Ibn 8in3 on tbe Now by Jon McGinnis Ibn Sina's treatise on the now is a philosophically deep analysis of Aristotle's temporal theory by one of the Arab world's most astute philosophers. It allows us to see how Aristotle's theory was understood and perhaps more importantly modified within the Islamic milieu. The treatise has been translated and commented on by Yegane Shayegan in her dissertation Avicenna on Time.} However, Shayegan used an uncritical edition,2 and in places her translation and commentary seem to distort Ibn Sinä's meaning. In what follows I offer a new presentation ofIbn Sinä's account ofthe now. My translation is based on the edition established by Said Zayed, which, despite numerous typographical errors, still stands as a critical edition oflbn Sinä's Physics. 3 Further, I have compared Zayed's edition once again with the Teheran edition and also with the Latin translation oflbn Sina's Physics, the Sufficientia. 4 Iy. Shayegan "Avicenna on Time" (Ph.O. diss., Harvard University, 1986). 2Kittib ash-Shifa', as-Samtic a!-.tabff, lithograph (Teheran: n.p., 1886). c 3Ash-Shifti " a.t-.tabfCiyyat, vol. 1 as-samti a!-!abfCf, ed. Said Zayed (Cairo: The General Egyptian Book Organization, 1983); all future references to the Shifti' are to the !abfiyytit vol. 1 as-samac a!-!abff. Zayed' s edition is based on five different manuscripts and their marginalia. Unfortunately, Zayed does not provide exact locations for the manuscripts he utilized; however, we can tentatively identify them based on the bibliographies ofBrockelmann, Anawati, Mahdavi and Ergin: al-Azhar (and marginalia) [331 (185-226)], Dar al-Kutub [H. 262, H. 753, H. 172 (P. VII)], Damad al-jadidah [822, 823,824,825], Teheran (and marginalia) [I, 144/6 (?)], the British Museum [Suppt. 711]. 4p or Teheran edition see footnote 2; A vicennaeperhypateticiphilosophi ac medicorum facile primi opera ... (Venice: 1508) (reprint by Minerva, 1961); henceforth referred to as the Sufflcientia. Copyright 1999, American Catholic Philosophical Quarterly, Vol. LXXIII, No.l 74 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLY I have not attempted to translate Ibn Slnä's crabbed and contorted Arabic absolutely literally, which would undoubtedly lead to an incomprehensible and unreadable text of little value. But neither have I literary freedom, which might not capture Ibn allowed myself ｵｮｬｩｭ ｴ･ｾ Slnä's intended meaning. Rather, I have tried to take the middle path. Thus to the best of my abilities I have rendered Ibn Slnä's Arabic into natural English and yet made no sustained effort to simplify the philosophical reconditeness of the text. Hopefully my commentary will straighten up the more oblique passages. I. Translation: Concerning an Elucidation ofthe Now: (160.4-7) We say: the now is known from knowing time. Thus since time is continuous, necessarily it has a division which is imagined and is called the now. This now is absolutely not something in act existing in time itself, otherwise it would sever the continuity of time. Its existence, rather, is only as the estimative faculty imagines it,5 namely, a connector in a linear extension. 6 For the connector is not something actually existing in a linear extension insofar as it is a connector; otherwise the connectors wou1d be infinite, as we shall make clear later. (160.7-161.1) Indeed [the now] would only be in act, ifit were to sever time with a kind of discontinuation. But it is impossible that it sever the continuity of time, because if a discontinuation is attributed to time, then that discontinuation must be at either [I] the beginning or [11] the ending of the time. [I] On the one hand, if it is at the beginning ofthe time, then from that it is necessary that no "before" belonged to that time. If no "before" belonged to it, then it is necessary that it was not something nonexisting, SCala an yatawahhamahu al-wahm; lit. as estimation esteems it. "Estimation" is a complex notion for Ibn Sina. Roughly estimation is one ofthe internal sense faculties which has intentions (maCanf; see below) for it proper objects. See Deborah Black's "Estimation (Wahm) in Avicenna: The Logical and Psychological Dimensions" in Dialogue XXXII (Spring 1993): 219-258. I have chosen to use the English "imagine" instead of"esteem" to \express the activity of the Avicennian estimative faculty or its operation, since "imagine" ,seems to make more sense in English; nevertheless, one should not confuse my use of !imagine with the Avicennian imaginative faculty (mutakhayyilah) or its operation. These lare two distinct faculties. 6Literally, "something straight in extension." IBN SINÄ ON THE Now 75 and then it exists; for when there is something nonexisting and then it exists, its existence is after its nonexistence. Thus its nonexistence would be before its existence. Hence a "before" would necessarily belong to it and that "before" would be an intention7 other than the "nonexistence" characterized according to the manner which we asserted in this situation. 8 So this thing of which this species of beforeness is predicated would be when this time was not. Thus before this time fully realized Ｈｾ､ｩｬ｡ｮＩＬ there would be a time continuous with [this time]-that one before and this one after-and this division would join the two, whereas it was posited as a division, so this is a contradiction. [11] Likewise, if [the now] imposed a division in the manner ofan end point, then either [A] there would be the possibility of something existing after it, or [B] there would not be. [B] Now on the one hand, if it were not possible that something exists after it, not even that whose existence is necessary,9 (so that it is impossible that something exists with the nonexistence which is reached after the end point), then absolute possibility and that something necessary exists necessarily would have been eliminated; but necessary existence and absolute possibility are not eliminated. 1O [A] On the other hand, ifthat [that is, the possibility ofthe existence of something] were after it, then it would have an after so that it would be before rand argument [I] applies]. Thus the now is a connector, not a divider. 7Ma cana (lit. concept) often translates the Greek ａＶｹｯｾ or is translated by the Latin intentio and occasionally ratio and can have much the same variety of meanings as these tenns. See Richard Frank, "Al-macana: Some Reflections on the Technical Meanings of the Tenn in the Kalam and its Use in the Physics of Mucammar," Journal 0/the American Oriental Society 87 (July-September, 1967): 248-59. We can take it here to mean those properties which though not essentially material, neverthelss belong to sensible fonns. Ibn Sinä's canonical example is hostility in a wolfwhich the sheep recognizes via estimation; however, one can also see how motion could be considered a mifnii insofar as motion is not nlaterial yet it cannot exist apart from a mobile; see D. Black's "Estimation (Wahm) in Avicenna." 8Excising bihi with the manuscripts. 9The phrase employed here is wiijib al-wujud. Wajib al-wujud is the technical tenninology for God, yet as professor Mannura has pointed out to me the context virtually demands that Ibn Sina be discussing existents within the temporal order. Consequently, wiijib al-wujud here should be taken as short hand for wiijib al-wujud bi ghayrihi, the necessary existent through another. IOReading la yartafiCiin with the Teheran manuscript. 76 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLY (161.1-7) Hence tinle, in relation to itself, does not have a now existing in act, but rather [the now exists] in potency. I mean by ["in potency"], potency proximate to act, that is, time is always disposed to the now being posited in it, either by sonleone positing it or by the motion coming to a concurrent, undivided boundary, like the starting point (mabda') ofthe rising and setting [ofthe sun] orthe like. This does not really produce a division in the essence of time itself, but rather in its relation to motions, like the relative divisions produced in other magnitudes. For example, one part of a body is divided from an other part by [the one part being] parallel to or in contact with [the other] or by someone positing it without an actual division having occurred in it in reality; rather a division occurs in it through a comparison to something else. When this now occurs by means ofthis relation, then its nonexisting is only in the totality of time after it. (161.7-12) One [can only] say "[the now] is corrupted in the immediately following now or a now which does not immediately follow it" after committing [oneself] to [the now] having a corruption which begins at a now, or even the beginning of its corruption is at the limit of time during the whole ofwhich it is nonexistent. 11 However, nothing more is understood by "corruption" than that something is rionexistent after its existence. [The now's] existence in this situation is that it is a limit oftime [but] during [time] it is somethingnonexisting; as ifyou said that [thenow] is an existing thing at the limit oftime [but] during [time] it is something nonexisting. Now its corruption does not have a beginning which is the first now in which it is corrupted; 12 on the contrary, its existence is nothing otherthan a division between [time's] existence and its nonexistence. And you will leam that there does not belong to being moved and resting and generating and corrupting a first now in which there is being moved or resting or generating or corrupting, since potentia11y time is infmitely divisible. (161.12-162.10) Should someone suppose on the basis ofthis that he can say either that the now becomes nonexistent gradually (so that its setting off into nonexistence extends over aspace of time) or that it llReading baI for bila with the Teheran manuscript. 12Literally, "belonging to its corruption there is not a beginning of corruption, which is the first now in which it was corrupted." IBN SINÄ ON THE Now 77 beeomes nonexistent "all at onee" (so that its nonexistenee is in a now), the falsity of [this] assertion will need to be explained. We say that the nonexistent or existent happening "all at onee" (in the . sense of oeeurring in a single now) is not neeessarily the opposite ofwhat either gradually eonles to be or eeases to be, but rather it is more speeifie than that opposite. That opposite [that is, the opposite ofwhat comes to be gradually] is what does not go gradually to existence or nonexistence or alteration or the like. This holds true [1] of what oeeurs "all at onee"; and it holds true [2a] of the thing which is nonexisting in all of a certain time, but is existing in [time's] limit whieh is not time, or [2b] the thing which is existing in all of a eertain time but is not existing in [time's] limit which is not in time. For indeed it is not the case that these two exist or not exist gradually, and the first, that is, that ofwhieh the existence or nonexistence is in a now, is also thus. The latter viewpoint [2], however, is distinet from that first viewpoint, because the first viewpoint has assumed that the judgment conceming the now oftime, which is essentially [time's] end point, is like the judgment eoneerning all time. i3 On the other hand, in the latter viewpoint [2] it has been assumed that the judgment about the now is different from the judgment about time, from [the fact that] one now is not placed after a different now (otherwise the nows would be adjoining);14 however, [aecording to the seeond view] that now is nothing other than a limit. Our debate does not concern whether this seeond viewpoint turns out to be true or not; for we are not debating it with a view to affirming its existence, but rather we speak about it insofar as a eertain negation is predicated of it, namely, the negation that it comes to exist or not exist gradually. Now there belongs in that [negation] a partner (sharik); but that partner is more particular than this negation and the more particular is not intrinsic to the more general, nor is it neeessary that something insofar as it is eoneeptualized as a subjeet or predieate be such that it is affirmed or not affinned in its existence-this had been learned in the art of logic. 