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Оглавление14 Aristot. De Interpr. p. 17, a. 37-b. 14: ἐπεὶ δ ἐστὶ τὰ μὲν καθόλου τῶν πραγμάτων, τὰ δὲ καθ ἕκαστον (λέγω δὲ καθόλου μὲν ὃ ἐπὶ πλειόνων πέφυκε κατηγορεῖσθαι, καθ ἕκαστον δὲ ὃ μὴ, οἷον ἄνθρωπος μὲν τῶν καθόλου, Καλλίας δὲ τῶν καθ ἕκαστον)ˇ &c. Ammonius (in Schol. p. 113, a. 38) says that what is predicated, either of many subjects or of one, must be μία φύσις.
The warning against quantifying the predicate appears in this logical treatise of Aristotle, and is repeated in the Analytica Priora, I. xxvii. p. 43, b. 17. Here we have: οὐδεμία κατάφασις ἀληθὴς ἔσται, ἐν ᾗ τοῦ κατηγορουμένου καθόλου τὸ καθόλου κατηγορεῖται, οἷον ἔστι πᾶς ἄνθρωπος πᾶν ζῷον (b. 14).
15 Ibid. b. 16–29.
16 Ibid. p. 17, b. 29–37. Mr. John Stuart Mill (System of Logic, Bk. I. ch. iv. s. 4) cites and approves Dr. Whatelys observation, that the recognition of a class of Propositions called indefinite is a solecism, of the same nature as that committed by grammarians when in their list of genders they enumerate the doubtful gender. The speaker must mean to assert the proposition either as an universal or as a particular proposition, though he has failed to declare which.
But Aristotle would not have admitted Dr. Whatelys doctrine, declaring what the speaker must mean. Aristotle fears that his class, indefinite, will appear impertinent, because many speakers are not conscious of any distinction or transition between the particular and the general. The looseness of ordinary speech and thought, which Logic is intended to bring to view and to guard against, was more present to his mind than to that of Dr. Whately: moreover, the forms of Greek speech favoured the ambiguity.
Aristotles observation illustrates the deficiencies of common speaking, as to clearness and limitation of meaning, at the time when he began to theorize on propositions.
I think that Whatelys assumption the speaker must mean is analogous to the assumption on which Sir W. Hamilton founds his proposal for explicit quantification of the predicate, viz., that the speaker must, implicitly or mentally, quantify the predicate; and that his speech ought to be such as to make such quantification explicit. Mr. Mill has shewn elsewhere that this assumption of Sir. W. Hamiltons is incorrect.
It thus appears that there is always one negation corresponding to one and the same affirmation; making up together the Antiphasis, or pair of contradictory opposites, quite distinct from contrary opposites. By one affirmation we mean, that in which there is one predicate only, and one subject only, whether taken universally or not universally:
| E.g. | Omnis homo est albus | Non omnis homo est albus. | |
| Est homo albus | Non est homo albus. | ||
| Nullus homo est albus | Aliquis homo est albus. |
But this will only hold on the assumption that album signifies one and the same thing. If there be one name signifying two things not capable of being generalized into one nature, or not coming under the same definition, then the affirmation is no longer one.17 Thus if any one applies the term himation to signify both horse and man, then the proposition, Est himation album, is not one affirmation, but two; it is either equivalent to Est homo albus and Est equus albus or it means nothing at all; for this or that individual man is not a horse. Accordingly, in this case also, as well as in that mentioned above, it is not indispensable that one of the two propositions constituting the Antiphasis should be true and the other false.18
17 Aristot. De Interpr. p. 18, a. 13, seq.: μία δέ ἐστι κατάφασις καὶ ἀπόφασις ἡ ἓν καθ ἑνὸς σημαίνουσα, ἢ καθόλου ὄντος καθόλου ἢ μὴ ὁμοίως, οἷον πᾶς ἄνθρωπος λευκός ἐστιν εἰ τὸ λευκὸν ἓν σημαίνει. εἰ δὲ δυοῖν ἓν ὄνομα κεῖται, ἐξ ὧν μή ἐστιν ἕν, οὐ μία κατάφασις, &c., and the Scholion of Ammonius, p. 116, b. 6, seq.
18 Aristot. De Interpr. p. 18, a. 26. The example which Aristotle here gives is one of a subject designated by an equivocal name; when he had begun with the predicate. It would have been more pertinent if he had said at first, εἰ ὁ ἄνθρωπος ἓν σημαίνει.
