.[44] At best, it can only be understood as a limit in the mathematical sense; a terminus towards which potentiality may come constantly nearer and nearer, but which it can never reach. The first, or bilateral potentiality, is the only sense at once consistent, legitimate, and conformable to ordinary speech. Aristotle himself admits that the second and third are equivocal meanings,[45] departing from the first as the legitimate meaning; but if equivocal departure to so great an extent were allowed, the term, put to such multifarious service, becomes unfit for accurate philosophical reasoning. And we find this illustrated by the contradiction into which Aristotle himself falls in the course of a few lines. The sentence of First Philosophy (which I translated in the last page) is a correction of the logical statement immediately preceding it, in so far as it suppresses the necessary Possible, or the unilateral potentiality. But on the other hand the same sentence introduces a new confusion by its third variety--the impossible Potential, departing from all clear and consistent meaning of potentiality, and coinciding only with the explanation of Non-Ens, as given by Aristotle elsewhere.[46]

[Footnote 44: M. Barthélemy St. Hilaire, in the note to his translation (p. 197) calls it justly--"le possible qui n'est jamais; et qui par cela même, porte en lui une sorte d'impossibilité." It contradicts both the two explanations of [Greek: dunato\n] which Aristotle had given a few lines before. 1. [Greek: dunato\n o(/ti e)nergei=]. 2. [Greek: dunato\n o(/ti e)nergê/seien a)/n] (p. 23, a. 10).]

[Footnote 45: Aristot. De Interpr. p. 23, a. 5. [Greek: tou=to me\n tou/tou cha/rin ei)/rêtai, o(/ti ou) pa=sa du/namis tô=n a)ntikeime/nôn, ou)d' o(/sai le/gontai kata\ to\ au)to\ ei)=dos. e)/niai de\ duna/meis o(mô/numoi/ ei)sin; to\ ga\r dunato\n ou)ch a(plô=s le/getai, a)lla\ to\ me\n o(/ti a)lêthe\s ô(s e)nergei/a| o)/n], &c.

If we read the thirteenth chapter of Analytica Priora I. (p. 32, a. 18-29) we shall see that [Greek: to\ e)ndecho/menon] is declared to be [Greek: ou)k a)nagkai=on], and that in the definition of [Greek: to\ e)ndecho/menon], the words [Greek: ou(= mê\ o)/ntos a)nagkai/ou] are expressly inserted. When [Greek: to\ a)nagkai=on] is said [Greek: e)nde/chesthai], this is said only in an equivocal sense of [Greek: e)nde/chesthai--to\ ga\r a)nagkai=on o(mônu/môs e)nde/chesthai le/gomen.]

On the meaning of [Greek: to\ e)ndecho/menon], translated above, in the table, "possible (logically) to be," and its relation to [Greek: to\ dunato/n], see Waitz, ad Organ. I. pp. 375-8. Compare Prantl. Gescht. der Logik, I. pp. 166-8.]

[Footnote 46: Aristot. De Interpr. p. 21, a. 32: [Greek: to\ de\ mê\ o)/n, o(/ti doxasto/n, ou)k a)lêthe\s ei)pei=n o)/n ti; do/xa ga\r au)tou= ou)k e)/stin o(/ti e)/stin, a)ll' o(/ti ou)k e)/stin. To\ mê\ o)/n] is the true description of that which Aristotle improperly calls [Greek: du/namis ê(\ ou)de/pote e)ne/rgeia/ e)stin].

The triple enumeration given by Aristotle (1. Actuality without Potentiality. 2. Actuality with Potentiality. 3. Potentiality without Actuality) presents a neat symmetry which stands in the place of philosophical exactness.]

The contrast of Actual and Potential stands so prominently forward in Aristotle's First Philosophy, and is, when correctly understood, so valuable an element in First Philosophy generally, that we cannot be too careful against those misapplications of it into which he himself sometimes falls. The sense of Potentiality, as including the alternative of either affirmative or negative--may be or may not be--is quite essential in comprehending the ontological theories of Aristotle; and when he professes to drop the may not be and leave only the may be, this is not merely an equivocal sense of the word, but an entire renunciation of its genuine sense. In common parlance, indeed, we speak elliptically, and say, It may be, when we really mean, It may or may not be. But the last or negative half, though not expressly announced, is always included in the thought and belief of the speaker and understood by the hearer.[47]

[Footnote 47: See Trendelenburg ad Aristot. De Animâ, pp. 303-307.]

Many logicians, and Sir William Hamilton very emphatically, have considered the Modality of propositions as improper to be included in the province of Logic, and have treated the proceeding of Aristotle in thus including it, as one among several cases in which he had transcended the legitimate boundaries of the science.[48] This criticism, to which I cannot subscribe, is founded upon one peculiar view of the proper definition and limits of Logic. Sir W. Hamilton lays down the limitation peremptorily, and he is warranted in doing this for himself; but it is a question about which there has been great diversity of view among expositors, and he has no right to blame others who enlarge it. My purpose in the present volume is to explain how the subject presented itself to Aristotle. He was the first author that ever attempted to present Logic in a scientific aspect; and it is hardly fair to try him by restrictions emanating from critics much later. Yet, if he is to be tried upon this point, I think the latitude in which he indulges preferable to the restricted doctrine of Sir W. Hamilton.

[Footnote 48: See pp. 143-5 of the article, "Logic," in Sir William Hamilton's Discussions on Philosophy--a very learned and instructive article, even for those who differ from most of its conclusions. Compare the opposite view, as advocated by M. Barthélemy St. Hilaire, Logique d'Aristote, Préface, pp. **lxii.-lxviii.]

In the treatise now before us (De Interpretatione) Aristotle announces his intention to explain the Proposition or Enunciative Speech, the conjunction of a noun and a verb; as distinguished, first, from its two constituents (noun and verb) separately taken; next, from other modes of speech, also combining the two (precative, interrogative, &c.). All speech (he says), the noun or verb separately, as well as the proposition conjointly, is, in the first instance, a sign of certain mental states common to the speaker with his hearers; and, in the second instance, a sign of certain things or facts, resembling (or correlating with) these mental states.[49] The noun, pronounced separately, and the verb, pronounced separately, are each signs of a certain thought in the speaker's mind, without either truth or falsehood; the Proposition, or conjunction of the two, goes farther and declares truth or falsehood. The words pronounced (he says) follow the thoughts in the mind, expressing an opinion (i.e. belief or disbelief) entertained in the mind; the verbal affirmation or negation gives utterance to a mental affirmation or negation--a feeling of belief or disbelief--that something is, or that something is not.[50] Thus, Aristotle intends to give a theory of the Proposition, leaving other modes of speech to Rhetoric or Poetry:[51] the Proposition he considers under two distinct aspects. In its first or subjective aspect, it declares the state of the speaker's mind, as to belief or disbelief. In its second or objective aspect, it declares a truth or falsehood correlating with such belief or disbelief, for the information of the hearer. Now the Mode belonging to a proposition of this sort, in virtue of its form, is to be true or false. But there are also other propositions--other varieties of speech enunciative--which differ from the Simple or Assertory Proposition having the form is or is not, and which have distinct modes belonging to them, besides that of being true or false. Thus we have the Necessary Proposition, declaring that a thing is so by necessity, that it must be so, or cannot but be so; again, the Problematical Proposition, enunciating that a thing may or may not be so. These two modes attach to the form of the proposition, and are quite distinct from those which attach to its matter as simply affirmed or denied; as when, instead of saying, John is sick, we say, John is sick of a fever, John is dangerously sick, with a merely material modification. Such adverbs, modifying the matter affirmed or denied, are numerous, and may be diversified almost without limit. But they are not to be placed in the same category with the two just mentioned, which modify the form of the proposition, and correspond to a state of mind distinct from simple belief or disbelief, expressed by a simple affirmation or negation.[52] In the case of each of the two, Aristotle has laid down rules (correct or incorrect) for constructing the legitimate Antiphasis, and for determining other propositions equipollent to, or following upon, the propositions given; rules distinct from those applying to the simple affirmation. When we say of anything, It may be or may not be, we enunciate here only one proposition, not two; we declare a state of mind which is neither belief nor disbelief, as in the case of the Simple Proposition, but something wavering between the two; yet which is nevertheless frequent, familiar to every one, and useful to be made known by a special form of proposition adapted to it--the Problematical. On the other hand, when we say, It is by necessity--must be--cannot but be--we declare our belief, and something more besides; we declare that the supposition of the opposite of what we believe, would involve a contradiction--I would contradict some definition or axiom to which we have already sworn adherence. This again is a state of mind known, distinguishable, and the same in all, subjectively; though as to the objective correlate--what constitutes the Necessary, several different opinions have been entertained.

[Footnote 49: Aristot. De Interpr. p. 16, a. 3-8: [Greek: e)/sti me\n ou)=n ta\ e)n tê=| phônê=| tô=n e)n tê=| psuchê=| pathêma/tôn su/mbola--ô(=n me/ntoi tau=ta sêmei=a prô/tôs, tau)ta\ pa=si pathê/mata tê=s psuchê=s, kai\ ô(=n tau=ta o(moiô/mata, pra/gmata ê)/dê tau)ta/.] Ibid. a. 13: [Greek: ta\ me\n ou)=n o)no/mata au)ta\ kai\ ta\ r(ê/mata e)/oike tô=| a)/neu sunthe/seôs kai\ diaire/seôs noê/mati--ou)/te ga\r pseu=dos ou)/t' a)lêthe/s pô.] Ib. p. 17, a. 2: [Greek: lo/gos a)pophantiko\s, e)n ô(=| to\ a)lêtheu/ein ê)\ pseu/desthai u(pa/rchei]. Compare p. 20, a. 34.]

[Footnote 50: Aristot. De Interpret. p. 23, a. 32: [Greek: ta\ me\n e)n tê=| phônê=| a)kolouthei= toi=s e)n tê=| dianoi/a|, e)kei= de\ e)nanti/a do/xa ê( tou= e)nanti/ou], &c. Ib. p. 24, b. 1: [Greek: ô(/ste ei)/per e)pi\ do/xês ou(/tôs e)/chei, ei)si\ de\ ai( e)n tê=| phônê=| katapha/seis kai\ a)popha/seis su/mbola tô=n e)n tê=| psuchê=|, dê=lon o(/ti kai\ katapha/sei e)nanti/a me\n a)po/phasis ê(/ peri\ tou= au)tou= katho/lou], &c. Ib. p. 17, a. 22: [Greek: e)/sti de\ ê( a(plê= a)po/phansis phônê\ sêmantikê\ peri\ tou= u(pa/rchein ti ê)\ mê\ u(pa/rchein], &c.]

[Footnote 51: Ibid. p. 17, a. 5. [Greek: oi( me\n ou)=n a)/lloi (lo/goi) a)phei/sthôsan; r(êtorikê=s ga\r ê)\ poiêtikê=s oi)keiote/ra ê( ske/psis; o( de\ a)pophantiko\s tê=s nu=n theôri/as.]]

[Footnote 52: Ammonius (in the Scholia on De Interpret. p. 130, a. 16, seq., Brand.) ranks all modal propositions under the same category, and considers the number of them to be, not indeed infinite, but very great. He gives as examples: "The moon changes fast; Plato loves Dion vehemently." Sir W. Hamilton adopts the same view as Ammonius: "Modes may be conceived without end--all must be admitted, if any are; the line of distinction attempted to be drawn is futile." (Discussions on Phil. ut sup. p. 145.) On the other hand, we learn from Ammonius that most of the Aristotelian interpreters preceding him reckoned the simple proposition [Greek: to\ u(pa/rchein] as a modal; and Aristotle himself seems so to mention it (Analytica Priora, I. ii. p. 25, a. 1); besides that he enumerates true and false, which undoubtedly attach to [Greek: to\ u(pa/rchein], as examples of modes (De Interpret. c. 12, p. 22, a. 13). Ammonius himself protests against this doctrine of the former interpreters.

Mr. John Stuart Mill (System of Logic, Bk. I. ch. iv. s. 2) says:--"A remark of a similar nature may be applied to most of those distinctions among propositions which are said to have reference to their modality; as difference of tense or time; the sun did rise, is rising, will rise. . . . The circumstance of time is properly considered as attaching to the copula, which is the sign of predication, and not to the predicate. If the same cannot be said of such modifications as these, Cæsar is perhaps dead; it is possible that Cæsar is dead; it is only because these fall together under another head; being properly assertions not of anything relating to the fact itself, but of the state of our own mind in regard to it; namely, our absence of disbelief of it. Thus, Cæsar may be dead, means, I am not sure that Cæsar is alive."

I do not know whether Mr. Mill means that the function of the copula is different in these problematical propositions, from what it is in the categorical propositions: I think there is no difference. But his remark that the problematical proposition is an assertion of the state of our minds in regard to the fact, appears to me perfectly just. Only, we ought to add, that this is equally true about the categorical proposition. It is equally true about all the three following propositions:--1. The three angles of a triangle may or may not be equal to two right angles. 2. The three angles of a triangle are equal to two right angles. 3. The three angles of a triangle are necessarily equal to two right angles. In each of these three propositions, an assertion of the state of our minds is involved, and a different state of mind in each. This is the subjective aspect of the proposition; it belongs to the form rather than to the matter, and may be considered as a mode. The commentators preceding Ammonius did so consider it, and said that the categorical proposition had its mode as well as the others. Ammonius differed from them, treating the categorical as having no mode--as the standard unit or point of departure.

The propositions now known as Hypothetical and Disjunctive, which may also be regarded as in a certain sense Modals, are not expressly considered by Aristotle. In the Anal. Prior. I. xliv. p. 50 a. 16-38, he adverts to hypothetical syllogisms, and intimates his intention of discussing them more at length: but this intention has not been executed, in the works that we possess.]

In every complete theory of enunciative speech, these modal propositions deserve to be separately explained, both in their substantive meaning and in their relation to other propositions. Their characteristic property as Modals belongs to form rather than to matter; and Aristotle ought not to be considered as unphilosophical for introducing them into the Organon, even if we adopt the restricted view of Logic taken by Sir W. Hamilton, that it takes no cognizance of the matter of propositions, but only of their form. But though I dissent from Hamilton's criticisms on this point, I do not concur with the opposing critics who think that Aristotle has handled the Modal Propositions in a satisfactory manner. On the contrary, I think that the equivocal sense which he assigns to the Potential or Possible, and his inconsistency in sometimes admitting, sometimes denying, a Potential that is always actual, and a Potential that is never actual--are serious impediments to any consistent Logic. The Problematical Proposition does not admit of being cut in half; and if we are to recognize a necessary Possible, or an impossible Possible, we ought to find different phrases by which to designate them.

