CHAPTER 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 109number of general heads all our predicates must be included, whether our propositions be true or false in each particular case.

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 110that it properly belongs.4 He thus recognizes the legitimate dependence of Logic on Psychology or Mental Philosophy.

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 111distinguished from the Noun by connoting time, and also by always serving as predicate to some noun as subject.7

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 (πράγματα) as universal or singular, 112according 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.

113It 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:—

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 114our 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

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 Aplanēs) 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 movement115 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 116spent 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 117Nature 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.

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, 118supposed 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 —

119

Affirmative.		Contradictory Negative.
Est omnis homo	… … … …	Non est omnis homo.
Est omnis non homo	… … … …	Non est omnis non homo.

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

(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, 120is 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

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

121Here 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.

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

122It 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 (ἐκ μεταθέσεως, 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

123After this very subtle and obscure distinction between propositions secundi adjacentis, and those tertii adjacentis, in respect to 124the 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 (ἐκ μεταθέσεως, 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

Neither the indefinite noun (οὐκ ἄνθρωπος) nor the indefinite verb (οὐ τρέχει — οὐ δίκαιος) 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 makeup an Antiphasis.31

In one and the same proposition, it is indispensable that the 125subject 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

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 126questions 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.

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

Aristotle now discusses the so-called Modal Propositions — the Possible and the Necessary. What is the appropriate form of 127Antiphasis 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.	3.
1. Possible (physically) to be.	1. Not possible (physically) to be.
2. Possible (logically) to be.	2. Not possible (logically) to be.
3. Not impossible to be.	3. Impossible to be.
4. Not necessary to be.	4. Necessary not to be.
2.	4.
1. Possible (physically) not to be.	1. Not possible (physically) not to be.
2. Possible (logically) not to be.	2. Not possible (logically) not to be.
3. Not impossible not to be.	3. Impossible not to be.
4. Not necessary 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 128which 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

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 129the 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

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, 130we 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

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 131either 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 132down 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 133the objective correlate — what constitutes the Necessary, several different opinions have been entertained.

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 134merely 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.

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.

135If, 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 contradiction136 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

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 137of 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.

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 (οὐ), 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 138Proposition 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.

[END OF CHAPTER IV]

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