With these exceptions Aristotle lays it down, that, in every Antiphasis, one proposition must be true and the other must be false. But (he goes on to say) this is only true in regard to matters past or present; it is not true in regard to events particular and future. To admit it in regard to these latter, would be to affirm that the sequences of events are all necessary, and none of them casual or contingent; whereas we know, by our own personal experience, that many sequences depend upon our deliberation and volition, and are therefore not necessary. If all future sequences are necessary, deliberation on our part must be useless. We must therefore (he continues) recognize one class of sequences which are not uniform not predetermined by antecedents; events which may happen, but which also may not happen, for they will not happen. Thus, my coat may be cut into two halves, but it never will be so cut; it will wear out without any such bisection occurring.19
19 Aristot. De Interpr. p. 18, a. 28-p. 19, b. 4.
If you affirm the reality of a fact past or present, your affirmation is of necessity determinately true, or it is determinately false, i.e. the contradictory negation is determinately true. But if you affirm the reality of a fact to come, then your affirmation is not by necessity determinately true, nor is the contradictory negation determinately true. Neither the one nor the other separately is true: nothing is true except the disjunctive antithesis as a whole, including both. If you say, To-morrow there will either be a sea-fight, or there will not be a sea-fight, this disjunctive or indeterminate proposition, taken as a whole, will be true. Yet neither of its constituent parts will be determinately true; neither the proposition, To-morrow there will be a sea-fight, nor the proposition, To-morrow there will not be a sea-fight. But if you speak with regard to past or present if you say, Yesterday either there was a sea-fight or there was not a sea-fight then not only will the disjunctive as a whole be true, but also one or other of its parts will be determinately true.20
20 Ibid. p. 18, b. 29. Ammonius (Scholia ad De Interpret. p. 119, bb. 18, 28, seq.) expresses Aristotles meaning in terms more distinct than Aristotle himself: μὴ πάντως ἔχειν τὸ ἕτερον μόριον τῆς ἀντιφάσεως ἀφωρισμένως ἀληθεῦον, &c. (b. 43).
This remarkable logical distinction is founded on Aristotles ontological or physical doctrines respecting the sequence and conjunction of events. He held (as we shall see more fully in the Physica and other treatises) that sequences throughout the Kosmos were to a certain extent regular, to a certain extent irregular. The exterior sphere of the Kosmos (the Aplanēs) with the countless number of fixed stars fastened into it, was a type of regularity and uniformity; eternal and ever moving in the same circular orbit, by necessity of its own nature, and without any potentiality of doing otherwise. But the earth and the elemental bodies, organized and unorganized, below the lunar sphere and in the interior of the Kosmos, were of inferior perfection and of very different nature. They were indeed in part governed and pervaded by the movement and influence of the celestial substance within which they were comprehended, and from which they borrowed their Form or constituent essence; but they held this Form implicated with Matter, i.e. the principle of potentiality, change, irregularity, generation, and destruction, &c. There are thus in these sublunary bodies both constant tendencies and variable tendencies. The constant Aristotle calls Nature; which always aspires to Good, or to perpetual renovation of Forms as perfect as may be, though impeded in this work by adverse influences, and therefore never producing any thing but individuals comparatively defective and sure to perish. The variable he calls Spontaneity and Chance, forming an independent agency inseparably accompanying Nature always modifying, distorting, frustrating, the full purposes of Nature. Moreover, the different natural agencies often interfere with each other, while the irregular tendency interferes with them all. So far as Nature acts, in each of her distinct agencies, the phenomena before us are regular and predictable; all that is uniform, and all that (without being quite uniform) recurs usually or frequently, is her work. But, besides and along with Nature, there is the agency of Chance and Spontaneity, which is essentially irregular and unpredictable. Under this agency there are possibilities both for and against; either of two alternative events may happen.
It is with a view to this doctrine about the variable kosmical agencies or potentialities that Aristotle lays down the logical doctrine now before us, distinguishing propositions affirming particular facts past or present, from propositions affirming particular facts future. In both cases alike, the disjunctive antithesis, as a whole, is necessarily true. Either there was a sea-fight yesterday, or there was not a sea-fight yesterday: Either there will be a sea-fight to-morrow, or there will not be a sea-fight to-morrow both these disjunctives alike are necessarily true. There is, however, a difference between the one disjunctive couple and the other, when we take the affirmation separately or the negation separately. If we say, There will be a sea-fight to-morrow, that proposition is not necessarily true nor is it necessarily false; to say that it is either the one or the other (Aristotle argues) would imply that every thing in nature happened by necessary agency that the casual, the potential, the may be or may not be, is stopped out and foreclosed. But this last is really the case, in regard to a past fact. There was a sea-fight yesterday, is a proposition either necessarily true or necessarily false. Here the antecedent agencies have already spent themselves, blended, and become realized in one or other of the two alternative determinate results. There is no potentiality any longer open; all the antecedent potentiality has been foreclosed. The proposition therefore is either necessarily true or necessarily false; though perhaps we may not know whether it is the one or the other.