13Reading an for an. 14Mushafaca, which I have translated "adjoining," is not a standard Arabic term and possibly Ibn Stna coined it. In Shifa ' 111.2, 181.9-10 Ibn Sina defines tashafzf as astate of touching the following [thing] qua following; wa amma at-tashafucufa huwa ｾ｡ｬ mumassi ta/in min ｾ｡ｹｴｨｵ huwa taUn. Thus given the similarity ofmeaning between forms 111 (mCala) and VI (tafäCala) mushafaca could mean to bring about this state ofbeing in contact with what is next. 78 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLY Henee ifthe elaim "it eomes to exist or not exist gradually" is more general than the elaim "it eomes to exist ornot exist 'all at onee'" (in the sense that that thing's state is in an initial now), then the assertion that "either it is gradually or it is 'all at onee'" (in this [previously mentioned] sense) does not hold true through the validity of a disjunetion eovering either the two extremes of the eontrary, or the eontrary and what is intrinsie to its eontrary. (162.10-14) And again: the opposite of what exists "all at onee" is what does not exist "all at onee," that is, it does not exist in an initial now. But it is not neeessarily intrinsie to [the opposite of that whieh exists or does not exist "all at onee"] that it exists or not exists gradually; indeed that whieh is in aeeordanee with the aforementioned viewpoint [nanlely, 2] might be truly asserted in relation to it. Unless of eourse by "something existing 'all at onee'" one means that whieh does not exist now unless (a) existenee is fully realized in it, and (b) there does not exist a now at whieh it is still in proeess. It is also likewise for "something not existing 'all at onee'" aeeording to [what has been said]. For ifthis is the meaning, then this is intrinsieally the opposite and the premise is valid. Yet it is not neeessary that [without these stipulations this opposite's] initial existenee or eeasing to be is "all at onee." (162.14-163.11) Here is something important, and even if it does not fit in this plaee, it is appropriate that we mention it in order to verify what we have said. That is to say it is worth our whi1e to investigate whether [given] two times, in one ofwhieh things are in one state and in the other in another state, then eould things in the now eommon to [the two times] be entirely laeking both states? Or is it in [the now] aeeording to one ofthe two states without the other? Now if the two things are potentially mutually exelusive, sueh as the eontiguous and the noneontiguous or the existent and the nonexistent and the like, then it is impossible that the thing with respeet to the posited now be entirely laeking one or the other ofthem. Henee it neeessarily follows that it is aeeording to one ofthem, and 1 wish I knew whieh one ofthem it is! So we say that it is neeessary that something eomes to the existing thing [that is, the thing existing in a partieular state], and makes it eease to be [existing in that state]. So either [1] that thing whieh arrives is among those whose being found in a now is permissible, that is, something whose I state remains the same in any now you take during the time ofits existenee, land it does not need a now which corresponds to an interval of time IB·N SINÄ ON THE Now 79 (muddah) in order to be. 15 Now whatever is such, the thing in the common division is described by [the state], like the contiguous and the quadrupie and other [states] of a fixed disposition, whose existence remains the same in each now during the time of their existence. Or [2] [that which comes to the thing existing in a particular state] is something contrary to this description. So that its existence will occur in a time, yet it will not occur in a now; and its existence will be in the second time alone, and it will not be possible [that it exist in] the now dividing the two [times]. For in it there is an opposition (muqdbalah)16 like separation or loss of contiguity andmotion. For some ｯｦｴｨ･ｳｾ then, their state can remain the same during the nows oftheir time, leaving aside the nows ofthe occurrence initially; and for some ofthem, their states can absolutely not remain the same. As for the one which can [remain the same], it is like the noncontiguous, which is to be apart; for it does not occur except by motion and variation of state. Yet it remains not touching; indeed, it is apart for a time during which it remains the same, even if its states vary from other perspectives; for that is not from the perspective that they are separate and not touching. As forthose which cannot [remain the same], they are like motion. For its state does not remain the same in any now, but rather in every now there is a renewal ofneamess and remoteness, both being among the states ofthe motion. Hence the immobile thing when it is set in motion and the contiguous when it is made no longer to touch is such that there is in the now which is the division between [the changing thing's] two times contiguity and lack of motion (since in it there is neither a beginning of separation nor motion). Even if this [issue] is extemal to our goal, it is useful conceming [this issue] and conceming other issues. (163.11-164.1) That which we have discussed is the now surrounded by the past and future; as if time occurred and then after its occurrence it was marked off by this now. But a different now may be imagined 15Readingfi an for fi an; see the Latin "non est necesse ut in quantum sit comitetur eam tempus" [it is not necessary that in as far as it is it accompanies its time] (Sufficientia, 35r). Y. Shayegan translates: "it does not need to be in a 'now' whose [stretch] to another 'now' corresponds to duration" (67). This translation requires us to take ila as syntactically which seem unlikely. Further her translation countenances independent ofthe verb ｹ｡ｾＨｩｪｵＬ the existence of "stretches" (her addition) between nows which are not periods oftime, a position which is dubious. See the commentary for a discussion. 16See the Arabic translation of Aristotle's Posterior Analytics 72a12-l3 where the Arabic muqabalah translates the Greek ￤ｶＧｴＨ･｡ｾＮ 80 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLY according to a different description. Hence the limit of a mobile (and let [this] be some point) [1] assumes a certain spatial magnitude, 17 even indeed a certain line, in its motion and flow (as ifit-that is, that limit-is something borne along) and then [2] in that line points are assumed which do not actually make the line, but rather are imagined connected with it. Likewise it appears that something like that [that is, the moving point] is in time and in motion (in the sense of a traversal), and also something like the interior points in the line which did not n1ake [up the line]. That is because being borne along and a time are imagined as existing lS with reference to a spatial magnitude. Therefore a continuous time is congruent with what is borne along because of a continuous transition along a continuaus spatial n1agnitude; for that which is borne along, or rather the state which attends it with the motion, is an indivisible limit, which through its flow makes a continuity. From the spatial magnitude there corresponds to [that which is borne along] a point and from time a now; however no line of spatial magnitude accompanies [that which is borne along] (for [that] had followed it) nor motion in the sense of a traversal (for [that] had come to an end) nor time (for [that] had passed). Rather what does accompany [that which is borne along] from each of [these, that iS,spatial magnitude, motion and time] is an indivisible limit belonging to [each ofthese three] which is not divisible the way [each ofthem] are. 19 (164.1-4) Thus accompanying [that which is borne along] from time there is always the now, and from the traversal the thing which we in fact showed to be motion (so long as the thing is moving), and from spatial magnitude the boundary, whether a point or the like. Each one ofthese is an end point. Even what is borne along is an end point in its own right insofar as it is borne along; as if [being borne along] were something in a spatial magnitude extending from the beginning to wherever it reaches. Thus, insofar as it is what is borne along, it is something extending from the beginning to the end; and the essence of the persistent existing thing 17Masiifa, which I have translated here as "spatial magnitude," can also be rendered "interval," "stretch" or "distance." Indeed, certain later claims require translating masafa as "interval" or "stretch." 18Reading wujida with Zayed for the Teheran manuscript's wa ｾ｡､Ｎ 19Inqisiim; Ibn Sina has preferred ｪ￤ｾｬ or ｦ｡ｾｩｬ to indicate a division in time (or any continuum) throughout his account ofthe now. This is one ofthe few occasions where he deviates from this tendency. IBN SiNA ON THE Now 81 now20 is a boundary and an end point essentially insofar as it has been carried to this boundary. (164.4-13) Thus it is appropriate for us to consider: whether just as the essence of what is borne along is one and makes its boundary and end point and also the interval by its flow, so likewise with respect to time is there something that is the now which flows? Thus it would essentially be indivisible qua it, that is, it would remain the very same insofar as it is that, and yet it wouldnot remain the same insofar as it is the now. For it is only a now when it is taken to mark off time, just as the former one is [only] what is borne along when it marks off what it marks off, but in itself it is a point or the like. Just as that which is borne along qua that which is borne along may happen not2 ! to exist twice but rather passes away with the passing away of its being borne along, so the now qua now does not exist twice. However, the thing (which for whatever reason became a now) could exist several times, just as that which is borne along qua a thing which happens to be borne along could exist several times. Thus if something like this exists, then it would be true that the now, through its flowing, would make time, but this now would not be that one which is posited connecting two times, just as the point which is imagined to make an interval by means of its motion is different from the point imagined in the interva1. 