We must observe that the distinction of Problematical and Necessary Propositions corresponds, in the mind of Aristotle, to that capital and characteristic doctrine of his Ontology and Physics, already touched on in this chapter. He thought, as we have seen, that in the vast circumferential region of the Kosmos, from the outer sidereal sphere down to the lunar sphere, celestial substance was a necessary existence and energy, sempiternal and uniform in its rotations and influence; and that through its beneficent influence, pervading the concavity between the lunar sphere and the terrestrial centre (which included the four elements with their compounds) there prevailed a regularizing tendency called Nature: modified, however, and partly counteracted by independent and irregular forces called Spontaneity and Chance, essentially unknowable and unpredictable. The irregular sequences thus named by Aristotle were the objective correlate of the Problematical Proposition in Logic. In these sublunary sequences, as to future time, may or may not was all that could be attained, even by the highest knowledge; certainty, either of affirmation or negation, was out of the question. On the other hand, the necessary and uniform energies of the celestial substance, formed the objective correlate of the Necessary Proposition in Logic; this substance was not merely an existence, but an existence necessary and unchangeable. I shall say more on this when I come to treat of Aristotle as a kosmical and physical philosopher; at present it is enough to remark that he considers the Problematical Proposition in Logic to be not purely subjective, as an expression of the speaker's ignorance, but something more, namely, to correlate with an objective essentially unknowable to all.

The last paragraph of the treatise De Interpretatione discusses the question of Contraries and Contradictories, and makes out that the greatest breadth of opposition is that between a proposition and its contradictory (Kallias is just--Kallias is not just), not that between, a proposition and what is called its contrary (Kallias is just--Kallias is unjust); therefore, that according to the definition of contrary, the true contrary of a proposition is its contradictory.[53] This paragraph is not connected with that which precedes; moreover, both the reasoning and the conclusion differ from what we read as well in this treatise as in other portions of Aristotle. Accordingly, Ammonius in the Scholia, while informing us that Porphyry had declined to include it in his commentary, intimates also his own belief that it is not genuine, but the work of another hand. At best (Ammonius thinks), if we must consider it as the work of Aristotle, it has been composed by him only as a dialectical exercise, to debate an unsettled question.[54] I think the latter hypothesis not improbable. The paragraph has certainly reference to discussions which we do not know, and it may have been composed when Aristotle had not fully made up his mind on the distinction between Contrary and Contradictory. Considering the difficult problems that he undertook to solve, we may be sure that he must have written down several trains of thought merely preliminary and tentative. Moreover, we know that he had composed a distinct treatise 'De Oppositis,'[55] which is unfortunately lost, but in which he must have included this very topic--the distinction between Contrary and Contradictory.

[Footnote 53: Aristot. De Interpr. p. 23, a. 27, seq.]

[Footnote 54: Scholia ad Arist. pp. 135-139, Br. [Greek: gumna/sai mo/non boulêthe/ntos tou\s e)ntugcha/nontas pro\s tê\n e)pi/krisin tô=n pithanô=s me\n ou) me/ntoi a)lêthô=s legome/nôn lo/gôn] &c. (p. 135, b. 15; also p. 136, a. 42).]

[Footnote 55: Scholia ad Categorias, p. 83, a. 17-19, b. 10, p. 84, a. 29, p. 86, b. 42, p. 88, a. 30. It seems much referred to by Simplikius, who tells us that the Stoics adopted most of its principles (p. 83, a. 21, b. 7).]

Whatever may have been the real origin and purpose of this last paragraph, I think it unsuitable as a portion of the treatise De Interpretatione. It nullifies, or at least overclouds, one of the best parts of that treatise, the clear determination of Anaphasis and its consequences.

If, now, we compare the theory of the Proposition as given by Aristotle in this treatise, with that which we read in the Sophistes of Plato, we shall find Plato already conceiving the proposition as composed indispensably of noun and verb, and as being either affirmative or negative, for both of which he indicates the technical terms.[56] He has no technical term for either subject or predicate; but he conceives the proposition as belonging to its subject:[57] we may be mistaken in the predicates, but we are not mistaken in the subject. Aristotle enlarges and improves upon this theory. He not only has a technical term for affirmation and negation, and for negative noun and verb, but also for subject and predicate; again, for the mode of signification belonging to noun and verb, each separately, as distinguished from the mode of signification belonging to them conjointly, when brought together in a proposition. He follows Plato in insisting upon the characteristic feature of the proposition--aptitude for being true or false; but he gives an ampler definition of it, and he introduces the novel and important distribution of propositions according to the quantity of the subject. Until this last distribution had been made, it was impossible to appreciate the true value and bearing of each Antiphasis and the correct language for expressing it, so as to say neither more nor less. We see, by reading the Sophistes, that Plato did not conceive the Antiphasis correctly, as distinguished from Contrariety on the one hand, and from mere Difference on the other. He saw that the negative of any proposition does not affirm the contrary of its affirmative; but he knew no other alternative except to say, that it affirms only something different from the affirmative. His theory in the Sophistes recognizes nothing but affirmative propositions, with the predicate of contrariety on one hand, or of difference on the other;[58] he ignores, or jumps over, the intermediate station of propositions affirming nothing at all, but simply denying a pre-understood affirmative. There were other contemporaries, Antisthenes among them, who declared contradiction to be an impossibility;[59] an opinion coinciding at bottom with what I have just cited from Plato himself. We see, in the Theætêtus, the Euthydêmus, the Sophistes, and elsewhere, how great was the difficulty felt by philosophers of that age to find a proper locus standi for false propositions, so as to prove them theoretically possible, to assign a legitimate function for the negative, and to escape from the interdict of Parmenides, who eliminated Non-Ens as unmeaning and incogitable. Even after the death of Aristotle, the acute disputation of Stilpon suggested many problems, but yielded few solutions; and Menedêmus went so far as to disallow negative propositions altogether.[60]

[Footnote 56: Plato, Sophistes, pp. 261-262. [Greek: pha/sin kai\ a)po/phasin].--ib. p. 263 E. In the so-called Platonic 'Definitions,' we read [Greek: e)n katapha/sei kai\ a)popha/sei] (p. 413 C); but these are probably after Aristotle's time. In another of these Definitions (413 D.) we read [Greek: a)po/phasis], where the word ought to be [Greek: a)po/phansis].]

[Footnote 57: Plato, Sophist. p. 263 A-C.]

[Footnote 58: Ibid. p. 257, B: [Greek: Ou)k a)r', e)nanti/on o(/tan a)po/phasis le/gêtai sêmai/nein, sugchôrêso/metha, tosou=ton de\ mo/non, o(/ti tô=n a)/llôn ti mênu/ei to\ mê\ kai\ to\ ou)/ protithe/mena tô=n e)pio/ntôn o)noma/tôn, ma=llon de\ tô=n pragma/tôn, peri\ a(/tt' a)\n ke/êtai ta\ e)piphtheggo/mena u(/steron tê=s a)popha/seôs o)no/mata.]

The term [Greek: a)nti/phasis], and its derivative [Greek: a)ntiphatikô=s], are not recognized in the Platonic Lexicon. Compare the same dialogue, Sophistes, p. 263; also Euthydêmus, p. 298, A. Plato does not seem to take account of negative propositions as such. See 'Plato and the Other Companions of Sokrates,' vol. II. ch. xxvii. pp. 446-455.]

[Footnote 59: Aristot. Topica, I. xi. p. 104, b. 20; Metaphys. [Greek: D]. p. 1024, b. 32; Analytic. Poster. I. xxv. p. 86, b. 34.]

[Footnote 60: Diogon. Laert. ii. 134-135. See the long discussion in the Platonic Theætêtus (pp. 187-196), in which Sokrates in vain endeavours to produce some theory whereby [Greek: pseudê\s do/xa] may be rendered possible. Hobbes, also, in his Computation or Logic (De Corp. c. iii. § 6), followed by Destutt Tracy, disallows the negative proposition per se, and treats it as a clumsy disguise of the affirmative [Greek: e)k metathe/seôs], to use the phrase of Theophrastus. Mr. John Stuart Mill has justly criticized this part of Hobbes's theory (System of Logic, Book I. ch. iv. § 2).]

Such being the conditions under which philosophers debated in the age of Aristotle, we can appreciate the full value of a positive theory of propositions such as that which we read in his treatise De Interpretatione. It is, so far as we know, the first positive theory thereof that was ever set out; the first attempt to classify propositions in such a manner that a legitimate Antiphasis could be assigned to each; the first declaration that to each affirmative proposition there belonged one appropriate negative, and to each negative proposition one appropriate counter-affirmative, and one only; the earliest effort to construct a theory for this purpose, such as to hold ground against all the puzzling questions of acute disputants.[61] The clear determination of the Antiphasis in each case--the distinction of Contradictory antithesis from Contrary antithesis between propositions--this was an important logical doctrine never advanced before Aristotle; and the importance of it becomes manifest when we read the arguments of Plato and Antisthenes, the former overleaping and ignoring the contradictory opposition, the latter maintaining that it was a process theoretically indefensible. But in order that these two modes of antithesis should be clearly contrasted, each with its proper characteristic, it was requisite that the distinction of quantity between different propositions should also be brought to view, and considered in conjunction with the distinction of quality. Until this was done, the Maxim of Contradiction, denied by some, could not be shown in its true force or with its proper limits. Now, we find it done,[62] for the first time, in the treatise before us. Here the Contradictory antithesis (opposition both in quantity and quality) in which one proposition must be true and the other false, is contrasted with the Contrary (propositions opposite in quality, but both of them universal). Aristotle's terminology is not in all respects fully developed; in regard, especially, to the quantity of propositions it is less advanced than in his own later treatises; but from the theory of the De Interpretatione all the distinctions current among later logicians, take their rise.

[Footnote 61: Aristot. De Interpr. p. 17, a. 36: [Greek: pro\s ta\s sophistika\s e)nochlê/seis].]

[Footnote 62: We see, from the argument in the Metaphysica of Aristotle, that there were persons in his day who denied or refused to admit the Maxim of Contradiction; and who held that contradictory propositions might both be true or both false (Aristot. Metaph. [Greek: G]. p. 1006, a. 1; p. 1009, a. 24). He employs several pages in confuting them.

See the Antinomies in the Platonic Parmenides (pp. 154-155), some of which destroy or set aside the Maxim of Contradiction ('Plato and the Other Companions of Sokrates,' vol. II. ch. xxv. p. 306).]

The distinction of Contradictory and Contrary is fundamental in ratiocinative Logic, and lies at the bottom of the syllogistic theory as delivered in the Analytica Priora. The precision with which Aristotle designates the Universal proposition with its exact contradictory antithesis, is remarkable in his day. Some, however, of his observations respecting the place and functions of the negative particle ([Greek: ou)]), must be understood with reference to the variable order of words in a Greek or Latin sentence; for instance, the distinction between Kallias non est justus and Kallias est non justus does not suggest itself to one speaking English or French.[63] Moreover, the Aristotelian theory of the Proposition is encumbered with various unnecessary subtleties; and the introduction of the Modals (though they belong, in my opinion, legitimately to a complete logical theory) renders the doctrine so intricate and complicated, that a judicious teacher will prefer, in explaining the subject, to leave them for second or ulterior study, when the simpler relations between categorical propositions have been made evident and familiar. The force of this remark will be felt more when we go through the Analytica Priora. The two principal relations to be considered in the theory of Propositions--Opposition and Equipollence--would have come out far more clearly in the treatise De Interpretatione, if the discussion of the Modals had been reserved for a separate chapter.

[Footnote 63: The diagram or parallelogram of logical antithesis, which is said to have begun with Apuleius, and to have been transmitted through Boethius and the Schoolmen to modern times (Ueberweg, System der Logik, sect. 72, p. 174) is as follows:--

A. Omnis homo est justus. --- E. Nullus homo est justus. |X| I. Aliquis homo est justus. --- O. Aliquis homo non est justus.

But the parallelogram set out by Aristotle in the treatise De Interpretatione, or at least in the Analytica Priora, is different, and intended for a different purpose. He puts it thus:--

1. Omnis homo est justus . . . . . 2. Non omnis homo est justus. 4. Non omnis homo est non justus . 3. Omnis homo est non justus.

Here Proposition (1) is an affirmative, of which (2) is the direct and appropriate negative: also Proposition (3) is an affirmative (Aristotle so considers it), of which (4) is the direct and appropriate negative. The great aim of Aristotle is to mark out clearly what is the appropriate negative or [Greek: A)po/phasis] to each [Greek: Kata/phasis (mi/a a)po/phasis mia=s katapha/seôs], p. 17, b. 38), making up together the pair which he calls [Greek: A)nti/phasis], standing in Contradictory Opposition; and to distinguish this appropriate negative from another proposition which comprises the particle of negation, but which is really a new affirmative.

The true negatives of homo est justus--Omnis homo est justus are, Homo non est justus--Non omnis homo est justus. If you say, Homo est non justus--Omnis homo est non justus, these are not negative propositions, but new affirmatives ([Greek: e)k metathe/seôs] in the language of Theophrastus).]

Spotted a typo or a problem in this chapter? Tell us

V. ANALYTICA PRIORA I

Reviewing the treatise De Interpretatione, we have followed Aristotle in his first attempt to define what a Proposition is, to point out its constituent elements, and to specify some of its leading varieties. The characteristic feature of the Proposition he stated to be--That it declares, in the first instance, the mental state of the speaker as to belief or disbelief, and, in its ulterior or final bearing, a state of facts to which such belief or disbelief corresponds. It is thus significant of truth or falsehood; and this is its logical character (belonging to Analytic and Dialectic), as distinguished from its rhetorical character, with other aspects besides. Aristotle farther indicated the two principal discriminative attributes of propositions as logically regarded, passing under the names of quantity and quality. He took great pains, in regard to the quality, to explain what was the special negative proposition in true contradictory antithesis to each affirmative. He stated and enforced the important separation of contradictory propositions from contrary; and he even parted off (which the Greek and Latin languages admit, though the French and English will hardly do so) the true negative from the indeterminate affirmative. He touched also upon equipollent propositions, though he did not go far into them. Thus commenced with Aristotle the systematic study of propositions, classified according to their meaning and their various interdependences with each other as to truth and falsehood--their mutual consistency or incompatibility. Men who had long been talking good Greek fluently and familiarly, were taught to reflect upon the conjunctions of words that they habitually employed, and to pay heed to the conditions of correct speech in reference to its primary purpose of affirmation and denial, for the interchange of beliefs and disbeliefs, the communication of truth, and the rectification of falsehood. To many of Aristotle's contemporaries this first attempt to theorize upon the forms of locution familiar to every one would probably appear hardly less strange than the interrogative dialectic of Sokrates, when he declared himself not to know what was meant by justice, virtue, piety, temperance, government, &c.; when he astonished his hearers by asking them to rescue him from this state of ignorance, and to communicate to him some portion of their supposed plenitude of knowledge.

