[51] Ibid. p. 17, a. 5. οἱ μὲν οὖν ἄλλοι (λόγοι) ἀφείσθωσαν· ῥητορικῆς γὰρ ἢ ποιητικῆς οἰκειοτέρα ἡ σκέψις· 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.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 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, Cæsar is perhaps dead; it is possible that Cæsar is dead; it is only because these fall together under another head; being properly assertions not of anything relating to the fact itself, but of the state of our own mind in regard to it; namely, our absence of disbelief of it. Thus, Cæsar may be dead, means, I am not sure that Cæsar is alive.�
I do not know whether Mr. Mill means that the function of the copula is different in these problematical propositions, from what it is in the categorical propositions: I think there is no difference. But his remark that the problematical proposition is an assertion of the state of our minds in regard to the fact, appears to me perfectly just. Only, we ought to add, that this is equally true about the categorical proposition. It is equally true about all the three following propositions:— 1. The three angles of a triangle may or may not be equal to two right angles. 2. The three angles of a triangle are equal to two right angles. 3. The three angles of a triangle are necessarily equal to two right angles. In each of these three propositions, an assertion of the state of our minds is involved, and a different state of mind in each. This is the subjective aspect of the proposition; it belongs to the form rather than to the matter, and may be considered as a mode. The commentators preceding Ammonius did so consider it, and said that the categorical proposition had its mode as well as the others. Ammonius differed from them, treating the categorical as having no mode — as the standard unit or point of departure.
The propositions now known as Hypothetical and Disjunctive, which may also be regarded as in a certain sense Modals, are not expressly considered by Aristotle. In the Anal. Prior. I. xliv. p. 50 a. 16-38, he adverts to hypothetical syllogisms, and intimates his intention of discussing them more at length: but this intention has not been executed, in the works that we possess.
In every complete theory of enunciative speech, these modal propositions deserve to be separately explained, both in their substantive meaning and in their relation to other propositions. Their characteristic property as Modals belongs to form rather than to matter; and Aristotle ought not to be considered as unphilosophical for introducing them into the Organon, even if we adopt the restricted view of Logic taken by Sir W. Hamilton, that it takes no cognizance of the matter of propositions, but only of their form. But though I dissent from Hamilton’s criticisms on this point, I do not concur with the opposing critics who think that Aristotle has handled the Modal Propositions in a satisfactory manner. On the contrary, I think that the equivocal sense which he assigns to the Potential or Possible, and his inconsistency in sometimes admitting, sometimes denying, a Potential that is always actual, and a Potential that is never actual — are serious impediments to any consistent Logic. The Problematical Proposition does not admit of being cut in half; and if we are to recognize a necessary Possible, or an impossible Possible, we ought to find different phrases by which to designate them.
We must observe that the distinction of Problematical and Necessary Propositions corresponds, in the mind of Aristotle, to that capital and characteristic doctrine of his Ontology and Physics, already touched on in this chapter. He thought, as we have seen, that in the vast circumferential region of the Kosmos, from the outer sidereal sphere down to the lunar sphere, celestial substance was a necessary existence and energy, sempiternal and uniform in its rotations and influence; and that through its beneficent influence, pervading the concavity between the lunar sphere and the terrestrial centre (which included the four elements with their compounds) there prevailed a regularizing tendency called Nature: modified, however, and partly counteracted by independent and irregular forces called Spontaneity and Chance, essentially unknowable and unpredictable. The irregular sequences thus named by Aristotle were the objective correlate of the Problematical Proposition in Logic. In these sublunary sequences, as to future time, may or may not was all that could be attained, even by the highest knowledge; certainty, either of affirmation or negation, was out of the question. On the other hand, the necessary and uniform energies of the celestial substance, formed the objective correlate of the Necessary Proposition in Logic; this substance was not merely an existence, but an existence necessary and unchangeable. I shall say more on this when I come to treat of Aristotle as a kosmical and physical philosopher; at present it is enough to remark that he considers the Problematical Proposition in Logic to be not purely subjective, as an expression of the speaker’s ignorance, but something more, namely, to correlate with an objective essentially unknowable to all.
The last paragraph of the treatise De Interpretatione discusses the question of Contraries and Contradictories, and makes out that the greatest breadth of opposition is that between a proposition and its contradictory (Kallias is just — Kallias is not just), not that between a proposition and what is called its contrary (Kallias is just — Kallias is unjust); therefore, that according to the definition of contrary, the true contrary of a proposition is its contradictory.[53] This paragraph is not connected with that which precedes; moreover, both the reasoning and the conclusion differ from what we read as well in this treatise as in other portions of Aristotle. Accordingly, Ammonius in the Scholia, while informing us that Porphyry had declined to include it in his commentary, intimates also his own belief that it is not genuine, but the work of another hand. At best (Ammonius thinks), if we must consider it as the work of Aristotle, it has been composed by him only as a dialectical exercise, to debate an unsettled question.[54] I think the latter hypothesis not improbable. The paragraph has certainly reference to discussions which we do not know, and it may have been composed when Aristotle had not fully made up his mind on the distinction between Contrary and Contradictory. Considering the difficult problems that he undertook to solve, we may be sure that he must have written down several trains of thought merely preliminary and tentative. Moreover, we know that he had composed a distinct treatise ‘De Oppositis,’[55] which is unfortunately lost, but in which he must have included this very topic — the distinction between Contrary and Contradictory.
[53] Aristot. De Interpr. p. 23, a. 27, seq.
[54] Scholia 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).