I. The logical category of quantity

In the Science of Logic, Hegel asserts that time and space exemplify the logical structure of quantity (SL: 199/21: 230),Footnote ⁴ which he defines as the ‘being-for-itself which is absolutely identical with being-for-another; the repulsion of the many ones which is immediate non-repulsion, their continuity’ (SL: 152/21: 173). The purpose of this section is to explain this definition as a series of logical relations, which will elucidate time's exemplification of it.Footnote ⁵ A focus on quantity does not imply that this category alone captures all complications regarding temporal existence. But following Hegel, it captures the general formal determinations under which all temporal existence falls, particularly those concerning time's passing and the formation of a magnitude of concern in our paradox. Although Hegel only briefly mentions the connection between quantity and time, we will find a clear parallel between his descriptions of time and this logical analysis.

Let us begin with the category of being-for-itself.Footnote ⁶ This category expresses a logical relation whereby a limit to something presents not only a negation of that being but is also internalized by it, meaning that this being has an inner self-reference to that limit. Indeed, as a limited something, this being cannot be itself without the limit. The limit is not merely an external imposition but also belongs to the limited something as its own. So, the mere externality or negativity of this limit is transcended by recognizing it affirms this being. Hegel calls transcending this mere externality ‘the posited negation of negation’ or a simple self-reference (einfache Beziehung auf sich) in relation to otherness (SL: 126/21: 144).

Both the negativity of the external limitation and the negation of that negativity or externality, as a ‘turning back into itself’ (SL: 127/21: 145), equally belong to the definition of being-for-itself. While being-for-itself is the negation of what is posited as a merely external negation, it can only turn back into itself under the condition that it is indeed limited, hence negated by externality. Although the limit may not be something merely external to being-for-self, it also implies this externality as such. Being-for-itself is therefore the ‘absolute union of the reference to another and the reference to itself’ (SL: 133/21: 152). Nevertheless, by focusing on a being's exclusion of otherness as an affirmation of itself, its dependence on externality may be abstracted from or conceived as nothing but this affirmation from its standpoint.

Following a detailed account of this reduction of externality to an empty being-for-one, meaning nothing but an affirmation of that one being determined as being-for-itself, Hegel articulates the dialectic between the one and the many ones. The being-for-itself of some particular being, which is determined as one in so far as it refers simply to itself in the exclusion of otherness, can be itself or ‘immediately present’ only in so far as ‘its negative reference to itself is at the same time reference to an existent’ (SL: 135/21: 155). Because the one, as being-for-itself, involves a negative self-reference to otherness, which is not nothing, the externality limiting the one must be conceived as something existing of its own. Because the one's own conceptual determinations imply an externality, it ‘repels itself from itself’ into another one (SL: 136/21: 156). By turning to this external being, we discover that the same determinations applicable to our initial being-for-itself apply to it in turn: this external being is itself limited by the limit of the initial being-for-itself, is negated, and therefore reanimates the logical determinations with which we began. This externality proves to be another being-for-itself and thus another one. We may posit as many ones as we wish, prolonging this repeating chain of logical determinations ad infinitum. For Hegel, the concept of the one thus implies many ones.

Hegel develops an extensive analysis of repulsion and attraction (Repulsion und Attraction), which follow from the relationship between the one and the many ones. On the one hand, because each of the many ones is equally determined as being-for-itself, they are equally determined as other-excluding. Although that exclusion might be initially considered as non-relational indifference or self-containment, repulsion is not a ‘liberation from what is repelled and fled from’ (SL: 142/21: 163). Each of the many ones can be itself only through relations to the others excluding it, in relation to which it is negated and able to turn back into itself. Exclusion is itself a form of relation: any one is that unique one and not any other unique one. The many ones exist only in relation to one another yet in so far as they are different. On the other hand, each of the many ones is equally determined as one. That is, each of the many ones contains all the logical determinations of oneness as such. The category of attraction consequently arises when we think the many as ‘one one’, meaning as the self-same form of the many ones. As there can be no attraction without different ones to attract, the one one ‘does not swallow the attracted ones within it as into one point’ (SL: 141/21: 162). Rather, the one one reflects how the many ones affirm and continue the same determination of oneness through them. Hegel claims that repulsion and attraction are therefore connected, each presupposing the other, with the many of repulsion ‘falling back upon itself and the positing of itself as its other, as a one’ and the one one of attraction being likewise ‘only the positing of itself as its other, as the many’ (SL: 144/21: 164). Repulsion refers to attraction in so far as its many ones must be, in their plurality, equally ones; attraction refers to repulsion in so far as its oneness refers to many in a plurality.