Aristotle tells us expressly that the theory of the Syllogism, both demonstrative and dialectic, on which we are now about to enter, was his own work altogether and from the beginning; that no one had ever attempted it before; that he therefore found no basis to work upon, but was obliged to elaborate his own theory, from the very rudiments, by long and laborious application. In this point of view, he contrasts Logic pointedly with Rhetoric, on which there had been a series of writers and teachers, each profiting by the labours of his predecessors.[1] There is no reason to contest the claim to originality here advanced by Aristotle. He was the first who endeavoured, by careful study and multiplied comparison of propositions, to elicit general truths respecting their ratiocinative interdependence, and to found thereupon precepts for regulating the conduct of demonstration and dialectic.[2]

[Footnote 1: See the remarkable passage at the close of the Sophistici Elenchi, p. 183, b. 34-p. 184, b. 9: [Greek: tau/tês de\ tê=s pragmatei/as ou) to\ me\n ê)=n to\ de\ ou)k ê)=n proexeirgasme/non, a)ll' ou)de\n pantelô=s u(pê=rche--kai\ peri\ me\n tô=n r(êtorikô=n u(pê=rche polla\ kai\ palaia\ ta\ lego/mena, peri\ de\ tou= sullogi/zesthai pantelô=s ou)de\n ei)/chomen pro/teron a)/llo le/gein, a)ll' ê)\ tribê=| zêtou=ntes polu\n chro/non e)ponou=men.]]

[Footnote 2: Sir Wm. Hamilton, Lectures on Logic, Lect. v. pp. 87-91, vol. III.:--"The principles of Contradiction and Excluded Middle can both be traced back to Plato, by whom they were enounced and frequently applied; though it was not till long after, that either of them obtained a distinctive appellation. To take the principle of Contradiction first. This law Plato frequently employs, but the most remarkable passages are found in the Phædo (p. 103), in the Sophista (p. 252), and in the Republic (iv. 436, vii. 525). This law was however more distinctively and emphatically enounced by Aristotle. . . . . Following Aristotle, the Peripatetics established this law as the highest principle of knowledge. From the Greek Aristotelians it obtained the name by which it has subsequently been denominated, the principle, or law, or axiom, of Contradiction ([Greek: a)xi/ôma tê=s a)ntipha/seôs]). . . . . The law of Excluded Middle between two contradictories remounts, as I have said, also to Plato; though the Second Alcibiades, in which it is most clearly expressed (p. 139; also Sophista, p. 250), must be admitted to be spurious. . . . . This law, though universally recognized as a principle in the Greek Peripatetic school, and in the schools of the middle ages, only received the distinctive appellation by which it is now known at a comparatively modern date."

The passages of Plato, to which Sir W. Hamilton here refers, will not be found to bear out his assertion that Plato "enounced and frequently applied the principles of Contradiction and Excluded Middle." These two principles are both of them enunciated, denominated, and distinctly explained by Aristotle, but by no one before him, as far as our knowledge extends. The conception of the two maxims, in their generality, depends upon the clear distinction between Contradictory Opposition and Contrary Opposition; which is fully brought out by Aristotle, but not adverted to, or at least never broadly and generally set forth, by Plato. Indeed it is remarkable that the word [Greek: A)nti/phasis], the technical term for Contradiction, never occurs in Plato; at least it is not recognized in the Lexicon Platonicum. Aristotle puts it in the foreground of his logical exposition; for, without it, he could not have explained what he meant by Contradictory Opposition. See Categoriæ, pp. 13-14, and elsewhere in the treatise De Interpretatione and in the Metaphysica. Respecting the idea of the Negative as put forth by Plato in the Sophistes (not coinciding either with Contradictory Opposition or with Contrary Opposition), see 'Plato and the Other Companions of Sokrates,' vol. II. ch. xxvii. pp. 449-459. I have remarked in that chapter, and the reader ought to recollect, that the philosophical views set out by Plato in the Sophistes differ on many points from what we read in other Platonic dialogues.]

He begins the Analytica Priora by setting forth his general purpose, and defining his principal terms and phrases. His manner is one of geometrical plainness and strictness. It may perhaps have been common to him with various contemporary geometers, whose works are now lost; but it presents an entire novelty in Grecian philosophy and literature. It departed not merely from the manner of the rhetoricians and the physical philosophers (as far as we know them, not excluding even Demokritus), but also from Sokrates and the Sokratic school. For though Sokrates and Plato were perpetually calling for definitions, and did much to make others feel the want of such, they neither of them evinced aptitude or readiness to supply the want. The new manner of Aristotle is adapted to an undertaking which he himself describes as original, in which he has no predecessors, and is compelled to dig his own foundations. It is essentially didactic and expository, and contrasts strikingly with the mixture of dramatic liveliness and dialectical subtlety which we find in Plato.

The terminology of Aristotle in the Analytica is to a certain extent different from that in the treatise De Interpretatione. The Enunciation ([Greek: A)po/phanis]) appears under the new name of [Greek: Pro/tasis], Proposition (in the literal sense) or Premiss; while, instead of Noun and Verb, we have the word Term ([Greek: O(/ros]), applied alike both to Subject and to Predicate.[3] We pass now from the region of declared truth, into that of inferential or reasoned truth. We find the proposition looked at, not merely as communicating truth in itself, but as generating and helping to guarantee certain ulterior propositions, which communicate something additional or different. The primary purpose of the Analytica is announced to be, to treat of Demonstration and demonstrative Science; but the secondary purpose, running parallel with it and serving as illustrative counterpart, is, to treat also of Dialectic; both of them[4] being applications of the inferential or ratiocinative process, the theory of which Aristotle intends to unfold.

[Footnote 3: Aristot. Analyt. Prior. I. i. p. 24, b. 16: [Greek: o(/ron de\ kalô= ei)s o(\n dialu/etai ê( pro/tasis, oi(=on to/ te katêgorou/menon kai\ to\ kath' ou(= katêgorei=tai], &c.

[Greek: O(/ros]--Terminus--seems to have been a technical word first employed by Aristotle himself to designate subject and predicate as the extremes of a proposition, which latter he conceives as the interval between the termini--[Greek: dia/stêma]. (Analyt. Prior. I. xv. p. 35, a. 12. [Greek: sterêtikô=n diastêma/tôn], &c. See Alexander, Schol. pp. 145-146.)

In the Topica Aristotle employs [Greek: o(/ros] in a very different sense--[Greek: lo/gos o( to\ ti/ ê)=n ei)=nai sêmai/nôn] (Topic. I. v. p. 101, b. 39)--hardly distinguished from [Greek: o(rismo/s]. The Scholia take little notice of this remarkable variation of meaning, as between two treatises of the Organon so intimately connected (pp. 256-257, Br.).]

[Footnote 4: Analyt. Prior. I. i. p. 24, a. 25.]

The three treatises--1, Analytica Priora, 2, Analytica Posteriora, 3, Topica with Sophistici Elenchi--thus belong all to one general scheme; to the theory of the Syllogism, with its distinct applications, first, to demonstrative or didactic science, and, next, to dialectical debate. The scheme is plainly announced at the commencement of the Analytica Priora; which treatise discusses the Syllogism generally, while the Analytica Posteriora deals with Demonstration, and the Topica with Dialectic. The first chapter of the Analytica Priora and the last chapter of the Sophistici Elenchi (closing the Topica), form a preface and a conclusion to the whole. The exposition of the Syllogism, Aristotle distinctly announces, precedes that of Demonstration (and for the same reason also precedes that of Dialectic), because it is more general: every demonstration is a sort of syllogism, but every syllogism is not a demonstration.[5]

[Footnote 5: Ibid. I. iv. p. 25, b. 30.]

As a foundation for the syllogistic theory, propositions are classified according to their quantity (more formally than in the treatise De Interpretatione) into Universal, Particular, and Indefinite or Indeterminate;[6] Aristotle does not recognize the Singular Proposition as a distinct variety. In regard to the Universal Proposition, he introduces a different phraseology according as it is looked at from the side of the Subject, or from that of the Predicate. The Subject is, or is not, in the whole Predicate; the Predicate is affirmed or denied respecting all or every one of the Subject.[7] The minor term of the Syllogism (in the first mode of the first figure) is declared to be in the whole middle term; the major is declared to belong to, or to be predicable of, all and every the middle term. Aristotle says that the two are the same; we ought rather to say that each is the concomitant and correlate of the other, though his phraseology is such as to obscure the correlation.

[Footnote 6: Ibid. I. i. p. 24, a. 17. The Particular ([Greek: e)n me/rei]), here for the first time expressly distinguished by Aristotle, is thus defined:--[Greek: e)n me/rei de\ to\ tini\ ê)\ mê\ tini\ ê)\ mê\ panti\ u(pa/rchein.]]

[Footnote 7: Ibid. b. 26: [Greek: to\ d' e)n o(/lô| ei)nai e(/teron e(te/rô|, kai\ to\ kata\ panto\s katêgorei=sthai thate/rou tha/teron, tau)to/n e)sti--tau)to\n], i.e. [Greek: a)ntestramme/nôs], as Waitz remarks in note. Julius Pacius says:--"Idem re, sed ratione differunt ut ascensus et descensus; nam subjectum dicitur esse vel non esse in toto attributo, quia attributum dicitur de omni vel de nullo subjecto" (p. 128).]

The definition given of a Syllogism is very clear and remarkable:--"It is a speech in which, some positions having been laid down, something different from these positions follows as a necessary consequence from their being laid down." In a perfect Syllogism nothing additional is required to make the necessity of the consequence obvious as well as complete. But there are also imperfect Syllogisms, in which such necessity, though equally complete, is not so obviously conveyed in the premisses, but requires some change to be effected in the position of the terms in order to render it conspicuous.[8]

[Footnote 8: Aristot. Anal. Prior. I. i. p. 24, b. 18-26. The same, with a little difference of wording, at the commencement of Topica, p. 100, a. 25. Compare also Analyt. Poster. I. x. p. 76, b. 38: [Greek: o(/sôn o)/ntôn tô=| e)kei=na ei)=nai gi/netai to\ sumpe/rasma.]]

The term Syllogism has acquired, through the influence of Aristotle, a meaning so definite and technical, that we do not easily conceive it in any other meaning. But in Plato and other contemporaries it bears a much wider sense, being equivalent to reasoning generally, to the process of comparison, abstraction, generalization.[9] It was Aristotle who consecrated the word, so as to mean exclusively the reasoning embodied in propositions of definite form and number. Having already analysed propositions separately taken, and discriminated them into various classes according to their constituent elements, he now proceeds to consider propositions in combination. Two propositions, if properly framed, will conduct to a third, different from themselves, but which will be necessarily true if they are true. Aristotle calls the three together a Syllogism.[10] He undertakes to shew how it must be framed in order that its conclusion shall be necessarily true, if the premisses are true. He furnishes schemes whereby the cast and arrangement of premisses, proper for attaining truth, may be recognized; together with the nature of the conclusion, warrantable under each arrangement.

[Footnote 9: See especially Plato, Theætêt. p. 186, B-D., where [Greek: o( sullogismo\s] and [Greek: ta\ a)nalogi/smata] are equivalents.]

[Footnote 10: Julius Pacius (ad Analyt. Prior. I. i.) says that it is a mistake on the part of most logicians to treat the Syllogism as including three propositions (ut vulgus logicorum putat). He considers the premisses alone as constituting the Syllogism; the conclusion is not a part thereof, but something distinct and superadded. It appears to me that the vulgus logicorum are here in the right.]

In the Analytica Priora, we find ourselves involved, from and after the second chapter, in the distinction of Modal propositions, the necessary and the possible. The rules respecting the simple Assertory propositions are thus, even from the beginning, given in conjunction and contrast with those respecting the Modals. This is one among many causes of the difficulty and obscurity with which the treatise is beset. Theophrastus and Eudemus seem also to have followed their master by giving prominence to the Modals:[11] recent expositors avoid the difficulty, some by omitting them altogether, others by deferring them until the simple assertory propositions have been first made clear. I shall follow the example of these last; but it deserves to be kept in mind, as illustrating Aristotle's point of view, that he regards the Modals as principal varieties of the proposition, co-ordinate in logical position with the simple assertory.

[Footnote 11: Eudemi Fragmenta, cii.-ciii. p. 145, ed. Spengel.]

Before entering on combinations of propositions, Aristotle begins by shewing what can be done with single propositions, in view to the investigation or proving of truth. A single proposition may be converted; that is, its subject and predicate may be made to change places. If a proposition be true, will it be true when thus converted, or (in other words) will its converse be true? If false, will its converse be false? If this be not always the case, what are the conditions and limits under which (assuming the proposition to be true) the process of conversion leads to assured truth, in each variety of propositions, affirmative or negative, universal or particular? As far as we know, Aristotle was the first person that ever put to himself this question; though the answer to it is indispensable to any theory of the process of proving or disproving. He answers it before he enters upon the Syllogism.

The rules which he lays down on the subject have passed into all logical treatises. They are now familiar; and readers are apt to fancy that there never was any novelty in them--that every one knows them without being told. Such fancy would be illusory. These rules are very far from being self-evident, any more than the maxims of Contradiction and of the Excluded Middle. Not one of the rules could have been laid down with its proper limits, until the discrimination of propositions, both as to quality (affirmative or negative), and as to quantity (universal or particular), had been put prominently forward and appreciated in all its bearings. The rule for trustworthy conversion is different for each variety of propositions. The Universal Negative may be converted simply; that is, the predicate may become subject, and the subject may become predicate--the proposition being true after conversion, if it was true before. But the Universal Affirmative cannot be thus converted simply. It admits of conversion only in the manner called by logicians per accidens: if the predicate change places with the subject, we cannot be sure that the proposition thus changed will be true, unless the new subject be lowered in quantity from universal to particular; e.g. the proposition, All men are animals, has for its legitimate converse not, All animals are men, but only, Some animals are men. The Particular Affirmative may be converted simply: if it be true that Some animals are men, it will also be true that Some men are animals. But, lastly, if the true proposition to be converted be a Particular Negative, it cannot be converted at all, so as to make sure that the converse will be true also.[12]

[Footnote 12: Aristot. Analyt. Prior. I. ii. p. 25, a. 1-26.]

