Lecture 7 — How time is measured

It is most necessary, however, to know time, either with a measure or infinitely.

There is, however, something by which one judges the greater and lesser: moreover, it is able to be put into a ratio, (Latin rationabile; cf. Euclid, Elements 5, def. 4: “Magnitudes are said to have a ratio to one another which are capable, when multiplied, of exceeding one another” (tr. T. L. Heath).) just like magnitudes. For one understands great ones even far off, not by extending one’s understanding out yonder, as some might say of sight (for even when they are not, it similarly understands), but by a proportional motion. For there are similar figures and motions in it.

For (The Leonine text of Aristotle reads “for” (enim) at 452b13; our Greek MS tradition reports “consequently” (oun).) by what does it differ when it understands the greater ones?

Or is it that (The Leonine text of Aristotle at 452b13 reads “that” or “because” (quia), following the Greek MSS that read hoti, instead of those that read hotan, “when.”) it understands those that are less? For all those that are within are lesser; and those that are outside are also proportionately. But perchance it is able to get a proportional just as also with the species, but in it, so too with the distances.

So just as if something is moved according to AB, BE it makes GD: for AG and GD are proportional. What then makes GD rather than ZI? Or as AG is to AB, so is KT to TM; hence it is being moved with respect to those together; but if one wants to understand according to AZ, ZI, he understands similarly to GB, BE. But instead of TC, he will understand KLM. For these are related as ZA to BA.

So when a motion of both the thing and of the time comes about together, then memory is acting. He might think, however, that he remembers while not doing so; for nothing keeps someone from being deceived and to seem to remember even while not remembering. It is not, however, possible for one acting in his memory not to think that he does so but rather not to notice what is remembered: for this was just what remembering is.

But if the that belongs to the thing should come into being without the one that belongs to the time, or the latter without the former, he does not recollect.

But the one that belongs to time is twofold. For sometimes he does not remember it with a measure, e.g. that it was two days ago, but that he did do it at some time or other. Sometimes however also with a measure.

But he does remember although not with a measure; for men are accustomed to say that they remember but do not know when, whenever they do not know its quantity with a metron.

386. It is most necessary, however, to know (452b7). After the Philosopher has shown the mode of recalling from the side of the things to be recalled, here he determines the mode of recalling from the side of time.

And first, he sets out what he intends to do.

Second, he clarifies what he had set out, where he says there is, however, something by which one judges (452b8; [387]).

He says first, therefore, that in recollecting it is most necessary to know time, namely the past, which memory is concerned with, which recollection is a search for; past time is known by one who is recollecting sometimes under a determinate measure, for instance when one knows that one has sensed this item two days ago, and sometimes it is known infinitely, that is indeterminately, for instance if one remembers that he has sensed this item at some unspecified time. (Cf. Aristotle below at 453a1.)

387. Then, when he says there is, however, something by which one judges (452b8), he clarifies what he had set out.

First, he shows how the soul knows the measure of time.

Second, he clarifies the principal point which he had set out, namely that the person who recollects must know time, where he says so when a motion of both the thing and of time (452b23; [396]).

In regard to the first, he does two things.

First, he clarifies what he had set out.

Second, he solves a certain question where he says for by what does it differ (452b13; [389]).

For he says first that there is something in the soul whereby it judges a greater or lesser measure of time. And this is to be able to be put into a ratio with respect to time just as it is also in respect to bodily magnitudes: which the soul understands to be both large with respect to the quantity of the bodies seen, and far off with respect to the quantity of local distance, to which the quantity of time is made proportionate, which is grasped according to its distance from the present moment.

388. The soul knows such magnitudes not by extending one’s understanding out yonder, as if the soul knows magnitudes by getting in contact with them according to the intellect (which is something that he seems to be saying on account of Plato, (Cf. Albert the Great, De memoria 2.5 (p. 114b).) as is clear in the first book of On the Soul (Aristotle, On the Soul 1.3, 407a10–18; cf. Aquinas, Commentary on Aristotle’s On the Soul, bk. 1, lect. 4, nn. 46–51; lect. 8.)); and in this way some people also say that vision comes into being because a visual ray crosses the whole distance up to the thing seen, as is said in the book On Sense and What Is Sensed. (Aristotle, On Sense and What Is Sensed 1.2, 437b10–438a3; 438a25–27; cf. Aquinas, Commentary on Sense and What is Sensed, ch. 7, nn. 105–7.) But it cannot be that magnitudes are known by the soul through contact with the intelligence, since in that way the soul could understand only existent magnitudes, but as the case now stands we see that it understands magnitudes that do not exist. For nothing keeps the soul from understanding a quantity twice that of the heavens. Therefore the soul does not know a magnitude by extending itself to it, but because a certain movement left in the soul by the sensible thing is proportional to an exterior magnitude: for there are in the soul certain forms and motions similar to the things through which it knows things.