22 Hence ifthis thing exists, then its existence is somethingjoined to the intention23 (which in what preceded we confirmed to be motion) without [being joined to] before or after or coinciding. (164.13-165.5) Now just as [that which is borne along] possessing a "where" when it continues to flow in spatial magnitude produces motion, likewise, it possessing this intention which we call the "now" when it continues [to flow] in the before and after ofmotion produces time. Thus the relation ofthis thing to the before and after is [that] its being is a now, which in itself is something making time, and it numbers time by means of boundaries in [the motion] which are produced when we take a now. Thus dhatuhu al-mawjudah ｡ｬＭｭｵｴｾｳｩｨ al-an. 21Reading annahu la with the Teheran manuscript. 22Literally, "different from the point of the distance imagined in it (m.)" The antecedent of "it" injihf, however, is unclear. Since the most obvious antecedents are all feminine, we should most likely emend the text to jiha. 23See above for discussion of"intention." 20 wa 82 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLY it produces numerable befores and afters, like points number the line, in that each point is common between two lines by means of two relations. Now the actual numberer is that which first gives the thing unity and then gives it multiplicity and number through repetition. , Thus the now,which is associated with this description numbers time; so that unless there is a now, time is not numbered. The before and after also number time according to the second viewpoint, that is, that they are its parts. [Time's] quality ofbeing partitioned occurs by means ofthe existence of the now, because the before and after are parts of time, and each part of it has a natural propensity for being divided just like the parts ofa line. Thus the now is better suited for the unit, and the unit is more appropriate for enumerating. Hence the now numbers according to the way in which the point numbers and yet is not divided. The motion numbers time by producing the before and after on account of the spatial magnitude. Thus by means of the magnitude of the nl0tion there will be the number of before and after, so the motion numbers the time according as it produces the number oftime, that is, before and after. Time numbers motion in that [time] is a number belonging to [motion] itself. (165.5-9) An example ofthis is people who owing to their existence are the causes of the existence of their number, which is for instance ten; and due to their existence, their "tenness" exists. The "tenness" does not make the peop1e existing beings or things; however [it does make them] things which are countable, that is, endowed with a number. When the soul counts the people, what it counts is not the nature ofthe human being, but rather [it counts] the "tenness" produced by the distinction which occurs in the men' s nature, for instance. Thus the soul by means ofthe men numbers the "tenness,"just as motion numbers time according to the aforementioned intention. Were it not for the motion in connection with the boundaries of before and after made in spatial magnitude, then a number would not exist for time. (165.9-14) Tinle, however, measures motion and motion measures time. Now time measures motion according to two modes. The first is that it makes [motion] possess a measure. The second is that it indicates the quantity of its measure. Motion measures time according as it indicates [time's] measure by means ofthe before and after existing in it. But there is a difference between the two situations [that is, time measuring motion _ --------------- - - - - - - - - - - - - - - - - - - - - - - IBN SINA. ON THE Now 83 and motion measuring time]. As for indicating the measure,24 sometimes it is just as the measure of wheat indicates the holding capacity for the wheat and sometimes it is just as the holding capacity for the wheat indicates the measure ofthe wheat [being held]. Likewise sometimes the spatial magnitude indicates the measure of motion and sometimes the motion [indicates] the measure ofspatial magnitude. Thus sometimes one speaks of a distance oftwo parasangs [approx. 8 miles] and sometimes "a stone' s throw" (masdfat ramya). However, that which gives the magnitude (miqddr) to the other is one of the two, and it is the one that in itself is a measure. (165.14-17) Because time is continuous in its very being (fi jauharihi), it is pennissible to assert [that it is] long and short. And because it is a number in relation to the before and after according to what we have set forth, it is permissible to assert [it is] few and many. [This is] likewise [true] for motion, since continuity and discontinuity occur in it; hence the properties of continuity and discontinuity are asserted of it. However that occurs in [motion] extraneously, while what is most proper to it is fastness and slowness. Thus we have indicated the manner ofthe existence ofthe now in act, if existing in act belongs to it; and [we have indicated] the way it exists in potency. 11. Commentary: Ibn Sinä's account ofthe now takes place against the backdrop ofhis theory oftime. A thorough account ofhis temporal theory would merit a study of its own; thus we must content ourselves with abrief summary, which Ibn Sinä himselfprovides in the following passage. To be divided into before and after is concomitant with motion. The before existing in [motion] is only what pertains to [motion] on behalf of the before in spatial magnitude (masdfa), and the after is only what pertains to it on behalf of the after in spatial magnitude. However, from that it does not follow that the before belonging to motion is found with the after of [motion], as the 24Reading qadr with the Teheran manuscript for Zayed' s qudra; also see the Latin mensuram (Sufficientia, 35r). 84 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLY before and after in spatial magnitude are found together. It is not possible that what is congruent with the before belonging to motion through a spatial magnitude becomes after nor what is congruent with the after of it [becomes] before, as is possible in spatial magnitude. So a property belongs to the before and after in motion which is concomitant with them on the part of their belonging to motion, but not on the part of their belonging to spatial magnitude. Now the two are numbered by motion; for motion by means of its parts indeed numbers before and after. ofthe before and after Thus a number belongs to motion ｢･ｾ｡ｵｳ belonging to it in spatial magnitude. Also a magnitude belongs to [motion] parallel to the magnitude ofthe spatial magnitude. Time is this number and magnitude; for time is the number of motion when [motion] is divided into before and after-not by time but rather by spatial magnitude, otherwise the definition would be circular. 25 Much like Aristotle' s temporal theory, Ibn Sinä's rests on a correspondence Although the between spatial magnitude, motion and time. 26 correspondence is not exact, it does allow divisions exißting in spatial magnitude to mark off divisions in motion, such that motion can be measured and numbered. Time just is this measure and number ofmotion. Ibn Sinä's treatise on the now, in its turn, is an explanation ofthe nature of these divisions and how they allow us to measure and number motion and consequently time. (160.4-8) Ibn Sinä begins with an observation about the relation between the now and time and then a defmition of the now. Our knowledge concerning the now comes from our knowledge of time; for time is continuous and everything which is continuous is divisible, and the now just is the dividing point between past and future. This now is in potency. It must be in potency and not in act, since there cannot be an actual division in time; for time is continuous and the continuous is infmitely divisible (at least potentially).27 Ifthe now actually divided time and time is infinitely divisible, there would be an actually infinite number 25 Shifä' 11.11, 156.18-57.7. 26See Physics IV, 11, 219al O-b2. 27Physics VI, 1-2, 231a21-33b32. IBN SINÄ ON THE Now 85 ofnows. However, there is never an actual infmite and so the nows cannot be actual divisions within time itself, but only potential divisions. 28 The now, then, is only a conceptual division, which the soul imagines or esteems in the time. 29 How the soul can imagine this division will be explained in the sequel (161.1-7). This argument is interesting. It is clearly Aristotelian, but it does not seem to be one that either Aristotle or at least two of his commentators employed. Aristotle certainly makes the point that the now is only a potential division in time, but he does not seem to have argued explicitly for it. 30 Alexander of Aphrodisias, on the other hand argues: If [time] were divisible in actuality, then in between its parts there would be an interval which is not time. Time, however, is one in actuality, although it is divisible in potentiality.31 The argument is mutatis mutandis, one Aristotle employed at Physics VIII, 8 (262a19-b4) to show that in any motion along a straight line a point lying between two extremes is a potential, but not actual, division ofthe motion. Philoponus likewise contends that the now can only mark a potential division in time; however, he argues from the nature ofthe motion which time measures. 32 Time, it is maintained, primarily measures the motion of the outermost sphere of the fixed stars. Now if there were an actual division in time, there must be an actual division in the motion which time measures; however, there is only an actual division in a motion if the 28 Physics BI, 6, 206bI2-13; IV, 13, 222aIO-20. 29See footnote 5 for a discussion of estimation. 30Perhaps Aristotle's comments at IV, 11, 220a4-21 and 13, 222a10-20 are intended to show why the now can only be a potential division; however, if so, Aristotle does not make this point explicit. 31 De tempore 21.14-16 [13]; Alexander' s De tempore is now lost in Greek, but extant in Arabic and Latin translations. The Arabic can be found in Commentaires sur Aristote Perdus en Grec et Autres Epitres, ed. A. Badawi (Beirut: Dar el-Mashreq, 1971), 19-24; the sur Latin in G. Thery, "Autour du decret de 1210: 11, Alexandre d'Aphrodise, ａｰ･ｲｾｵ I'influence de sa noetique," Bibliotheque Thomiste 7 (1926): 92-97; an English translation of the Latin can be found in R. W. Sharples, "Alexander of Aphrodisias, On Time," Phronesis 27 (1982): 58-81. (All translations are my own and from the Arabic; bracketed numbers refer 10 Sharples' translation from the Latin text). 32Philoponus, In Aristotelis Physicorum Commentaria, ed. H. Vitelli (Berlin: George Reimer, 1888) 732, 5-733, 36. 