Here then are four separate rules laid down, one for each variety of propositions. The rules for the second and third variety are proved by the rule for the first (the Universal Negative), which is thus the basis of all. But how does Aristotle prove the rule for the Universal Negative itself? He proceeds as follows: "If A cannot be predicated of any one among the B's, neither can B be predicated of any one among the A's. For if it could be predicated of any one among them (say C), the proposition that A cannot be predicated of any B would not be true; since C is one among the B's."[13] Here we have a proof given which is no proof at all. If I disbelieved or doubted the proposition to be proved, I should equally disbelieve or doubt the proposition given to prove it. The proof only becomes valid, when you add a farther assumption which Aristotle has not distinctly enunciated, viz.: That if some A (e.g. C) is B, then some B must also be A; which would be contrary to the fundamental supposition. But this farther assumption cannot be granted here, because it would imply that we already know the rule respecting the convertibility of Particular Affirmatives, viz., that they admit of being converted simply. Now the rule about Particular Affirmatives is afterwards itself proved by help of the preceding demonstration respecting the Universal Negative. As the proof stands, therefore, Aristotle demonstrates each of these by means of the other; which is not admissible.[14]

[Footnote 13: Ibid. p. 25, a. 15: [Greek: ei) ou)=n mêdeni\ tô=n B to\ A u(pa/rchei, ou)de\ tô=n A ou)deni\ u(pa/rxei to\ B. ei) ga\r tini, oi(=on tô=| G, ou)k a)lêthe\s e)/stai to\ mêdeni\ tô=n B to\ A u(pa/rchein; to\ ga\r G tô=n B ti/ e)stin.]

Julius Pacius (p. 129) proves the Universal Negative to be convertible simpliciter, by a Reductio ad Absurdum cast into a syllogism in the First figure. But it is surely unphilosophical to employ the rules of Syllogism as a means of proving the legitimacy of Conversion, seeing that we are forced to assume conversion in our process for distinguishing valid from invalid syllogisms. Moreover the Reductio ad Absurdum assumes the two fundamental Maxims of Contradiction and Excluded Middle, though these are less obvious, and stand more in need of proof than the simple conversion of the Universal Negative, the point that they are brought to establish.]

[Footnote 14: Waitz, in his note (p. 374), endeavours, but I think without success, to show that Aristotle's proof is not open to the criticism here advanced. He admits that it is obscurely indicated, but the amplification of it given by himself still remains exposed to the same objection.]

Even the friends and companions of Aristotle were not satisfied with his manner of establishing this fundamental rule as to the conversion of propositions. Eudêmus is said to have given a different proof; and Theophrastus assumed as self-evident, without any proof, that the Universal Negative might always be converted simply.[15] It appears to me that no other or better evidence of it can be offered, than the trial upon particular cases, that is to say, Induction.[16] Nothing is gained by dividing (as Aristotle does) the whole A into parts, one of which is C; nor can I agree with Theophrastus in thinking that every learner would assent to it at first hearing, especially at a time when no universal maxims respecting the logical value of propositions had ever been proclaimed. Still less would a Megaric dialectician, if he had never heard the maxim before, be satisfied to stand upon an alleged à priori necessity without asking for evidence. Now there is no other evidence except by exemplifying the formula, No A is B, in separate propositions already known to the learner as true or false, and by challenging him to produce any one case, in which, when it is true to say No A is B, it is not equally true to say, No B is A; the universality of the maxim being liable to be overthrown by any one contradictory instance.[17] If this proof does not convince him, no better can be produced. In a short time, doubtless, he will acquiesce in the general formula at first hearing, and he may even come to regard it as self-evident. It will recall to his memory an aggregate of separate cases each individually forgotten, summing up their united effect under the same aspect, and thus impressing upon him the general truth as if it were not only authoritative but self-authorized.

[Footnote 15: See the Scholia of Alexander on this passage, p. 148, a. 30-45, Brandis; Eudemi Fragm. ci.-cv. pp. 145-149, ed. Spengel.]

[Footnote 16: We find Aristotle declaring in Topica, II. viii. p. 113, b. 15, that in converting a true Universal Affirmative proposition, the negative of the Subject of the convertend is always true of the negative of the Predicate of the convertend; e.g. If every man is an animal, every thing which is not an animal is not a man. This is to be assumed (he says) upon the evidence of Induction--uncontradicted iteration of particular cases, extended to all cases universally--[Greek: lamba/nein d' e)x e)pagôgê=s, oi(=on ei) o( a)/nthrôpos zô=|on, to\ mê\ zô=|on ou)k a)/nthrôpos; o(moi/ôs de\ kai\ e)pi\ tô=n a)/llôn. . . . . e)pi\ pa/ntôn ou)=n to\ toiou=ton a)xiôte/on.]

The rule for the simple conversion of the Universal Negative rests upon the same evidence of Induction, never contradicted.]

[Footnote 17: Dr. Wallis, in one of his acute controversial treatises against Hobbes, remarks upon this as the process pursued by Euclid in his demonstrations:--"You tell us next that an Induction, without enumeration of all the particulars, is not sufficient to infer a conclusion. Yes, Sir, if after the enumeration of some particulars, there comes a general clause, and the like in other cases (as here it doth), this may pass for a proofe till there be a possibility of giving some instance to the contrary, which here you will never be able to doe. And if such an Induction may not pass for proofe, there is never a proposition in Euclid demonstrated. For all along he takes no other course, or at least grounds his Demonstrations on Propositions no otherwise demonstrated. As, for instance, he proposeth it in general (i. c. 1.)--To make an equilateral triangle on a line given. And then he shows you how to do it upon the line A B, which he there shows you, and leaves you to supply: And the same, by the like means, may be done upon any other strait line; and then infers his general conclusion. Yet I have not heard any man object that the Induction was not sufficient, because he did not actually performe it in all lines possible."--(Wallis, Due Correction to Mr. Hobbes, Oxon. 1656, sect. v. p. 42.) This is induction by parity of reasoning.

So also Aristot. Analyt. Poster. I. iv. p. 73, b. 32: [Greek: to\ katho/lou de\ u(pa/rchei to/te, o(/tan e)pi\ tou= tucho/ntos kai\ prô/tou deiknu/êtai.]]

Aristotle passes next to Affirmatives, both Universal and Particular. First, if A can be predicated of all B, then B can be predicated of some A; for if B cannot be predicated of any A, then (by the rule for the Universal Negative) neither can A be predicated of any B. Again, if A can be predicated of some B, in this case also, and for the same reason, B can be predicated of some A.[18] Here the rule for the Universal Negative, supposed already established, is applied legitimately to prove the rules for Affirmatives. But in the first case, that of the Universal, it fails to prove some in the sense of not-all or some-at-most, which is required; whereas, the rules for both cases can be proved by Induction, like the formula about the Universal Negative. When we come to the Particular Negative, Aristotle lays down the position, that it does not admit of being necessarily converted in any way. He gives no proof of this, beyond one single exemplification: If some animal is not a man, you are not thereby warranted in asserting the converse, that some man is not an animal.[19] It is plain that such an exemplification is only an appeal to Induction: you produce one particular example, which is entering on the track of Induction; and one example alone is sufficient to establish the negative of an universal proposition.[20] The converse of a Particular Negative is not in all cases true, though it may be true in many cases.

[Footnote 18: Aristot. Analyt. Prior. I. ii. p. 25, a. 17-22.]

[Footnote 19: Ibid. p. 25, a. 22-26.]

[Footnote 20: Though some may fancy that the rule for converting the Universal Negative is intuitively known, yet every one must see that the rule for converting the Universal Affirmative is not thus self-evident, or derived from natural intuition. In fact, I believe that every learner at first hears it with great surprise. Some are apt to fancy that the Universal Affirmative (like the Particular Affirmative) may be converted simply. Indeed this error is not unfrequently committed in actual reasoning; all the more easily, because there is a class of cases (with subject and predicate co-extensive) where the converse of the Universal Affirmative is really true. Also, in the case of the Particular Negative, there are many true propositions in which the simple converse is true. A novice might incautiously generalize upon those instances, and conclude that both were convertible simply. Nor could you convince him of his error except by producing examples in which, when a true proposition of this kind is converted simply, the resulting converse is notoriously false. The appeal to various separate cases is the only basis on which we can rest for testing the correctness or incorrectness of all these maxims proclaimed as universal.]

From one proposition taken singly, no new proposition can be inferred; for purposes of inference, two propositions at least are required.[21] This brings us to the rules of the Syllogism, where two propositions as premisses conduct us to a third which necessarily follows from them; and we are introduced to the well-known three Figures with their various Modes.[22] To form a valid Syllogism, there must be three terms and no more; the two, which appear as Subject and Predicate of the conclusion, are called the minor term (or minor extreme) and the major term (or major extreme) respectively; while the third or middle term must appear in each of the premisses, but not in the conclusion. These terms are called extremes and middle, from the position which they occupy in every perfect Syllogism--that is in what Aristotle ranks as the First among the three figures. In his way of enunciating the Syllogism, this middle position formed a conspicuous feature; whereas the modern arrangement disguises it, though the denomination middle term is still retained. Aristotle usually employs letters of the alphabet, which he was the first to select as abbreviations for exposition;[23] and he has two ways (conforming to what he had said in the first chapter of the present treatise) of enunciating the modes of the First figure. In one way, he begins with the major extreme (Predicate of the conclusion): A may be predicated of all B, B may be predicated of all C; therefore, A may be predicated of all C (Universal Affirmative). Again, A cannot be predicated of any B, B can be predicated of all C; therefore, A cannot be predicated of any C (Universal Negative). In the other way, he begins with the minor term (Subject of the conclusion): C is in the whole B, B is in the whole A; therefore, C is in the whole A (Universal Affirmative). And, C is in the whole B, B is not in the whole A; therefore, C is not in the whole A (Universal Negative). We see thus that in Aristotle's way of enunciating the First figure, the middle term is really placed between the two extremes,[24] though this is not so in the Second and Third figures. In the modern way of enunciating these figures, the middle term is never placed between the two extremes; yet the denomination middle still remains.

[Footnote 21: Analyt. Prior. I. xv. p. 34, a. 17; xxiii. p. 40, b. 35; Analyt. Poster. I. iii. p. 73, a. 7.]

[Footnote 22: Aristot. Analyt. Prior. I. iv. p. 25, b. 26, seq.]

[Footnote 23: M. Barthélemy St. Hilaire (Logique d'Aristote, vol. ii. p. 7, n.), referring to the examples of Conversion in chap. ii., observes:--"Voici le prémier usage des lettres représentant des idées; c'est un procédé tout à fait algébrique, c'est à dire, de généralisation. Déjà, dans l'Herméneia, ch. 13, § 1 et suiv., Aristote a fait usage de tableaux pour représenter sa pensée relativement à la consécution des modales. Il parle encore spécialement de figures explicatives, liv. 2. des Derniers Analytiques, ch. 17, § 7. Vingt passages de l'Histoire des Animaux attestent qu'il joignait des dessins à ses observations et à ses théories zoologiques. Les illustrations pittoresques datent donc de fort loin. L'emploi symbolique des lettres a été appliqué aussi par Aristote à la Physique. Il l'avait emprunté, sans doute, aux procédés des mathématiciens."

We may remark, however, that when Aristotle proceeds to specify those combinations of propositions which do not give a valid conclusion, he is not satisfied with giving letters of the alphabet; he superadds special illustrative examples (Analyt. Prior. I. v. p. 27, a. 7, 12, 34, 38).]

[Footnote 24: Aristot. Analyt. Prior. I. iv. p. 25, b. 35: [Greek: kalô= de\ me/son, o(\ kai\ au)to\ e)n a)/llô| kai\ a)/llo e)n tou/tô| e)sti/n, o(\ kai\ tê=| the/sei gi/netai me/son.]]

The Modes of each figure are distinguished by the different character and relation of the two premisses, according as these are either affirmative or negative, either universal or particular. Accordingly, there are four possible varieties of each, and sixteen possible modes or varieties of combinations between the two. Aristotle goes through most of the sixteen modes, and shows that in the first Figure there are only four among them that are legitimate, carrying with them a necessary conclusion. He shows, farther, that in all the four there are two conditions observed, and that both these conditions are indispensable in the First figure:--(1) The major proposition must be universal, either affirmative or negative; (2) The minor proposition must be affirmative, either universal or particular or indefinite. Such must be the character of the premisses, in the first Figure, wherever the conclusion is valid and necessary; and vice versâ, the conclusion will be valid and necessary, when such is the character of the premisses.[25]

[Footnote 25: Aristot. Analyt. Prior. I. iv. p. 26, b. 26, et sup.]

In regard to the four valid modes (Barbara, Celarent, Darii, Ferio, as we read in the scholastic Logic) Aristotle declares at once in general language that the conclusion follows necessarily; which he illustrates by setting down in alphabetical letters the skeleton of a syllogism in Barbara. If A is predicated of all B, and B of all C, A must necessarily be predicated of all C. But he does not justify it by any real example; he produces no special syllogism with real terms, and with a conclusion known beforehand to be true. He seems to think that the general doctrine will be accepted as evident without any such corroboration. He counts upon the learner's memory and phantasy for supplying, out of the past discourse of common life, propositions conforming to the conditions in which the symbolical letters have been placed, and for not supplying any contradictory examples. This might suffice for a treatise; but we may reasonably believe that Aristotle, when teaching in his school, would superadd illustrative examples; for the doctrine was then novel, and he is not unmindful of the errors into which learners often fall spontaneously.[26]

[Footnote 26: Analyt. Poster. I. xxiv. p. 85, b. 21.]

