Chapter IV: De Interpretatione (2)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[Footnote 36: Ibid. a. 27.]

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

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

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

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

1.

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

2.

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

3.

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

4.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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