Jacques Maritain Center: Thomistic Institute


Steven C. Snyder, Ph.D.
Pontifical College Josephinum
July, 2000

One profitable way of studying Thomas Aquinas' understanding of the natural philosophy of time is to place him in dialogue with some near contemporaries, in this paper Averroes, Albert the Great, and Robert Kilwardby. To write his Physics commentary Thomas carefully read Averroes' and Albert's commentaries; we do not know whether Thomas read Kilwardby's insightful and for our purposes very helpful opusculum De tempore. Each of these four philosophers is interpreting and weighing the truth of Aristotle's Physics IV.10-14,(1) which is organized in this way: a dialectical beginning which focuses our attention on the key stumbling block, time's successive being, prepares the way for Aristotle's scientific determination of time's being (an sit) and definition (quid sit). With that foundation Aristotle discusses at length what it means for things to exist "in time," and he concludes this section with an explanation of how common language about time accords with his conclusions. In the final chapter he asks two questions, about the possible dependence of time on a soul's numbering temporal events and about the unity of time, viz. whether there is one time for all motions or as many times as there are motions. These two questions elicit open disagreement among our four philosophers and result in a dialogue on time which is of enduring and not just historical value.

Prior to any disagreements, these four thinkers--Averroes, Kilwardby, Albert, and Thomas--agree on Aristotle's explanation of time's mode of being and definition. They agree that time's mode of being is the flowing, successive being which motion has (esse successivum, actus imperfectus), not the stable, enduring being of material substances (esse permanens, actus perfectus). All of time that exists in physical reality is the flowing, present moment or now, which is always "other and other."(2) The sophistical dialectical arguments with which Aristotle introduces his analysis of time in Physics IV.10 all err because they fail to recognize time's successive mode of being, which follows upon motion's successive mode of being because time is an attribute of motion. We remember that the Parmenidean sophistical arguments which opened the Physics erred similarly by misunderstanding motion's flowing, imperfect actuality. The four physicists also agree that Aristotle rightly defines time as "the number of motion according to before and after."(3)

As the number of motion, time is by nature not an abstract counting number but the number precisely of events of the material universe.(4)

There is, then, verbal agreement among the four on time's mode of being and definition; but there is significant disagreement on the meaning of the words they have agreed to, as we can see by turning to the two questions of time and the soul and the unity of time, beginning with Averroes. The argument in Aristotle that Albert considers dialectical, "... if nothing can do the numbering except a soul or the intellect of a soul, no time can exist without the existence of a soul ...",(5) Averroes takes as demonstrative: time is made actual by the intellective soul's act of numbering events of the world. It does so by marking off earlier and later now-s as the termini of the temporal extent belonging to a motion in the world; having established the time of that motion, the mind also has a fixed time period by which to measure other motions. For example, the intellective soul marks off the start and finish of one diurnal motion as one day: time is thus measured, and a measure now exists for measuring other motions also, for example one day's worth of study. Time exists materially and potentially in events of the world; it is given formal being by the soul's act of numbering. This is Averroes' position on time and the soul, and it is Thomas Aquinas' position in the Sentences.(6)

For Averroes, the "motion" named in time's definition, "the number of motion according to prior and posterior," is that motion which when temporally marked off by the intellective soul has a nature to be the measuring rod for all events of the world--by its measure all events of the world are at least potentially measured. The regular and observable rotational movement of the ultimate celestial sphere, the motion of the primum mobile of the shared geocentric cosmology of Aristotle and our four medieval thinkers, is for Averroes the motion named in Aristotle's definition. There is only one time because there is this one motion by reference to which the soul can measure all other subordinate motions. For Averroes, the proper way to understand Aristotle's definition of time is "the number <supplied by the intellective soul's measuring> the motion, according to prior and posterior, of the sphere of the fixed stars primarily and secondarily all other motions."