When he deals with the remaining or invalid modes of the First figure, his manner of showing their invalidity is different, and in itself somewhat curious. "If (he says) the major term is affirmed of all the middle, while the middle is denied of all the minor, no necessary consequence follows from such being the fact, nor will there be any syllogism of the two extremes; for it is equally possible, either that the major term may be affirmed of all the minor, or that it may be denied of all the minor; so that no conclusion, either universal or particular, is necessary in all cases."[27] Examples of such double possibility are then exhibited: first, of three terms arranged in two propositions (A and E), in which, from the terms specially chosen, the major happens to be truly affirmable of all the minor; so that the third proposition is an universal Affirmative:--

Major and } } Animal is predicable of every Man; Middle. }

Middle and } } Man is not predicable of any Horse; Minor }

Major and } } Animal is predicable of every Horse. Minor }

Next, a second example is set out with new terms, in which the major happens not to be truly predicable of any of the minor; thus exhibiting as third proposition an universal Negative:--

Major and } } Animal is predicable of every Man; Middle. }

Middle and } } Man is not predicable of any Stone; Minor }

Major and } } Animal is not predicable of any Stone. Minor }

Here we see that the full exposition of a syllogism is indicated with real terms common and familiar to every one; alphabetical symbols would not have sufficed, for the learner must himself recognize the one conclusion as true, the other as false. Hence we are taught that, after two premisses thus conditioned, if we venture to join together the major and minor so as to form a pretended conclusion, we may in some cases obtain a true proposition universally Affirmative, in other cases a true proposition universally Negative. Therefore (Aristotle argues) there is no one necessary conclusion, the same in all cases, derivable from such premisses; in other words, this mode of syllogism is invalid and proves nothing. He applies the like reasoning to all the other invalid modes of the first Figure; setting them aside in the same way, and producing examples wherein double and opposite conclusions (improperly so called), both true, are obtained in different cases from the like arrangement of premisses.

[Footnote 27: Analyt. Prior. I. iv. p. 26, a. 2, seq.]

This mode of reasoning plainly depends upon an appeal to prior experience. The validity or invalidity of each mode of the First figure is tested by applying it to different particular cases, each of which is familiar and known to the learner aliunde; in one case, the conjunction of the major and minor terms in the third proposition makes an universal Affirmative which he knows to be true; in another case, the like conjunction makes an universal Negative, which he also knows to be true; so that there is no one necessary (i.e. no one uniform and trustworthy) conclusion derivable from such premisses.[28] In other words, these modes of the First figure are not valid or available in form; the negation being sufficiently proved by one single undisputed example.

[Footnote 28: Though M. Barthélemy St. Hilaire (note, p. 19) declares Aristotle's exposition to be a model of analysis, it appears to me that the grounds for disallowing this invalid mode of the First figure (A--E--A, or A--E--E) are not clearly set forth by Aristotle himself, while they are rendered still darker by some of his best commentators. Thus Waitz says (p. 381): "Per exempla allata probat (Aristoteles) quod demonstrare debebat ex ipsâ ratione quam singuli termini inter se habeant: est enim proprium artis logicæ, ut terminorum rationem cognoscat, dum res ignoret. Num de Caio prædicetur animal nescit, scit de Caio prædicari animal, si animal de homine et homo de Caio prædicetur."

This comment of Waitz appears to me founded in error. Aristotle had no means of shewing the invalidity of the mode A E in the First figure, except by an appeal to particular examples. The invalidity of the invalid modes, and the validity of the valid modes, rest alike upon this ultimate reference to examples of propositions known to be true or false, by prior experience of the learner. The valid modes are those which will stand this trial and verification; the invalid modes are those which will not stand it. Not till such verification has been made, is one warranted in generalizing the result, and enunciating a formula applicable to unknown particulars (rationem terminorum cognoscere, dum res ignoret). It was impossible for Aristotle to do what Waitz requires of him. I take the opposite ground, and regret that he did not set forth the fundamental test of appeal to example and experience, in a more emphatic and unmistakeable manner.

M. Barthélemy St. Hilaire (in the note to his translation, p. 14) does not lend any additional clearness, when he talks of the "conclusion" from the propositions A and E in the First figure. Julius Pacius says (p. 134): "Si tamen conclusio dici debet, quæ non colligitur ex propositionibus," &c. Moreover, M. St. Hilaire (p. 19) slurs over the legitimate foundation, the appeal to experience, much as Aristotle himself does: "Puis prenant des exemples où la conclusion est de toute évidence, Aristote les applique successivement à chacune de ces combinaisons; celles qui donnent la conclusion fournie d'ailleurs par le bon sens, sont concluantes ou syllogistiques, les autres sont asyllogistiques."]

We are now introduced to the Second figure, in which each of the two premisses has the middle term as Predicate.[29] To give a legitimate conclusion in this figure, one or other of the premisses must be negative, and the major premiss must be universal; moreover no affirmative conclusions can ever be obtained in it--none but negative conclusions, universal or particular. In this Second figure too, Aristotle recognizes four valid modes; setting aside the other possible modes as invalid[30] (in the same way as he had done in the First figure), because the third proposition or conjunction of the major term with the minor, might in some cases be a true universal affirmative, in other cases a true universal negative. As to the third and fourth of the valid modes, he demonstrates them by assuming the contradictory of the conclusion, together with the major premiss, and then showing that these two premisses form a new syllogism, which leads to a conclusion contradicting the minor premiss. This method, called Reductio ad Impossibile, is here employed for the first time; and employed without being ushered in or defined, as if it were familiarly known.[31]

[Footnote 29: Analyt. Prior. I. v. p. 26, b. 34. As Aristotle enunciates a proposition by putting the predicate before the subject, he says that in this Second figure the middle term comes [Greek: prô=ton tê=| the/sei]. In the Third figure, for the same reason, he calls it [Greek: e)/schaton tê=| the/sei], vi. p. 28, a. 15.]

[Footnote 30: Analyt. Prior. I. v. p. 27, a. 18. In these invalid modes, Aristotle says there is no syllogism; therefore we cannot properly speak of a conclusion, but only of a third proposition, conjoining the major with the minor.]

[Footnote 31: Ibid. p. 27, a. 15, 26, seq. It is said to involve [Greek: u(po/thesis], p. 28, a. 7; to be [Greek: e)x u(pothe/seôs] xxiii. p. 41, a. 25; to be [Greek: tou= e)x u(pothe/seôs], as opposed to [Greek: deiktiko/s], xxiii. p. 40, b. 25.

M. B. St. Hilaire remarks justly, that Aristotle might be expected to define or explain what it is, on first mentioning it (note, p. 22).]

Lastly, we have the Third figure, wherein the middle term is the Subject in both premisses. Here one at least of the premisses must be universal, either affirmative or negative. But no universal conclusions can be obtained in this figure; all the conclusions are particular. Aristotle recognizes six legitimate modes; in all of which the conclusions are particular, four of them being affirmative, two negative. The other possible modes he sets aside as in the two preceding figures.[32]

[Footnote 32: Ibid. I. vi. p. 28, a. 10-p. 29, a. 18.]

But Aristotle assigns to the First figure a marked superiority as compared with the Second and Third. It is the only one that yields perfect syllogisms; those furnished by the other two are all imperfect. The cardinal principle of syllogistic proof, as he conceives it, is--That whatever can be affirmed or denied of a whole, can be affirmed or denied of any part thereof.[33] The major proposition affirms or denies something universally respecting a certain whole; the minor proposition declares a certain part to be included in that whole. To this principle the four modes of the First figure manifestly and unmistakably conform, without any transformation of their premisses. But in the other figures such conformity does not obviously appear, and must be demonstrated by reducing their syllogisms to the First figure; either ostensively by exposition of a particular case, and conversion of the premisses, or by Reductio ad Impossibile. Aristotle, accordingly, claims authority for the Second and Third figures only so far as they can be reduced to the First.[34] We must, however, observe that in this process of reduction no new evidence is taken in; the matter of evidence remains unchanged, and the form alone is altered, according to laws of logical conversion which Aristotle has already laid down and justified. Another ground of the superiority and perfection which he claims for the First figure, is, that it is the only one in which every variety of conclusion can be proved; and especially the only one in which the Universal Affirmative can be proved--the great aim of scientific research. Whereas, in the Second figure we can prove only negative conclusions, universal or particular; and in the Third figure only particular conclusions, affirmative or negative.[35]

[Footnote 33: Ibid. I. xli. p. 49, b. 37: [Greek: o(/lôs ga\r o(\ mê/ e)stin ô(s o(/lon pro\s me/ros kai\ a)/llo pro\s tou=to ô(s me/ros pro\s o(/lon, e)x ou)deno\s tô=n toiou/tôn dei/knusin o( deiknu/ôn, ô(/ste ou)de\ gi/netai sullogismo/s.]

He had before said this about the relation of the three terms in the Syllogism, I. iv. p. 25, b. 32: [Greek: o(/tan o(/roi trei=s ou(/tôs e)/chôsi pro\s a)llê/lous ô(/ste to\n e)/schaton e)n o(/lô| ei)=nai tô=| me/sô| kai\ to\n me/son e)n o(/lô| tô=| prô/tô| ê)\ ei)=nai ê)\ mê\ ei)=nai, a)na/gkê tô=n a)/krôn ei)=nai sullogismo\n te/leion] (Dictum de Omni et Nullo).]

[Footnote 34: Analyt. Prior. I. vii. p. 29, a. 30-b. 25.]

[Footnote 35: Ibid. I. iv. p. 26, b. 30, p. 27, a. 1, p. 28, a. 9, p. 29, a. 15. An admissible syllogism in the Second or Third figure is sometimes called [Greek: dunato\s] as opposed to [Greek: te/leios], p. 41, b. 33. Compare Kampe, Die Erkenntniss-Theorie des Aristoteles, p. 245, Leipzig, 1870.]

Such are the main principles of syllogistic inference and rules for syllogistic reasoning, as laid down by Aristotle. During the mediæval period, they were allowed to ramify into endless subtle technicalities, and to absorb the attention of teachers and studious men, long after the time when other useful branches of science and literature were pressing for attention. Through such prolonged monopoly--which Aristotle, among the most encyclopedical of all writers, never thought of claiming for them--they have become so discredited, that it is difficult to call back attention to them as they stood in the Aristotelian age. We have to remind the reader, again, that though language was then used with great ability for rhetorical and dialectical purposes, there existed as yet hardly any systematic or scientific study of it in either of these branches. The scheme and the terminology of any such science were alike unknown, and Aristotle was obliged to construct it himself from the foundation. The rhetorical and dialectical teaching as then given (he tells us) was mere unscientific routine, prescribing specimens of art to be committed to memory: respecting syllogism (or the conditions of legitimate deductive inference) absolutely nothing had been said.[36] Under these circumstances, his theory of names, notions, and propositions as employed for purposes of exposition and ratiocination, is a remarkable example of original inventive power. He had to work it out by patient and laborious research. No way was open to him except the diligent comparison and analysis of propositions. And though all students have now become familiar with the various classes of terms and propositions, together with their principal characteristics and relations, yet to frame and designate such classes for the first time without any precedent to follow, to determine for each the rules and conditions of logical convertibility, to put together the constituents of the Syllogism, with its graduation of Figures and difference of Modes, and with a selection, justified by reasons given, between the valid and the invalid modes--all this implies a high order of original systematizing genius, and must have required the most laborious and multiplied comparisons between propositions in detail.

[Footnote 36: Aristot. Sophist. Elench. p. 184, a. 1, b. 2: [Greek: dio/per tachei=a me\n a)/technos d' ê)=n ê( didaskali/a toi=s mantha/nousi par' au)tô=n; ou) ga\r te/chnên a)lla\ ta\ a)po\ tê=s te/chnês dido/ntes paideu/ein u(pela/mbanon . . . . peri\ de\ tou= sullogi/zesthai pantelô=s ou)de\n ei)/chomen pro/teron a)/llo le/gein, a)ll' ê)\ tribê=| zêtou=ntes polu\n chro/non e)ponou=men.]]

The preceding abridgment of Aristotle's exposition of the Syllogism applies only to propositions simply affirmative or simply negative. But Aristotle himself, as already remarked, complicates the exposition by putting the Modal propositions (Possible, Necessary) upon the same line as the above-mentioned Simple propositions. I have noticed, in dealing with the treatise De Interpretatione, the confusion that has arisen from thus elevating the Modals into a line of classification co-ordinate with propositions simply Assertory. In the Analytica, this confusion is still more sensibly felt, from the introduction of syllogisms in which one of the premisses is necessary, while the other is only possible. We may remark, however, that, in the Analytica, Aristotle is stricter in defining the Possible than he has been in the De Interpretatione; for he now disjoins the Possible altogether from the Necessary, making it equivalent to the Problematical (not merely may be, but may be or may not be).[37] In the middle, too, of his diffuse exposition of the Modals, he inserts one important remark, respecting universal propositions generally, which belongs quite as much to the preceding exposition about propositions simply assertory. He observes that universal propositions have nothing to do with time, present, past, or future; but are to be understood in a sense absolute and unqualified.[38]

[Footnote 37: Analyt. Prior. I. viii. p. 29, a. 32; xiii. p. 32, a. 20-36: [Greek: to\ ga\r a)nagkai=on o(mônu/môs e)nde/chesthai le/gomen]. In xiv. p. 33, b. 22, he excludes this equivocal meaning of [Greek: to\ e)ndecho/menon--dei= de\ to\ e)nde/chestha lamba/nein mê\ e)n toi=s a)nagkai/ois, a)lla\ kata\ to\n ei)rême/non diorismo/n.] See xiii. p. 32, a. 33, where [Greek: to\ e)nde/chesthai u(pa/rchein] is asserted to be equivalent to or convertible with [Greek: to\ e)nde/chesthai mê\ u(pa/rchein]; and xix. p. 38, a. 35: [Greek: to\ e)x a)na/gkês ou)k ê)=n e)ndecho/menon]. Theophrastus and Eudemus differed from Aristotle about his theory of the Modals in several points (Scholia ad Analyt. Priora, pp. 161, b. 30; 162, b. 23; 166, a. 12, b. 15, Brand.). Respecting the want of clearness in Aristotle about [Greek: to\ e)ndecho/menon], see Waitz's note **ad p. 32, b. 16. Moreover, he sometimes uses [Greek: u(pa/rchon] in the widest sense, including [Greek: e)ndecho/menon] and [Greek: a)nagkai=on], xxiii. p. 40, b. 24.]

[Footnote 38: Analyt. Prior. I. xv. p. 34, b. 7.]

