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Diverse Writings 5

 Appraising Heidegger's Interpretations of Movement and Time(1)

Michael Eldred

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    Table of contents

    0. Abstract

    1. The late Heidegger on time 

    2. Time and movement in Aristotle's thinking

     3. The aporetic nature of Aristotelean time and its consequences through Cartesian mathematical science and up to Sein und Zeit 

      4. Time in our global capitalist economy

    5. Recovery of the three-dimensional, complexly interwoven social time of who-interplay 

     

    0. Abstract 

    The early Heidegger mines the wealth to be found in Aristotle's thinking on movement and time and, with Husserl's aid, regains a phenomenologically more adequate ontology of time as three-dimensional, ecstatic time. He thus overcomes the inadequacy of Aristotle's conception of time as the counting number abstracted from movement which dovetails ultimately with the Cartesian cast of time as a linear, continuous variable so amenable to the modern sciences. The later Heidegger reiterates the three-dimensionality of time, but this conception remains divorced from the movement of social interplay exemplified by the gainful capitalist power play of value. 

    1. The late Heidegger on time 

    Heidegger's concern with time and being is well-known from his early thinking right up to the late paper and seminar on Time and Being in 1962.(2)  The coupling of movement and time in his thinking, by contrast, is not as familiar, although the early Heidegger has left behind a profusion of lecture scripts in which also the movement of factical life is at the focus of attention. His conception of movement grows above all out of interpretations of Aristotle, his Physics, his Metaphysics, his Ethics. Heidegger's 1962 paper, by contrast, does not concern itself with the phenomenon of movement, but with the giving of being and the giving of time by the Ereignis, by propriation. Time is accordingly the three-dimensional "reaching" (Reichen, SD:14) of the three ecstasies of time, past, present and future. This reaching, which Heidegger also characterizes as a "giving" (Geben, SD:16) is, in turn, given by propriation. Hence, time proper is a giving given by the giving of propriation, that is, the giving of a giving (Geben eines Gebens, SD:16). Likewise, being itself is given by propriation as the giving of presence that in turn enables the presence of what is given, namely, beings, in their epochal castings. 

    Heidegger's effort is directed at thinking being and time non-metaphysically, which for him means thinking both being and time not in relation to beings, but in themselves, or rather, from propriation. This accounts for the lack of movement in the time-space that Heidegger conceives as the clearing opened by the giving of time and being. Time itself is the givenness of presence in the unity of presence and absence, which is the three-dimensional reaching to one another of beenness as the denial (Verweigerung, SD:16) of presence, future as the withholding (Vorenthalt, SD:16) of presence and the third dimension of presence itself. Heidegger therefore characterizes time as this overarching, unified reaching itself as four-dimensional. Can this four-dimensional reaching itself be regarded as a movement, just as perhaps the sending of being can? The giving of time and being by propriation reaches human being. Otherwise, the human would not be a human being. Human being, or Dasein is cast as stretching out into the three ecstasies of time. Hence, Heidegger can characterize the future itself as a "coming-toward-us" (Auf-uns-zukommen, SD:18). Is this future as coming-toward-us itself a movement, or is only that which comes toward us from the temporal dimension of the future in movement as an arriving epochal casting of being? How does this coming-toward-us of the future relate to the temporal stretching of the life-movement of human being itself? Isn't the withheld presence of the future itself only the dimension within which movement takes place, albeit a movement of another kind than the movements of beings pure and simple? Does human being itself move toward the future in receiving the epochal casting of being that comes toward us, withheld by the future? In any case, if there is movement in the time-space given by propriation, it is a strange kind of movement, apart from the movements of the factical life of human beings and also apart from the movements of physical beings as a whole. 

    Let these questions stand for the moment and allow them to "puzzle the will" (Shakespeare). 

    2. Time and movement in Aristotle's thinking 

    If in the modern age, the phenomenon of movement has been reduced to a differential ratio dm/dt, where m is the magnitude lifted off any phenomenon at all, and t is the continuous variable measuring the uniform, that is, linear passage of the time variable conceived as a continuum of instants, for ancient Greek philosophy, all the terms in this conception, i.e. movement, magnitude, continuum, time, were still questionable phenomena with which it grappled. Returning to the scene of this questioning may allow us to come to a more adequate understanding of movement and time, of their paradoxicality that defies an all too self-confident, arrogantly narrow-minded, 'logical' rationality. Aristotle's Physics represents the culmination and consummation of Greek attempts to think through the ontology of the fu/sei o)/nta, i.e. of physical beings, whose being is characterized by their being kinou/mena (Phys. A 2;185a13) or moving, movable. During his time in Marburg, Heidegger devoted much of his lectures to the interpretation of Aristotle's thinking in general, and his thinking on movement and time, in particular. I will draw on the pertinent volumes of the Gesamtausgabe(3) in recounting how Aristotle, as the acme of ancient Greek thinking who drew the threads together, developed concepts of time and movement in his Physics. The first book of the Physics starts with a critical review of Aristotle's predecessors' thinking on the being of movement, ki/nhsij, including that of Parmenides with his mono-archic determination e(/n to\ o)/n, "being is one", which leads to a denial of the possibility of movement altogether. 