86 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLY mobile actually comes to a rest. Since the sphere ofthe fixed stars never actually comes to a rest, there cannot be an actual division in time. Hence this division is only potential and in our minds. Although it would be hasty to say Ibn Sina' s argument for the potentiality of the now is unique, it is different from various ancient arguments, which would have been accessible to hirn. 33 (160.8-161.1) Ibn Sina proffers a secondargument, an argument, we might add, which is more properly Avicennian. 34 Ifthe now were an actual division in time, then there would have to be a discontinuation in time and this severance oftime's continuity would come either at the beginning or the ending of the time. 35 The first horn assurnes that the now belongs to the beginning of a period oftime. Now either (a) there is a time which is before this time or (b) there is not. If (a) there is a time before the time which begins with the now, then the two times are continuous and one and the same now would join the two times while simultaneously separating them, which is absurd. In concrete terms, if 12:00-12:30 and 12:30-1:00 are actually divided at 12:30, then the two times are actually joined and actually separated simultaneouslyat 12:30, which is impossible. On the otherhand, if (b) there is not a time before this time, then it is impossible that the tinle beginning with the now not have existed, and then existed. For its nonexistence would be before its existence, which is just to say there was a time before this time. Hence if there is no time before, then this time would have always existed and consequently there is not some now which is its beginning point. 36 Nor could one say that between the two times there 33For ancient commentators' positions conceming the potential division of continua see D. Furley, "The Greek Commentators' Treatment of Aristotle's Theory of the Continuous," in Infinity and Continuity in Ancient and Medieval Thought, ed. N. Kretzmann (Ithaca: Comell University Press, 1982), 17-36. 34At least part of this argument, however, can be traced back to Alexander's De tempore 24.3-6 [27]. 35Although I reconstruct Ibn Stna's argument in tenns of a particular time in order to show why the now cannot mark areal severance in time' s continuity, the argument can also be framed in tenns of an absolute beginning and ending of time. In this latter sense, Ibn Stna could use the argument to show the etemity of time and consequently the cosmos. 36See De tempore 24.3-6 [27]. "If someone says that this time was not before, since it was something generated (ka'in) orthat it will not be after, since it is something generated, then he has necessitated that before time there is a time and that after the end of time there will be a time; [for] ifbefore, after, was and was not were not to require ｾＡｬｊ｟ｩｨｾＭ IBN SINÄ ON THE Now 87 is only an interval, as for instance between 12:29:59 and 12:30:00; for that interval is either a time and thus argument (a) applies, or it is not a time, but it would still be before the time and thus argument (b) app1ies. The second horn assurnes that the now is at an end point oftime. Now at this end point, there is either (a) the possibility of something existing or (b) there is not. If there is the possibility of something existing after this end point, then mutatis mutandis the arguments ofthe fIrst horn apply. On the other hand, to maintain that it is not possible for anything to exist involves an implicit contradiction; for one must deny the possibility ofboth what is necessary (wajib al-wujud) and absolute possibility.37 Clearly, it is impossible that what is necessary not exist. For even ifwajib al-wujud is taken in the weak sense of "what is necessary through another" as I suggested in footnote 9, insofar as the wajib al-wujud is necessary it must be. Hence to say that which is necessary might not be is tantamount to saying that which must be might not be, which clearly is false. Furthennore, when Ibn Sina speaks of absolute possibility, he is referring to whether something may or may not exist; hence if something has existed, then there must be an absolute possibility for its existence, otherwise it could not have been. 38 Thus one cannot deny the existence of absolute possibility without simultaneously implying that at some point all would hour, day and month require a time." See G. VIastos' "Disorderly Motion in Plato's Timaeus" [in Studies in Greek Philosophy, vol. 11: Socrates, Plato and Their Tradition, ed. D. Graham (Princeton: Princeton IJniversity Press, 1995), 247-64 (especially 253-55)] for a discussion of why the claim "before the beginning of time" would not imply an inconsistency for Aristotle. 37For a detailed discussion of the necessary and the possible in Ibn Stna see A.M. Goichon, La Distinction de I 'Essence et de I 'Existence d 'apres Ibn Sfna (Paris: ･ｾＨｽ｣ｳｄ de Brouwer, 1937), 156-180; for a more recent discussion see G. Finianos, Les Grandes Divisions de I 'Etre Hmawjud" selon Ibn Sfnd (Fribourge: Editions Universitaires Fribourge Suisso, 1976), 222-38. 38Ibn Si'na distinguishes two meanings of the term possible: (I) that which is not impossible and (2) that which may or may not exist, which he tenns "absolute possibility" here, but "Real possibility" elsewhere. The first sense of possibility might be thought of as logical possibility and the latter as physical possibility, that is, that which truly could exist. For instance, infonnation travelling at velocities greater than the speed of light is logically possible, but it is physically impossible (barring the existence oftheoretical tachyons). See Avicenna's Treatise on Logic: Part One ofDanesh-Name Alai, trans. F. Zabeeh (The Hague: Matinus Nijhoff, 1971),24; and al-Isharat wat-Tanbfhat, al-Man!iq, 00. S. Dunyä (Cairo: Dar al-Ma'ärif, 1971), IV.3, 272; Remarks andAdmonitions: Part One: Logic, trans. S. Inati (Wetteren: Universa Press, 1984), 95. 88 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLY that has been, could not have been. Both necessary existence and absolute possibility cannot be denied. Therefore something must exist after any now. (161.1-7) Having shown that the now is not an actual division in time, Ibn Sina explains how the now is in time potentially. Time, we are told, is predisposed to one assuming a division in it or positing a division in it. Hence, one can posit a division in time in much the same way an examiner divides the time before a test from the tinle of a test, by saying "begin"; or we can talk about the moment the sun crests or sinks below the horizon, etc. None of these indicate an actual division in time itself, but only a relative division-either relative to us or some extrinsic boundary. The case is similar to that of a continuous plane ABCD. Although the lines AB and CD are parallel to one another and thus separate, we do not think the plane is divided on that account. Nor do we think that ifwe imagine a line, EF, between AB and CD that ABEF and EFCD are separated by an actual division, EF, in the plane, but rather only that there is a conceptual division between them. The same is true with time and its division, the now. (161.7-162.14) In the next three sections Ibn Sina addresses a puzzle posed by Aristotle (Physics IV, 10, 218all-21), whichRichard Sorabji has dubbed the "paradox ofthe ceasing instant."39 The puzzle runs as foliows. Aristotle assumes: (1) successive nows cannot exist simultaneously (that is, the instant right now cannot have existed with any past or future instant(s)); (2) the prior now must have ceased to exist; fmally (3) nows, like points, cannot exist immediately adjacent to one another (that is, between any two points/nows there are an infmite number of other points/nows). Assunle the now is perpetually different (äAAO Kat äAAO); but ifthe now is perpetually different, then the prior now must have ceased to exist (2). The prior now, however, could not have ceased to exist while it existed (for it was existing). On the other hand, it could not have ceased to exist in the immediately adjacent now, for there are no immediately adjacent nows (3). Further, if it were to cease in any now other than itself, it would be simultaneous with the infmite number of nows between any two nows (3), but it is impossible that the now exists simultaneously with 39R. Sorabji, Time, Creation and the Continuum: Theories in Antiquity and the Early Middle Ages (lthaca: Comell University Press, 1983), 7-12; also see Sorabji, "Aristotle on the Instant ofChange" in Artieles on Aristotle: 3. Metaphysies, ed. 1. Barnes, M. Schofield and R. Sorabji (London: Duckworth, 1979), 159-77. IBN SINA ON THE Now 89 any other now, let alone an infinite nunlber ofnows (1). Therefore, the apparently paradoxical conclusion emerges that the past now and the present now are different, but could not have changed. (161.7-12) Ibn Sina begins with a pathology. The paradox only works if one assumes that the now is corrupted or ceases to be in a now or more exactly in time's limit. This assumption is unnecessary. The now simply is the division between time's existence and nonexistence and hence the now has its existence in time's limit and thus cannot be ceasing at that limit; rather its nonexistence is in the totality of time. One might protest that this explanation provides no account ofwhen the now is corrupted, but Ibn Sina points out that "corruption" means nothing more than something no longer is after it was. Hence it is not required that there always be a first instant of corruption. In fact, a number of states, such as motion and coming to rest or generation and corruption, do not have a first instant in which the process occurs. Ibn Sina clearly has Aristotle's argument at Physics VI, 5, 236a727 in mind. Since this argument also provides the background for a later section (162.14-163.ll) we should consider it briefly. Aristotle contends that there can be neither a first instant nor a first period of time in which a process ofchange begins. Weshall just consider the claim that in a process of change there is no first instant. Imagine aperiod oftime ABC in which a mobile, x, is in astate, SI, in the entirety ofAB and then changes to S2 in Be (where SI and S2 are contradictory states, for example, moving and being at rest). BC cannot be an indivisible instant otherwise x wou1d simultaneously be both SI and S2; since it was SI in all of AB, which inc1udes B, whi1e at C x had changed to S2' but BC was assumed to be an indivisible instant and thus C and Bare actually identical. Nor can there be an instant B'C such that x was SI in all of AB, but at B'C x was S2. For B'C is either immediate1y adjacent to B and thus two instants are immediately adjacent, which is false; or there is an interval between B and B'C in which x is neither SI nor S2' which is impossible since SI and S2 were assumed to be contradictories such that one had to obtain. Therefore there can be no first instant of change. Fakhr ad-din ar-Razi in his ｡ｬＭｍ｢ｾｩｴｨ al-mashriqiyya points to an apparent inconsistency in Ibn Sina's position. 40 At Physics 11.3 of the 4°F. Räzi, ｨｴｩｾ ｢｡