29Aristot. De Interpet. p. 20, a. 16-30.
29Aristot. 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; butnon homo, if nothing be appended to it, is not more true or false (indeed less so) thanhomo.30
30Ibid. a. 31, seq.
30Ibid. a. 31, seq.
The transposition of substantive and adjective makes no difference in the meaning of the phrase;Est albus homois equivalent toEst 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 anAntiphasis.31
31Ibid. 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).
31Ibid. 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 thesubject 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 termshomo,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
32Aristot. De Interpr. p. 20, b. 13-22.
32Aristot. 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,Whatis Rhetoric? so as to put him under the necessity of enunciating an explanation of his own.33
33See the Scholia of Ammonius, p. 127, Br.
33See 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: ifhimationmeans both horse and man, it will often happen thatquestions respectinghimationcannot 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 intohomo, and may be employed either as one subject or as one predicate; buthomo,albus,ambulans, do not coalesce into one; so that if we say,Kallias est homo, albus, ambulans, the proposition is not one but three.34Accordingly, 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.
34Aristot. De Interpret. p. 20, b. 2. seq.; Ammonius, Schol. pp. 127-128, a. 21, Br. Compare De Sophist. Elench. p. 169, a. 6-15.
34Aristot. 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.35Kallias is acurrier, Kallias isgood— both these propositions may be true; yet the proposition, Kallias is agood 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, Homeris a poet; but we cannot truly say, Homeris.36We see by this last remark,37how distinctly Aristotle assigned a double meaning toest: 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 sayNon-Ens est, because the real meaning of the first of these propositions is,Non-Ens est opinabile non esse.38
35Aristot. De Interpr. p. 21, a. 7, seq.
35Aristot. De Interpr. p. 21, a. 7, seq.
36Ibid. a. 27.
36Ibid. a. 27.
37Compare 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.
37Compare 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.
38Aristot. 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.
38Aristot. 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-calledMODALPropositions — the Possible and the Necessary. What is the appropriate form ofAntiphasisin the case of such propositions, wherepossible to be, ornecessary to be, is joined to the simpleis. After a chapter of some length, he declares that the form ofAntiphasissuitable 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.39From theAntiphasisin Modals Aristotle proceeds to legitimate sequences admissible in such propositions, how far any one of them can be inferred from any other.40He 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.
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.41He then discusses whether we can correctly say that thenecessary to beis alsopossible to be. If not, then we might say correctly that thenecessary to beisnot possible to be; for one side or other of a legitimateAntiphasismay always be truly affirmed. Yet this would be absurd: accordingly we must admit that thenecessary to beis alsopossible to be. Here, however, we fall seemingly into a different absurdity; for thepossible to beis alsopossible not to be; and how can we allow that what isnecessary to beis at the same timepossible not to be? To escape from such absurdities on both sides, we must distinguish two modes of the Possible: one, inwhich 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
39Aristot. 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.
39Aristot. 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.
40Aristot. De Interpr. p. 22, a. 14-b. 28.
40Aristot. De Interpr. p. 22, a. 14-b. 28.
41Aristot. 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.
41Aristot. 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.
42Aristot. De Interpret. p. 22, b. 29-p. 23, a. 15.
42Aristot. De Interpret. p. 22, b. 29-p. 23, a. 15.
Having thus stated thatpossible to be, in this unilateral and equivocal sense but in no other, is a legitimate consequence ofnecessary 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
43Ibid. p. 23, a. 21-26.
43Ibid. 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, thenecessary to beincluded and implied thepossible 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 animpossiblePossible; it seems a self-contradictory description.44At best, it can only be understood as a limit inthe 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,45departing 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 thenecessaryPossible, or the unilateral potentiality. But on the other hand the same sentence introduces a new confusion by its third variety — theimpossiblePotential, departing from all clear and consistent meaning of potentiality, and coinciding only with the explanation ofNon-Ens, as given by Aristotle elsewhere.46
44M. 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.â€� 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).
44M. 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.â€� 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).
45Aristot. 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 εἰσιν· 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 anequivocalsense of ἐνδέχεσθαι — τὸ γὰρ ἀναγκαῖονὁμωνύμωςἐνδέχεσθαι λέγομεν.On the meaning of τὸ ἐνδεχόμενον, translated above, in the table, “possible (logically) to be,â€� and its relation to τὸ δυνατόν, see Waitz, ad Organ. I. pp. 375-8. Compare Prantl. Gescht. der Logik, I. pp. 166-8.
45Aristot. 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 εἰσιν· 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 anequivocalsense of ἐνδέχεσθαι — τὸ γὰρ ἀναγκαῖονὁμωνύμωςἐνδέχεσθαι λέγομεν.
On the meaning of τὸ ἐνδεχόμενον, translated above, in the table, “possible (logically) to be,â€� and its relation to τὸ δυνατόν, see Waitz, ad Organ. I. pp. 375-8. Compare Prantl. Gescht. der Logik, I. pp. 166-8.
46Aristot. De Interpr. p. 21, a. 32: τὸ δὲ μὴ ὄν, ὅτι δοξαστόν, οὐκ ἀληθὲς εἰπεῖν ὄν τι· 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.