In defending his position regarding this question, Aristotle denies (what he represents his opponents as maintaining) that all events happen by necessity. He points to the notorious fact that we deliberate and take counsel habitually, and that the event is frequently modified, according as we adopt one mode of conduct or another; which could not be (he contends), if the event could be declared beforehand by a proposition necessarily or determinately true. What Aristotle means by necessity, however, is at bottom nothing else than constant sequence or conjunction, conceived by him as necessary, because the fixed ends which Nature is aiming at can only be attained by certain fixed means. To this he opposes Spontaneity and Chance, disturbing forces essentially inconstant and irregular; admitting, indeed, of being recorded when they have produced effects in the past, yet defying all power of prediction as to those effects which they will produce in the future. Hence arises the radical distinction that he draws in Logic, between the truth of propositions relating to the past (or present) and to the future.
But this logical distinction cannot be sustained, because his metaphysical doctrine (on which it is founded) respecting the essentially irregular or casual, is not defensible. His opponents would refuse to grant that there is any agency essentially or in itself irregular, casual, and unpredictable.21 The aggregate of Nature consists of a variety of sequences, each of them constant and regular, though intermixed, co-operating, and conflicting with each other, in such manner that the resulting effects are difficult to refer to their respective causes, and are not to be calculated beforehand except by the highest scientific efforts; often, not by any scientific efforts. We must dismiss the hypothesis of Aristotle, assuming agencies essentially irregular and unpredictable, either as to the past or as to the future. The past has been brought about by agencies all regular, however multifarious and conflicting, and the future will be brought about by the like: there is no such distinction of principle as that which Aristotle lays down between propositions respecting the past and propositions respecting the future.
21 The Stoics were opposed to Aristotle on this point. They recognized no logical difference in the character of the Antiphasis, whether applied to past and present, or to future. Nikostratus defended the thesis of Aristotle against them. See the Scholia of Simplikius on the Categorić, p. 87, b. 30-p. 88, a. 24. αἱ γὰρ εἰς τὸν μέλλοντα χρόνον ἐγκλινόμεναι προτάσεις οὔτε ἀληθεῖς εἰσὶν οὔτε ψευδεῖς διὰ τὴν τοῦ ἐνδεχομένου φύσιν.
The remarks of Hobbes, upon the question here discussed by Aristotle, well deserve to be transcribed (De Corpore, part II. ch. X. s. 5):
But here, perhaps, some man may ask whether those future things, which are called contingents, are necessary. I say, therefore, that generally all contingents have their necessary causes, but are called contingents in respect of other events, upon which they do not depend; as the rain, which shall be to-morrow, shall be necessary, that is, from necessary causes; but we think and say, it happens by chance, because we do not yet perceive the causes thereof, though they exist now. For men commonly call that casual or contingent, whereof they do not perceive the necessary cause; and in the same manner they use to speak of things past, when not knowing whether a thing be done or no, they say, it is possible it never was done.
Wherefore, all propositions concerning future things, contingent or not contingent as this, It will rain to-morrow, or this, To-morrow the sun will rise are either necessarily true, or necessarily false; but we call them contingent, because we do not yet know whether they be true or false; whereas their verity depends not upon our knowledge, but upon the foregoing of their causes. But there are some, who, though they confess this whole proposition, To-morrow it will either rain or not rain, to be true, yet they will not acknowledge the parts of it, as To-morrow it will rain, or To-morrow it will not rain, to be either of them true by itself; because they say neither this nor that is true determinately. But what is this determinately true, but true upon our knowledge, or evidently true? And therefore they say no more, but that it is not yet known whether it be true or no; but they say it more obscurely, and darken the evidence of the truth with the same words with which they endeavour to hide their own ignorance.
Compare also the fuller elucidation of the subject given by Mr. John Stuart Mill, in his System of Logic, Bk. III. ch. xvii. s. 2: An event occurring by chance may be better described as a coincidence from which we have no ground to infer an uniformity; the occurrence of an event in certain circumstances, without our having reason on that account to infer that it will happen again in those circumstances. This, however, when looked closely into, implies that the enumeration of the circumstances is not complete. Whatever the fact was, since it has occurred once, we may be sure that if all the circumstances were repeated, it would occur again; and not only if all, but there is some particular portion of those circumstances, on which the phenomenon is invariably consequent. With most of them, however, it is not connected in any permanent manner: its conjunction with those is said to be the effect of chance, to be merely casual. Facts casually conjoined are separately the effect of causes, and therefore of laws; but of different causes, and causes not connected by any law. It is incorrect then to say that any phenomenon is produced by chance; but we may say that two or more phenomena are conjoined by chance, that they co-exist or succeed one another only by chance.