Having finished with the Modals, Aristotle proceeds to lay it down, that all demonstration must fall under one or other of the three figures just described; and therefore that all may be reduced ultimately to the two first modes of the First figure. You cannot proceed a step with two terms only and one proposition only. You must have two propositions including three terms; the middle term occupying the place assigned to it in one or other of the three figures.[39] This is obviously true when you demonstrate by direct or ostensive syllogism; and it is no less true when you proceed by Reductio ad Impossibile. This last is one mode of syllogizing from an hypothesis or assumption:[40] your conclusion being disputed, you prove it indirectly, by assuming its contradictory to be true, and constructing a new syllogism by means of that contradictory together with a second premiss admitted to be true; the conclusion of this new syllogism being a proposition obviously false or known beforehand to be false. Your demonstration must be conducted by a regular syllogism, as it is when you proceed directly and ostensively. The difference is, that the conclusion which you obtain is not that which you wish ultimately to arrive at, but something notoriously false. But as this false conclusion arises from your assumption or hypothesis that the contradictory of the conclusion originally disputed was true, you have indirectly made out your case that this contradictory must have been false, and therefore that the conclusion originally disputed was true. All this, however, has been demonstration by regular syllogism, but starting from an hypothesis assumed and admitted as one of the premisses.[41]

[Footnote 39: Ibid. xxiii. p. 40, b. 20, p. 41, a. 4-20.]

[Footnote 40: Ibid. p. 40, b. 25: [Greek: e)/ti ê)\ deiktikô=s ê)\ e)x u(pothe/seôs; tou= d' e)x u(pothe/seôs me/ros to\ dia\ tou= a)duna/tou.]]

[Footnote 41: Ibid. p. 41, b. 23: [Greek: pa/ntes ga\r oi( dia\ tou= a)duna/tou perai/nontes to\ me\n pseu=dos sullogi/zontai, to\ d' e)x a)rchê=s e)x u(pothe/seôs deiknu/ousin, o(/tan a)du/nato/n ti sumbai/nê| tê=s a)ntipha/seôs tethei/sês.]

It deserves to be remarked that Aristotle uses the phrase [Greek: sullogismo\s e)x u(pothe/seôs], not [Greek: sullogismo\s u(pothetiko/s]. This bears upon the question as to his views upon what subsequently received the title of hypothetical syllogisms; a subject to which I shall advert in a future note.]

Aristotle here again enforces what he had before urged--that in every valid syllogism, one premiss at least must be affirmative, and one premiss at least must be universal. If the conclusion be universal, both premisses must be so likewise; if it be particular, one of the premisses may not be universal. But without one universal premiss at least, there can be no syllogistic proof. If you have a thesis to support, you cannot assume (or ask to be conceded to you) that very thesis, without committing petitio principii, (i.e. quæsiti or probandi); you must assume (or ask to have conceded to you) some universal proposition containing it and more besides; under which universal you may bring the subject of your thesis as a minor, and thus the premisses necessary for supporting it will be completed. Aristotle illustrates this by giving a demonstration that the angles at the base of an isosceles triangle are equal; justifying every step in the reasoning by an appeal to some universal proposition.[42]

[Footnote 42: Analyt. Prior. I. xxiv. p. 41, b. 6-31. The demonstration given (b. 13-22) is different from that which we read in Euclid, and is not easy to follow. It is more clearly explained by Waitz (p. 434) than either by Julius Pacius or by M. Barth. St. Hilaire (p. 108).]

Again, every demonstration is effected by two propositions (an even number) and by three terms (an odd number); though the same proposition may perhaps be demonstrable by more than one pair of premisses, or through more than one middle term;[43] that is, by two or more distinct syllogisms. If there be more than three terms and two propositions, either the syllogism will no longer be one but several; or there must be particulars introduced for the purpose of obtaining an universal by induction; or something will be included, superfluous and not essential to the demonstration, perhaps for the purpose of concealing from the respondent the real inference meant.[44] In the case (afterwards called Sorites) where the ultimate conclusion is obtained through several mean terms in continuous series, the number of terms will always exceed by one the number of propositions; but the numbers may be odd or even, according to circumstances. As terms are added, the total of intermediate conclusions, if drawn out in form, will come to be far greater than that of the terms or propositions, multiplying as it will do in an increasing ratio to them.[45]

[Footnote 43: Ibid. I. xxv. p. 41, b. 36, seq.]

[Footnote 44: Ibid. xxv. p. 42, a. 23: [Greek: ma/tên e)/stai ei)lêmme/na, ei) mê\ e)pagôgê=s ê)\ kru/pseôs ê)/ tinos a)/llou tô=n toiou/tôn cha/rin.] Ib. a. 38: [Greek: ou(=tos o( lo/gos ê)\ ou) sullelo/gistai ê)\ plei/ô tô=n a)nagkai/ôn ê)rô/têke pro\s tê\n the/sin.]]

[Footnote 45: Ibid. p. 42, b. 5-26.]

It will be seen clearly from the foregoing remarks that there is a great difference between one thesis and another as to facility of attack or defence in Dialectic. If the thesis be an Universal Affirmative proposition, it can be demonstrated only in the First figure, and only by one combination of premisses; while, on the other hand, it can be impugned either by an universal negative, which can be demonstrated both in the First and Second figures, or by a particular negative, which can be demonstrated in all the three figures. Hence an Universal Affirmative thesis is at once the hardest to defend and the easiest to oppugn: more so than either a Particular Affirmative, which can be proved both in the First and Third figures; or a Universal Negative, which can be proved either in First or Second.[46] To the opponent, an universal thesis affords an easier victory than a particular thesis; in fact, speaking generally, his task is easier than that of the defendant.

[Footnote 46: Analyt. Prior. I. xxvi. p. 42, b. 27, p. 43, a. 15.]

In the Analytica Priora, Aristotle proceeds to tell us that he contemplates not only theory, but also practice and art. The reader must be taught, not merely to understand the principles of Syllogism, but likewise where he can find the matter for constructing syllogisms readily, and how he can obtain the principles of demonstration pertinent to each thesis propounded.[47]

[Footnote 47: Ibid. I. xxvii. p. 43, a. 20: [Greek: pô=s d' eu)porê/somen au)toi\ pro\s to\ tithe/menon a)ei\ sullogismô=n, kai\ dia\ poi/as o(dou= lêpso/metha ta\s peri\ e(/kaston a)rcha/s, nu=n ê)/dê lekte/on; ou) ga\r mo/non i)/sôs dei= tê\n ge/nesin theôrei=n tô=n sullogismô=n, a)lla\ kai\ tê\n du/namin e)/chein tou= poiei=n.] The second section of Book I. here begins.]

A thesis being propounded in appropriate terms, with subject and predicate, how are you the propounder to seek out arguments for its defence? In the first place, Aristotle reverts to the distinction already laid down at the beginning of the Categoriæ.[48] Individual things or persons are subjects only, never appearing as predicates--this is the lowest extremity of the logical scale: at the opposite extremity of the scale, there are the highest generalities, predicates only, and not subjects of any predication, though sometimes supposed to be such, as matters of dialectic discussion.[49] Between the lowest and highest we have intermediate or graduate generalities, appearing sometimes as subjects, sometimes as predicates; and it is among these that the materials both of problems for debate, and of premisses for proof, are usually found.[50]

[Footnote 48: Ibid. I. xxvii. p. 43, a. 25, seq.]

[Footnote 49: Ibid. p. 43, a. 39: [Greek: plê\n ei) mê\ kata\ do/xan]. Cf. Schol. of Alexander, p. 175, a. 44, Br.: [Greek: e)ndo/xôs kai\ dialektikô=s, ô(/sper ei)=pen e)n toi=s Topikoi=s], that even the principia of science may be debated; for example, in book B. of the Metaphysica. Aristotle does not recognize either [Greek: to\ o)/n] or [Greek: to\ e(/n] as true genera, but only as predicates.]

[Footnote 50: Ibid. a. 40-43.]

You must begin by putting down, along with the matter in hand itself, its definition and its propria; after that, its other predicates; next, those predicates which cannot belong to it; lastly, those other subjects, of which it may itself be predicated. You must classify its various predicates distinguishing the essential, the propria, and the accidental; also distinguishing the true and unquestionable, from the problematical and hypothetical.[51] You must look out for those predicates which belong to it as subject universally, and not to certain portions of it only; since universal propositions are indispensable in syllogistic proof, and indefinite propositions can only be reckoned as particular. When a subject is included in some larger genus--as, for example, man in animal--you must not look for the affirmative or negative predicates which belong to animal universally (since all these will of course belong to man also) but for those which distinguish man from other animals; nor must you, in searching for those lower subjects of which man is the predicate, fix your attention on the higher genus animal; for animal will of course be predicable of all those of which man is predicable. You must collect what pertains to man specially, either as predicate or subject; nor merely that which pertains to him necessarily and universally, but also usually and in the majority of cases; for most of the problems debated belong to this latter class, and the worth of the conclusion will be co-ordinate with that of the premisses.[52]** Do not select predicates that are predicable[53] both of the predicate and subject; for no valid affirmative conclusion can be obtained from them.

[Footnote 51: Analyt. Prior. I. xxvii. p. 43, b. 8: [Greek: kai\ tou/tôn poi=a doxastikô=s kai\ poi=a kat' a)lê/theian.]]

[Footnote 52: Ibid. I. xxvii. p. 43, b. 10-35.]

[Footnote 53: Ibid. b. 36: [Greek: e)/ti ta\ pa=sin e(po/mena ou)k e)klekte/on; ou) ga\r e)/stai sullogismo\s e)x au)tô=n.] The phrase [Greek: ta\ pa=sin e(po/mena], as denoting predicates applicable both to the predicate and to the subject, is curious. We should hardly understand it, if it were not explained a little further on, p. 44, b. 21. Both the Scholiast and the modern commentators understand [Greek: ta\ pa=sin e(po/mena] in this sense; and I do not venture to depart from them. At the same time, when I read six lines afterwards (p. 44, b. 26) the words [Greek: oi(=on ei) ta\ e(po/mena e(kate/rô| tau)ta/ e)stin]--in which the same meaning as that which the commentators ascribe to [Greek: ta\ pa=sin e(po/mena] is given in its own special and appropriate terms, and thus the same supposition unnecessarily repeated--I cannot help suspecting that Aristotle intends [Greek: ta\ pa=sin e(po/mena] to mean something different; to mean such wide and universal predicates as [Greek: to\ e(\n] and [Greek: to\ o)/n] which soar above the Categories and apply to every thing, but denote no real genera.]

Thus, when the thesis to be maintained is an universal affirmative (e.g. A is predicable of all E), you will survey all the subjects to which A will apply as predicate, and all the predicates applying to E as subject. If these two lists coincide in any point, a middle term will be found for the construction of a good syllogism in the First figure. Let B represent the list of predicates belonging universally to A; D, the list of predicates which cannot belong to it; C, the list of subjects to which A pertains universally as predicate. Likewise, let F represent the list of predicates belonging universally to E; H, the list of predicates that cannot belong to E; G, the list of subjects to which E is applicable as predicate. If, under these suppositions, there is any coincidence between the list C and the list F, you can construct a syllogism (in Barbara, Fig. 1), demonstrating that A belongs to all E; since the predicate in F belongs to all E, and A universally to the subject in C. If the list C coincides in any point with the list G, you can prove that A belongs to some E, by a syllogism (in Darapti, Fig. 3). If, on the other hand, the list F coincides in any point with the list D, you can prove that A cannot belong to any E: for the predicate in D cannot belong to any A, and therefore (by converting simply the universal negative) A cannot belong as predicate to any D; but D coincides with F, and F belongs to all E; accordingly, a syllogism (in Celarent, Fig. 1) may be constructed, shewing that A cannot belong to any E. So also, if B coincides in any point with H, the same conclusion can be proved; for the predicate in B belongs to all A, but B coincides with H, which belongs to no E; whence you obtain a syllogism (in Camestres, Fig. 2), shewing that no A belongs to E.[54] In collecting the predicates and subjects both of A and of E, the highest and most universal expression of them is to be preferred, as affording the largest grasp for the purpose of obtaining a suitable middle term.[55] It will be seen (as has been declared already) that every syllogism obtained will have three terms and two propositions; and that it will be in one or other of the three figures above described.[56]

[Footnote 54: Analyt. Prior. I. xxviii. p. 43, b. 39-p. 44, a. 35.]

[Footnote 55: Ibid. p. 44, a. 39. Alexander and Philoponus (Scholia, p. 177, a. 19, 39, Brandis) point out an inconsistency between what Aristotle says here and what he had said in one of the preceding paragraphs, dissuading the inquirer from attending to the highest generalities, and recommending him to look only at both subject and predicate in their special place on the logical scale. Alexander's way of removing the inconsistency is not successful: I doubt if there be an inconsistency. I understand Aristotle here to mean only that the universal expression KZ ([Greek: to\ katho/lou Z]) is to be preferred to the indefinite or indeterminate (simply Z, [Greek: a)dio/riston]), also K[Greek: G] ([Greek: to\ katho/lou G]) to simple [Greek: G (a)dio/riston)]. This appears to me not inconsistent with the recommendation which Aristotle had given before.]

[Footnote 56: Ibid. p. 44, b. 6-20.]

The way just pointed out is the only way towards obtaining a suitable middle term. If, for example, you find some predicate applicable both to A and E, this will not conduct you to a valid syllogism; you will only obtain a syllogism in the Second figure with two affirmative premisses, which will not warrant any conclusion. Or if you find some predicate which cannot belong either to A or to E, this again will only give you a syllogism in the Second figure with two negative premisses, which leads to nothing. So also, if you have a term of which A can be predicated, but which cannot be predicated of E, you derive from it only a syllogism in the First figure, with its minor negative; and this, too, is invalid. Lastly, if you have a subject, of which neither A nor E can be predicated, your syllogism constructed from these conditions will have both its premisses negative, and will therefore be worthless.[57]

[Footnote 57: Analyt. Prior. I. xxviii. p. 44, b. 25-37.]

In the survey prescribed, nothing is gained by looking out for predicates (of A and E) which are different or opposite: we must collect such as are identical, since our purpose is to obtain from them a suitable middle term, which must be the same in both premisses. It is true that if the list B (containing the predicates universally belonging to A) and the list F (containing the predicates universally belonging to E) are incompatible or contrary to each other, you will arrive at a syllogism proving that no A can belong to E. But this syllogism will proceed, not so much from the fact that B and F are incompatible, as from the other fact, distinct though correlative, that B will to a certain extent coincide with H (the list of predicates which cannot belong to E). The middle term and the syllogism constituted thereby, is derived from the coincidence between B and H, not from the opposition between B and F. Those who derive it from the latter, overlook or disregard the real source, and adopt a point of view merely incidental and irrelevant.[58]

[Footnote 58: Ibid. p. 44, b. 38-p. 45, a. 22. [Greek: sumbai/nei dê\ toi=s ou(/tôs e)piskopou=si prosepible/pein a)/llên o(do\n tê=s a)nagkai/as, dia\ to\ lantha/nein tê\n tau)to/têta tô=n B kai\ tô=n Th.]]