    On pronouncing that "it must not remain hidden what movement is" (dei= mh\ lanqa/nein ti/ e)sti ki/nhsij. Phys. G 1;200b13), Aristotle proceeds in the third book to introduce the ontological concepts that will allow him to overcome the shortcomings of his predecessors, namely, above all, the famous triad du/namij, e)ne/rgeia and e)ntele/xeia, a triad as hackneyed as any other from ancient Greece in our snotty unphilosophical times. Although we are entirely familiar with the phenomenon of movement, Aristotle claims that it remains hidden to us. This is the classic situation of philosophical thinking: it starts with what is most familiar, and thus in some sense known, in order then to show that we have always already skipped over the simplest of questions and appeased the understanding with only apparently adequate notions that take the phenomenon in question for granted. 

    Now for a condensed re-run of Aristotle's stepwise unfolding of the required ontological concepts of movement. Ontological concepts grasp the phenomena in view as modes of being which means, for Greek thinking, the ways in which the phenomena themselves come to presence and present themselves. 

    Movement concerns all beings in the world, not just beings in some kind of 'nature'. It is a misinterpretation to regard early Greek thinking as natural philosophy. For the Greek understanding of being, that which is present is, and what is present most of all is the ei)=doj, look or sight that a being presents of itself. The ei)=doj is e(/n, one, that is a well-defined, single look or Gestalt that can also be addressed by the lo/goj through the manifold of simple categories that define (o(ri/zein), or predicate the being in how it stands in presence in its predicament. Movement is the phenomenon of change (metabolh/), and that with respect to four categories or predicaments: a being can change with respect to what it is (to/de ti, ou)si/a) associated with the phenomenon of becoming and decay, how it is (poio/n) associated with mutation, how much it is (poso/n) associated with waxing and waning, and, finally, where it is (pou, kata\ to/pon) associated with the phenomenon of locomotion. 

    The peculiarity of the phenomenon of movement, as Aristotle treats it in the Physics, is that it cannot be pinned down to the present. Anything in movement has a twofold (dixw=j) presence: first of all it shows itself in the look of its ei)=doj, but secondly, it also has a lack (ste/rhsij) that points to something absent which it could also be, i.e. which could also be brought into presence. For instance, a full moon has the lack that it could also be a new moon, or vice versa. In what it is, it is also in a certain way, i.e. potentially or 'absently', what it is not, a mh\ o)/n. Mh\ o)/n is the pivotal concept for Plato's thinking on movement in The Sophist. Or a piece of timber presents itself in its ei)=doj both as timber and also as lacking what it could also be, namely, a table, for instance. What/how/how much/where something could be through the appropriate movement is its du/namij, i.e. its potential, potency or power to be something else, which is more than a merely formal or so-called 'logical' possibility. The thing itself has an inherent tendency to become other than it is; it is not yet finished and so in a certain sense, it is what it is not. Aristotle conceives the lack in the twofold presence of a being in movement through the pair of concepts, du/namij and e)ntele/xeia. A being with a potential, a duna/mei o)/n, has the power to become something else, but as it is in its presence, it is still a)telh/j, unfinished. It could only have itself in its finished presence in achieving e)ntele/xeia, i.e. through its having-itself-in-its-end. 

    Thus does Aristotle come to his first definition of the being of movement. It is the presence of the potential being as such, stretching itself toward its finished presence, and thus a peculiar twofold presence of both presence and absence in which the potential being is on its way to becoming other than it is, attaining a finished state in which the movement will come into its end. In achieving its presence as a potential being, but not yet as finished, the du/namij is already fully present, i.e. in its e)ntele/xeia, insofar as it is duna/mei o)/n, but it has not yet attained finished presence as something else in its realized potential. In movement, the potential being is still exercising its power of change. Hence Aristotle writes, "The finished presence of the potential being insofar as it is such is movement." (h( tou= duna/mei o)/n e)ntele/xeia, $(= toiou=ton, ki/nhsij e)stin. Phys. G 1;201a10f). In movement, the being's power to be what it can be is at work, i.e. it is e)ne/rgeia or energy. Therefore, Aristotle can say that movement is the e)ne/rgeia of a du/namij in its e)ntele/xeia. Movement itself is a phenomenon that cannot be defined by a single category; it has, at least, a twofold presence and therefore must be addressed by a double concept, i.e. by a pair of ontological concepts, du/namij and e)ntele/xeia as lack (ste/rhsij), whose unified twofold presence is a third phenomenon, namely, the at-work-ness of the potential under way or in transition to finished presence, which is movement itself. Because the tacit underlying Greek understanding of being is standing presence, to conceptualize movement, it is forced to resort to a double or even ambivalent conceptualization. 

    {Now, if the being does not have the source of its movement within itself, which would make it an ensouled (e)/myuxon), animated being, or a physical being in the highest Aristotelean sense, it suffers itself to be moved by something else. A being with the potential to be moved has a du/namij paqhtikh/, a pathetic potential, whereas a being that is potentially a mover has a du/namij poihtikh/, or a productive potential. A piece of timber has the passive potential, or power, to suffer itself to be transmuted into a table, and the know-how of carpentry has the active power to move or transmute the timber into a table. Despite this twofold, passive-and-active, aspect of movement, the movement at work, its e)ne/rgeia, is still just one movement, and not two. 