ｍＭｬ 1924/25), 674. al-mashriqfyya, voI. 1 (Hydarabad: Majlis dä'irat aI-macärif, 90 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLY Shifa ' Ibn Sina had argued that the processes of generation and eorruption must oeeur 'all at onee' (du/a); for substantial forms do not allow of degrees of intensity.41 Substantial forms might be eompared to whole numbers; for example, there are no varying shades oftwo which eventually fade into three. Sinee there are not degrees of intensity in substantial forms, substantial eoming to be or passing away eannot be a gradual proeess; for there is no intermediary between the being and non-being of a substanee. On the other hand, Ibn Sina has just claimed that certain processes, such as generation and eorruption, do not oeeur in an instant or now. The ineonsisteney comes in the immediately following section (161.12-162.9) where Ibn Sinädefmes dufa as change in an instant ornow. In short, Ibn Sinä argues that generation and corruption must occur "all at onee," and then claims that they cannot occur in an instant. Shayegan has tried to exeulpate Ibn Sina on the ground "that Avieenna's intention in this passage is not substantial generation, [rather] he is merely coneemed with logieal notions of eeasing and beginning."42 The rejoinder fails. What this solution implicitly sanctions is that logical impossibilities n1ight be physically possible; for it is a physical fact that substantial forms do not allow of degrees of intensity, but a logieal impossibility that two opposing tennini eould exist simu1taneous1y in the same thing, in the same way. Indeed what is logieally possible may be physieally impossible, but the eonverse is not true. Thus another solution must be sought. Ibn Sina is not guilty of ineonsisteney, I maintain, but only of earelessness. We should understand "all at onee" (dufa) at 11.3 as only meaning "not gradually," whereas at 161.13 "all at onee" expresses the more teehnieal sense of "that which oceurs in an instant or now." The exaet distinetion between these two will be made elear in the following seetion. For our purpose it is suffieient to note that there are two possible meanings for "all at once." Therefore, Razi's critique rests on an equivocation between a technical and non-technical use of du/a. (161.12-162.9) Ibn Sina now responds to an objeetion in what quite possibly is his most original eontribution to the diseussion ofthe now. The objeetion is that the now must either be eorrupted gradually or "all at 41 Shifa' II.3, 98.10-18. 42Shayegan, HAvicenna on Time, 158. IBN SINA ON THE Now 91 once," that is, in a now. 43 Hence, ifthe now is corrupted gradually, then it will exist simultaneously with other nows, which is impossible. Or if it is corrupted in a now, then it will be corrupted in either the immediately adjacent now, which is impossible since there are no immediately adjacent nows, or in itself, which is likewise impossible, since it is then existing. This objection only follows if the disjunction between corrupted gradually and "all at once" is areal disjunction. Now, areal disjunction is one in which the two disjuncts are exhaustive, such as "every number is either odd or even."44 Thus, the real disjunct of"is corrupted gradually" is "is not corrupted gradually." In contrast to real disjunctions, there are also unreal disjunctions, whose disjuncts can either both be false or both be true. 45 Thus both disjuncts are false in the proposition "either this is inanimate or an animaI" when it is predicated of a tree; while in the proposition "either this is not inanimate or not an animai" both disjuncts are true ofa tree. We are only concemed with the unreal disjunct in which both disjuncts might be false. This state can occur when one of the disjuncts is narrower than the opposite ofthe other; for instanee, "animai" is narrower than the opposite of inanimate, namely, animate, since more things than animals are animate, namely, plants and angels or intelligences. Now (1) "to be corrupted in a now or 'all at onee, '" maintains Ibn Sina, is more particular or narrower than "not to be corrupted gradually"; for those things which either (2a) have their existence in time, but not in time's limit 43Shayegan is undoubtedly correct to relate the following sections to the fourteenth century Latin discussions ofthe primo et ultimo instanti and incipit et desinit. Still we must be careful to what extent we can honestly attribute the discoveries of fourteenth century natural philosophers to Ibn Stna and to what extent we are merely reading back their advancements. See 1. Murdoch "Infinity and Continuity" in The Cambridge History 0/ Later Medieval Philosophy, ed. N. Kretzmann, A. Kenny and 1. Pinborg (Cambridge: Cambridge University Press, 1982), 564-591 (especially 585-87) for a survey of fourteenth century developments. 44Shija', al-Qiyas, ed. Zayed (Cairo: The General Egyptian Book Organization, 1964), 242.9-243.2; The Propositional Logic 0/Avicenna, trans. N. Shehaby (Boston: D. Reidel PublishingCo., 1973),44. Alsoseeal-Isharatwat-Tanbfhat, al-Man!iq, III.8,250;Remarks and Admonitions: Part One: Logic, 87. It should also be noted that zero would not have been considered a number, since numbers were viewed as collections of units; hence the proposition "all numbers are odd or even" is exhaustive. 45Shija', al-Qiyas, 243.2-244.17; The Propositional Logic 0/Avicenna, 44-46. And also al-Isharat wat-Tanbfhat, al-Man.tiq, III.8, 251-255; Inati, Remarks and Admonitions, 87-88. 92 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLY or (2b) exist in time's limit, but not in tinle, also are not corrupted gradually, yet they do not cease to be in a now. That (1) and (2) are distinct Ibn Sinä makes clear by observing that our judgments conceming thenl are different. When we say that (1) the now is corrupted "all at once," that is, in an instant, we are committed to judgments about the now being similar to those made about tinle. For instance, just as two times can adjoin, so two nows could adjoin; or also, just as any part oftime is in time, so the now is in time. On the other hand, when we say (2) the now is not in time, but is time's limit, our judgments conceming the now are different from our judgments conceming time. Thus, two nows cannot adjoin, or a now is not in time the way a particular tinle iso One way to clarify this distinction is to envision two linear coordinate systems, where viewpoint (1) is captured by treating the nows as closed intervals on a line and viewpoint (2) by treating the nows as open intervals (see figure 1).46 It is not important that we either prove that a • 2--0-------:::> a : b • • figure 1. b the now fits one or the other of these models or completely clarify what is intended by either model. It suffices that we grasp that the two nlodels are different and that either one could describe the now. Given the distinction between 1 and 2, Ibn Sinä reasons as foliows. One cannot argue that the now must either cease to be gradually or "all at once," since the real opposite of"to cease to be gradually" is "not to cease to be gradually." However, "not to cease to be gradually" can be broken down into (1) ceasing to be "all at once," that is, in a now or, (2) not existing in time, but existing in time's limit. Hence, one cannot argue by a disjunctive syllogism that since the now does not cease to be gradually it must cease to be in a now. (162.10-14) Ibn Sinä employs the same argument to show that the opposite ofwhat does exist or does not exist "all at once" must exist or not exist gradually. One can, hqwever, sufficiently stipulate "existing 'all at once '" such that its opposite is "to exist gradually." Thus something would 46 J. Dubois wants to draw a similar picture for Aristotle when he distinguishes between the now qua "limite" and "terme"; Le Temps et l'Instant selon Aristote (Paris: Desclee de Brouwer, 1967), 192-93. IBN SiNA ON THE Now 93 only be said to exist "all at once," if (a) that thing were fully actual Ｈｾ｡ｩｬＩ as opposed to a limit or a merely potential division; and (b) there are no other nows at which this thing is coming to be, that is, its coming to be does not involve a process. Given these stipulations, then the opposite of to come to be "all at once" is to come to be gradually; however, there is nothing inherent in the notion of coming to be "all at once," such that we must take coming to be gradually as its opposite. (162.14-163.11) The following section corresponds to Aristotle's Physics VI, 5 (235b6-236b 18), which might explain Ibn Sinä's apology for discussing the topic out of place, despite the fact that it is germane to the present subject. 47 The following question may be posed as folIows: if something has changed from one state to another in a time ABC, such that in the first part ofthe time the thing was in the first state, but in the second part it was in the second state, then in which state is the thing at the now, B, which potentially divides the two times? It must be in one of the two states since ifthe states are mutually exclusive (such as being or not being, or being in motion or at rest) then it is impossible that the thing not be in one ofthe states. For everything must be or not be, and everything capable of motion must either be moving or at rest. 48 Therefore, that which undergoes change must be in one ofthe two states at B, but which one? In a change something arrives, namely, a new state, and causes the old state no longer to exist. 49 There are two general types of states: (1) those which can be in a now and (2) those which cannot. Further, among those states which cannot be in a now, there are (2a) those states which cannot initially be in a now, but later can and (2b) those which can never be in a now. Those states which can be in a now, (1), must meet two criteria. First, during the time ofthe state's existence the exact same state must be found at any now taken during that time. For instance, during the time AF if something possesses astate which can be found in a now, for example, being a square, then at any instant during AF, say B, C, D, or E, the state ofbeing a square obtains. Second, the state must not require some interval of time, or a now which has a duration, in order to be. This second 47See the discussion at section 161.7-12 for the Aristotelian background. 48See Physics VI, 5, 235bI3-16. 49Where Ibn Stna has framed his thesis in tenns of something "arriving" (yaridu), Aristotle cast his claim in tenns of"retiring from" or "leaving" Ｈ･ｾ iotatat or Ct1toAei1tet v; Physics VI, 5, 235b8). 