Although motion itself--as material and potential principle of time--is all of time that Averroes thinks exists extra mentem, Robert Kilwardby, who distinguishes what time is from the way we perceive time, concludes that apart from the mind's act of numbering there exists individually in each event of the universe some real temporal extent, having a ratio distinct from motion. He calls this time in reality tempus illimitatum et indeterminatum; it is the quantity of time belonging as a proper attribute and measure of each event of the world without the soul's act of numbering. Each event has its own tempus illimitatum.(7) However, Aristotle's definition refers to time not just as measure but as number, which for Kilwardby is arithmetical number caused by an intellective soul alone.(8) Soul by its numbering brings into existence tempus limitatum et determinatum, the fixed time periods of a day and its multiples and parts (e.g. weeks or hours).(9)

For Kilwardby, Averroes has incorrectly limited the definition of time to the proper number of one motion alone, that of the sphere of the fixed stars. Since each and every motion possesses temporal extent as a proper attribute, each and every motion can properly be numbered by the soul. Since our minds supply the formal number of time and thus make the temporal yardstick, we can use any motion to measure time. There is no privileged motion by reference to which all others are temporally measured and determined. And so there should be as many times-time as illimitatum-as there are motions and observers. However, Kilwardby's geocentric cosmology meant for him that all of these various human measures of time are translatable into one all-embracing and best known measure of times, the soul's measure of the time of the motion of the sphere of the fixed stars.(10) There are not many times corresponding to the diverse motions chosen as standards by different observers, because all temporal measures can be reduced to the ultimate time which measures the motion of the fixed stars. Therefore, there is for Kilwardby ultimately one time for the whole universe, because there is one time to which all the various humanly generated times can in practice be reduced.

Albert and Thomas argue that time is not made by the soul: time exists as an ens naturae, as the number of motion, in the flowing successive being of the present now. The mind fashions temporal extents, of course, like one week or one second; but it can only do so because time already exists in re. Further, there is but one real time of the universe, they argue, although of course our ways of perceiving that time can be various and many.

The error of Averroes, adopted by Kilwardby, arose because they misunderstood the nature of number. Albert says that Averroes certainly was in error in ascribing the origin of temporal number to the soul, and Aristotle seems to have made the same error. But against this error Albert points out that "... the soul never numbers anything unless there is in it a ratio of number taken from things themselves."(11) Each and every concept of number which we have is derived from our experience of real number in nature. We can count ten horses in a herd because there are really outside the mind ten distinct horses that exist as ten whether we count them or not. Number exists already in nature when there is real otherness, real distinction, in nature.(12)

Where there is distinction in nature, there is number in nature. Horses in reality are enduring beings and so we have them all before us as we discern--count--their number. Motion's being is successive and flowing and motion's parts do not co-exist for us to discern--count--their number. To perceive a temporal extent we must mark off and hold in the memory earlier and later now-s. But we can number in this way only because there is real temporal number, real temporal distinction, in the flowing present now which is all of time that is real in the world. Each present moment, just because it is flowing, distinguishes past from future, earlier from later. Because the present moment not only continues time but also distinguishes past from future, there is real temporal distinction and order, and so real temporal number, belonging to events themselves. The order of prior and posterior in the flowing now is time in nature.(13)

And so Albert concludes,

. . . in order "to number," three things are needed: namely, numbered matter, formal number, and a soul numbering not formally but efficiently. Therefore, if there were no soul, there still is number according to formal being and numbered matter . . . and so, when no soul exists, number exists not only in potency but also according to an accidental form of discretion belonging to the things numbered; and in this way also time exists entirely outside the soul. And since for the existence of a thing in itself all that is needed is form and matter, soul is not needed for the existence of time in itself. But soul by the act of numbering does establish and cause our own comprehension of time . . .(14)

Temporal extents like one year do exist in the mind, but these extents are our way of holding together in our perceptions a reality which in nature is not an extent but only a flow. Our temporal measuring, our chronometrics, would be pure fiction, unrelated to physical reality, unless prior to chronometrics there is real chronos, real time existing in nature with its own proper mode of physical being. Real distinction of earlier and later, and so real temporal number, exists in physical reality in the indivisible, flowing now. Natural time exists in the flowing now's distinction of before from after. No more of time need or can exist naturally. Successive beings have their being in their proper indivisible principle.(15)

This position on the extra-mental reality of time is held by both Albert and Thomas in their Physics commentaries. In this commentary Thomas has abandoned the Averroistic position on time and the soul he had held in the Sentences and adopted in the Physics Albert's position.(16) But in one point Thomas differs from Albert. Albert allowed that Aristotle seemed to have made the Averroistic error of saying the soul supplies the formal principle of time; Thomas intends his careful line by line commentary to demonstrate that Aristotle avoided this erroneous innovation from first to last in Physics IV. For Thomas, both Aristotle and the truth hold that time has real successive being, form and matter, in the events of the material universe.