    Moreover, movement is a continuous (sunexe/j, Phys. G 1;200b19) phenomenon which means that it is connected (e)xo/menon) and also that it holds itself together within itself (sune/xein). The continuum is that which can be divided limitlessly (a)/peiron diaireto/n, 200b21), i.e. for which there is no discrete limit where the division has to stop. The indefinite, double or twofold determination of movement as both du/namij and e)ntele/xeia at once would seem to have to do with its continuous, limitlessly divisible nature. The presence of the du/namij cannot be separated from the likewise present absence or lack of the e)ntele/xeia as the perfect, finished present toward which the du/namij in its e)ne/rgeia is stretched. Instead of a well-defined, unambiguous presence of one (e(/n) that could be captured by a single concept, we have an ambiguous, inseparable or infinitesimally close presence in its being-at-work of both a power and the not-yet-finished end-presence. Even more than that, with the advent of e)ne/rgeia, there is a triad of elements whose unity constitutes the full ontological structure of movement of all four Aristotelean kinds. 

    With this triad, Aristotle has all the elements in his hand to think through also the ontology of the phenomenon of time, albeit he goes a completely different path in his chapters on time in Phys. D Chaps. 10-14. Traditional commentators on Aristotle have not made the connection, or rather misconnection, between the ontological concepts Aristotle develops in order to grasp the phenomenon of movement and his investigation of time. Not even Heidegger, in his thorough-going interpretations of the Physics on movement and time in Gesamtausgabe Band 18 and Band 24(4) makes the link between the triad of concepts fashioned to capture movement and the triad of temporal dimensions into which time stretches. In Book Delta, Aristotle notes that "it is obvious that time is not without movement and metabolism/change" (fanero\n o(/ti ou)k e)/stin a)/neu kinh/sewj kai\ metablolh=j xro/noj. D 11 219a1). Time and movement go hand in hand, a phenomenological finding that even modern physics does not want to deny when considering, for instance, the supposed non-reversibility of time in connection with entropic movement and the Second Law of Thermodynamics.} The gateway to the ontology of time for Aristotle and those coming after him is {thus} through the phenomenon of movement: Something present has the potential, the power to be something else, which it can become through the appropriate movement which itself comes to presence when the potential achieves its finished presence as a potential, namely, in being at work as movement itself toward its end. What was (in the past) a potential power at rest is now (in the present) a power at work toward a (future) realization of the potential in a perfect presence. The three ontological elements of movement thus map onto the three dimensions or 'ecstasies' of time itself which, two-and-a-half millennia later, and foreshadowed by Husserl's phenomenology of time, will be explicated as the temporality of Dasein in Sein und Zeit, whereas the Aristotelean conception of quantifiable time, now designated by Heidegger as the "vulgar conception of time" (vulgäres Zeitverständnis, SZ:428 §82a), will be shown to be derivative of a more primordial conception of the phenomenon of time (cf. Sein und Zeit Division 2, Chap. 6). 

    When a power is at work, all three elements of movement are present, albeit that two of them, namely, the power as potential and the power realized in a finished presence, are present as absence, i.e. as no longer and not yet. This ontology of time is therefore thought on the basis of the paradigm of production, a particular kind of movement. A piece of timber, for instance, has the potential to be a table. This potential becomes present as such when the timber is being worked upon by the carpenter on its way to attaining a perfected presence in a finished table. The piece of timber as in movement is thus stretched in time between what it was potentially and what it will be finally, and only in this transition as a simultaneity of presence and absence is it in movement. Being itself is thought in Greek ontology as a pro-duction, a Her-Stellung, namely, as a coming from an origin, a whence (a)rxh/, ge/noj, ti\ h)=n) into the perfected presence of its sight (i)de/a, ei)=doj) {most succinctly summed up in Aristotle's famous formula for the beingness (ou)si/a) of a being: to\ ti/ h)=n ei)=nai, or the what-it-was-being of a being.} 

    3. The aporetic nature of Aristotelean time and its consequences through Cartesian mathematical science and up to Sein und Zeit 

    Aristotle eschews the possibility residing in the triad of concepts he has fashioned to grasp the ontology of movement, and famously determines time instead quantitatively as the number (a)riqmo/j, 219b2) or measure (me/tron, 221a1) of movement. Thus he writes, "This namely is time, the number of movement with respect to earlier and later. Time is therefore not movement but movement insofar as it has a number." (tou=to ga/r e)stin o( xro/noj, a)riqmoj kinh/sewj kata\ to pro/teron kai\ u(/steron. Ou)k a)/ra ki/nhsij o( xro/noj, a)ll" $(= a)riqmo\n e)/xei h( ki/nhsij. 219b1ff).(5) And further, "time is the measure of movement" (o(/ xro/noj me/tron kinh/sewj, 221a1). The now or instant (to\ nu=n) divides the earlier from the later like a point (stigmh/, 219b18) divides a line (grammh/) into two parts (220a21). An instant is literally that which 'stands in' presence. The succession of nows counted off as 'now', and 'now', and 'now' is the progress of time coming to presence and simultaneously disappearing from presence, this coming and disappearing itself being already a hint of time's twofold nature as both presence and absence. Aristotle raises the aporia that only the now is, so that time consists predominantly of that which is not, namely, the no-longer and the not-yet. He lets this aporia stand, however. 