94 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLY criterion excludes both nows considered as atoms of time possessing a certain duration, and states such as motion which require a certain interval in order to be. With regard to the states, which we nlight call states with a fixed disposition, that which has changed must at the now at which it first changed be in that state to which it has changed. While Ibn Sina does not offer an explicit proof for this thesis, we can fmd at least one in Aristotle's Physics, which fits premises provided by Ibn Sina. First, it is necessary that some new state come (yaridu) to the thing existing in a particular state and make the first state cease to be (162.19); but "coming" if not identical with change at least follows upon change (235b9-11). Every change, however, changes from something, A, to something, C, (235b6-7). Now if the thing were not C at the now at which the thing has changed to C, then "the thing which has changed, when it has changed, is changing to that which has changed; but this is impossible" (235b22-26). Whether this argument or another is the one Ibn Sina had in mind is irrelevant; what is clear is that Ibn Sina thought that at the now dividing two states, the thing which undergoes change will be in the second state, when the state is one of a fixed disposition. Now among those states which cannot be in a now, there are (2a) those states which cannot initially be in a now, but later can. Loss of contiguity is such astate. There is the initial now when two things (A and B) lose contiguity, but at any now after the initial now of separation, A and B will not be touching, even if, for example, Ais moving away from B. For when A is moving away from B, the relation between A and B will be constantly changing, but that A and B are not touching will not change. On the other hand, other states are such that (2b) at any now one should take, the state ofthe thing undergoing change will be different. For instance, consider the .motion along a distance AF. At any now in the motion across AF, e.g. the mobile at B, C, D or E, the relation of the mobile to A or F will be different. At B the mobile will be closer to A than that to F; whereas at C the mobile will have drawn closer to F, but retreated from A and so on. What both 2a and 2b have in common is that they involve an opposition. That is to say, the state itself is from something to something different, whether it be from touching to not touching or from some point A to anotherpoint B. We may referto 2a and 2b as states with, at least initially, an unfixed disposition. When astate with an unfixed disposition comes to that which is undergoing change, then, according to Ibn Sina, that which is undergoing change remains in the state with the fixed disposition at the initial moment IBN SiNA. ON THE Now 95 of change. We may reconstruct the argument as foliows. In states with an unfixed disposition, there is an inherent opposition, since the state itself involves a terminus a quo and a terminus ad quem, and these two are different. Thus it is impossible for that which is undergoing change to be in both termini simultaneously; and thus that which is undergoing change cannot be in astate with an unfixed disposition at the initial now, or at any now. However, at the initial now that which is undergoing change is at the terminus a quo, but the terminus a quo just was the state with a fixed disposition. "Hence the thing is immobile when it is set in motion and contiguous when it is made no longer to touch" (163.9-10). Ibn Si'nä's position seems contradictory or at least unclear. For at 163.4 he had said those states with an unfixed disposition have their existence in time and not in a now "and hence their existence is in the second time (az-zaman ath-thanf) alone." This claim seems to affinn the Aristotelian doctrine that with respect to that which changes the now always belongs to the latertime (vor:epov).50 However, at 163.9-10 Ibn Si'nä claims that "the thing is immobile when it is set in motion and contiguous when it is made no longer to touch." This position suggests that at the initial moment of change the changing things remains in the state belonging to the first time. As a possible solution to this apparent inconsistency I suggest that Ibn Sinä is retaining Aristotelian tenninology, while generalizing Aristotle's point. Conceming Aristotle's argument Sorabji rightly observes "it is crucial to understanding the passage to notice that the earlier state, ofwhich there is no last instant, is one which involves changing while the later state does not. "51 Ibn Smä's point is that whenever there is a change from one state to another and one of the states involves change, the state at the moment of change will always follow that state which does not involve change, that is, the state with the fixed disposition. Thus Aristotle' s position requires that during the first time the state involves change, while during the second time the state does not involve change, whereas Ibn Sinä's fOTIllUlation includes both Aristotle's case and the case where during the first time the state does not involve change, but the state during the second time does. 50 Physics VIII, 8, 263b 10-11. on the Instant ofChange," 172. It should be noted the passage Sorabji is discussing is Physics VIII, 8, 263 b 15-264a6, although he notes that this argument had been generalized at VI, 5, 235b-32. 5 I"Aristotle 96 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLY Shayegan has offered an alternative interpretation of tbis passage based on her translation of 163.3-5. 52 She translates our passage: Or else the thing is different from tbis qualification and it exists in time not in the 'now'; it will then come to exist in the second ofthe two times only. The 'now' which divides the two is not necessarily predicated of it; and there will be in it [the 'now'] the opposite characteristic such as distinction and lack ofcontact and movement (67). Shayegan sees in this passage the introduction of a nunc differens. 53 Tlle nunc differens is different from the now which potentially divides time; for the nunc differens is a "temporal 'now' [which] exists in a stretch oftime," or more specifically the "second time" and its states are constantly changing. The nunc differens must be extended, or temporal, since "the opposite characteristic such as distinction and lack of contact and movement" can be found in it. This interpretation has problems. The first difficulty, which I shall merely mention, is the philosophical morass inherent in the notion of an extended now. In fact, Aristotle gives several explicit arguments against an extended now at Physics IV, 10 and VI, 3. 54 Certainly Ibn Sina is no lackey to Aristotle and thus a mere appeal to authority would bear no weight; nevertheless, when Ibn Sina does significantly diverge from Aristotle he is quick to point out the errors of his predecessor. Since to introduce an extended now would be a radical shift, we should rightly expect some defense ofit by Ibn Sinä. None is forthcoming. There is also a contextual difficulty with this reading. As both Norman Kretzmann and Shayegan herself observe there is a close association between the nunc 52Shayegan, 192-93. 53There are passages in Aristotle which might lead one to posit a nunc diffirens; for example, Aristotle says the now in one sense is just the same, but in another it is not the same in much the same way that Coriscus in the Market and Coriscus in the Lyceum are one and the same and yet different (Physics IV, 11, 219b 12-21). Shayegan does not solely view the nunc differens in this sense, as will be made clear in the body. For a discussion and critique of the nunc diffirens see N. Kretzmann, "Time Exists-but Hardly, or Obscurely (Physics IV, 10, 217b29-218a33)," TheAristotelian Society Supplementary vol. 50 (1976): 91-114 (especially, 100-107). 54218811-30; 234all-24. IBN SiNA ON THE Now 97 dijJerens and the nuncjluens (an sayalan), or flowing now. ss Hence the context ofthis passage would have had to shift from the now which is the potential division between past and future to the un-introduced nuncjluens. In almost the next line, however, Ibn 8inä explicitly states "that which we discussed is the now sUITounded bythe past and future" (163.11-12). Only then will he begin to discuss a different description ofthe now, namely, the nunc jluens, or flowing now. The conception of a nunc differens, or extended now, does not emerge clearly from the text and would require much philosophical elucidation if it did. Thus we can rightly reject its introduction as a means of explaining the text. (163.11-164.4) To this point Ibn 8ma has only considered the now as a potential division in time. The analogue is with a point in a line which does not make up or compose the line. The relation ofthe point to the line, however, can be considered differently; for we can also think of the point which describes a line through its flow or motion. Likewise, suggests Ibn Sinä, perhaps the now can be considered as a temporal analogue to the moving point-a flowing now. Before we continue we should briefly consider the origin of the "flowing now" thesis. It seems unlikely that Aristotle held the view. s6 A complete discussion of Aristotle's position is beyond the scope of this paper, but a few brief comments are warranted. First, nowhere in Aristotle' s discussion ofthe now does he use the word puate;, that is, flow, or any other tenn which might suggest a moving now. S7 Only the mobile is characterized as moving. Further, it would seem impossible on philosophical grounds that the now move or change; for the now is indivisible (Physics VI, 3), yet everything that changes must be divisible (VI, 4). Aristotle gives an explicit version ofthis argument at De anima I, 55Kretzmann, "Time Exists," 106-07; Shayegan 192-93. 56See W. Wieland, Die aristotelische Physik (Göttingen: Vandenhoeck & Ruprecht, 1962), 324-27 and Kretzmann, "Time Exists," for interpretations which deny the doctrine ofthe flowing now to Aristotle; and F. Miller, "Aristotle on the Reality ofTime," Archivfür Geschichte der Philosophie 56 (1974): 132-155, for an interpretation which attributes the view to Aristotle. 57The phrase &AAO KUt &AAO which is said of the now throughout IV, 10 and 11, simply means "other and other"; and although one could understand it to mean "perpetual change," one could as easily understand it as "to be distinct." In the latter sense the phrase need not imply motion. 98 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLY 4, 409al-2 against any unit-point or now-being moved. 58 Although I do not believe Aristotle is the author ofthe theory of a "flowing now," it does seem to have been ascribed to him early on. Alexander in his De tempore says that "the now when itflows (stil) makes time."59 Similar views are also found in both Simplicius and Philoponus. 6o Since Ibn Sinä's order of presentation and argumentation on several occasions resemble those found in both Alexander and Philoponus, it is highly likely that one or both of these philosophers influenced his understanding ofthe now and particularly his postulation of a flowing now. Ibn Sinä himself countenances the comparison between a moving point producing a line and a flowing now producing time by indicating the relation between being borne along, time and spatial magnitude; for a time is proportional to the motion on account of the continuous motion along a spatial magnItude. In other words, spatial magnitude, motion and time are three linear extensions, all ofwhich can be plotted against one another such that for any "point" on one continuum a corresponding "point" can be found on the others. 