  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 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. 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. 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 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 phantasm5 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 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. 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 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 (p???ata) as universal or singular, It seems (as Ammonius observes, Schol. p. 112, a. 33) that ??t?fas?? in this sense was a technical term, introduced by Aristotle. 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: ??de?a ?at?fas?? ?????? ?sta?, ?? ? t?? ?at?????????? ?a????? t? ?a????? ?at????e?ta?, ???? ?st? p?? ?????p?? p?? ???? (b. 14). 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.
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 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 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 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 Aplanes) 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 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 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 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, 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 —
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 —
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 First, let us assume homo as subject. We have then
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,
As the words t? ?? d?? refer to the second contradictory pair (that is, C and D) in the first Quaternion, so the words t? d? d??, ?? 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 (t? d? d??, ??) which they bear to A and B, the first contradictory pair of the first Quaternion. d???? ?????ta? a? ??t???se?? (line 20) is explained and illustrated by line 37 — a?ta? ?? ??? d?? ??t??e??ta?, ???a? d? d?? p??? t? ??? ?????p?? ?? ?p??e?e??? t? p??ste???. 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 —
p?e???? d? t??t?? ??? ?s??ta? ??t???se??. a?ta? d? ????? ??e???? a?ta? ?a?’ ?a?t?? ?s??ta?, ?? ???at? t? ??? ?????p?? ???e?a?. The second a?ta? alludes to this last quaternion, ??e???? 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 —
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 Waitz in his note suggests that instead of t?ta?ta? we ought to read tet????. 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.) — ?ta? d? t? ?st? t??t?? p??s?at?????ta?, ?d? d???? ?????ta? a? ??t???se??. ???? d? ???? ?st? d??a??? ?????p??· t? ?st? t??t?? f?? s???e?s?a? ???a ? ??a ?? t? ?ataf?se?. ?ste d?? t??t? t?tta?a ?sta? ta?ta, ?? t? ?? d?? p??? t?? ?at?fas?? ?a? ?p?fas?? ??e? ?at? t? st?????? ?? a? ste??se??, t? d? d??, ??. ???? d’ ?t? t? ?st?? ? t? d??a?? p??s?e?seta? ? t? ?? d??a?? (25), ?ste ?a? ? ?p?fas??. t?tta?a ??? ?sta?. (Here follow the first pairs of Antitheses, or the first Quaternion of propositions in the order as given) —
t? ??? ?st?? ??ta??a ?a? t? ??? ?st? t? d??a?? p??s?e?seta? ?a? t? ?? d??a?? (30). — ??ta? ?? ??? d?? ??t??e??ta?, ???a? d? d?? p??? t? ??? ?????p?? ?? ?p??e?e??? t? (38) p??ste???. (Here follow the second pairs of Antitheses, or the second Quaternion of propositions, again in the order from which I have departed above) —
p?e???? d? t??t?? ??? ?s??ta? ??t???se??. a?ta? d? (the second Quaternion) ????? ??e???? (first Quaternion) a?ta? ?a?’ ?a?t?? ?s??ta?, ?? ???at? t? ??? ?????p?? ???e?a?. In this text Waitz makes three alterations:— 1. In line 24, instead of ? t? d??a?? p??s?e?seta? ? t? ?? d??a?? — he reads, ? t? ?????p? p??s?e?seta? ? t? ??? ?????p?. 2. In line 30 he makes a similar change; instead of t? d??a?? p??s?e?seta? ?a? t? ?? d??a?? — he reads, t? ?????p? p??s?e?seta? ?a? t? ??? ?????p?. In line 38, instead of p??ste???, he reads p??ste???t??. 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 — ???? d’ ?t? t? ?st?? ? t? d??a?? p??s?e?seta? ? t? ?? d??a??, ?a? ? t? ?????p? ? t? ??? ?????p?, ?ste ?a? ? ?p?fas??. t?tta?a ??? ?sta?. Here Aristotle declares the reason why (???) there come to be four couples of propositions; that reason is, because ?st? and ??? ?st? may be joined either with d??a??? or ?? d??a??? and either with ?????p?? or with ??? ?????p??. 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 t? ??? ?st?? ??ta??a (in the first Quaternion, which has just been enunciated) ?a? t? ??? ?st?? t? ?????p? p??s?e?seta? ?a? t? ??? ?????p?. These last words are incorrect in fact, for ??? ?????p?? 