It follows for Albert and Thomas that there is one time and not many times belonging naturally to the universe. Time is one, numerically one in the universe, because the universe is one. There is ultimately a single temporal becoming common to the whole universe. Time is the number of the fundamental becoming of the whole. For, individual motions not only have their own proper becoming but also partake of the becoming of the system they are in. The earth, for example, partakes of its own motion and the motion of our solar system and the motion of our galaxy and, indeed, the motion--the most fundamental becoming--of the universe as a whole. Thomas says,

There is one first motion, which is the cause of every other motion. Whence whatever things have changeable being have this changeable being from that first motion, which is the motion of the outer sphere of the fixed stars. Moreover, whoever perceives any motion whether existing in sensible things or in the soul, perceives transmutable being, and as a result perceives the first motion which time follows upon . . . time follows upon only one motion by which all others are caused and measured; and thus there remains only one time.(17)

It is because the inferior motions are part of a single universe, have their start and finish as part of one flowing whole and partake of the becoming of the whole, that all motions are in the one time of the universe. We defined time as the number of motion. The motion named in this definition is the motion which is causally first, the fundamental becoming of the universe. Time is the number of the becoming which belongs to the universe as a whole, a becoming in which all events of the universe share. Time is the number of the events of the universe insofar as they belong to one universe.

Albert and Thomas thought the source and course of the fundamental becoming of the whole universe was readily observable by us as the motion of the fixed stars,(18)

and so they concluded that the absolute time of the universe is immediately measurable by all observers. Our astronomy now recognizes the error of asserting a sphere of the fixed stars. But this modern correction does not change what is essential to Albert's and Thomas' position, that the universe is one, it has a continuous history. The becoming of the whole, shared in by all its parts, is the natural subject unifying time, even if the source and course of that underlying becoming of the whole is not directly observable or measurable by us.(19)

Kilwardby's analysis of the unity of time has the merit of anticipating modern recognition of the relativity of human perceptions of time. But Albert and Thomas argue more effectively than does Kilwardby against the error of mistaking our way of perceiving time for time's mode of being as a flowing reality in nature. The Averroistic error on time and the soul is unavoidable if we do not acknowledge along with Albert and Thomas a real temporal becoming proper to the universe as a whole. Our science of time-measure, chronometrics, is dependent on their being a real time, a real chronos, which is being measured, even if only indirectly through secondary motions dependent on this primary temporal becoming of the universe. If time is denied real albeit flowing and successive being in the material world and is made primarily a mental construct, then it will logically follow that motion, too, must be denied real being in the world and must be treated primarily as a mental construct. Such a notion is repugnant to the natural philosopher. Moreover, in this respect we are all natural philosophers, for the existence of motion is an immediate, per se nota truth, as is the existence of time. Making time depend on the soul in the Averroistic way will eventually lose for us nature itself. And losing nature means losing God. Upon first turning to the question of time and the soul, Thomas says,

... if there are numbered things, there must be number. Hence, both numbered things and their number depend on one who numbers. Now the existence of numbered things does not depend on an intellect unless there is some intellect which is the cause of things, as is the divine intellect. However, their existence does not depend on the intellect of the soul. Only numeration itself, which is an act of the soul, depends on the intellect of the soul.(20)

Time and motion lead to natural knowledge of God. By losing true understanding of time as a successive being real in the world, we would lose understanding of motion, which is also a successive being, as real in the world. Our victory over Parmenidean skepticism in Physics I would in the end be given away in Physics IV. Losing nature we would lose God and lose ourselves. Thus it is essential that we study carefully the legacy on the nature of time bequeathed by Thomas Aquinas and Albert his teacher.(21)