    Time does not lie before us like a u(pokei/menon to be spoken about; it is not a something (ti/, ou)si/a) lying before us to be addressed by the lo/goj, for a something lying present at hand is only present, which would reduce time proper to the instantaneous now (nu=n) which, tellingly, has the ambiguous ontological characteristics of both discrete presence-at-hand or standing presence, and fleeting continuity or non-being. Time is and, simultaneously, is not. Heidegger notes, "From the hegemony of this concept of being [as standing presence] it becomes clear why Aristotle interprets time itself starting from the present, the 'now'." (Aus der Herrschaft dieses Seinsbegriffs [als ständige Anwesenheit] wird deutlich, warum Aristoteles die Zeit selbst aus der Gegenwart, dem 'Jetzt', auslegt. GA19:633) Heidegger hence takes up the Aristotelean aporia, time's 'illogical' nature as both present and absent, and this is central to his program to break the hegemony of the lo/goj by finding a prelogical access to being. 

    As a quantity lifted off the phenomenon of movement, Aristotle can say, "we measure" (metrou=men, 220b15) time; it is a number, a measure, a magnitude (me/geqoj, 220b27), and, like movement itself, it is continuous. Insofar as it is simply a number, time is unmoving, i.e. outside time, so it is crucial that the counting of nows in the progress of a movement refers to the transitional character of the nows that they are underway from...to, i.e. always both present and absent. As a continuous magnitude, there is no smallest time, because any continuous magnitude can be divided further, but as a number (a)riqmo/j, 219b2), there is a smallest one, which Aristotle takes to be two (220a28) because that is the first number one comes to in the act of counting, starting with the one (mona/j). Time is counted by saying 'now' at least twice in succession, thus marking an earlier and a later. This raises the aporia in the nature of numbers as either countable and discrete or as endlessly divisible and continuous, an aporia which was solved in mathematics as late as the nineteenth century with the concept of mathematical limit (Cauchy, Weierstrass)(6) which allowed the infinitesimally small to be coherently calculated without assuming the infinitesimals as infinitely small magnitudes smaller than any real number. Infinitesimals can be dealt with as the limits of countable, infinite sequences of rational numbers, thus bringing countability and continuity together. The mathematical concept of limit says roughly that by counting you can get as close as you like without actually getting there, thus, once again a twofold of both presence and absence. 

    But why should time be quantitative at all? In his detailed interpretation of Aristotle's ontology of time in Gesamtausgabe Band 24, Heidegger himself does not question the quantitative nature of Aristotelean time, but, on the contrary, takes some interpretative pains to justify it phenomenologically.(7) For Aristotle, time is something lifted off (a)fai/resij) movement itself in its transitional character and, as such, it is an abstraction. Saying 'now', or a succession of 'nows', is an abstraction from any particular quality of the movement concerned, capturing only the phenomenal moment of transition from what was to what is to what will be. The only difference between successive 'nows' is earlier and later, which makes of the counting of now-moments or instants passing through, the abstracting counting of time itself. Hegel saw that quantity is the abstraction from all quality,(8) and the counting process of successive 'nows' is indeed an abstraction from all quality of movement apart from its transitional, never-to-be-pinned-down character 'between', underway, or as both presence and absence. A kind of ordinal counting as a steady drumbeat of successive nows can therefore be phenomenally justified, and the successive nows can be added up to attain a succession of (ordinal) counting numbers going on indefinitely, which is the counting of time that can be made mechanical and arbitrarily refined in ever more sophisticated clocks (beyond the rough counting of days, months, years, which are all regular movements of celestial bodies). The difference between any two counted now-moments can be measured, and since they are read off movement, which is continuous, the measured magnitude of time itself is also regarded as continuous. 

    {The continuity of time already represents a dilemma or aporia for the conception of time as an ariqmo/j or counting number lifted off movement because the counting numbers are not continuous. One paradox arising from this is that any finite time interval is continuous and therefore can be infinitely divided, so that the counting of these divisions one after the other itself is infinite, but within a finite time interval. How is this possible? Furthermore, continuity goes hand in hand with the transitional nature of time in its twofold presence as here-and-gone. This means that infinitely close to any instant is already its disappearance. When, therefore, Aristotle provides a definition of time as "the number of movement with respect to earlier and later", the qualification "with respect to earlier and later" is crucial because it indicates the fleeting nature of time. So the phenomenon of time, even if quantified, cannot be reduced to number pure and simple. Even the counting of time by a clock with its discrete, countable ticking evaporates into nothingness if the clock stops ticking, i.e. if its own movement stops, and time can never be fixed in presence, say, by writing it down.} 

    We should note that the quantitative, Cartesian or Newtonian ontology of time has its origin already with Aristotle's counted time. A four-dimensional Cartesian mathematical space-time is fully characterized by just four continuous variables in a quadruple (x, y, z, t) of real numbers. Such a four-dimensional space-time is by no means put into question by relativity or quantum physics, both of which continue to operate with the mathematical language of four-dimensional vectors for space-time. {A plurality of vector spaces arises by relativizing absolute time, thus making time relative to the frame of reference, the only absolute being the finite speed of movement of light, c. The qualifying reference to "earlier and later" in the Aristotelean definition of time becomes buried in the continuous nature of four-dimensional space-time and the differential calculus which operates with points in space-time infinitely close to a given quadruple. If a given co-ordinate quadruple is regarded as here-and-now, it is infinitely close to being already there-and-gone.} The phenomena of fleeting movement and vanishing time are captured implicitly in the differential calculus of movement and at the same time they are obscured, especially by the perplexing infinitesimals that for a long time defied mathematical logic. 