61 The "one_to_one" correspondence occurs between the three since that which is borne along and its various dispositions, namely, to have a "where" and a "when," that is, a now, seem to produce their respective continua through their motion. That is to say, the flow of the mobile produces motion, the flow of the "where" produces (or better yet describes) a spatial magnitude and the flow ofthe now produces time. 62 58The passage immediately following 409a1-2 is often given as an alternative definition for the line. "Further, since they say a moving line makes a surface while a [nl0ving] point [makes] a line, the movenlents of the units will also be lines" (409a4). We nlust bear in mind the context of this passage. Aristotle is refuting the theory that the soul is a self-moving number. Hence when he says "they say" (<J>aol.) he means the proponents of this theory and he is pointing out that their definition of the soul and of a line are mutually incoherent. He is not necessarily sanctioning this definition. 59De tempore 21. 13 [13]. 6°Simplicius In Aristotelis Physicorum Commentaria, ed. H. Diels (Berlin: George Reimer, 1882), 722, 28-34; Philoponus In phys., 272, 20. 61Aristotle first mentions the procedure at IV, 11, 219a1 0-19 and 219b 12-220a21; he more fully develops it at VI, 1,231 b 18-232a22; also see G.E.L. Owen, "Aristotle on Time" in Articles on Aristotle: 3. Metaphysics, 140-158 (especially the section "priorities and paralleIs between space and time"). 62For discussions and critiques of the analogy between spatial extension, motion and time see G.E.L. Owen, "Aristotle on Time," 154-158; E. Hussey, Aristotle's Physics Books I/I and IV (Oxford: Clarendon Press, 1983), 154-156; and M. Inwood, "Aristotle on the Reality of Time" in Aristotle's Physics: A Collection 0/ Essays, ed. L. Judson (Oxford: IBN SINÄ ON THE Now 99 (164.1-4) Ibn Sinä points to another simi1arity between that which is borne a10ng, the point and the now; they are all end points of their respective continua. 1t is re1ative1y clear how a now and a point can be end points of time and a line or a spatial magnitude, but it is not so clear how that which moves along is an end point of motion or being borne along. Think of the motion as stretching from the mobile's starting point to wherever it has reached. Further, imagine an invisible string extending from the mobile's terminus a quo to the mobile itself. The mobile, then, can be viewed as the end point ofthis invisible string, that is, the end point of motion qua an extension. (164.4-13) The preceding sections were not so much a proof ofthe existence ofthis flowing now, as an enumeration ofthe various similarities between spatial magnitude/motion/time and the point/that which is borne along/the now. Ibn Sinä next poses the question whether there might in fact be a now which through its flow produces time in the way a moving point produces a 1ine. He begins by indicating the various implications for a theory oftime and more specifically a theory ofthe now, ifthere should be such a flowing now. These implications include the following. That which is borne along can be viewed from two perspectives: first, as an object and second as a moving thing. 63 Now insofar as that which is borne a10ng is an object it remains one and the same, for example, the train in Philadelphia and then in New Y ork are one and the same train. On the other hand, insofar as that which is borne along is moving, it can be differently described; for examp1e, the train passing through Princeton Junction is not the same as the train passing through Newark. Simi1arly, if there were a now which produced time through its flowing, then insofar as it is what is flowing, it wou1d remain one and the same, just as the object which happens to be moving remains one and the same. On the other hand, insofar as it is jlowingit can bedifferent1ycharacterized, forexample, 12:00:00, 12:00:01, 12:00:02 etc., and as such the now would be like that which is borne along qua moving. A second implication is this. That which is borne along qua moving cannot exist twice with the same description or characterization, otherwise it would not be moving. For instance, imagine something, x, which is Clarendon Press, 1991), 151-178 (especially 165-168). 63See Physics IV, 11 219b12-33. 100 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLY borne along a distanee AF. Now during the motion aeross AF, x ean be eharaeterized as x-A, x-B, x-C, ete. to x-Fe (Where "x-A" means "x potentially at loeation A" and similarly for the rest.) Thus if x were eharaeterized twiee as x-A, we would say x was at rest at A and not moving. Nevertheless, x eonsidered merely as x, ean and does perdure or exist several times; for the x at A, B, C ete. is the same x. Onee again, the now from the viewpoint of what is flowing would perdure. Only the now as variously eharaeterized would not exist twiee; thus, for instanee, there eould not be two instanees of 12:00:00 p.m. 25 Deeember 1997. This implieation raises the question: "what is this temporal entity, the now, whieh supposedly perdures and produees tinle by its flow?" A partial answer to the question just raised is that the flowing now whieh produees time would be other than the now posited eonneetmg before and after; for just as the moving point whieh produees a line is other than any of the points within that line, so the flowing now would be different than the now whieh eonneets before and after. The differenee between the two nows is that the now qua potential division is joined with before, after and eoineiding, that is, being simultaneous, while the now qua flowing would be joined with motion and thus that whieh is borne along; for there is no motion separate from that whieh is borne along. 64 Consequently, the flowing now would be neither before, after or eoineiding, but the eause of being before, after or eoineiding. (164.13-165.9) Ibn Sina next turns to two questions whieh the foregoing has raised: first, what is the flowing now's manner ofexistenee? And seeond, how does it produee the before and after? The flowing now, we said, is joined with that whieh is borne along. Now that whieh is borne along possesses a "where" that is, a spatial loeation, at any point in its traversal. With the motion of the mobile, this ''where'' deseribes a spatial interval in whieh we ean mark off eertain boundaries, whieh are spatial befores and afters. An analogous phenomenon oeeurs at the temporal level. That whieh is borne along possesses a "when" at any point in its traversal; for just as a mobile must be spatially loeated, so likewise must the mobile be temporally loeated. The flowing now is not eoneeived as some aetual 64See Physics III, I, 200b32-2041 a3; III, 3, 202aI3-16. IBN SINA ON THE Now 101 entity or object in its own right; nonetheless, it is areal state belonging to that which is borne along. 6s Where I have argued that for Ibn Sinä the now, though not an actual object or entity in its own right, nevertheless is something real inherent in that which is borne along, Shayegan believes that the flowing now and the flowing point "are pure conjectures and are references to geometrical objects, not to actual thingS."66 There is obvious merit in this suggestion; for understanding the flowing now as a mere mathematical abstraction would avoid the difficulties in explaining the philosophically embarrassing nature of a now, which seems to be a physical or at least actual object. 67 Unfortunately, treating the flowing now as a mere mathematical abstraction has problems ofits own. Fakhr ad-Din Räzl observes that motion (ormore specifically the motion of the flowing now), according to Ibn Sinä, is the producer (muhilf)68 and cause oftime; however, ifthe flowing now is not something existing (maCdum), then how can it be the producer and cause of something that does exist, namely, time. One ofcourse could say that time 651nwood argues that treating the now as "instantaneous states of the moving object" offends against Aristotle, since (I) it carves up objects along temporallines and it does not "account for those features of our experience-such as our ability to perceive movement and the smoothly continuous rather than jerky character ofour temporal experience" ("Aristotle on the Reality ofTime," 167). The objection only works ifwe construe instantaneous states of the moving object as temporal analogues to frames in a motion picture. Thus as the ｦｲ｡ｭ･ｾ of the movie make up the movie, so these instantaneous states of the moving object would make up time. This understanding of instantaneous states of the moving object is clearly not what Ibn Stna has in mind nor is he implicitly committed to it. Rather, to use Kretzmann' s picturesque example ("Time Exists" 97-8), instantaneous states ofthe moving object should be imagined as analogous to potential cuts (as opposed to slices) in a salami sausage. Such an understanding neither actually carves up objects along temporallines nor gives our temporal experience a ')erky character." 66Shayegan, 205. 67See F. Miller, "Aristotle on the Reality of Time," 145-46 for various attempts to characterize the nature of a flowing now. Miller suggests that perhaps the flowing now "could be characterized as the sort of material point that would occupy not a geometrical point but a three dimensional place" (145). 68The Arabic Ｂｍｾｌ which I am translating "producer" most naturally would be rearl as ｭ｡ｾｬ［ however, ｭ｡ｾｬ means "a location or site," which make no sense in the context. Therefore, I have opted to rearl Ｂｌｾｍ as Ｌｬｩｾｵｭ the active participle of the verb Ｇ｡ｾｬＬ which can mean "to cause to set in or occur, bring about, produce" which the context, in fact, requires. 102 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLY has no existence independent of the mind and thus also is a mathematical abstraction, but Razi is quick to add that Ibn 8inä is not among these. 69 8hayegan, following Räzi, makes some remarks about Ibn Sina's "doctrine of coincidental super addition of existence to essence," but it is not clear how these remarks are intended to absolve Ibn Sina from Razi' s charge. 70 On the other hand, to construe the flowing now as the mobile's temporallocation and as areal state inhering in the mobile deflects Räzi' s critique and also avoids committing Ibn Sina to the existence of a now which is an actual object. 71 Ibn Sina then turns to the second question: "how does the flowing now produce the before and after?" As the mobile is borne along, the "now" associated with it, describes an interval and this interval is time. We can mark offboundaries, or befores and afters, in the time corresponding to the various locations ofthat which is borne along insofar as it possesses a now. The way that we mark off these boundaries is akin to the way we number a line; for although a line does not intrinsically possess a number it is inherently numerable. Ifwe consider the line AD which was described by some mobile x crossing a spatial magnitude, we can posit a point B in the line, which corresponds to a location where x was during its traversal. The line can then be conceptually divided into the units AB and BD, and hence the line will be two insofar as there are two conceptually distinct parts. Or again, we can conceptually divide AD at B and C, which also correspond to various locations ofx during its traversal. In this case, there are the three conceptually distinct parts AB, BC and CD; and thus AD is three, and so on. Similarly the flowing now, which is associated with the motion of that which is born along, will produce befores and afters, which correspond to the spatial befores and afters passed through during the motion of x. These derivative befores and afters are potential divisions in the motion and allow ofbeing numbered as the line was numbered. Time, 69ｨｴｩｾ｡