There is, indeed, one distinction between inferences as to the past and inferences as to the future, which may have contributed to suggest, though it will not justify, the position here laid down by Aristotle. In regard to the disjunctive To-morrow there will be a sea-fight, or there will not be a sea-fight nothing more trustworthy than inference or anticipation is practicable: the anticipation of a sagacious man with full knowledge is more likely to prove correct than that of a stupid man with little knowledge; yet both are alike anticipations, unverifiable at the present moment. But if we turn to the other disjunctive Yesterday there was a sea-fight, or there was not a sea-fight we are no longer in the same position. The two disputants, supposed to declare thus, may have been far off, and may have no other means of deciding the doubt than inference. But the inference here is not unverifiable: there exist, or may exist, witnesses or spectators of the two fleets, who can give direct attestation of the reality, and can either confirm or refute the inference, negative or affirmative, made by an absentee. Thus the proposition, Yesterday there was a sea-fight, or the other, Yesterday there was not a sea-fight, will be verifiable or determinably true. There are indeed many inferences as to the past, in regard to which no direct evidence is attainable. Still this is an accident; for such direct evidence may always be supposed or imagined as capable of being brought into court. But, in respect to the future, verification is out of the question; we are confined to the region of inference, well or ill-supported. Here, then, we have a material distinction between the past and the future. It was probably present to the mind of Aristotle, though he misconceives its real extent of operation, and makes it subservient to his still more comprehensive classification of the different contemporaneous agencies (regular and irregular) which he supposes to pervade the Kosmos.
In the treatise before us, he next proceeds to state what collocation of the negative particle constitutes the special or legitimate negation to any given affirmation, or what are the real forms of proposition, standing in contradictory opposition to certain other forms, so as to make up one Antiphasis.22 The simplest proposition must include a noun and a verb, either definite or indefinite: non homo is a specimen of an indefinite noun non currit, of an indefinite verb. There must be, in any one proposition, one subject and one predicate; even the indefinite noun or verb signifies, in a certain sense, one thing. Each affirmation comprises a noun, or an indefinite noun, with a verb; the special corresponding or contradictory negation (making up the Antiphasis along with the former) comprises a noun (or an indefinite noun) with an indefinite verb. The simplest proposition is
| Affirmative. | Contradictory Negative. | |
| Est homo | Non est homo. | |
| Est non homo | Non est non homo. |
Here are only two pairs of antithetic propositions, or one quaternion. The above is an indefinite proposition (which may be either universal or not). When we universalize it, or turn it an universal proposition, we have
| Affirmative. | Contradictory Negative. | |
| Est omnis homo | Non est omnis homo. | |
| Est omnis non homo | Non est omnis non homo. |
22 Aristot. De Interpr. p. 19, b. 5, seq.
The above are specimens of the smallest proposition; but when we regard larger propositions, such as those (called tertii adjacentis) where there are two terms besides est, the collocation of the negative particle becomes more complicated, and requires fuller illustration. Take, as an example, the affirmative Est justus homo, the true negation of this is, Non est justus homo. In these two propositions, homo is the subject; but we may join the negative with it, and we may consider non homo, not less than homo, as a distinct subject for predication, affirmative or negative. Farther, we may attach est and non est either to justus or to non justus as the predicate of the proposition, with either homo, or non homo, as subject. We shall thus obtain a double mode of antithesis, or two distinct quaternions, each containing two pairs of contradictory propositions. The second pair of the first quaternion will not be in the same relation as the second pair of the second quaternion, to the proposition just mentioned, viz. (A) Est justus homo; with its negative, (B) Non est justice homo.23
23 Aristot. De Interpr. p. 19, b. 19. ὅταν δὲ τὸ ἔστι τρίτον προσκατηγορῆται, ἤδη διχῶς λέγονται αἱ ἀντιθέσειςˇ λέγω δὲ οἷον ἔστι δίκαιος ἄνθρωποςˇ τὸ ἔστι τρίτον φημὶ συγκεῖσθαι ὄνομα ἢ ῥῆμα ἐν τῇ καταφάσει. ὥστε διὰ τοῦτο τέτταρα ἔσται ταῦτα, ὧν τὰ μὲν δύο πρὸς τὴν κατάφασιν καὶ ἀπόφασιν ἕξει κατὰ τὸ στοιχοῦν ὡς αἱ στερήσεις, τὰ δὲ δύο, οὔ. [λέγω δὲ ὅτι τὸ ἔστιν ἢ τῷ δικαίῳ προσκείσεται ἢ τῷ οὐ δικαίῳ], ὥστε καὶ ἡ ἀπόφασις. τέτταρα οὖν ἔσται. νοοῦμεν δὲ τὸ λεγόμενον ἐκ τῶν ὑπογεγραμμένων. In this passage the words which I have enclosed between brackets are altered by Waitz: I shall state presently what I think of his alteration. Following upon these words there ought to be, and it seems from Ammonius (Schol. p. 121, a. 20) that there once was, a scheme or table arranging the four propositions in the order and disposition which we read in the Analytica Priora, I. xlvi. p. 51, b. 37, and which I shall here follow. But no such table now appears in our text; we have only an enumeration of the four propositions, in a different order, and then a reference to the Analytica.