The precept here delivered--That in order to obtain middle terms and good syllogisms, you must study and collect both the predicates and the subjects of the two terms of your thesis--Aristotle declares to be equally applicable to all demonstration, whether direct or by way of Reductio ad Impossibile. In both the process of demonstration is the same--involving two premisses, three terms, and one of the three a suitable middle term. The only difference is, that in the direct demonstration, both premisses are propounded as true, while in the Reductio ad Impossibile, one of the premisses is assumed as true though known to be false, and the conclusion also.[59] In the other cases of hypothetical syllogism your attention must be directed, not to the original quæsitum, but to the condition annexed thereto; yet the search for predicates, subjects, and a middle term, must be conducted in the same manner.[60] Sometimes, by the help of a condition extraneous to the premisses, you may demonstrate an universal from a particular: e.g., Suppose C (the list of subjects to which A belongs as predicate) and G (the list of subjects to which E belongs as predicate) to be identical; and suppose farther that the subjects in G are the only ones to which E belongs as predicate (this seems to be the extraneous or extra-syllogistic condition assumed, on which Aristotle's argument turns); then, A will be applicable to all E. Or if D (the list of predicates which cannot belong to A) and G (the list of subjects to which E belongs as predicate) are identical; then, assuming the like extraneous condition, A will not be applicable to any E.[61] In both these cases, the conclusion is more universal than the premisses; but it is because we take in an hypothetical assumption, in addition to the premisses.

[Footnote 59: Ibid. I. xxix. p. 45, a. 25-b. 15.]

[Footnote 60: Ibid. I. xxix. p. 45, b. 15-20. This paragraph is very obscure. Neither Alexander, nor Waitz, nor St. Hilaire clears it up **completely. See Schol. pp. 178, b., 179, a. Brandis.

Aristotle concludes by saying that syllogisms from an hypothesis ought to be reviewed and classified into varieties--[Greek: e)piske/psasthai de\ dei= kai\ dielei=n posachô=s oi( e)x u(pothe/seôs] (b. 20). But it is doubtful whether he himself ever executed this classification. It was done in the Analytica of his successor Theophrastus (Schol. p. 179, a. 6, 24). Compare the note of M. Barthélemy St. Hilaire, p. 140.]

[Footnote 61: Analyt. Prior. I. xxix. p. 45, b. 21-30.]

Aristotle has now shown a method of procedure common to all investigations and proper for the solution of all problems, wherever soluble. He has shown, first, all the conditions and varieties of probative Syllogism, two premisses and three terms, with the place required for the middle term in each of the three figures; next, the quarter in which we are to look for all the materials necessary or suitable for constructing valid syllogisms. Having the two terms of the thesis given, we must study the predicates and subjects belonging to both, and must provide a large list of them; out of which list we must make selection according to the purpose of the moment. Our selection will be different, according as we wish to prove or to refute, and according as the conclusion that we wish to prove is an universal or a particular. The lesson here given will be most useful in teaching the reasoner to confine his attention to the sort of materials really promising, so that he may avoid wasting his time upon such as are irrelevant.[62]

[Footnote 62: Ibid. b. 36-xxx. p. 46, a. 10.]

This method of procedure is alike applicable to demonstration in Philosophy or in any of the special sciences,[63] and to debate in Dialectic. In both, the premisses or principia of syllogisms must be put together in the same manner, in order to make the syllogism valid. In both, too, the range of topics falling under examination is large and varied; each topic will have its own separate premisses or principia, which must be searched out and selected in the way above described. Experience alone can furnish these principia, in each separate branch or department. Astronomical experience--the observed facts and phenomena of astronomy--have furnished the data for the scientific and demonstrative treatment of astronomy. The like with every other branch of science or art.[64] When the facts in each branch are brought together, it will be the province of the logician or analytical philosopher to set out the demonstrations in a manner clear and fit for use. For if nothing in the way of true matter of fact has been omitted from our observation, we shall be able to discover and unfold the demonstration, on every point where demonstration is possible; and, wherever it is not possible, to make the impossibility manifest.[65]

[Footnote 63: Ibid. p. 46, a. 8**: [Greek: kata\ me\n a)lê/theian e)k tô=n kat' a)lê/theian diagegramme/nôn u(pa/rchein, ei)s de\ tou\s dialektikou\s sullogismou\s e)k tô=n kata\ do/xan prota/seôn.]

Julius Pacius (p. 257) remarks upon the word [Greek: diagegramme/nôn] as indicating that Aristotle, while alluding to special sciences distinguishable from philosophy on one side, and from dialectic on the other, had in view geometrical demonstrations.]

[Footnote 64: Analyt. Prior. I. xxx. p. 46, a. 10-20**: [Greek: ai( d' a)rchai\ tô=n sullogismô=n katho/lou me\n ei)/rêntai--i)/diai de\ kath' e(ka/stên ai( plei=stai. dio\ ta\s me\n a)rcha\s ta\s peri\ e(/kaston e)mpeiri/as e)/sti paradou=nai. le/gô d' oi(=on tê\n a)strologikê\n me\n e)mpeiri/an tê=s a)strologikê=s e)pistê/mês; lêphthe/ntôn ga\r i(kanô=s tô=n phainome/nôn ou(/tôs eu(re/thêsan ai( a)strologikai\ a)podei/xeis. o(moi/ôs de\ kai\ peri\ a)/llên o(poianou=n e)/chei te/chnên te kai\ e)pistê/mên.]

What Aristotle says here--of astronomical observation and experience as furnishing the basis for astronomical science--stands in marked contrast with Plato, who rejects this basis, and puts aside, with a sort of contempt, astronomical observation (Republic, vii. pp. 530-531); treating acoustics also in a similar way. Compare Aristot. Metaphys. [Greek: L]. p. 1073, a. 6, seq., with the commentary of Bonitz, p. 506.]

[Footnote 65: Analyt. Prior. I. xxx. p. 46, a. 22-27**: [Greek: ô(/ste a)\n lêphthê=| ta\ u(pa/rchonta peri\ e(/kaston, ê(me/teron ê)/dê ta\s a)podei/xeis e(toi/môs e)mphani/zein. ei) ga\r mêde\n kata\ tê\n i(stori/an paraleiphthei/ê tô=n a)lêthô=s u(parcho/ntôn toi=s pra/gmasin, e(/xomen peri\ a(/pantos ou(= me\n e)/stin a)po/deixis, tau/tên eu(rei=n kai\ a)podeiknu/nai, ou(= de\ mê\ pe/phuken a)po/deixis, tou=to poiei=n phanero/n.]

Respecting the word [Greek: i(stori/a]--investigation and record of matters of fact--the first sentence of Herodotus may be compared with Aristotle, Histor. Animal. p. 491, a. 12; also p. 757, b. 35; Rhetoric. p. 1359, b. 32.]

For the fuller development of these important principles, the reader is referred to the treatise on Dialectic, entitled Topica, which we shall come to in a future chapter. There is nothing in all Aristotle's writings more remarkable than the testimony here afforded, how completely he considered all the generalities of demonstrative science and deductive reasoning to rest altogether on experience and inductive observation.

We are next introduced to a comparison between the syllogistic method, as above described and systematized, and the process called logical Division into genera and species; a process much relied upon by other philosophers, and especially by Plato. This logical Division, according to Aristotle, is a mere fragment of the syllogistic procedure; nothing better than a feeble syllogism.[66] Those who employed it were ignorant both of Syllogism and of its conditions. They tried to demonstrate--what never can be demonstrated--the essential constitution of the subject.[67] Instead of selecting a middle term, as the Syllogism requires, more universal than the subject but less universal (or not more so) than the predicate, they inverted the proper order, and took for their middle term the highest universal. What really requires to be demonstrated, they never demonstrated but assume.[68]

[Footnote 66: Analyt. Prior. I. xxxi. p. 46, a. 33. Alexander, in Scholia, p. 180, a. 14. The Platonic method of [Greek: diai/resis] is exemplified in the dialogues called Sophistês and Politicus; compare also Philêbus, c. v., p. 15.]

[Footnote 67: Ibid. p. 46, a. 34: [Greek: prô=ton d' au)to\ tou=to e)lelê/thei tou\s chrôme/nous au)tê=| pa/ntas, kai\ pei/thein e)pechei/roun ô(s o)/ntos dunatou= peri\ ou)si/as a)po/deixin gi/nesthai kai\ tou= ti/ e)stin.]]

[Footnote 68: Ibid. p. 46, b. 1-12.]

Thus, they take the subject man, and propose to prove that man is mortal. They begin by laying down that man is an animal, and that every animal is either mortal or immortal. Here, the most universal term, animal, is selected as middle or as medium of proof; while after all, the conclusion demonstrated is, not that man is mortal, but that man is either mortal or immortal. The position that man is mortal, is assumed but not proved.[69] Moreover, by this method of logical division, all the steps are affirmative and none negative; there cannot be any refutation of error. Nor can any proof be given thus respecting genus, or proprium, or accidens; the genus is assumed, and the method proceeds from thence to species and differentia. No doubtful matter can be settled, and no unknown point elucidated by this method; nothing can be done except to arrange in a certain order what is already ascertained and unquestionable. To many investigations, accordingly, the method is altogether inapplicable; while even where it is applicable, it leads to no useful conclusion.[70]

[Footnote 69: Ibid. p. 46, b. 1-12.]

[Footnote 70: Ibid. b. 26-37. Alexander in Schol. p. 180, b. 1.]

We now come to that which Aristotle indicates as the third section of this First Book of the Analytica Priora. In the first section he explained the construction and constituents of Syllogism, the varieties of figure and mode, and the conditions indispensable to a valid conclusion. In the second section he tells us where we are to look for the premisses of syllogisms, and how we may obtain a stock of materials, apt and ready for use when required. There remains one more task to complete his plan--that he should teach the manner of reducing argumentation as it actually occurs (often invalid, and even when valid, often elliptical and disorderly), to the figures of syllogism as above set forth, for the purpose of testing its validity.[71] In performing this third part (Aristotle says) we shall at the same time confirm and illustrate the two preceding parts; for truth ought in every way to be consistent with itself.[72]

[Footnote 71: Analyt. Prior. I. xxxii. p. 47, a. 2: [Greek: loipo\n ga\r e)/ti tou=to tê=s ske/pseôs; ei) ga\r tê/n te ge/nesin tô=n sullogismô=n theôroi=men kai\ tou= eu(ri/skein e)/choimen du/namin, e)/ti de\ tou\s gegenême/nous a)nalu/oimen ei)s ta\ proeirême/na schê/mata, te/los a)\n e)/choi ê( e)x a)rchê=s pro/thesis.]]

[Footnote 72: Ibid. a. 8.]

When a piece of reasoning is before us, we must first try to disengage the two syllogistic premisses (which are more easily disengaged than the three terms), and note which of them is universal or particular. The reasoner, however, may not have set out both of them clearly: sometimes he will leave out the major, sometimes the minor, and sometimes, even when enunciating both of them, he will join with them irrelevant matter. In either of these cases we must ourselves supply what is wanting and strike out the irrelevant. Without this aid, reduction to regular syllogism is impracticable; but it is not always easy to see what the exact deficiency is. Sometimes indeed the conclusion may follow necessarily from what is implied in the premisses, while yet the premisses themselves do not form a correct syllogism; for though every such syllogism carries with it necessity, there may be necessity without a syllogism. In the process of reduction, we must first disengage and set down the two premisses, then the three terms; out of which three, that one which appears twice will be the middle term. If we do not find one term twice repeated, we have got no middle and no real syllogism. Whether the syllogism when obtained will be in the first, second, or third figure, will depend upon the place of the middle term in the two premisses. We know by the nature of the conclusion which of the three figures to look for, since we have already seen what conclusions can be demonstrated in each.[73]

[Footnote 73: Ibid. a. 10-b. 14.]

Sometimes we may get premisses which look like those of a true syllogism, but are not so in reality; the major proposition ought to be an universal, but it may happen to be only indefinite, and the syllogism will not in all cases be valid; yet the distinction between the two often passes unnoticed.[74] Another source of fallacy is, that we may set out the terms incorrectly; by putting (in modern phrase) the abstract instead of the concrete, or abstract in one premiss and concrete in the other.[75] To guard against this, we ought to use the concrete term in preference to the abstract. For example, let the major proposition be, Health cannot belong to any disease; and the minor. Disease can belong to any man; Ergo, Health cannot belong to any man. This conclusion seems valid, but is not really so. We ought to substitute concrete terms to this effect:--It is impossible that the sick can be well; Any man may be sick; Ergo, It is impossible that any man can be well. To the syllogism, now, as stated in these concrete terms, we may object, that the major is not true. A person who is at the present moment sick may at a future time become well. There is therefore no valid syllogism.[76] When we take the concrete man, we may say with truth that the two contraries, health-sickness, knowledge-ignorance, may both alike belong to him; though not to the same individual at the same time.

[Footnote 74: Ibid. I. xxxiii. p. 47, b. 16-40: [Greek: au(/tê me\n ou)=n ê( a)pa/tê gi/netai e)n tô=| para\ mikro/n; ôs ga\r ou)de\n diaphe/ron ei)pei=n to/de tô=|de u(pa/rchein, ê)\ to/de tô=|de panti\ u(pa/rchein, sugchôrou=men.]

M. B. St. Hilaire observes in his note (p. 155): "L'erreur vient uniquement de ce qu'on confond l'universel et l'indeterminé séparés par une nuance très faible d'expression, qu'on ne doit pas cependant negliger." Julius Pacius (p. 264) gives the same explanation at greater length; but the example chosen by Aristotle ([Greek: o( A)ristome/nês e)sti\ dianoêto\s A)ristome/nês]) appears open to other objections besides.]

[Footnote 75: Analyt. Prior. I. xxxiv. p. 48, a. 1-28.]

[Footnote 76: Ibid. a. 2-23. See the Scholion of Alexander, p. 181, b. 16-27, Brandis.]

