[36] Ibid. a. 27.
[37] Compare Schol. (ad Anal. Prior. I.) p. 146, a. 19-27; also Eudemi Fragment. cxiv. p. 167, ed. Spengel.
Eudemus considered ἔστιν as one term in the proposition. Alexander dissented from this, and regarded it as being only a copula between the terms, συνθέσεως μηνυτικὸν μόριον τῶν ἐν τῇ προτάσει ὅρων.
[38] Aristot. De Interpr. p. 21, a. 32; compare Rhetorica, ii. p. 1402, a. 5. The remark of Aristotle seems to bear upon the doctrine laid down by Plato in the Sophistes, p. 258 — the close of the long discussion which begins, p. 237, about τὸ μὴ ὄν, as Ammonius tells us in the Scholia, p. 112, b. 5, p. 129, b. 20, Br. Ammonius also alludes to the Republic; as if Plato had delivered the same doctrine in both; which is not the fact. See ‘Plato and the Other Companions of Sokrates,’ vol. II. ch. xxvii. [pp. 447-458], seq.
Aristotle now discusses the so-called MODAL Propositions — the Possible and the Necessary. What is the appropriate form of Antiphasis in the case of such propositions, where possible to be, or necessary to be, is joined to the simple is. After a chapter of some length, he declares that the form of Antiphasis suitable for the Simple proposition will not suit for a Modal proposition; and that in the latter the sign of negation must be annexed to the modal adjective — possible, not possible, &c. His reasoning here is not merely involved, but substantially incorrect; for, in truth, both in one and in the other, the sign of contradictory negation ought to be annexed to the copula.[39] From the Antiphasis in Modals Aristotle proceeds to legitimate sequences admissible in such propositions, how far any one of them can be inferred from any other.[40] He sets out four tables, each containing four modal determinations interchangeable with each other.
1. 3. 1. Possible (physically) to be. 1. Not possible (physically) to be. 2. Possible (logically) to be. 2. Not possible (logically) to be. 3. Not impossible to be. 3. Impossible to be. 4. Not necessary to be. 4. Necessary not to be. 2. 4. 1. Possible (physically) not to be. 1. Not possible (physically) not to be. 2. Possible (logically) not to be. 2. Not possible (logically) not to be. 3. Not impossible not to be. 3. Impossible not to be. 4. Not necessary not to be. 4. Necessary to be.
| 1. | 3. |
|---|---|
| 1. Possible (physically) to be. | 1. Not possible (physically) to be. |
| 2. Possible (logically) to be. | 2. Not possible (logically) to be. |
| 3. Not impossible to be. | 3. Impossible to be. |
| 4. Not necessary to be. | 4. Necessary not to be. |
| 2. | 4. |
| 1. Possible (physically) not to be. | 1. Not possible (physically) not to be. |
| 2. Possible (logically) not to be. | 2. Not possible (logically) not to be. |
| 3. Not impossible not to be. | 3. Impossible not to be. |
| 4. Not necessary not to be. | 4. Necessary to be. |
Aristotle canvasses these tables at some length, and amends them partly by making the fourth case of the second table change place with the fourth of the first.[41] He then discusses whether we can correctly say that the necessary to be is also possible to be. If not, then we might say correctly that the necessary to be is not possible to be; for one side or other of a legitimate Antiphasis may always be truly affirmed. Yet this would be absurd: accordingly we must admit that the necessary to be is also possible to be. Here, however, we fall seemingly into a different absurdity; for the possible to be is also possible not to be; and how can we allow that what is necessary to be is at the same time possible not to be? To escape from such absurdities on both sides, we must distinguish two modes of the Possible: one, in which the affirmative and negative are alike possible; the other in which the affirmative alone is possible, because it is always and constantly realized. If a man is actually walking, we know that it is possible for him to walk; and even when he is not walking, we say the same, because we believe that he may walk if he chooses. He is not always walking; and in his case, as in all other intermittent realities, the affirmative and the negative are alike possible. But this is not true in the case of necessary, constant, and sempiternal realities. With them there is no alternative possibility, but only the possibility of their doing or continuing to do. The celestial bodies revolve, sempiternally and necessarily; it is therefore possible for them to revolve; but there is no alternative possibility; it is not possible for them not to revolve. Perpetual reality thus includes the unilateral, but not the bilateral, possibility.[42]
[39] Aristot. De Interpret. p. 21, a. 34-p. 22, a. 13. See the note of Waitz, ad Organ. I. p. 359, who points out the error of Aristotle, partly indicated by Ammonius in the Scholia.
The rule does not hold in propositions with the sign of universality attached to the subject; but it is at least the same for Modals and Non-modals.