First, let us assume homo as subject. We have then
| (QUATERNION I.) | ||
|---|---|---|
| (A) Est justus homo | (B) Non est justus homo. | |
| (D) Non est non justus homo | (C) Est non justus homo. |
Examining the relation borne by the last two among these four propositions (C and D), to the first two (A and B), the simple affirmative and negative, we see that B is the legitimate negative of A, and D that of C. We farther see that B is a consequence of C, and D a consequence of A, but not vice versâ: that is, if C is true, B must certainly be true; but we cannot infer, because B is true, that C must also be true: while, if A is true, D must also be true; but D may perhaps be true, though A be not true. In other words, the relation of D to A and of C to B, is the same as it would be if the privative term injustus were substituted in place of non justus; i.e. if the proposition C (Est injustus homo) be true, the other proposition B (Non est justus homo) must certainly be true, but the inference will not hold conversely; while if the proposition A (Est justus homo) be true, it must also be true to say D (Non est injustus homo), but not vice versâ.24
24 Referring to the words cited in the preceding note, I construe τὰ δὲ δύο, οὔ as Boethius does (II. pp. 384–385), and not in agreement with Ammonius (Schol. p. 122, a. 26, Br.), who, however, is followed both by Julius Pacius and Waitz (p. 344). I think it impossible that these words, τὰ δὲ δύο, οὔ, can mean (as Ammonius thinks) the κατάφασις and ἀπόφασις themselves, since the very point which Aristotle is affirming is the relation of these words, πρὸς τὴν κατάφασιν καὶ ἀπόφασιν, i.e. to the affirmative and negative started from
| (A) Est justus homo | (B) Non est justus homo. |
As the words τὰ μὲν δύο refer to the second contradictory pair (that is, C and D) in the first Quaternion, so the words τὰ δὲ δύο, οὔ designate the second contradictory pair (G and H) in the second Quaternion. Though G and H are included in the second Quaternion, they are here designated by the negative relation (τὰ δὲ δύο, οὔ) which they bear to A and B, the first contradictory pair of the first Quaternion. διχῶς λέγονται αἱ ἀντιθέσεις (line 20) is explained and illustrated by line 37 αὗται μὲν οὖν δύο ἀντίκεινται, ἄλλαι δὲ δύο πρὸς τὸ οὐκ ἄνθρωπος ὡς ὑποκείμενόν τι προστεθέν. Lastly, Aristotle expressly states that the second Quaternion will stand independently and by itself (p. 20, a. 1), having noticed it in the beginning only in relation to the first.
Such is the result obtained when we take homo as the subject of the proposition; we get four propositions, of which the two last (C and D) stand to the two first (B and A) in the same relation as if they (C and D) were privative propositions. But if, instead of homo, we take non homo as Subject of the proposition (justus or non justus being predicates as before), we shall then obtain two other pairs of contradictory propositions; and the second pair of this new quaternion will not stand in that same relation to these same propositions B and A. We shall then find that, instead of B and A, we have a different negative and a different affirmative, as the appropriate correlates to the third and fourth propositions. The new quaternion of propositions, with non homo as subject, will stand thus
| (QUATERNION II.) | ||
|---|---|---|
| (E) Est justus non homo | (F) Non est justus non homo. | |
| (H) Non est non justus non homo | (G) Est non justus non homo.25 |
Here we see that propositions G and H do not stand to B and A in the same relations as C and D stand to B and A; but that they stand in that same relation to two perfectly different propositions, F and E. That is, if in place of non justus, in propositions G and H, we substitute the privative term injustus (thus turning G into Est injustus non homo, and turning H into Non est injustus non homo), the relation of G, when thus altered, to F, and the relation of H, when thus altered, to E, will be the same as it was before. Or, in other words, if G be true, F will certainly be true, but not vice versâ; and if E be true, H will certainly be true, but not vice versâ.
25 Aristot. De Interpr. p. 19, b. 36. αὗται μὲν οὖν δύο ἀντίκεινται (the two pairs A B and C D of the first quaternion), ἄλλαι δὲ δύο πρὸς τὸ οὐκ ἄνθρωπος ὡς ὑποκείμενόν τι προστεθένˇ
| (E) ἔστι δίκαιος οὐκ ἄνθρωπος | (F) οὐκ ἔστι δίκαιος οὐκ ἄνθρωπος. | |
| (H) οὐκ ἔστιν οὐ δίκαιος οὐκ ἄνθρωπος | (G) ἔστιν οὐ δίκαιος οὐκ ἄνθρωπος. |
πλείους δὲ τούτων οὐκ ἔσονται ἀντιθέσεις. αὗται δὲ χωρὶς ἐκείνων αὐταὶ καθ ἑαυτὰς ἔσονται, ὡς ὀνόματι τῷ οὐκ ἄνθρωπος χρώμεναι. The second αὗται alludes to this last quaternion, ἐκείνων to the first. I have, as in the former case, transposed propositions three and four of this second quaternion, in order that the relation of G to F and of H to E may be more easily discerned.