389. Then, when he says for by what does it differ (452b13a), he settles a question about what was set out before. And concerning this he does three things.

First, he proposes a question.

Second, he solves it, where he says or is it that it understands those that are less (452b13b; [390]).

Third, he gives an example of the answer in letters where he says so, therefore, if one is moved (452b17; [391]).

So first, he asks this question: when the soul knows a magnitude through the likeness of the magnitude which it has, in what does that by which it knows a greater or lesser magnitude differ? For they seem not to have a different likeness, in that they do not differ in species.

390. Then, when he says or is it that it understands those that are less (452b13b), he resolves the question. And he says that the soul, through a similar figure or form, knows the lesser ones, that is, a smaller quantity, just as through a similar form it also knows a larger magnitude. For the interior forms and movements correspond proportionately to the exterior magnitudes, and perchance the same thing happens with magnitudes or distances of places and times as also happens in regard to the species of things, so that just as in it, the one knowing, there are various likenesses and movements corresponding proportionately to the various species of things, for example to a horse or a cow, so also do they correspond to various quantities.

391. Then, when he says so just as if something is moved (452b17), he shows such a various proportion through an example with letters.

To make this clear one must realize that since he said above that there are in the intelligence figures similar to and movements proportional to the things, he uses here, for the sake of an example, the similarity of figures as the geometers use them, amongst whom figures are called similar whose sides are proportional and angles equal, as is clear in the sixth book of Euclid. (Euclid, Elements 6, def. 1: “Similar rectileal figures are such as have their angles severally equal and the sides about the equal angles proportional” (T. L. Heath tr.). Heath renders the Greek term homoia as “similar” and analogon as “proportional.” In this chapter, Aquinas will be using Latin vocabulary that tracks Euclidean usage rather closely. Hence it is worth noting a couple of definitions from Euclid, that for logos, which will show up in Aquinas’s vocabulary as “proportio” or “ratio,” and that assigning the description analogon, which will appear chiefly in adjectival forms like “proportionales” or the adverbial form “proportionaliter.” Here are the two key definitions from Heath’s translation. Euclid, Elements 5, def. 1: “A ratio is a sort of relation in respect of size between two magnitudes of the same kind”; ibid., def. 6: “Let magnitudes which have the same ratio be called proportional.” For a more metaphysical view of analogy, see B. Montagnes, O.P., La doctrine de l’analogie de l’être d’après saint Thomas d’Aquin (Louvain: Publications Universitaires, 1963).)

392. Therefore, let triangle BAE be described, the base of which is BE. Then from a point G marked in the side BA let a line be drawn equidistant from the base and right up to the other side; this line is GD. And, similarly, in the triangle GAD let a line ZI be drawn equidistant from the base. It was demonstrated in the first book of Euclid (Gauthier cites Euclid, Elements 1, Prop. 26 and the translation by Adelard of Bath under Prop. 29, that if a line meets two parallel lines, then the two “coalternate angles” will be equal. Euclid (1, Prop. 27) has the conditional pointing in the opposite direction: “If a straight line falling on two straight lines makes the alternate angles equal to one another, the straight lines will be parallel to one another” (Heath tr.).) that a straight line falling upon two equidistant lines makes the opposite angles equal. Therefore, angle AGD is equal to angle ABE, and angle ADG is equal to angle AEB. But angle A is common; therefore, the three angles of triangle GAD are equal to the angles of triangle BAE. Therefore the lines that subtend the equal angles are proportional, according to the fourth proposition of the sixth book of Euclid; (Euclid, Elements, 6, Prop. 4: “In equiangular triangles the sides about the equal angles are proportional, and those are corresponding sides which subtend the equal angles” (Heath tr.). Gauthier’s note quotes Adelard’s Latin. Accordingly, the Greek, Latin, and English terms line up as follows: analogon, proportionalia, proportional; homologoi, respicientia, corresponding.) therefore, what is the proportion (In this chapter the Latin word proportio is used as a synonym for mathematical ratio; there are also a couple of instances in this chapter where Aquinas employs ratio in this sense.) of AB to AG is the same as the proportion of BE to GD; therefore, alternately, the proportion from AB to BE is the same as the proportion from AG to GD; and thus the two aforementioned triangles are similar figures. Through the line AB and its parts are understood the movements of the soul by which the soul knows; and through the lines BE, GD, and ZI, which are the bases of the triangles, are understood the various quantities differing in greatness and smallness.