1. Aristotle. Physics 4.10-14 (217b30-224a16), translations of which are taken from Aristotle. Physics. Tr. Hippocrates G. Apostle. Grinnell, IA: Peripatetic Press, 1980. Averroes. In 4 Physicorum comm.87-134, in Aristotelis Opera cum Averrois commentariis, vol. 4 (Venice, 1562-1574; repr. Frankfurt a. M., 1962); Robert Kilwardby, Tractatus de tempore, in On Time and Imagination, ed. P. Osmund Lewry, O.P. Oxford: Oxford University Press, 1987, which is translated as Robert Kilwardby. On Time and Imagination, Part 2: Introduction and Translation. Tr.. Alexander Broadie. Oxford: Oxford University Press, 1993; Albertus Magnus, Physica lib.4, tr.3, cc.1-17, ed. P. Hossfeld. Cologne, 1987, vol.4/1 of Opera Omnia, pp.259-293; and Thomas Aquinas, In 4 Physicorum lectiones 15-23 (Rome: Marietti, 1965), a translation of which is to be found in Thomas Aquinas. Commentary on Aristotle's Physics. Tr. Richard J. Blackwell et al. New Haven: Yale University Press, 1963. All references, unless otherwise noted, shall be to these texts and editions. For a clear and insightful overview of the physics of time in the middle ages, see Anneleise Maier, Metaphysische Hintergründe der spätscholastichen Naturphilosophie. Rome, 1955, pp. 47-137.

2. See, for example, Aris., Physics 4.11 (219b9-10); Aver. comm. 103 (f.182G); Kilw. q.1, nn.7-9; Alb. 4.3.7 (4/1:272.4-83); and Th. l.18, nn.1-11 (nn.582-592).

3. Aris. 4.11 (219b2-3); Aver. comm.101 (f.181C-H); Kilw. q.2, nn.10-12; Alb. 4.3.5-6 (4/1:267-271); and Th. l.17, nn.1-11 (nn.571-581).

4. Aris. 4.11 (219b7-10); Aver. comm.102 (f.181K-182E); Kilw. q.6, nn.26-27; Alb. 4.3.6 (4/1:269.69-270.37); and Th. l.17, n.11 (n.581). Almost inevitably the term "number" conjures for us the concept of mathematical number, the counting numbers 1, 2, 3, etc. Mathematical number, however, is arrived at by abstraction from a more basic plurality or "number" real in things. Aristotle distinguishes concrete number and plurality real in things (numbered number) from the mathematical number abstracted from this real plurality (number by which we number). Time is concrete number, the numbered number of motion. Time is a plurality that numbers naturally the real distinction of start and finish, and parts between, of motion.

5. Aris. Phy. IV.14 (223a25-26).

6. Aver. comm 109 (f.187C) and 131 (f.202C-F). Cf. Thomas in the Sentences: Cum igitur unicuique rei respondeat propria mensura, oportet quod secundum conditionem actus mensurati accipiatur essentialis differentia ipsius mensurae. Invenitur autem in actu qui motus est, successio prioris et posterioris. Et haec duo, scilicet prius et posterius, secundum quod numerantur per animam, habent rationem mensurae per modum numeri, quae est tempus ... Ex quo patet quod illud quod est de tempore quasi materiale, fundatur in motu, scilicet prius et posterius; quod autem est formale, completur in operatione animae numerantis: propter quod dicit Philosophus, IV Physic., text. 131, quod si non esset anima, non esset tempus. 1 Sent. d.19, q.2, a.1, sol. [Mandonnet 1:467].

... eorum quae signficantur nominibus, invenitur triplex diversitas. Quaedam enim sunt quae secundum esse totum completum sunt extra animam; et hujusmodi sunt entia completa, sicut homo et lapis. Quaedam autem sunt quae nihil habent extra animam, sicut somnia et imaginatio chimerae. Quaedam autem sunt quae habent fundamentum in re extra animam, sed complementum rationis eorum quantum ad id quod est formale, est per operationem animae, ut patet in universali ... et similiter est de tempore, quod habet fundamentum in motu, scilicet prius et posterius ipsius motus; sed quantum ad id quod est formale in tempore, scilicet numeratio, completur per operationem intellectus numerantis. ibid., q.5, a.1, sol. [Mandonnet 1: 486].

