Cursus Philosophicus Thomisticus, Secunda Pars Artis Logicae

The Philosopher explicitly enumerated all these, except motion, among the species of quantity in the Categories,¹ but rejected them in 5. Metaph.,² lect. 15. in St. Thomas.³ He places motion neither in the Metaphysics nor here, in his explanation of this category, among the species of quantity. We will fully gather the reason for this variation from the words of St. Thomas to be cited below.

Some define place, time, and motion here, but this question lies outside the present topic, since they should properly be treated in the Physics. Briefly, it suffices to transfer their definitions from there to here, so that we may at least taste, as it were, what they are. Place is defined in 4. Phys.⁴ as follows: “Place is the first unmoving surface of the containing body,” that is, a surrounding surface together with an immobility of distance. Motion is called “the act of a being in potency, insofar as it is in potency”⁵, that is, an act that passes successively, in which something is in potency and something in act. Time is “the number of motion according to before and after”⁶, that is, the measure of the duration of motion according to its earlier and later parts.

There is not, then, one OPINION AMONG AUTHORS, including Thomists, CONCERNING THE EXCLUSION of these species from quantity. As for place and motion, almost everyone agrees that they must be rejected from quantity, though they do not agree on the reason for rejecting them. But concerning time and speech, some admit time as a continuous successive quantity and speech as belonging to discrete quantity, while others exclude them.

I SAY, THEN, FIRST: According to St. Thomas’s opinion, motion, time, and place are not per se species of quantity but quantities per accidens⁷; and the Angelic Doctor excludes one and the other in the same way.

This is the opinion of many Thomists, as can be seen in Sanchez, lib. 5. q. 14., and Araujo, 5. Metaph. q. 3. art. 5. Yet in this matter the testimony of St. Thomas is clearer than daylight, so it is surprising that some of his disciples have doubted it. In 5. Metaph., lect. 15., § Distinguit modos, etc.,⁸ he says: “He posits two modes of quantity per accidens. In one way, some things are called quantities per accidens simply because they are accidents of something quantitative, as white and musical are accidents of a subject that is quantitative. In another way, some things are called quantities per accidens, not because of the subject in which they are, but because they are divided according to the quantity of some other quantity, as motion and time are said to be certain quantities and continuous because the things of which they are are divisible, and they themselves are divided according to the division of those things. For time is divisible and continuous because of motion, while motion is so because of magnitude—not indeed because of the magnitude of what is moved, but because of the magnitude of that in which it is moved. For motion is quantitative because that magnitude is quantitative. And because motion is quantitative, it follows that time is quantitative. Hence these can be called not only quantities per accidens, but quantities by posteriority, insofar as they derive the division of quantity from something prior.” Thus far St. Thomas. He concludes there that they are not posited as species of quantity because the species of quantity are considered according to quantity’s very being. Therefore, those things that have being as quantities only from another are not posited there as species of quantity, but are called quantities per accidens, as motion and time are.

From this it clearly follows that those who say St. Thomas does not deny that time and motion are quantities per se, but only that they have quantity in the most imperfect way because they are divided according to another quantity, are not glossing him correctly. They say these are not quantities by reason of their subject, as white is, which is required for being a quantity per accidens. But St. Thomas plainly calls both modes quantities per accidens, not one per accidens and the other per se, though imperfectly. Whatever one thinks about the mode of quantity per accidens, St. Thomas certainly holds that motion and time are quantities per accidens, and that they are therefore excluded from the category of quantity and its species. Hence they are quantities per accidens, as our purpose requires.

As for place, everyone easily rejects it, since it has nothing of quantity except either a surface or the character of encompassing and surrounding what is located. The first is not a quantity distinct from the species of quantity that is surface. In its character as an encompassing, it adds no new being or account of quantity, but only containment or application. Therefore, St. Thomas briefly rejected place from this category in the cited passage, saying that place is not placed among the species of quantity because it has another account of measure, but not another being of quantity.

As for motion and time, since they are successive, and all succession is either continuous or discrete, we speak especially here of continuous succession. For discrete succession, which excludes all continuity in its parts, consists only of indivisibles or instants and is thus found in spiritual things. Continuous succession, which has flowing and nonpermanent parts, can obtain quantity or extension from three sources. First, from the term or form, which comes about part by part; that it comes about part by part and not all at once may depend on the agent’s imperfection, which is unable to introduce the whole term at once, or on the resistance of a contrary in the patient, which is gradually overcome. Second, solely from the flow itself or the duration by which the parts pass successively. Third, from the space, whose magnitude and distance are overcome only by extension.