393. Therefore, by way of example, he concludes that if the soul is moved according to movement AB to know the quantity BE, this movement will also make quantity GD be known according to something belonging to itself, since the movement AG, which is contained in AB, and the magnitude GD are in the same proportion as the movement AB and the magnitude BE.

394. But then the question that was raised above will return: what more is required for knowing the quantity GD, which is greater, than for knowing the quantity ZI, which is less?

395. And in order that this might be seen more plainly, he takes indistinct movements, one of which is not contained in the other: therefore, let there be one line KM and let it be divided at point T in such a ratio (Here the Latin uses the expression tali ratione to express the term “ratio.”) that there is the same proportion of KT to TM as that of the line AG, according to which the quantity GD is known, to the line AB, according to which quantity BE is known; in this way, therefore, it is** being moved with respect** to these movements, since just as according to the movement AG the quantity GD is known, so according to the movement KT, and, just as according to the movement AB the quantity BE is known, so according to the movement TM. But if someone wants, according to the movement AZ, to know the quantity ZI, then GZ will have to be subtracted from AG, just as **GB **was added to it in order to know the quantity BE. But, if we wish to take distinct movements, we must take in place of the two movements KT and TM (in place of which he now puts TC, C and M may be inscribed on the same point) two other movements, one of which is KL and the other LM, so that the line KM is divided at point L according to this ratio, (Here secundum hanc rationem.) so that the proportion of KL to LM is as the proportion of AZ to AB. Hence, just as through the movement LM one knows the quantity BE, so through the movement KL one knows quantity ZI.

396. Then, when he says so when a motion of both the thing and of the time comes about together (452b23), he goes on to explain the principal thing he had set out to do.

And first, he shows that the one who recollects must know time.

Second, he shows two ways of knowing time where he says but that which is of time (452b29; [397]).

Accordingly, he says first that when the movement of the thing to be remembered and of the past time occur in the soul together, then there is the act of memory. If, however, someone should think that it is so related and yet memory should not come into being in this way—because it lacks either the movement of the thing or the movement of the time—then there is no object remembered; for nothing keeps deception from existing in the memory, as when it seems to someone that he remembers something and he actually does not, since the past time occurs to him but not the thing that he saw, but another instead. (The Latin loco eius might also be rendered: “by means of its place,” perhaps alluding to the mnemonic method of “places.”)

In addition, sometimes one remembers and does not think that he does so, but it escapes his notice, because the thing occurred to him but not the time ; since, as noted above, (2.1, 450b20 to 451a12, 15–16; cf. ch. 3, n. 349.) remembering is to be intent on the phantasm of a thing inasmuch as it is the likeness of something previously apprehended. *(To be sure, a photocopy can be isomorphic with its original; but being a copy in this sense is not enough to induce either recollection. The Leonine edition here strongly echoes the vocabulary of “*eikōn-imago-likeness” as discussed in Chapter 3: Hoc est memorari intendere phantasmati alicuius rei prout est imago prius apprehensi. Aquinas’s point is that a phantasm or idea in and of itself is not enough to cause recollection: the phantasm or idea must be charged with eidetic intentionality.) Hence, if movement of the thing should come about without the movement of the time, or vice versa, one does not recollect.

397. Then when he says but the one which belongs to time (452b29), he shows the diverse manner in which those who recollect know time. For sometimes one does not record the time under a determinate measure; for example, that he did something two days ago, but rather that he did it at some time or other; however, sometimes he records it even under a certain measure of time; but it is in the memory if one records a past time, although not under a determinate measure. For men are accustomed to say that they do record a thing as past but do not know when it was, since they do not know the metron, (Here Aquinas glosses the hitherto un-translated Greek term metron from 453a4.) that is, the measure, of the time. And this happens because of a weak impression, as occurs in things that are seen by those who are far away and which are known indeterminately.