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29 Aristot. De Interpet. p. 20, a. 16–30.

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

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

31 Ibid. b. 1–12. That ἐστὶ λευκὸς ἄνθρωπος, and ἐστὶν ἄνθρωπος λευκός, 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 ἀπὸ τῶν πραγμάτων πιστοῦσθαι (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

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

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.

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

35 Aristot. De Interpr. p. 21, a. 7, seq.

36 Ibid. a. 27.

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

Eudemus considered ἔστιν as one term in the proposition. Alexander dissented from this, and regarded it as being only a copula between the terms, συνθέσεως μηνυτικὸν μόριον τῶν ἐν τῇ προτάσει ὅρων.

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 τὸ μὴ ὄν, 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.	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 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

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.

40 Aristot. De Interpr. p. 22, a. 14-b. 28.

41 Aristot. De Interpr. p. 22, b. 22, λείπεται τοίνυν &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.

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

43 Ibid. p. 23, a. 21–26.

Now the sentence just translated (enunciating a doctrine of Aristotles 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

44 M. Barthélemy St. Hilaire, in the note to his translation (p. 197) calls it justly le possible qui nest jamais; et qui par cela męme, porte en lui une sorte dimpossibilité. It contradicts both the two explanations of δυνατὸν which Aristotle had given a few lines before. 1. δυνατὸν ὅτι ἐνεργεῖ. 2. δυνατὸν ὅτι ἐνεργήσειεν ἄν (p. 23, a. 10).

45 Aristot. De Interpr. p. 23, a. 5. τοῦτο μὲν τούτου χάριν εἴρηται, ὅτι οὐ πᾶσα δύναμις τῶν ἀντικειμένων, οὐδ ὅσαι λέγονται κατὰ τὸ αὐτὸ εἶδος. ἔνιαι δὲ δυνάμεις ὁμώνυμοί εἰσινˇ τὸ γὰρ δυνατὸν οὐχ ἁπλῶς λέγεται, ἀλλὰ τὸ μὲν ὅτι ἀληθὲς ὡς ἐνεργείᾳ ὄν, &c.

If we read the thirteenth chapter of Analytica Priora I. (p. 32, a. 18–29) we shall see that τὸ ἐνδεχόμενον is declared to be οὐκ ἀναγκαῖον, and that in the definition of τὸ ἐνδεχόμενον, the words οὗ μὴ ὄντος ἀναγκαίου are expressly inserted. When τὸ ἀναγκαῖον is said ἐνδέχεσθαι, this is said only in an equivocal sense of ἐνδέχεσθαι τὸ γὰρ ἀναγκαῖον ὁμωνύμως ἐνδέχεσθαι λέγομεν.

On the meaning of τὸ ἐνδεχόμενον, translated above, in the table, possible (logically) to be, and its relation to τὸ δυνατόν, see Waitz, ad Organ. I. pp. 375–8. Compare Prantl. Gescht. der Logik, I. pp. 166–8.

46 Aristot. De Interpr. p. 21, a. 32: τὸ δὲ μὴ ὄν, ὅτι δοξαστόν, οὐκ ἀληθὲς εἰπεῖν ὄν τιˇ δόξα γὰρ αὐτοῦ οὐκ ἔστιν ὅτι ἔστιν, ἀλλ ὅτι οὐκ ἔστιν. Τὸ μὴ ὄν is the true description of that which Aristotle improperly calls δύναμις ἣ οὐδέποτε ἐνέργειά ἐστιν.

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 Aristotles 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

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.

48 See pp. 143–5 of the article, Logic, in Sir William Hamiltons 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 dAristote, 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 speakers 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 speakers 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.

49 Aristot. De Interpr. p. 16, a. 3–8: ἔστι μὲν οὖν τὰ ἐν τῇ φωνῇ τῶν ἐν τῇ ψυχῇ παθημάτων σύμβολα ὧν μέντοι ταῦτα σημεῖα πρώτως, ταὐτὰ πᾶσι παθήματα τῆς ψυχῆς, καὶ ὧν ταῦτα ὁμοιώματα, πράγματα ἤδη ταὐτά. Ibid. a. 13: τὰ μὲν οὖν ὀνόματα αὐτὰ καὶ τὰ ῥήματα ἔοικε τῷ ἄνευ συνθέσεως καὶ διαιρέσεως νοήματι οὔτε γὰρ ψεῦδος οὔτ ἀληθές πω. Ib. p. 17, a. 2: λόγος ἀποφαντικὸς, ἐν ᾧ τὸ ἀληθεύειν ἢ ψεύδεσθαι ὑπάρχει. Compare p. 20, a. 34.

50 Aristot. De Interpret. p. 23, a. 32: τὰ μὲν ἐν τῇ φωνῇ ἀκολουθεῖ τοῖς ἐν τῇ διανοίᾳ, ἐκεῖ δὲ ἐναντία δόξα ἡ τοῦ ἐναντίου, &c. Ib. p. 24, b. 1: ὥστε εἴπερ ἐπὶ δόξης οὕτως ἔχει, εἰσὶ δὲ αἱ ἐν τῇ φωνῇ καταφάσεις καὶ ἀποφάσεις σύμβολα τῶν ἐν τῇ ψυχῇ, δῆλον ὅτι καὶ καταφάσει ἐναντία μὲν ἀπόφασις ἥ περὶ τοῦ αὐτοῦ καθόλου, &c. Ib. p. 17, a. 22: ἔστι δὲ ἡ ἁπλῆ ἀπόφανσις φωνὴ σημαντικὴ περὶ τοῦ ὑπάρχειν τι ἢ μὴ ὑπάρχειν, &c.

51 Ibid. p. 17, a. 5. οἱ μὲν οὖν ἄλλοι (λόγοι) ἀφείσθωσανˇ ῥητορικῆς γὰρ ἢ ποιητικῆς οἰκειοτέρα ἡ σκέψιςˇ ὁ δὲ ἀποφαντικὸς τῆς νῦν θεωρίας.

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 τὸ ὑπάρχειν 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 τὸ ὑπάρχειν, as examples of modes (De Interpet. 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, Cćsar is perhaps dead; it is possible that Cćsar 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, Cćsar may be dead, means, I am not sure that Cćsar 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 Hamiltons 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 speakers 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.