There are few chapters in Aristotle more obscure and puzzling than the tenth chapter of the De Interpretatione. It was found so by Alexander, Herminus, Porphyry, Ammonius, and all the Scholiasts. Ammonius (Schol. pp. 121, 122, Br.) reports these doubts, and complains of it as a riddle almost insolvable. The difficulties remain, even after the long note of Waitz, and the literal translation of M. Barthélemy St. Hilaire.
The propositions which we have hitherto studied have been indefinite; that is, they might be universal or not. But if we attach to them the sign of universality, and construe them as universals, all that we have said about them would still continue to be true, except that the propositions which are diametrically (or diagonally) opposed would not be both true in so many instances. Thus, let us take the first quaternion of propositions, in which est is attached to homo, and let us construe these propositions as universal. They will stand thus
| (A) Omnis est homo justus | (B) Non omnis est homo justus. | |
| (D) Non omnis est homo non justus | (C) Omnis est homo non justus. |
In these propositions, as in the others before noticed, the same relation prevails between C and B, and between A and D; if C be true, B also is true, but not vice versâ; if A be true, D also will be true, but not vice versâ. But the propositions diagonally opposed will not be so often alike true:26 thus, if A be true (Omnis est homo justus), C cannot be true (Omnis est homo non justus); whereas in the former quaternion of propositions (indefinite, and therefore capable of being construed as not universal) A and C might both be alike true.27
26 Aristot. De Interpret. p. 19, b. 35. πλὴν οὐχ ὁμοίως τὰς κατὰ διάμετρον ἐνδέχεται συναληθεύεινˇ ἐνδέχεται δὲ ποτέ. The diameter or diagonal is to be understood with reference to the scheme or square mentioned p. 119, note, the related propositions standing at the angles, as above.
27 The Scholion of Ammonius, p. 123, a. 17, Br., explains this very obscure passage: ἀλλ ἐπὶ μὲν τῶν ἀπροσδιορίστων (indefinite propositions, such as may be construed either as universal or as particular), κατὰ τὴν ἐνδεχομένην ὕλην τάς τε καταφάσεις (of the propositions diagonally opposite), συναληθεύειν ἀλλήλαις συμβαίνει καὶ τὰς ἀποφάσεις, ἅτε ταῖς μερικαῖς ἰσοδυναμούσας. ἐπὶ δὲ τῶν προσδιωρισμένων (those propositions where the mark of universality is tacked to the Subject), περὶ ὧν νυνὶ αὐτῷ ὁ λόγος, τῆς καθόλου καταφάσεως καὶ τῆς ἐπὶ μέρους ἀποφάσεως, τὰς μὲν καταφάσεις ἀδύνατον συναληθεῦσαι καθ οἱανδήποτε ὕλην, τὰς μέντοι ἀποφάσεις συμβαίνει συναληθεύειν κατὰ μόνην τὴν ἐνδεχομένηνˇ &c.
It is thus that Aristotle explains the distinctions of meaning in propositions, arising out of the altered collocation of the negative particle; the distinction between (1) Non est justus, (2) Est non justus, (3) Est injustus. The first of the three is the only true negative, corresponding to the affirmative Est Justus. The second is not a negative at all, but an affirmative (ἐκ μεταθέσεως, or by transposition, as Theophrastus afterwards called it). The third is an affirmative, but privative. Both the second and the third stand related in the same manner to the first; that is, the truth of the first is a necessary consequence either of the second or of the third, but neither of these can be certainly inferred from the first. This is explained still more clearly in the Prior Analytics; to which Aristotle here makes express reference.28
28 Aristot. De Interpr. p. 19, b. 31. ταῦτα μὲν οὖν, ὥσπερ ἐν τοῖς Ἀναλυτικοῖς λέγεται, οὕτω τέτακται.
Waitz in his note suggests that instead of τέτακται we ought to read τετάχθω. But if we suppose that the formal table once existed in the text, in an order of arrangement agreeing with the Analytica, this conjectural change would be unnecessary.
Waitz has made some changes in the text of this chapter, which appear to me partly for the better, partly not for the better. Both Bekker and Bussemaker (Firmin Didot) retain the old text; but this old text was a puzzle to the ancient commentators, even anterior to Alexander of Aphrodisias. I will here give first the text of Bekker, next the changes made by Waitz: my own opinion does not wholly coincide with either. I shall cite the text from p. 19, b. 19, leaving out the portion between lines 30 and 36, which does not bear upon the matter here discussed, while it obscures the legitimate sequence of Aristotles reasoning.
