b. To the Second Proof

376. To the second proof of the antecedent [n.289] it is said that ‘the indivisible is nothing other than lack of the continuous, so that nothing save lack of continuous succession is formally an instant- and so a point is lack of length and states nothing positive’. And in that case the proposition that ‘the successive has precisely being because its indivisible exists’ [n.289] needs to be denied; rather it has precisely successive being because a part of it flows by, and never because an indivisible of it is something positive.

377. Many things seem to make for this opinion:

First, that, when the idea alone of the continuous is posited and everything absolute is removed, the continuous seems to have a term, provided it is not absolute; and it does not seem that God can separate finiteness from line nor - as a consequence - a point from it either, which does not seem likely were a point ‘an absolute essence’ different from line.

378. Likewise, if point and line were two absolute essences, it does not seem possible that some one thing would be made from them unless one of them were an accident of the other; for they are not one by perfect identity since they are posited as two absolute essences; nor possible that a single third thing would be made composed of them, because neither is act or potency with respect to the other. The indivisible then has being and not-being without generation and corruption, because if it is only in the middle of a continuous line it is only one point, but when the line is divided there are two points actually; so there is there some point that was not there before, and there without generation, because it does not seem probable that a generator has generated there some absolute essence.

379. Likewise, it seems, from the author of Six Principles about the figure of an incision,Book of Six Principles 1.4, “In the case of certain things there is doubt whether their beginning is from nature or from act, as in the figure of an incision; for no addition is made but a certain separation of parts.” ³⁴ that this is not something said positively, and yet there is a surface there in actuality that was not in actuality before.

380. But against this [nn.376-379]:

Then the result is that the generation of a substance that is not per se the term of a continuum will be nothing (or at any rate in nothing), because there is no positive measure of it; and so it is in the case of illumination and all sudden changes that are not the per se terms of motion. And although this result could be avoided in the case of changes that are terms of motion and come to be in an instant (as nothing in the case of nothing or privation of continuity in the case of privation of continuity), yet it seems absurd about the former cases, for they are not the per se terms of the continuity of any continuous thing, because they are nothing of anything continuous, whether positively or privatively.

381. Further, according to the Philosopher Posterior Analytics 1.4.7334-37, the idea of line comes from points, that is, point falls into the essential idea of line and is said of line in the first mode of saying per se [sc. the mode of per se when the predicate falls into the definition of the subject]; but no privation pertains per se to the idea of something positive;     therefore etc     . [sc. point must state something positive, contra n.376].

382. From the same [sc. statement of the Philosopher, n.381] the result also follows that, if a point is only a privation, line too will be only a privation, as well as surface and solid; for a termed thing is defined by what terminates it and something positive does not essentially include a privation.

383. Likewise the same result [n.382] follows (for another reason [sc. from what is said in n.376 and not from Aristotle’s statement in n.381]) that, if a point is only a lack of length, a line will be only a lack of width and a surface only a lack of depth; and then there will only be a single dimension, which solid would be posited to be, although however the dimension which is called ‘depth’ could in another respect be called ‘width’ (for the three dimensions are distinguished by imagining three lines intersecting each other at the same point).

384. And from this further is inferred something unacceptable, that if a surface is only the privation of depth, how will a point be the privation of a privation? For nothing seems to deprive a privation unless it is something formally positive.

385. In addition, there are on a surface many corporeal or sensible qualities, as it seems; therefore a surface is not merely a privation.

The antecedent is proved about colors and figures, each of which is per se visible and consequently something positive. The figure too [sc. of a surface] seems most properly to follow the kind or species, and so seems to be an accident manifestive of the species; but it does not seem probable that there is no positive entity to something that is such as to follow a species naturally and to manifest it.

386. If it be said differently [sc. to the proof, nn.289, 376] that ‘the indivisible by which the successive has being exists only in potency’ - this is no help, because, when the indivisible is gone, what succeeds to it in the way it has being in the whole? If another indivisible does, the argument [n.289] stands; if not, then the successive will not exist.

387. My response to the argument [n.289] is that, when the indivisible is gone, a continuous part flows by and not an indivisible; nor does anything succeed immediately, save as the continuous is immediate to the indivisible.

388. And if it be objected ‘therefore time does not always have being uniformly and equally (because, when the indivisible instant is posited, time exists, for its indivisible exists, but when the indivisible has gone, time immediately does not exist, because another indivisible of it does not exist)’ - I reply that, just as a line does not have being uniformly everywhere insofar as ‘everywhere’ distributes over the parts of a line and the indivisibles of a line (because a line has being in the former as it is in the parts and in the latter as it is in the ultimates), and yet a line exists everywhere uniformly to the extent that ‘everywhere’ distributes precisely over the latter or precisely over the former, so it is in the issue at hand of time; if the ‘always’ [at the beginning here, n.388] distributes precisely for the indivisibles or precisely for the parts, then time does have being uniformly; but if for both at once then it does not have being uniformly.