Although some recognize quantity per accidens in motion only from the first source, especially because of the agent’s weakness or the resistance of a contrary, and others only from the second, St. Thomas, leaving these aside, derived its magnitude and quantity solely from the space in which motion occurs. The reason is that motion, considered in relation to its term, is something incomplete, as it were the way and coming-to-be of the term itself; it is reduced to the genus or category of its term. But the term of motion is only where, quality, or quantity, as is proved in 5. Phys.⁹ Therefore motion cannot have a quantity that is a species of quantity by reason of its term, because not every motion has quantity as its term, and a motion that does have it is not constituted in the account of a distinct species of quantity from its term by reason of that term; it is simply called quantitative from it. But the succession of motion, taken according to the flow and duration of the motion itself, constitutes time. This does not provide quantity to motion; rather, it receives quantity from motion. Indeed, if motion were quantitative by reason of time, time and motion would not be two distinct species of quantity, since there would not be two quantities; motion would be quantitative through time. But it is incompatible with the nature of a thing that its duration should be quantity in the first and per se sense, since duration is nothing other than the continued being of a thing. That this continuation is divisible and quantitative, as it is in us, or indivisible, as it is in angels, does not follow from duration alone—which in both cases is continued being—but from the thing that endures. Therefore duration is not quantity of itself, but by reason of its subject. This is also clear from an indication: much motion can occur in little time, and vice versa; therefore the quantity of time does not quantify motion per se and primarily.

Hence St. Thomas rightly derived the quantity of motion from the quantity of that in which motion occurs, namely the space or distance between the terms between which there is motion. In local motion, this is a space consisting of several places; in qualitative motion, of several terminations or degrees in one and the same quality, or of passage from one quality to another in different subjects; in growth, of several parts of quantity. Motion has divisibility and quantity according to the distance to be traversed. For motion of itself says only that transition by which some being is in a state of coming-to-be, partly in potency and partly in act. Therefore this transition has quantity to the extent that there is divisibility and distance between the terms at which the transition occurs. If there is no distance, as between privation or negation and form, change from nonbeing to being occurs in an instant. If, however, change occurs between positive terms, motion is divisible precisely because there is distance between them. Motion therefore takes quantity from distance or space; of itself it does not provide it. It only makes the subject moved, not quantitative.

From this it is also shown that time is not quantity per se, but quantified by another. The quantity of time is the quantity of the duration of motion, and according to the before and after in motion there is a before and after in time, as is said in 4. Phys.¹⁰ Consequently, the divisibility and extension of time—which are nothing other than its before and after—are taken from the before and after in motion. Time therefore does not have divisibility and extension per se, but by reason of motion; hence it is quantitative per accidens, that is, through another, and so is not a per se species of quantity.

NOR IS IT VALID to answer, as some do, that time receives quantity from another, as it were efficiently and originally but not formally, because time has distinct indivisibles of its own, different from motion, namely instants, and consequently also distinct parts. The parts of motion, they say, are only presupposed to time, as a line is to a surface and a surface to a body; yet each of these is a per se species of quantity.

But the contrary is the case. Motion and time are related as duration and the thing that endures, and no thing causes its own duration, just as it does not cause its own being. Therefore neither can the quantity of motion cause the quantity of time. Moreover, for time to have a quantity per se distinct from motion, it would have to add a new extension, or parts to parts of motion, as a surface adds to a line and a body to a surface, and as number, by dividing a continuum, adds a new mode of extending and measuring discretely. But time has no divisibility and extension other than that of motion, since it is the before and after in motion. Otherwise, if it added distinct parts, it would be only the duration of motion, nor a number according to the before and after in motion: it would number something else, namely the parts it added over and above motion. We will say in the reply to the second argument how the indivisibles of time, which are instants, are not distinct from the indivisibles of motion.

I SAY, SECOND: Speech is not essentially and per se a species of quantity, but is so in a certain metaphorical way.

The Philosopher in 5. Metaph.¹¹ does not place speech among the species of quantity. Cajetan also holds this in his chapter on Quantity.

THE REASON IS that speech is called a quantity insofar as it consists of long and short syllables, which all pertains to the pronunciation of a voice in a faster or slower manner. But the voice itself is a quality, namely a sound uttered by an animal; pronunciation is motion; and speed and slowness are modes consequent upon motion. If these constituted quantity in speech, they would constitute it in motion too. Therefore, neither by reason of the voice, which is a quality, nor by reason of motion and its speed or slowness, which are quantities per accidens, are speech or its syllables per se species of quantity.

Others turn to the small durations of syllable pronunciation, which seem to imply a certain extension. But these little intervals are in reality nothing other than time, which is the duration of motion. We have placed time, with St. Thomas, among quantities per accidens. Hence St. Thomas in Opusc. 48, tract. On When, last chapter,¹² also reduces speech to a measure of discrete time, or to the pronunciation of that sound.