｢ ｍＭｬ｡ al-mashriqiyya, vol. 1, 551. 7°Shayegan, 208-9. 71Treating the now as a disposition in a mobile is not a philosophical panacea for a theory which posits a flowing now. One need merely ask whether there are as many nows as there are mobiles possessing this disposition? Further, ifthere are, do all these nows have different velocities corresponding to the velocities of the mobiles? If we claim that the "true" now is the state possessed by the outennost sphere, the now still seems to possess a velocity. Therefore, time would be produced at a certain velocity, but velocity presupposes time. I do not want to suggest that these difficulties are insunnountable, but rather they ｾｬｧ｛･ｳＭＢ ---indicate issues which a theory positing a ｦｬｯｷｩＡｉｾｅＱｵｌ IBN 8INÄ ON THE Now 103 ihowever, is the number ofmotion in respect ofbefore and after. 72 Hence, since the flowing now produces these numerable befores and afters in the motion, it produces time. Before we pass to the next issue, we should linger briefly over the question how we nUlTlber a line. At Physics IV, 11 (220a9-26) Aristotle had rejected two possible explanations. 73 According to the first means, we begin by imagining a line AE in which we conceptually mark off the midway point at C. We can say the line is two, because C is two, that is, the ending ofAC and the beginning ofCE; however, in order for C to make AE two we must take C twice, that is, it must exist twice. We have shown above though that the flowing now-the now which makes time numerable-cannot exist twice. Thus the now does not number time in this way. According to the second way we can number AE on account of its two parts, AC and CE. This suggestion also will not work for the reason given above and further the parts AC and CE properly correspond to time and not to the now. Aristotle's answer, and presumably Ibn Sinä's too, are embodied in the cryptic claim that just as time is a number so are the extremes of the line. 74 As a suggestion for how to understand what Aristotle and Ibn 8inä had in mind, let us divide AE into four segments AB, BC, CD and DE and then stipulate that we will count B, C and D only insofar as they are beginning points and not end points. Then the line AE is four, since we have only marked off four beginning points-A,. B, C and D. (We would not count E since it is not a beginning point.) The arbitrariness of taking the numerable now only as the beginning point of a period oftime is reduced when we remember that there are philosophical reasons for taking the now with the "second time." (165.5-9) Ibn Sinä next attempts to explain the way motion can number time and time can number motion with an example. Imagine a group of people. The existence of these people is explanatory of their number, for example, ten; for if the group did not exist or if there were fewer people in the group, the group would not be ten. The possibility of characterizing the group as ten does not make the group exist, but it does make it something that can be counted. Thus we count the group not qua human, for that is one, but qua characterizable by ten, that is, as individual 72See Shifa' lI.ll, 157.5-6 and Physics IV, 11, 219b 1-2. 73See F. Miller, "Aristotle on the Reality ofTime," 144-45. 74220a14-16; wo8' 6 ｘｰＶｶｯｾ ｡ｰｴＸｊｬ￶ｾ ... ｾｗ t"a eOX<Xt"<X ｾＱｩＢｴ ｾＱｩｬｊ ｘ＼ｐｙ •... 104 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLY units of counting. Analogously, motion is the cause of a number, or to be more exact that which is borne along possessing a now is the cause of a number; for as a mobile traverses a spatial magnitude, spatial befores and afters mark off potential divisions in the motion, which in turn correspond to temporal befores and afters. These temporal befores and afters can be assigned a number, which is time. Thus motion is the cause of a number, which is time. On the other hand, by means ofthe motion we can mark off boundaries of before and after and then by means of these boundaries we can ascribe a number to motion. The number is not the cause of the motion; nevertheless, the number, that is, time, does allow us to number the motion. Hence, time numbers motion. (165.9-18) Having shown how time numbers motion and motion numbers time, Ibn Sina turns to a related question: How does time measure motion and motion measure time? Time can measure motion in two ways. The first is that time makes motion measurable in a certain way. Time does so in much the same way that the tenness of the group made the group countable. Since the tenness belongs to the group, the group can be counted; likewise nlotion possesses a certain magnitude, which we call time, and since magnitudes can be measured, motion can be measured with respect to this magnitude, that is, time. 75 The second way time measures nlotion is that it actua11y indicates the quantity ofthe measure ofmotion. Hence we can indicate the length of a trip, for instance, as two days or a wa1k around the block as ten minutes. Thus according to the second way 75Ibn Sinä offers a proof in an-Najah [(Beirut, Dar al-äfäq al-jadidah, 1985): 152.18153 ..6] that a magnitude, namely, time, must belong to motion. Imagine two mobiles, x and y, which both have the same velocity, but their motions do not begin simultaneously (maCan), although they do end simultaneously. Let x begin first; clearly y will have traveled less distance than x; hence between a mobile's beginning and ending it possesses a certain capacity (imkan) for covering a distance. Now this capacity for covering a certain distance must allow of variation, that is, being greater or lesser; for if this capacity were fixed or unvarying, then any two mobiles which have the same velocity would cover the same distance regardless ofwhether they began moving together or not. For example, assume that the capacity for covering a certain distance does not admit ofvariation, then iftwo people were to travel from New York to Califomia, both going 65 m.p.h., but one leaves three days later than the first, they would still both arrive in Califomia simultaneously-a conclusion that is manifestly false. Thus the capacity of traveling a certain distance when the velocity is fixed must allow of increase (ziyada) and decrease (nuqsan); however, whatever allows of increase and decrease is a magnitude. Therefore, "this capacity possesses a magnitude which accompanies nlotion ｾ､ in which the motion occurs by means of [motion's] parts, which belong to it from the distance" (153.5-6). This magnitude isjust time. IBN SINÄ ON THE Now 105 we designate the extent or quantity of motion. Motion also measures time. It does so by specifying the extent of time according to the interval of motion which exists between a distinct before and after. Thus, for instance, we can measure a day as the interval between the sun's first appearance on the horizon and then its subsequent reappearance at the same place. Now both motion and time measure the other insofar as they indicate a measure. A measure, however, may be indicated in two ways.76 First, as a certain quantity is used to indicate that by which we measure; and second as that by which we measure a certain quantity. For instance, initially the meter was specified by the length of a certain rod, namely, the standard meter rod in Paris; hence a certain length (the length ofthe rod) was used to indicate that by which other lengths are measured (a meter). The meter, or that by which we measure, is then subsequently used to measure other rods and lengths. Similarly for time and motion. Traditionally the motion of the outermost celestial sphere was used to indicate a certain measure, namely, the day. The day in its turn was used to measure not only the motion of the outennost celestial sphere, but also other types of motion. This distinction between the ways ofindicating measures is not merely true oftime and motion, Ibn Sinä adds; it is similarly true ofany magnitude or measure. Hence we can indicate a certain distance by a motion or a certain motion by a distance. How long a drive is it from my horne to the university? 10 miles. How far is my horne from my neighbors? A stone's throw. In the first example, the extent ofthe motion from A to B is given by a spatial magnitude, whereas in the second the extent of a spatial magnitude is given by the magnitude of a motion. In all ofthese cases (whether distance, motion or time) we see that one ofthem is made measurable by one ofthe other two; thus by a relationship between one ofthese continua to a second we can specify the extent ofthe first. Imagine a child asking how long a trip from A to Bis. "How long is the trip?" asks the child. "One hundred miles," replies the father. "Oh... How long is one hundred miles?" the child inquisitively chimes out. "Two hours," the father abruptly responds. "But how long is two hours?" demands our young philospher. "It's as far as from our house to Grandma's ,house" the mother says. "Ahh, O.K." says the child, comprehending. So we see that each ofthese three is itself a measure and made measurable by one ofthe other two. 76See Philoponuslnphys., 741,21-742,14. 106 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLY (165.14-17) In this fmal section Ibn Sina enumerates a list of properties belonging to time and motion and also what distinguishes the two. First, since time and motion are continuous, they can both be said to be long and short as is true of any extent or interval. Further, since both time and motion can be cut up, at least potentially, into countable units, they can be few or many. Thus a week can be divided into few days, but into many minutes; and similarly a meter can be divided into a few decimeters, but into many millimeters. That property which is unique to motion and distinguishes it from time is that it is fast or slow; for fastness and slowness are defmed by time. Hence time could not be fast or slow without tinle being defmed by itself. 77 Thus concludes Ibn Sina's account of the now: how it exists as a potential division within time and in what sense, if any, one can speak of the now in act, that is, the flowing now. 78 University 0/Pennsylvania Philadelphia, Pennsylvania 77Physics IV, 10, 218bI3-18. 78 1 want to pay special thanks to Everett Rowson for his invaluable help and suggestions with the translation of this difficult text and likewise the beneficial comments ofProfessor Marmura. I would also like to mention James Ross and Susan Sauve Meyer, who provided numerous insights and criticisms conceming the philosophical content of an earlier draft ofthe translation, comments, which very much informed my own understanding ofthe text.