    It is as if modern physics again stumbles upon the twofold nature of movement and time as both present and absent in sub-atomic physics when it comes up against the dual nature of sub-atomic entities and electromagnetic radiation as both discrete particles and continuous waves. The fleeting being of movement comes back to haunt the mathematical Cartesian way of thinking with Heisenberg's indeterminacy principle, which rests on the dual nature of sub-atomic entities. {A moving being's position cannot be uniquely calculated without denying that it is moving.} This is the famous Heisenbergian discovery that the position and momentum, or the position and velocity of a sub-atomic entity such as an electron cannot both be mathematically calculated uniquely, but only within a certain range of probability. {This is often misinterpreted as meaning that the observation of, say, an electron's speed by means of an experimental set-up, which is itself a physical process, alters its position, and vice versa, but the indeterminacy lies already in the intrinsic nature of movement itself as both present and absent, and this applies not just to sub-atomic particles, but to moving beings in the world in general. The phenomenological insight does not have to be experimentally measurable to be true, but for modern physics it does.} 

    The ontology of time offered in Heidegger's Sein und Zeit breaks with the quantitative Aristotelean ontology, and therefore also with the later Cartesian mathematization of it, insofar as it shows that clock-time is phenomenologically derivative of the more originary, three-dimensional, ecstatic time of Dasein, but Dasein's Zeitlichkeit nevertheless remains captive to an ontology of time still determined by the paradigmatic movement of production underlying Aristotle's interpretation of movement through his famous triad of concepts. The twist with Sein und Zeit and other writings from that period, however, is that no longer is it a piece of timber that is produced into a table through the realization of a potential, but it is Dasein itself that casts its self into the future in a kind of self-production. Therefore Heidegger can write, "Preparing its potential for being, Dasein comes to itself." (Das Dasein kommt, sein Seinkönnen gewärtigend, auf sich zu. GA24:375) {How Dasein has always already been cast into an existential situation is the starting-point for its possibility or potential or power to cast itself anew out of the situation in which it finds itself. This renewed self-casting is pro-ductive in that it brings its self forth from out of the temporal ecstasy of the future, and it does so by grasping its ownmost potential for existing in refusing the self-image mirrored by others.} This conception of Dasein's self and its self-casting imbues Dasein with a will to productive power residing in its own resoluteness. Insofar, we could say that Sein und Zeit still has not broken with the metaphysical tradition. 

    The achievement of metaphysical thinking from its Greek inception on has been to grasp the phenomenon of movement in terms of both presence and absence (as ei)=doj and ste/rhsij) in such a way that what is present (to\ duna/mei o)/n) governs the pro-ductive movement of coming-to-presence of what is absent. This is the Western will to power over movement of all kinds. It must be qualified as a will to productive power over movement. {Access to the world through the lo/goj depends on beings' being grasped in a well-defined, discrete way as o)\n lego/menon, that is, as beings that are said in and grasped by language, and the discrete lo/goj, in turn, can be broken down ultimately into countable, finite, calculable number as binary code that articulates numerically a piece of world-understanding in executable digital pre-script or pro-gram that outsources our world-understanding into automated cybernetic processes/movements. Such logical pre-script is outside of time; it is timeless. Why? Because time is conceived simply as the real, linear variable, t, consisting of pure now-points which are either present or absent, but not both. The unity of time in its ambiguity as both presence and absence in simultaneity eludes pure number which, as the Greeks knew, is outside time. Despite the mathematization of time in the modern age, the aporias of time and movement continue to puzzle the modern mind in the guise, say, of Zenon's paradox that has been handed down from antiquity.} 

    It is {therefore} an historically momentous obscuring of the phenomena of time and movement to conceive time simply as a mathematical variable. If, however, human being itself is, in truth, exposed to three-dimensionally stretched, ecstatic time shared with others and also leading inevitably to death, then we have to return to reconsider movement and time, breaking both with the arithmetization and quantification of time, and also with the still productive conception of these phenomena remaining even in Heidegger's thinking. 