7. Kilw. q.14, n.77, & q.11, nn.44-51. Kilwardby's position on tempus illimitatum seems analogous to Averroes' postion that bodies have a quasi-substantial "form of corporeity" ontologically prior to their accidental form of determinate dimensions: see Henry J. Wolfson. Crescas' Critique of Aristotle. Cambridge, Mass: Harvard University Press, 1929, note 18, pp. 579-590.

8. Kilw. q.6, nn.25-28.

9. One advantage of this interpretation of time and the soul for Kilwardby is that it in some way saves Augustine's Confessions XI analysis of time (cf. Kilw. q.1, n.4; q.2, n.10; and q.13, n.72). Albert and Thomas, as we shall see, would say that Kilwardby is correct in asserting against Averroes that time really exists outside the mind (his tempus illimitatum), but he errs by saying time outside the mind is without number. Rather, the number of time in reality has esse successivum; but number conceived by the mind exists after the manner of a stable being, an ens permanens. Arithmetical number can exist in the mind, according to Albert, only because real number, i.e., real numerical distinction, already exists outside the mind. Albert, at least, has no interest in preserving Augustine's teaching authority on this question of natural philosophy. See Alb. 4.3.3 (4/1:264.62-81) & 4.3.4 (4/1:265.35-36).

10. Kilw., q.11, n.49.

11. Ecce, haec videtur esse sententia Aristotelis <viz., ... tempus in potentia est sine anima, actualem autem accipit perfectionem ab anima numerante>, et est expositio Averrois de hoc, qualiter tempus se habeat ad animam, et est imperfecta, ut mihi videtur. Cuius ratio est, quoniam anima numquam numerat aliquid, nisi sit in ipsa principium numeri, quod accipitur a rebus ipsis. Alb. 4.3.16 (4/1:289.61-69).

12. Aris., Categories c.6 (4b20-31); Metaphysics 14.1 (1087b34-1088a14) and 10.6 (1057a7-8); cf. Hippocrates Apostle, Aristotle's Philosophy of Mathematics. Chicago: The University of Chicago Press, 1952, p.5. See also Alb. 1 Metaph. tr.3, c.2 (ed. Colon. [1960] 16/1: 32.32) and 5 Metaph. tr.1, cc.8,10 (16/1: 227.41-229.26, 231.61-233.52); and A. George Molland, "Mathematics in the Thought of Albertus Magnus," in James A. Weisheipl, ed., Albertus Magnus and the Sciences. Toronto: Pontifical Institute of Mediaeval Studies, 1980, pp. 476-477.

13. Alb., 4.3.16 (4/1: 290.17-23) and c.12 (p. 283.2-88); cf. Th. 4 Phy. l. 23, n.5 (n. 629).

14. . . . ergo ad numerare tria exiguntur, scilicet materia numerata et numerus formalis et anima efficienter et non formaliter numerans; ergo si non sit anima, adhuc numerus est secundum esse formale et secundum materiam numeratam; ergo "quo numeratur" est duplex, scilicet "quo numeratur efficienter" et "quo numeratur formaliter". Non ergo secundum potentiam solum est numerus non existente anima, sed etiam secundum habitualem formam discretionis rerum numeratarum, et hoc modo penitus est etiam tempus extra animam, et cum ad esse rei in se non exigatur nisi forma et materia, non exigitur anima ad esse temporis in seipso. Sed anima actione numerantis ponit et causat temporis deprehensionem, et quoad hunc actum non est tempus extra animam. Alb. 4.3.16 (4/1:290.1-16. To avoid confusion over Albert's term habitualem, which is based on the Latin translation of Aristotle's Physics (223a18-19), we should note that Thomas glosses habitus as accidens motus, l.23, n.2 (n.626).

15. . . . tempus non habet esse extra animam, nisi secundum suum indivisibile; ipsa autem totalitas temporis accipitur per ordinationem animae numerantis prius et posterius in motu, ut supra <ed. note: l.17, n.2 seqq.> dictum est. Et ideo signanter dicit Philosophus quod tempus, non existente anima, est utcumque ens, id est, imperfecte; sicut et si dicatur quod motum contingit esse sine anima imperfecte. Th. l.23, n.5 (n.629).