(Bekker.) Ὅταν δὲ τὸ ἔστι τρίτον προσκατηγορῆται, ἤδη διχῶς λέγονται αἱ ἀντιθέσεις. λέγω δὲ οἷον ἔστι δίκαιος ἄνθρωποςˇ τὸ ἔστι τρίτον φημὶ συγκεῖσθαι ὄνομα ἢ ῥῆμα ἐν τῇ καταφάσει. ὥστε διὰ τοῦτο τέτταρα ἔσται ταῦτα, ὧν τὰ μὲν δύο πρὸς τὴν κατάφασιν καὶ ἀπόφασιν ἕξει κατὰ τὸ στοιχοῦν ὡς αἱ στερήσεις, τὰ δὲ δύο, οὔ. λέγω δ ὅτι τὸ ἔστιν ἢ τῷ δικαίῳ προσκείσεται ἢ τῷ οὐ δικαίῳ (25), ὥστε καὶ ἡ ἀπόφασις. τέτταρα οὖν ἔσται. (Here follow the first pairs of Antitheses, or the first Quaternion of propositions in the order as given)
| (A) ἔστι δίκιος ἄνθρωπος | (B) οὐκ ἔστι δίκιος ἄνθρωπος. | |
| (C) ἔστιν οὐ δίκαιος ἄνθρωπος | (D) οὐκ ἔστιν οὐ δίκαιος ἄνθρωπος. |
τὸ γὰρ ἔστιν ἐνταῦθα καὶ τὸ οὐκ ἔστι τῷ δικαίῳ προσκείσεται καὶ τῷ οὐ δικαίῳ (30). Αὗται μὲν οὖν δύο ἀντίκεινται, ἄλλαι δὲ δύο πρὸς τὸ οὐκ ἄνθρωπος ὡς ὑποκείμενόν τι (38) προστεθέν. (Here follow the second pairs of Antitheses, or the second Quaternion of propositions, again in the order from which I have departed above)
| (E) ἔστι δίκαιος οὐκ ἄνθρωπος | (F) Οὐκ ἔστι δίκαιος οὐκ ἄνθρωπος. | |
| (G) ἔστιν οὐ δίκαιος οὐκ ἄνθρωπος | (H) Οὐκ ἔστιν οὐ δίκαιος οὐκ ἄνθρωπος. |
πλείους δὲ τούτων οὐκ ἔσονται ἀντιθέσεις. αὗται δὲ (the second Quaternion) χωρὶς ἐκείνων (first Quaternion) αὐταὶ καθ ἑαυτὰς ἔσονται, ὡς ὀνόματι τῷ οὐκ ἄνθρωπος χρώμεναι.
In this text Waitz makes three alterations: 1. In line 24, instead of ἢ τῷ δικαίῳ προσκείσεται ἢ τῷ οὐ δικαίῳ he reads, ἢ τῷ ἀνθρώπῳ προσκείσεται ἢ τῷ οὐκ ἀνθρώπῳ.
2. In line 30 he makes a similar change; instead of τῷ δικαίῳ προσκείσεται καὶ τῷ οὐ δικαίῳ he reads, τῷ ἀνθρώπῳ προσκείσεται καὶ τῷ οὐκ ἀνθρώπῳ.
In line 38, instead of προστεθέν, he reads προστεθέντος.
Of these three alterations the first appears to me good, but insufficient; the second not good, though the passage as it stands in Bekker requires amendment; and the third, a change for the worse.
The purpose of Aristotle is here two-fold. First, to give the reason why, when the propositions were tertii adjacentis, there were two Quaternions or four couples of antithetical propositions; whereas in propositions secundi adjacentis, there was only one Quaternion or two couples of antithetical propositions. Next, to assign the distinction between the first and the second Quaternion in propositions tertii adjacentis.
Now the first of these two purposes is marked out in line 25, which I think we ought to read not by substituting the words of Waitz in place of the words of Bekker, but by retaining the words of Bekker and inserting the words of Waitz as an addition to them. The passage after such addition will stand thus λέγω δ ὅτι τὸ ἔστιν ἢ τῷ δικαίῳ προσκείσεται ἢ τῷ οὐ δικαίῳ, καὶ ἢ τῷ ἀνθρώπῳ ἢ τῷ οὐκ ἀνθρώπῳ, ὥστε καὶ ἡ ἀπόφασις. τέτταρα οὖν ἔσται. Here Aristotle declares the reason why (οὖν) there come to be four couples of propositions; that reason is, because ἔστι and οὐκ ἔστι may be joined either with δίκαιος or οὐ δίκαιος and either with ἄνθρωπος or with οὐκ ἄνθρωπος. Both these alternatives must be specified in order to make out a reason why there are two Quaternions or four couples of antithetical propositions. But the passage, as read by Bekker, gives only one of these alternatives, while the passage, as read by Waitz, gives only the other. Accordingly, neither of them separately is sufficient; but both of them taken together furnish the reason required, and thus answer Aristotles purpose.