Again, we must not suppose that we can always find one distinct and separate name belonging to each term. Sometimes one or all of the three terms can only be expressed by an entire phrase or proposition. In such cases it is very difficult to reduce the reasoning into regular syllogism. We may even be deceived into fancying that there are syllogisms without any middle term at all, because there is no single word to express it. For example, let A represent equal to two right angles; B, triangle; C, isosceles. Then we have a regular syllogism, with an explicit and single-worded middle term; A belongs first to B, and then to C through B as middle term (triangle). But how do we know that A belongs to B? We know it by demonstration; for it is a demonstrable truth that every triangle has its three angles equal to two right angles. Yet there is no other more general truth about triangles from which it is a deduction; it belongs to the triangle per se, and follows from the fundamental properties of the figure.[77] There is, however, a middle term in the demonstration, though it is not single-worded and explicit; it is a declaratory proposition or a fact. We must not suppose that there can be any demonstration without a middle term, either single-worded or many-worded.

[Footnote 77: Ibid. I. xxxv. p. 48, a. 30-39: [Greek: phanero\n o(/ti to\ me/son ou)ch ou(/tôs a)ei\ lêpte/on ô(s to/de ti, a)ll' e)ni/ote lo/gon, o(/per sumbai/nei ka)pi\ tou= lechthe/ntos.] A good Scholion of Philoponus is given, p. 181, b. 28-45, Brand.]

When we are reducing any reasoning to a syllogistic form, and tracing out the three terms of which it is composed, we must expose or set out these terms in the nominative case; but when we actually construct the syllogism or put the terms into propositions, we shall find that one or other of the oblique cases, genitive, dative, &c., is required.[78] Moreover, when we say, 'this belongs to that,' or 'this may be truly predicated of that,' we must recollect that there are many distinct varieties in the relation of predicate to subject. Each of the Categories has its own distinct relation to the subject; predication secundum quid is distinguished from predication simpliciter, simple from combined or compound, &c. This applies to negatives as well as affirmatives.[79] There will be a material difference in setting out the terms of the syllogism, according as the predication is qualified (secundum quid) or absolute (simpliciter). If it be qualified, the qualification attaches to the predicate, not to the subject: when the major proposition is a qualified predication, we must consider the qualification as belonging, not to the middle term, but to the major term, and as destined to re-appear in the conclusion. If the qualification be attached to the middle term, it cannot appear in the conclusion, and any conclusion that embraces it will not be proved. Suppose the conclusion to be proved is. The wholesome is knowledge quatenus bonum or quod bonum est; the three terms of the syllogism must stand thus:--

Major--Bonum is knowable, quatenus bonum or quod bonum est.

Minor--The wholesome is bonum.

Ergo--The wholesome is knowable, quatenus bonum, &c.

For every syllogism in which the conclusion is qualified, the terms must be set out accordingly.[80]

[Footnote 78: Analyt. Prior. I. xxxvi. p. 48, a. 40-p. 49, a. 5. [Greek: a(plô=s le/gomen ga\r tou=to kata\ pa/ntôn, o(/ti tou\s me\n o(/rous a)/ei thete/on kata\ ta\s klê/seis tô=n o)noma/tôn--ta\s de\ prota/seis lêpte/on kata\ ta\s e(ka/stou ptô/seis.] Several examples are given of this precept.]

[Footnote 79: Ibid. I. xxxvii. p. 49, a. 6-10. Alexander remarks in the Scholia (p. 183, a. 2) that the distinction between simple and compound predication has already been adverted to by Aristotle in De Interpretatione (see p. 20, b. 35); and that it was largely treated by Theophrastus in his work, [Greek: Peri\ Katapha/seôs], not preserved.]

[Footnote 80: Ibid. I. xxxviii. p. 49, a. 11-b. 2. [Greek: phanero\n ou)=n o(/ti e)n toi=s e)n me/rei sullogismoi=s ou(/tô lêpte/on tou\s o(/rous.] Alexander explains [Greek: oi( e)n me/rei sullogismoi/] (Schol. p. 183, b. 32, Br.) to be those in which the predicate has a qualifying adjunct tacked to it.]

We are permitted, and it is often convenient, to exchange one phrase or term for another of equivalent signification, and also one word against any equivalent phrase. By doing this, we often **facilitate the setting out of the terms. We must carefully note the different meanings of the same substantive noun, according as the definite article is or is not prefixed. We must not reckon it the same term, if it appears in one premiss with the definite article, and in the other without the definite article.[81] Nor is it the same proposition to say B is predicable of C (indefinite), and B is predicable of all C (universal). In setting out the syllogism, it is not sufficient that the major premiss should be indefinite; the major premiss must be universal; and the minor premiss also, if the conclusion is to be universal. If the major premiss be universal, while the minor premiss is only affirmative indefinite, the conclusion cannot be universal, but will be no more than indefinite, that is, counting as particular.[82]

[Footnote 81: Analyt. Prior. I. xxxix.-xl. p. 49, b. 3-13. [Greek: ou) tau)to\n e)sti to\ ei)=nai tê\n ê(donê\n a)gatho\n kai\ to\ ei)=nai tê\n ê(donê\n to\ a)gatho/n], &c.]

[Footnote 82: Ibid. I. xli. p. 49, b. 14-32. The Scholion of Alexander (Schol. p. 184, a. 22-40) alludes to the peculiar mode, called by Theophrastus [Greek: kata\ pro/slêpsin], of stating the premisses of the syllogism: two terms only, the major and the middle, being enunciated, while the third or minor was included potentially, but not enunciated. Theophrastus, however, did not recognize the distinction of meaning to which Aristotle alludes in this chapter. He construed as an universal minor, what Aristotle treats as only an indefinite minor. The liability to mistake the Indefinite for an Universal is here again adverted to.]

There is no fear of our being misled by setting out a particular case for the purpose of the general demonstration; for we never make reference to the specialties of the particular case, but deal with it as the geometer deals with the diagram that he draws. He calls the line A B, straight, a foot long, and without breadth, but he does not draw any conclusion from these assumptions. All that syllogistic demonstration either requires or employs, is, terms that are related to each other either as whole to part or as part to whole. Without this, no demonstration can be made: the exposition of the particular case is intended as an appeal to the senses, for facilitating the march of the student, but is not essential to demonstration.[83]

[Footnote 83: Ibid. I. xli. p. 50, a. 1: [Greek: tô=| d' e)kti/thesthai ou(/tô chrô/metha ô(/sper kai\ tô=| ai)stha/nesthai to\n mantha/nonta le/gontes; ou) ga\r ou(/tôs ô(s a)/neu tou/tôn ou)ch oi(=o/n t' a)podeichthê=nai, ô(/sper e)x ô(=n o( sullogismo/s.]

This chapter is a very remarkable statement of the Nominalistic doctrine; perceiving or conceiving all the real specialties of a particular case, but attending to, or reasoning upon, only a portion of them.

Plato treats it as a mark of the inferior scientific value of Geometry, as compared with true and pure Dialectic, that the geometer cannot demonstrate through Ideas and Universals alone, but is compelled to help himself by visible particular diagrams or illustrations. (Plato, Repub. vi. pp. 510-511, vii. p. 533, C.)]

Aristotle reminds us once more of what he had before said, that in the Second and Third figures, not all varieties of conclusion are possible, but only some varieties; accordingly, when we are reducing a piece of reasoning to the syllogistic form, the nature of the conclusion will inform us which of the three figures we must look for. In the case where the question debated relates to a definition, and the reasoning which we are trying to reduce turns upon one part only of that definition, we must take care to look for our three terms only in regard to that particular part, and not in regard to the whole definition.[84] All the modes of the Second and Third figures can be reduced to the First, by conversion of one or other of the premisses; except the fourth mode (Baroco) of the Second, and the fifth mode (Bocardo) of the Third, which can be proved only by Reductio ad Absurdum.[85]

[Footnote 84: Analyt. Prior. I. xlii., xliii. p. 50, a. 5-15. I follow here the explanation given by Philoponus and Julius Pacius, which M. Barthélemy St. Hilaire adopts. But the illustrative example given by Aristotle himself (the definition of water) does not convey much instruction.]

[Footnote 85: Ibid. xlv. p. 50, b. 5-p. 51, b. 2.]

No syllogisms from an Hypothesis, however, are reducible to any of the three figures; for they are not proved by syllogism alone: they require besides an extra-syllogistic assumption granted or understood between speaker and hearer. Suppose an hypothetical proposition given, with antecedent and consequent: you may perhaps prove or refute by syllogism either the antecedent separately, or the consequent separately, or both of them separately; but you cannot directly either prove or refute by syllogism the conjunction of the two asserted in the hypothetical. The speaker must ascertain beforehand that this will be granted to him; otherwise he cannot proceed.[86] The same is true about the procedure by Reductio ad Absurdum, which involves an hypothesis over and above the syllogism. In employing such Reductio ad Absurdum, you prove syllogistically a certain conclusion from certain premisses; but the conclusion is manifestly false; therefore, one at least of the premisses from which it follows must be false also. But if this reasoning is to have force, the hearer must know aliunde that the conclusion is false; your syllogism has not shown it to be false, but has shown it to be hypothetically true; and unless the hearer is prepared to grant the conclusion to be false, your purpose is not attained. Sometimes he will grant it without being expressly asked, when the falsity is glaring: e.g. you prove that the diagonal of a square is incommensurable with the side, because if it were taken as commensurable, an odd number might be shown to be equal to an even number. Few disputants will hesitate to grant that this conclusion is false, and therefore that its contradictory is true; yet this last (viz. that the contradictory is true) has not been proved syllogistically; you must assume it by hypothesis, or depend upon the hearer to grant it.[87]

[Footnote 86: Ibid. xliv. p. 50, a. 16-28.]

[Footnote 87: Analyt. Prior. I. xliv. p. 50, a. 29-38. See above, xxiii. p. 40, a. 25.

M. Barthélemy St. Hilaire remarks in the note to his translation of the Analytica Priora (p. 178): "Ce chapitre suffit à prouver qu'Aristote a distingué très-nettement les syllogismes par l'absurde, des syllogismes hypothétiques. Cette dernière dénomination est tout à fait pour lui ce qu'elle est pour nous." Of these two statements, I think the latter is more than we can venture to affirm, considering that the general survey of hypothetical syllogisms, which Aristotle intended to draw up, either never was really completed, or at least has perished: the former appears to me incorrect. Aristotle decidedly reckons the Reductio ad Impossibile among hypothetical proofs. But he understands by Reductio ad Impossibile something rather wider than what the moderns understand by it. It now means only, that you take the contradictory of the conclusion together with one of the premisses, and by means of these two demonstrate a conclusion contradictory or contrary to the other premiss. But Aristotle understood by it this, and something more besides, namely, whenever, by taking the contradictory of the conclusion, together with some other incontestable premiss, you demonstrate, by means of the two, some new conclusion notoriously false. What I here say, is illustrated by the very example which he gives in this chapter. The incommensurability of the diagonal (with the side of the square) is demonstrated by Reductio ad Impossibile; because if it be supposed commensurable, you may demonstrate that an odd number is equal to an even number; a conclusion which every one will declare to be inadmissible, but which is not the contradictory of either of the premisses whereby the true proposition was demonstrated.]

Here Aristotle expressly reserves for separate treatment the general subject of Syllogisms from Hypothesis.[88]

[Footnote 88: The expressions of Aristotle here are remarkable, Analyt. Prior. I. xliv. p. 50, a. 39-b. 3: [Greek: polloi\ de\ kai\ e(/teroi perai/nontai e)x u(pothe/seôs, ou(\s e)piske/psasthai dei= kai\ diasêmê=nai katharô=s. ti/nes me\n ou)=n ai( diaphorai\ tou/tôn, kai\ posachô=s gi/netai to\ e)x u(pothe/seôs, u(/steron e)rou=men; nu=n de\ tosou=nton ê(mi=n e)/stô phanero/n, o(/ti ou)k e)/stin a)nalu/ein ei)s ta\ schê/mata tou\s toiou/tous sullogismou/s. kai\ di' ê(\n ai)ti/an, ei)rê/kamen.]

Syllogisms from Hypothesis were many and various, and Aristotle intended to treat them in a future treatise; but all that concerns the present treatise, in his opinion, is, to show that none of them can be reduced to the three Figures. Among the Syllogisms from Hypothesis, two varieties recognized by Aristotle (besides [Greek: oi) dia\ tou= a)duna/tou]) were [Greek: oi( kata\ meta/lêpsin] and [Greek: oi( kata\ poio/têta]. The same proposition which Aristotle entitles [Greek: kata\ meta/lêpsin], was afterwards designated by the Stoics [Greek: kata\ pro/slêpsin] (Alexander ap. Schol. p. 178, b. 6-24).

It seems that Aristotle never realized this intended future treatise on Hypothetical Syllogisms; at least Alexander did not know it. The subject was handled more at large by Theophrastus and Eudêmus after Aristotle (Schol. p. 184, b. 45. Br.; Boethius, De Syllog. Hypothetico, pp. 606-607); and was still farther expanded by Chrysippus and the Stoics.

Compare Prantl, Geschichte der Logik, I. pp. 295, 377, seq. He treats the Hypothetical Syllogism as having no logical value, and commends Aristotle for declining to develop or formulate it; while Ritter (Gesch. Phil. iii. p. 93), and, to a certain extent, Ueberweg (System der Logik, sect. 121, p. 326), consider this to be a defect in Aristotle.]

In the last chapter of the first book of the Analytica Priora, Aristotle returns to the point which we have already considered in the treatise De Interpretatione, viz. what is really a negative proposition; and how the adverb of negation must be placed in order to constitute one. We must place this adverb immediately before the copula and in conjunction with the copula: we must not place it after the copula and in conjunction with the predicate; for, if we do so, the proposition resulting will not be negative but affirmative ([Greek: e)k metathe/seôs], by transposition, according to the technical term introduced afterwards by Theophrastus). Thus of the four propositions:

1. Est bonum. 2. Non est bonum. 4. Non est non bonum. 3. Est non bonum.

No. 1 is affirmative; No. 3 is affirmative ([Greek: e)k metathe/seôs]); Nos. 2 and 4 are negative. Wherever No. 1 is predicable, No. 4 will be predicable also; wherever No. 3 is predicable, No. 2 will be predicable also--but in neither case vice versâ.[89] Mistakes often flow from incorrectly setting out the two contradictories.

[Footnote 89: Analyt. Prior. I. xlvi. p. 51, b. 5, ad finem. See above, Chap. IV. p. 118, seq.]

Spotted a typo or a problem in this chapter? Tell us

IV. DE INTERPRETATIONE…

Cite this passage

MLA

APA

Chicago

IV. DE INTERPRETATIONE

V. ANALYTICA PRIORA I