16. Albert's Physics commentary was written before Thomas wrote his own Sentences commentary. It should not surprise us, however, that a theology student had not thought deeper than the standard Averroistic position on time in order to write primarily on the angels. But when the mature scholar is writing his Physics commentary, he studied closely his teacher's own commentary on that work. On Thomas' regular practice of closely reading Albert's Aristotelian paraphrases, see James A. Weisheipl, "Thomas d'Aquino and Albert His Teacher," The 2nd Lecture of the Etienne Gilson Series, 6 March 1980. Toronto: PIMS, 1980, pp. 13-14.

17. Si autem tempus consequatur motum animae, sequetur quod res non comparentur ad tempus nisi mediante anima; et sic tempus erit non res naturae, sed intentio animae, ad modum intentionis generis et speciei. Si autem consequatur universaliter omnem motum, sequetur quod quot sunt motus, tot sint tempora: quod est impossibile, quia duo tempora non sunt simul, ut supra <ed. note: l.16, n.2, & l.15, n.5> habitum est.

Ad huius igitur evidentiam sciendum est, quod est unus primus motus, qui est causa omnis alterius motus. Unde quaecumque sunt in esse transmutabili, habent hoc ex illo primo motu, qui est motus primi mobilis. Quicumque autem percipit quemcumque motum, sive in rebus sensibilibus existentem, sive in anima, percipit esse transmutabile, et per consequens percipit primum motum quem sequitur tempus. Unde quicumque percipit quemcumque motum, percipit tempus; licet tempus non consequatur nisi unum primum motum, a quo omnes alii causantur et mensurantur; et sic remanet tantum unum tempus. Th. l.17, n.4 (n.574)

Cf. Albert: . . . tempus ut in causa et ut in subiecto est in primo mobili; et bene concedo, quod non est in motu primi mobilis, secundum quod est expansus in toto caelo, sed prout in ipso secundum naturam aliquid est, a quo incipit motus, et aliquid, per quod regyrat motus. Haec autem sunt dextrum et sinistrum, non distincta ab anima, sed in ipsa caeli existentia . . . Alb. 4.3.16 (4/1: 290.36-45).

18. Alb. 4.3.17 (4/1:291.46-292.8); Th l.23, n.11 (n.635).

19. Cf. John M. Quinn, who has written extensively on the natural philosophy of time: "Plainly, the ubiquity and uniformity of time are mediated by the primary motion of the universal physical cause. Insofar as its number resident in the primary motion is secondarily exhibited in every other motion, time stretches to the farthest reaches of the cosmos . . . Here warranted knowledge stops; man cannot put his finger on which motion is the primary subject of time." "Time," New Catholic Encyclopedia . New York: McGraw-Hill, 1967, 14:159.

20. ... positis rebus numeratis, necesse est poni numerum. Unde sicut res numeratae dependent a numerante, ita et numerus earum. Esse autem rerum numeratarum non dependet ab intellectu, nisi sit aliquis intellectus qui sit causa rerum, sicut est intellectus divinus; non autem dependet ab intellectu animae. Unde nec numerus rerum ab intellectu animae dependet; sed solum ipsa numeratio, quae est actus animae, ab intellectu animae dependet. Th. l.23, n.5 (n.629). Thomas' reference to God seems to be occassioned by Aristotle's reference to "... that which when existing, time exists, that is, if a motion can exist without a soul." Phy. IV.14 (223a28-29).

21. Underlying this conclusion is the general principle that Aristotelian natural philosophy, rightly understood as Albert and Thomas did and modified to accommodate new facts, is essentially true and philosophically necessary today. Succinct statement of this principle can be found in James A. Weisheipl, O.P. "The Validity and Value of Natural Philosophy," Atti del Congresso Internazionale, no.9 :Il Cosmo e la Scienz, 1979, pp.263-266; and Benedict Ashley, O.P. "The River Forest School and the Philosophy of Nature Today," in R. James Long, ed., Philosophy and the God of Abraham: Essays in Memory of James A. Weisheipl, O.P. Toronto: Pontifical Institute of Mediaeval Studies, 1991, pp.1-16. Besides studying the many works of Weisheipl and Ashley on natural philosophy, the reader can benefit from the works on natural philosophy by William Humbert Kane, O.P., William A. Wallace, O.P., Vincent Edward Smith, and Richard J. Connell.