46Aristot. De Interpr. p. 21, a. 32: τὸ δὲ μὴ ὄν, ὅτι δοξαστόν, οὐκ ἀληθὲς εἰπεῖν ὄν τι· 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 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 themay not beand leave only themay 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
47See Trendelenburg ad Aristot. De Animâ, pp. 303-307.
47See 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.48This 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.
48See 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.
48See 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.49The noun, pronounced separately, and the verb, pronounced separately, are each signs of a certain thought in the speaker’s mind, withouteither 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 somethingis, or that somethingis not.50Thus, Aristotle intends to give a theory of the Proposition, leaving other modes of speech to Rhetoric or Poetry:51the Proposition he considers under two distinct aspects. In its first orsubjectiveaspect, it declares the state of the speaker’s mind, as to belief or disbelief. In its second orobjectiveaspect, 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 itsform, is to betrueorfalse. But there are also other propositions — other varieties of speech enunciative — which differ from the Simple or Assertory Proposition having the formisoris 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 thingissoby necessity, that itmust beso, orcannot but beso; again, the Problematical Proposition, enunciating that a thingmay or may not be so. These two modes attach to theformof the proposition, and are quite distinct from those which attach to itsmatteras simply affirmed or denied; as when, instead of saying, John is sick, we say, John is sickof a fever, John isdangerouslysick, with a merely material modification. Such adverbs, modifying thematteraffirmed 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 theformof the proposition, and correspond to a state of mind distinct from simple belief or disbelief, expressed by a simple affirmation or negation.52In the case of each of the two, Aristotle has laiddown rules (correct or incorrect) for constructing the legitimateAntiphasis, 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 tothe objective correlate — what constitutes the Necessary, several different opinions have been entertained.
49Aristot. De Interpr. p. 16, a. 3-8: ἔστι μὲν οὖν τὰ ἐν τῇ φωνῇ τῶν ἐν τῇ ψυχῇ παθημάτων σύμβολα — ὧν μέντοι ταῦτα σημεῖαπρώτως, 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.
49Aristot. De Interpr. p. 16, a. 3-8: ἔστι μὲν οὖν τὰ ἐν τῇ φωνῇ τῶν ἐν τῇ ψυχῇ παθημάτων σύμβολα — ὧν μέντοι ταῦτα σημεῖαπρώτως, 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.
50Aristot. 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.
50Aristot. 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.
51Ibid. p. 17, a. 5. οἱ μὲν οὖν ἄλλοι (λόγοι) ἀφείσθωσαν· ῥητορικῆς γὰρ ἢ ποιητικῆς οἰκειοτέρα ἡ σκέψις· ὁ δὲ ἀποφαντικὸς τῆς νῦν θεωρίας.
51Ibid. p. 17, a. 5. οἱ μὲν οὖν ἄλλοι (λόγοι) ἀφείσθωσαν· ῥητορικῆς γὰρ ἢ ποιητικῆς οἰκειοτέρα ἡ σκέψις· ὁ δὲ ἀποφαντικὸς τῆς νῦν θεωρίας.
52Ammonius (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 changesfast; Plato loves Dionvehemently.â€� 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.â€� (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 enumeratestrueandfalse, 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 theirmodality; as difference of tense or time; the sundidrise,isrising,willrise.… 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 isperhapsdead; it ispossiblethat 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.â€�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.
52Ammonius (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 changesfast; Plato loves Dionvehemently.â€� 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.â€� (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 enumeratestrueandfalse, 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 theirmodality; as difference of tense or time; the sundidrise,isrising,willrise.… 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 isperhapsdead; it ispossiblethat 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 toformrather than tomatter; 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 anecessaryPossible, or animpossiblePossible, 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 notwas 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 notmerely 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.53This 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.54I 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,’55which is unfortunately lost, but in which he must have included this very topic — the distinction between Contrary and Contradictory.
53Aristot. De Interpr. p. 23, a. 27, seq.
53Aristot. De Interpr. p. 23, a. 27, seq.
54Scholia ad Arist. pp. 135-139, Br. γυμνάσαι μόνον βουληθέντος τοὺς ἐντυγχάνοντας πρὸς τὴν ἐπίκρισιν τῶν πιθανῶς μὲν οὐ μέντοι ἀληθῶς λεγομένων λόγων &c. (p. 135, b. 15; also p. 136, a. 42).
54Scholia ad Arist. pp. 135-139, Br. γυμνάσαι μόνον βουληθέντος τοὺς ἐντυγχάνοντας πρὸς τὴν ἐπίκρισιν τῶν πιθανῶς μὲν οὐ μέντοι ἀληθῶς λεγομένων λόγων &c. (p. 135, b. 15; also p. 136, a. 42).
55Scholia 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).
55Scholia 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 ofAnaphasisand 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.56He has no technical term for either subject or predicate; but he conceives the proposition as belonging to its subject:57we 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 eachAntiphasisand 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 theAntiphasiscorrectly, 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;58he 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 contradictionto be an impossibility;59an 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 properlocus standifor 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 eliminatedNon-Ensas 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