    4. Time in our global capitalist economy

    Significantly, although Aristotle casts an ontology of a rich variety of four kinds of movement, he does not consider anywhere, as a kind of movement sui generis, the change that takes place through the exchange (metabolh/, a)llagh/) of one thing for another, such as exchange in the market-place, which would have brought in the category of pro/j ti, or relation, and another kind of movement, namely, the social movement of interchange.(9) The ambiguity residing in that crucial, indeed pivotal Aristotelean term, metabolh/, occurring in Aristotle's principal definition of du/namij as a mode of being, which can mean both 'change' and 'exchange', has had fateful consequences for Western history up to the present day. {Replacing one light bulb by a new one is a banal example of movement as exchange which can still be thought as a composite movement composed of the two movements of the old and the new light bulb. But the social exchange among human beings in which goods exchange or in which mutual recognition and estimation takes place can by no means be thought through merely by composing individual movements, because the starting-points of the movement are multiple and also interlinked in a mirroring process (as captured, for instance, in the process of recognition in Hegel's Phänomenologie des Geists).} The metabolh/ of greeting each other on the street, for instance, is an interchange whose ontological structure is already more complex than the productivist movement of a du/namij being realized one-sidedly through its e)ne/rgeia in which a starting-point governs a change in something else. {As an aside: It is also an aporia whether the productivist conception of movement breaks down measurably also on the sub-atomic level where sub-atomic particles such as photons and gluons exchange their energies with one another.(10) In any case it can be said that human sociation is a reciprocating interplay, starting with "a mutual Complaisance and Intercourse of Civilities".(11)

    So what can be said ontologically about economic movement and time? Like all movement, insofar as it is determined and therefore measured according to the Aristotelean and Cartesian casts of time, the value-movement of capital is counted by time, which in this case is the turnover time of capital, the measure of a circular movement (kuklofori/a, Phys. D 14;223b19) from M to M'=M+DM, that is, from an advanced principal sum to its return augmented with a surplus. The shorter the turnover time for this circuit, i.e. the faster value moves through its circuit as capital, the greater the surplus achieved in any standard period such as a year. {The success or otherwise of the circuit of capital can be measured by the simple finite-difference formula dM/dt = (M'-M)/(t'- t), the augmentation of money divided by the time interval, where t and t' are the points in time at which a capital sum is advanced and returns. This measure of success is simply the augmentation of capital divided by the time taken for such augmentation. Such a formula measuring the result of the capitalist value-play relies, of course, on the reduction of the phenomenon of time to a linear variable consisting of now-points and also on the reduction of the phenomenon of value to a quantitatively determined money-value wherein the power play underlying value becomes invisible. The differential calculus developed by Cartesian (Newtonian/Leibnizian) mathematics in the modern age for physical movement is therefore made to apply also to the social movement of value as capital, albeit without necessarily requiring infinitesimals but only a calculus of finite differences.} 

    In decisive and essential contrast to the movement of physical bodies described by Newtonian (or even Einsteinian) laws of motion, however, there is no formula to compute the difference M'-M expressing the augmentation of money, because it is merely the outcome of a value power play in which exchange-values are actually exchanged through being mutually estimated. There is no intrinsic potential exchange-value inhering in a use-value that could predetermine its quantitative exchangeable value, simply because exchange-value itself only comes about or happens in a power play on the market among at least two, and usually many players. Such is the power play played by all the players in a capitalist economy in their plurality, whose ontology represents a rupture with traditional metaphysics because metaphysics can cope only with mono-archic movement, not with the poly-archic, 'playful' movement of social interchange. Capital is therefore definitely calculating in that it reckons with a surplus value at the end of its circuit, but it cannot precalculate this surplus with calculative certainty, for the gainful interplay on the markets is essentially risky and uncertain. 

    {Moreover, the time required for the movement an exchange transaction also has no ground in a law of social movement according to which it could be precalculated, nor is this time interval uniform because the movement from which it is abstracted is itself non-uniform. Commodities offered for sale on the market are at rest (h)remei=n, Phys. D 12;221b28) with respect to their value-transformation and only jolt into movement upon being sold. They are nevertheless at rest only within the overall movement of capital, so that this their being-at-rest is only a limiting case of their movement as value, just as, analogously, a piece of timber at rest on the carpenter's bench is still within the overall movement of being made into a table. The movement of a single capital involves many individual transactions and therefore many individual value transformations, each of which takes its own time, so that the overall movement of one turnover of capital depends on many, even myriad value transformations being achieved before the advanced money-capital returns. This circumstance implies already that the circular movement of even a single capital comprises a series of jerky movements of value transformation plus the movement of production itself, which may be organized technically to run smoothly. Especially at the interfaces where commodity-value has to be transformed into money-value, the movement of value comes to rest for a time which may be brief or extended depending upon market conditions.} 

    The circular movement of a single capital is {hence} both incalculable and uneven. The reproduction of an entire capitalist economy involves the intricate intermeshing of many individual circuits of capital. The turnover of the total social capital is therefore even more complicated and intricate than that of a single capital, so that the counted number or time associated with this total social movement is both incalculable and non-uniform, since the underlying movement of total social capital itself is both incalculable and uneven. This contrasts with Aristotle's determination of the measure of time as an "even circular motion" (kuklofori/a o(malh/j, Phys. D 14;223b19). The regular period of even circular motion makes counting easier and its number, viz. time, easier to deal with calculatively. A public measure of time in a standard periodic movement also facilitates the co-ordination of movements not only among capitals but among the economic players in general. A uniform measure of time, such as the year, can be imposed on the movements of value as capital, but this is only the abstract subsumption of many complicated, uneven movements under a convenient conventional standard. 