Others make the quantity of speech consist in a certain harmonious consonance of its parts. But this consonance or harmony is not quantity, but proportion, which pertains to relation or, at most, to quality. Indeed, if the proportion is metrical, as in verse, besides the fact that this all depends on convention, it is not common to every kind of speech but only to poetry. If the harmony and proportion of speech lie in the expression itself and the liveliness of apt signification, all this comes from human convention in the voice, not from real quantity. Proportion and harmony in the pronunciation of a voice do not make a species of quantity any more than the proportion of parts in any motion does.

Finally, others say that speech is a discrete quantity, but of an unnamed and unknown species. They defend themselves by ignorance, which cannot be refuted. Finally, if speech is not a significant voice uttered according to a proportion of short and long syllables, it does not have the character of a special number. But all this is not something natural; it depends on human convention. Therefore speech is a species of quantity only metaphorically.

BUT YOU WILL ASK: Why, then, do the Philosopher in the Categories and St. Thomas in Opusc. 48¹³ enumerate place, time, and speech among the species of quantity? St. Thomas answers in the cited 5. Metaph., lect. 15.,¹⁴ “that the Philosopher in the Categories posited time as a quantity per se, whereas in the Metaphysics he posits it as a quantity per accidens, because there he distinguished the species of quantity according to different accounts of measure. Time, which is an extrinsic measure, has one account of measure, and magnitude, which is an intrinsic measure, another. Here, however, he considers the species of quantity according to quantity’s very being. Therefore, those things that have being as quantities only from another are not posited here as species of quantity, but as quantities per accidens.” Thus St. Thomas.

And if you say: If time is a quantity per accidens, how does it have the account of a per se measure, since measure is a property of quantity? The answer is that different measures can arise from the same quantity according to its different modification and application, just as a quantity measures differently when it informs intrinsically and when it is applied extrinsically. Thus, because time and magnitude or motion have the same quantity, they do not constitute different species of quantity per se; yet they do constitute different measurements because they are applied in different ways. Number differs in this respect, since it not only has a different mode of measuring but also a different mode of extending from continuous quantity: it divides and dissolves continuity.

THE ARGUMENTS ARE ANSWERED.

First it is argued: Place, although materially the same as a surface, formally has a different account of measuring, because a surface extends by informing, while place extends by encompassing. But a surface too is materially composed of lines, and number of continuous quantities, while each constitutes a different species of quantity. Therefore place does as well.

THE REPLY is that the cases differ. A surface adds new parts and a new account of extension to a line, although it presupposes the line’s extension. Number also dissolves the mode of continuous extension and transfers it to a discrete mode, which differs from the continuous even in its account of extension. Place, however, adds nothing to a surface except the application of it to something extrinsic that it surrounds.

Second it is argued: Motion and time have parts extended in a new way, namely by the distinct durations and successions through which the parts flow. They also have different indivisibles by which the successive parts are joined: in motion, the “having-changed,” and in time, instants. Therefore, nothing is lacking in them for the account of quantity per se. For spatial extension is not required essentially for quantity; extension over a duration suffices. In this space, however, there is a true extension of successive parts, one of which does not penetrate another but succeeds it. That this successive quantity depends on continuous quantity does not prevent motion and time from being true quantities, just as a body depends on a surface and yet is a true quantity.

THE REPLY is that these successive parts of motion do not add a new extension to the parts of magnitude or space, but a new mode of opposition to permanence, insofar as the parts of motion—that is, the terms acquired in space or distance—do not exist all at once but pass away. This mode, however, does not formally express a new kind of extension, but a lack of permanence, as is clear in itself. Since motion does not express an account of extension distinct from magnitude, it follows that time, which is its duration, does not have a quantity distinct from motion. For time is the duration of motion and has no parts other than motion, whose number it is according to before and after, although any motion is time only in a more regular and uniform way. Herein lies the great difference between motion and time, on the one hand, and magnitude and body, on the other: although a body presupposes a surface, it adds new parts to it; time, however, adds no new parts to motion, nor does motion add new parts to the magnitude of the space or distance in which it is exercised.

As for the added point about the indivisibles of motion and time, it is answered that an instant of time is not distinct from the indivisibles of motion, which are the “having-changed” in the motion of which time is the subject. In the same way, the parts of time do not differ from the parts of motion. Likewise, the indivisibles of motion are not different from the indivisibles of space or of the term acquired through motion in space or distance; they merely connote succession and a negation of permanence in these indivisibles. But we will treat this at greater length in the Physics.¹⁵

Third it is argued: In metrical or harmonious speech, there are different parts according to the length and shortness of pronunciation, which have different durations, and a different order of before and after according to the number of utterances, which are measured by syllables just as number is measured by units. Why, then, would it not be a distinct species of number?

THE REPLY is that all this says nothing quantitatively distinct from discrete or continuous motion, or from its duration, which is time. Hence speech is quantified discretely by the discrete motion of vocal utterance; it does not itself quantify in a new way. As for the added harmony, high or low pitch, and fast or slow pronunciation of the voice, these are qualities rather than quantities of speech.