Aristotle now proceeds to enunciate the first of the two Quaternions, and then proceeds to line 30, where the reading of Bekker is irrelevant and unmeaning; but the amendment of Waitz appears to me still worse, being positively incorrect in statement of fact. Waitz reads τὸ γὰρ ἔστιν ἐνταῦθα (in the first Quaternion, which has just been enunciated) καὶ τὸ οὐκ ἔστιν τῷ ἀνθρώπῳ προσκείσεται καὶ τῷ οὐκ ἀνθρώπῳ. These last words are incorrect in fact, for οὐκ ἄνθρωπος does not appear in the first Quaternion, but is reserved for the second. While the reading of Waitz is thus evidently wrong, that of Bekker asserts nothing to the purpose. It is useless to tell us merely that ἔστι and οὐκ ἔστιν attach both to δίκαιος and to οὐ δίκαιος in this first Quaternion (ἐνταῦθα), because that characteristic is equally true of the second Quaternion (presently to follow), and therefore constitutes no distinction between the two. To bring out the meaning intended by Aristotle I think we ought here also to retain the words of Bekker, and to add after them some, though not all, of the words of Waitz. The passage would then stand thus τὸ γὰρ ἔστιν ἐνταῦθα καὶ τὸ οὐκ ἔστι τῷ δικαίῳ προσκείσεται καὶ τῷ οὐ δικαίῳ, καὶ τῷ ἀνθρώπῳ, ἀλλ οὐ τῷ οὐκ ἀνθρώπῳ. Or perhaps καὶ οὐ τῷ οὐκ ἀνθρώπῳ might suffice in the last clause (being a smaller change), though ἀλλ οὐ seem the proper terms to declare the meaning. In the reading which I propose, the sequence intended by Aristotle is clear and intelligible. Having first told us that ἔστιν and οὐκ ἔστι being joined alternately with δίκαιος and with οὐ δίκαιος and also with ἄνθρωπος and οὐκ ἄνθρωπος, make up two Quaternions, he proceeds to enunciate the distinctive character belonging to the first Quaternion of the two, viz., that in it ἔστι and οὐκ ἔστιν are joined both with δίκαιος and οὐ δίκαιος, and also with ἄνθρωπος but not with οὐκ ἄνθρωπος, This is exactly the truth.
Aristotle next proceeds to the second Quaternion, where he points out, as the characteristic distinction, that οὐκ ἄνθρωπος comes in and ἄνθρωπος disappears, while δίκαιος and οὐ δίκαιος remain included, as in the first. This is declared plainly by Aristotle in line 37: αὗται μὲν οὖν δύο ἀντίκεινται (referring to the two pairs of antithetical propositions in the first Quaternion), ἄλλαι δὲ πρὸς τὸ οὐκ ἄνθρωπος ὡς ὑποκείμενόν τι προστεθένˇ ἔστι δίκαιος οὐκ ἄνθρωπος, ἔστιν οὐ δίκαιος οὐκ ἄνθρωπος-οὐκ ἔστι δίκαιος οὐκ ἄνθρωπος, ἔστιν οὐ δίκαιος οὐκ ἄνθρωπος-οὐκ ἔστιν οὐ δίκαιος οὐκ ἄνθρωπος. When we read these words, ἄλλαι δὲ δύο πρὸς τὸ οὐκ ἄνθρωπος ὡς ὑποκείμενόν τι προστεθέν, as applied to the second Quaternion, we see that there must have been some words preceding which excluded οὐκ ἄνθρωπος from the first Quaternion. Waitz contends for the necessity of changing προστεθέν into προστεθέντος. I do not concur with his reasons for the change; the words that follow, p. 20, line 2, ὡς ὀνόματι τῷ οὐκ ἄνθρωπος χρώμεναι (προσχρώμεναἰ), are a reasonable justification of προστεθέν οὐκ ἄνθρωπος ὡς ὑποκείμενόν τι προστεθέν being very analogous to οὐκ ἄνθρωπος ὡς ὄνομα.
This long note, for the purpose of restoring clearness to an obscure text, will appear amply justified if the reader will turn to the perplexities and complaints of the ancient Scholiasts, revealed by Ammonius and Boethius. Even earlier than the time of Alexander (Schol. p. 122, b. 47) there was divergence in the MSS. of Aristotle; several read τῷ δικαίῳ (p. 19, b. 25), several others read τῷ ἀνθρώπῳ. I think that all of them were right in what they retained, and wrong by omission only or mainly.
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 (ἐκ μεταθέσεως, in the language of Theophrastus) corresponding to it will also be true; in universal propositions, the same will not always hold. Thus, if you ask, Is Sokrates wise? and receive for answer No, you are warranted in affirming, Sokrates is not wise (the indefinite affirmation). But if you ask, Are all men wise? and the answer is No, you are not warranted in affirming, All men are not wise. This last is the contrary of the proposition, All men are wise; and two contraries may both be false. You are warranted in declaring only the contradictory negative, Not all men are wise.29