    If the turnover of the total social capital is the basic, underlying movement of a capitalist economy, the measure of this turnover also provides the basic measure of time in such a society whose rhythm is determined by the circular, augmentative movement of capital. {As we have seen,} this underlying social movement is uneven, which implies that time in such societies is also uneven (not like the more regular movement of, say, a simple agricultural society in tune with the movements of the seasons). Time in a global capitalist economy may even falter and stumble when the underlying movement of global capital falters and stumbles in an economic crisis in which the gainful game turns sour. 

    {Furthermore, the measure of the success of a turnover of capital is not only the amount of surplus value it throws off on its return as money capital, but also the turnover time taken for this circular movement, i.e. the faster the turnover, the more profitable the capital. Since capital is this augmentative movement from money to more money, it achieves greater augmentation by shortening as far as possible its turnover time, thus reducing the denominator in the finite difference formula dM/dt = (M'-M)/(t'-t) and increasing it overall.} If the turnover time of total social capital is an underlying, basic measure of time in capitalist society, the inherent tendency of capital as the determining gainful movement to shorten the turnover time means that time in such a society becomes shorter and shorter. That is, a capitalist society tends to continually accelerate time, even though such acceleration is not precalculable (but at most postcalculable), depending as it does already on the simple, but nevertheless incalculable transformation of commodity-value into money-value {(sale of the finished product on the market)} and of money-value into commodity-value {(e.g. if supply on the market is short)}. 

    5. Recovery of the three-dimensional, complexly interwoven social time of who-interplay

    "Oh! do not attack me with your watch. A watch is always 
    too fast or too slow. I cannot be dictated to by a watch." 
    Jane Austen Mansfield Park
    {The global gainful game that assumes the form of the movement of value as capital has a Janus face. On the one hand, it shows the face of the striving for the limitless accumulation of value as capital, the modern consummation of Aristotle's chrematistics. On the other hand, the simplest of exchange relations in which one use-value is exchanged for another is already, at root, when deciphered, the interchange of human powers, i.e. of human abilities. To see this, three shifts of viewing angle are necessary. First, the status of commodities and capital as reified, alien powers standing over against human beings as their pitiable victims must be fluidized in value itself as a process, that is, as a power play of mutual estimation in which also human powers and abilities are mutually valued and estimated. Second, it must be acknowledged that it is not only capitalist entrepreneurs that are the perpetrators of the striving for gain, but all the players in a capitalist economy, each of whom has a part to play in this play. Third, the striving for gain is not restricted to the economic, but encompasses also all those striving movements of human beings for gain of whatever kind, be it a gain in knowledge and understanding, in reputation, in social recognition for one's abilities, merits and services, a gain in esteem within a friendship, etc. etc. 

    To restrict the viewing angle to the economic:} An interchange among economic players which is a power interplay for gain can be, and often is mutually beneficial. {This is the fair face of Janus. As the movement of social life itself, this interchange of powers on the basis of mutual estimation is endless, limitless, for there is no end to how human beings can exercise their powers for each others' benefit. Thus there are two different perspectives for looking upon the constellation of being called the gainful power play of value, one fair, and one not so fair, and sometimes even downright ugly, that consists in employing our powers against each other, to unfair advantage. There are countless ways of playing the gainful game unfairly, both subtle and blatant, and on the economic playing field these ugly ways include exploiting workers under demeaning working conditions for low pay.} 

    To bring the fair face in both economic power play and the more general social interplay of mutual estimation to the forefront requires, as an ontological condition of possibility, recovering the three-dimensional time that has been quantified as a mere mathematical (and hence timeless) variable, t, {in the formula given above for the success of a circuit of capital,} for the time in which we play the gainful game is our own, finite life-time of our own life-movements leading to death. Firstly, as elaborated in Sein und Zeit, the mathematical variable, t, has to become thought and experienced as the three-dimensional ecstatic, finite time of human being itself that casts its self into the open dimension of the future by retrieving who it has been and fashioning its ownmost, singular possibility of existing. Such self-casting, however, is close to being misunderstood as auto-production and thus as a perpetuation of the Western will to productive power. Therefore, in a further twist, this three-dimensionally stretched time, which accords with the life-movement of human being itself stretching toward its future, has to become thought and experienced as the intermeshing social time of social movement itself, which is not just the measurable movement of total social capital, but the immeasurable, complexly interwoven movements of social interplay in which each individual haphazardly comes to stand (or fall) for a time as somewho, to gain or lose its self, in the power play of social estimation and social validation of its powers and abilities. 

    The plural nature of such a power play is already beyond the reach of the calculating, epistemic power thought at the inception of metaphysics and emulated to the present day by both the natural and social sciences. The power interplay is played out as complex movements in life-time in which the players are not the underlying subjects, have no substance and, despite their self-deceptions, inherently cannot achieve a standing presence. What does this imply for those questions posed at the outset regarding Heidegger's late thinking on time? First, it implies that the movement of giving represented by the sendings of being as epochal castings of the world remains abstracted from what is cast in such a casting. Second, the movement of the reaching of time in which an epochal casting of being arrives from the future is the slow time of philosophical thinking itself. And third, this double movement of the sending of being and the reaching of time still has nothing to say about the interwoven movements of human power plays in which the values of things and persons come about fluidly through mutual evaluating, estimating, appraising, validating and esteeming. 