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 ?st? and ??? ?st?? attach both to d??a??? and to ?? d??a??? in this first Quaternion (??ta??a), 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 — t? ??? ?st?? ??ta??a ?a? t? ??? ?st? t? d??a?? p??s?e?seta? ?a? t? ?? d??a??, ?a? t? ?????p?, ???’ ?? t? ??? ?????p?. Or perhaps ?a? ?? t? ??? ?????p? might suffice in the last clause (being a smaller change), though ???’ ?? 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 ?st?? and ??? ?st? being joined alternately with d??a??? and with ?? d??a??? and also with ?????p?? and ??? ?????p??, make up two Quaternions, he proceeds to enunciate the distinctive character belonging to the first Quaternion of the two, viz., that in it ?st? and ??? ?st?? are joined both with d??a??? and ?? d??a???, and also with ?????p?? but not with ??? ?????p??, This is exactly the truth. Aristotle next proceeds to the second Quaternion, where he points out, as the characteristic distinction, that ??? ?????p?? comes in and ?????p?? disappears, while d??a??? and ?? d??a??? remain included, as in the first. This is declared plainly by Aristotle in line 37:— a?ta? ?? ??? d?? ??t??e??ta? (referring to the two pairs of antithetical propositions in the first Quaternion), ???a? d? p??? t? ??? ?????p?? ?? ?p??e?e??? t? p??ste???· ?st? d??a??? ??? ?????p??, ?st?? ?? d??a??? ??? ?????p??-??? ?st? d??a??? ??? ?????p??, ?st?? ?? d??a??? ??? ?????p??-??? ?st?? ?? d??a??? ??? ?????p??. When we read these words, ???a? d? d?? p??? t? ??? ?????p?? ?? ?p??e?e??? t? p??ste???, as applied to the second Quaternion, we see that there must have been some words preceding which excluded ??? ?????p?? from the first Quaternion. Waitz contends for the necessity of changing p??ste??? into p??ste???t??. I do not concur with his reasons for the change; the words that follow, p. 20, line 2, ?? ???at? t? ??? ?????p?? ???e?a? (p??s???e?a?), are a reasonable justification of p??ste??? — ??? ?????p?? ?? ?p??e?e??? t? p??ste??? being very analogous to ??? ?????p?? ?? ???a. 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 t? d??a?? (p. 19, b. 25), several others read t? ?????p?. I think that all of them were right in what they retained, and wrong by omission only or mainly. Neither the indefinite noun (??? ?????p??) nor the indefinite verb (?? t???e? — ?? d??a???) 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 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 In one and the same proposition, it is indispensable that the 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 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 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 Eudemus considered ?st?? as one term in the proposition. Alexander dissented from this, and regarded it as being only a copula between the terms, s????se?? ???t???? ????? t?? ?? t? p??t?se? ????. Aristotle now discusses the so-called MODAL Propositions — the Possible and the Necessary. What is the appropriate form of
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 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. 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. 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 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 If we read the thirteenth chapter of Analytica Priora I. (p. 32, a. 18-29) we shall see that t? ??de??e??? is declared to be ??? ??a??a???, and that in the definition of t? ??de??e???, the words ?? ? ??t?? ??a??a??? are expressly inserted. When t? ??a??a??? is said ??d??es?a?, this is said only in an equivocal sense of ??d??es?a? — t? ??? ??a??a??? ?????? ??d??es?a? ????e?. On the meaning of t? ??de??e???, translated above, in the table, “possible (logically) to be,” and its relation to t? d??at??, see Waitz, ad Organ. I. pp. 375-8. Compare Prantl. Gescht. der Logik, I. pp. 166-8. 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, 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. 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 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 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. 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. The term ??t?fas??, and its derivative ??t?fat????, 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. 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 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 (??), 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
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:—
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 ?p?fas?? to each ?at?fas?? (?a ?p?fas?? ??? ?ataf?se??, p. 17, b. 38), making up together the pair which he calls ??t?fas??, 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 (?? eta??se?? in the language of Theophrastus). | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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