      Notes
      1. Paper presented to the 27th North Texas Heidegger Symposium 17-18 April 2009 convened by Rod Coltman and Charles Bambach. Passages in curled brackets {} were not read out in Texas. For more detail, see my study The Digital Cast of Being: Metaphysics, Mathematics, Cartesianism, Cybernetics, Capitalism, Communication, available at the artefact web site. Back to 1

      2.  
      3. Martin Heidegger 'Zeit und Sein' in Zur Sache des Denkens Niemeyer, Tübingen 1st ed. 1969 2nd printing 1976 SD:1-25. Back to 2

      4.  
      5. Cf. M. Heidegger Grundbegriffe der aristotelischen Philosophie Marburger Vorlesung SS 1924 Gesamtausgabe Band 18, ed. Mark Michalski 2002 § 26. Bewegung als e)ntelexei/a tou= duna/mei o)/ntoj (Phys. G 1) et seq. Cf. also Die Grundprobleme der Phänomenologie Marburger Vorlesung SS 1927 ed. F-W. v. Herrmann 1975 § 19 a) b) Auslegung des Aristotelischen Zeitbegriffs GA24:336ff, Platon: Sophistes Marburger Vorlesung WS 1924/25 Gesamtausgabe Band 19 ed. Ingeborg Schüßler 1992 GA19:100ff and Die Grundbegriffe der antiken Philosophie Marburger Vorlesung SS 1926 Gesamtausgabe Band 22, ed. Franz-Karl Blust, Viertes Kapital Das Problem der Bewegung und seine ontologische Bedeutung. Ursprung, Sinn und Funktion von du/namij und e)ne/rgeia §§ 61-64 GA22:170ff.. References to M. Heidegger Sein und Zeit (Being and Time) Niemeyer, Tübingen 1984 are given in the form SZ:151. Back to 3

      6.  
      7. Cf. M. Heidegger Die Grundprobleme der Phänomenologie Marburger Vorlesung SS 1927 Gesamtausgabe Band 24 ed. F-W. v. Herrmann 1975 § 19 a) b) Auslegung des Aristotelischen Zeitbegriffs GA24:336ff). Back to 4

      8.  
      9. Although M. Roubach cites this famous core Aristotelean definition of time in the chapter he devotes to "Number and Time in Being and Time" (p.55, mistranslating ki/nhsij as motion, i.e. locomotion, rather than the more encompassing phenomenon of movement), he discusses neither Aristotle's deep ontological analysis of movement in four senses (with its famous triad of characteristic concepts), nor Heidegger's extensive and continuing interpretations of Aristotelean movement in the 1920s (e.g. GA18, GA22, GA24) and thereafter. He therefore fails to make any connection whatsoever between the enigmatic twofold present-absent nature of movement itself and the fleeting present-absent nature of time itself, but instead deals with time only insofar as it is a finite or infinite number, i.e. only in relation to the finite and infinite in mathematics. But number itself, as unmoving, is outside time altogether, whereas number, according to Aristotle, counts time. The 'nows' themselves, therefore, must be, in some sense, moving, transitional the enigmatic ontology of movement and time. Cf. Michael Roubach Being and Number in Heidegger's Thought Continuum, London 2008. Back to 5

      10.  
      11. (Added July 2009 Ver. 1.1) Albeit that the aporia returns at the beginning of the twentieth century with the crisis in the foundations of mathematics involving questions concerning how the continuum of real numbers necessary for mathematical analysis can be derived logically from primitive elements, plus, perhaps, the arithmetical basis of the natural numbers taken as given: "... it is when we come to the real numbers that we get into serious problems about the logical foundations of mathematics..." (Solomon Feferman 'The Significance of Hermann Weyl's Das Kontinuum' second of three lectures for the conference Proof Theory: Historical and Philosophical Significance held at the University of Roskilde in Denmark 31 October - 01 November 1997, accessed July 2009). For more details, see Postscript 1 to The Digital Cast of Being. Back to 6

      12.  
      13. § 19 a) b) Auslegung des Aristotelischen Zeitbegriffs GA24:336ff op. cit. Back to 7

      14.  
      15. Cf. G.W.F. Hegel Enzyklopädie I §99 Werke Bd. 8 Suhrkamp, Frankfurt/M. 1970. Back to 8

      16.  
      17. Cf. on social interchange M. Eldred Social Ontology: Recasting Political Philosophy Through a Phenomenology of Whoness ontos verlag, Heusenstamm 2008 xiv+688 pp., esp. Chapter 5. In the Politics, Aristotle himself speaks of the making of money "through exchanging goods" (dia\ xrhma/twn metabolh=j Pol. 1257b20-25), thus employing the fateful term metabolh/ in its signification as 'exchange', not 'change'. (This in response to a question from Walter Brogan.) Back to 9

      18.  
      19. Cf. Encyclopaedia Britannica 2008 "subatomic particle". Back to 10

      20.  
      21. Joseph Addison 'Country manners' The Spectator No. 119 July 1711 in Joseph Addison, Sir Richard Steele & Eustace Budgell Sir Roger de Coverly Folio Society, London 1967 p. 81. Back to11

      22.  


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