The initial definition of quantity can now be clarified. While attraction corresponds to the determination of continuity as a self-continuing oneness through any limit, repulsion corresponds to the determination of discreteness or limit through which this self-continuation is possible (SL: 154/21: 176). Quantity is continuous because it is ‘simple, self-same reference to itself unbroken by any limit or exclusion’, as any limit is overcome in an affirmation of oneness (SL: 154/21: 176). Nevertheless, plurality or limitation is also posited in quantity because ‘the many are each what the others are, each is like the other, and the plurality is, consequently, simple and undifferentiated equality’ (SL: 154/21: 176). Continuity is not opposed to discreteness but ‘the self-continuation of the different ones into the ones from which they are distinguished’, that is, in affirming the oneness to which they belong (SL: 154/21: 176). As such, with quantity, there is an ‘unbroken continuity’ in the one ‘coming-out-of-itself’ as a plurality of many ones passing from one to the next one so as to remain a one (SL: 155/21: 177). Hegel also ultimately rejects a void as an intermediary or non-one between the many ones (SL: 154/21: 177); as an abstract or ‘indeterminate’ negation (SL: 136/21: 155), it proves to be no determinate being between them.

After describing pure quantity (die reine Quantität) in terms of this ‘self-equality […] of many that do not become exclusive’ and a ‘discreteness of confluents’ (SL: 154/21: 177), hence the reconciliation of repulsion and attraction in this logical determination, Hegel examines the distinction between continuous and discrete magnitude (kontinuierliche und discrete Größe). With magnitude, we think the many ones as a plurality in a more encompassing one.

Both continuity and discreteness apply to both kinds of magnitudes, albeit differently. With continuous magnitudes, the principle of discreteness or limitation is expressed as ‘the ubiquitous real possibility of the one’ posited anywhere in it (SL: 155/21: 177). That is, a limit may be posited anywhere in a continuous magnitude given its homogeneity; it is not composed of more fundamentally self-enclosed units marking the limit of divisibility. This also implies that the magnitude is ‘unbroken’ by any posited limit immediately shared between parts (SL: 154/21: 176). With discrete magnitudes, the principle of continuity is expressed ‘in the ones being the same as one another, or in that they have the same unity […] the one-outside-the-other of the many ones as of a same’ or one one (SL: 166/21: 190). But the many ones are an ‘outsideness-of-one-another as discontinuous, as broken off’ (SL: 166/21: 190). As I understand Hegel, the concept of a limit of one transitions to another limit of another one, albeit without conceptual intermediary, hence still continuously as ones. In turn, discrete magnitude posits an aggregate of many ones marking an absolute limit of division. Their limits relate them in a greater magnitude without being immediately shared. In either case, both continuity and discreteness, and thus all that quantity is, must be posited, making both expressions of quantity (SL: 167/21: 192).

II. The quantitative logic of time's passing

Because Hegel's logic examines logical determinations qua logical determinations rather than their application to any worldly content, Hegel only passingly mentions how the category of quantity applies to time in the Science of Logic. Let us undertake this task, examining the nature of time's passing before turning to the question of temporal magnitude in the following sections. Without pretending to exhaust his analysis of time in all respects, I examine Hegel's specific comments on time's passing in the Phenomenology of Spirit and the Philosophy of Nature, which together with his logic exhaust his mature reflections on the matter.Footnote ⁷ Together, these texts demonstrate how time's passing instantiates a quantitative logic in Hegel's own words.

The reader might be sceptical of examining Hegel's phenomenology alongside his reflections on the natural determination of time. However, there is no conflict between these analyses given our analytic concerns. First, we are concerned not with developing a detailed phenomenology of time consciousness but with considering the basic temporal form of our existence.Footnote ⁸ Any more phenomenologically complex, ‘spiritual’ expressions and representations of time must be grounded on these more general determinations expressed in his natural account of time. Second, as such, we as temporal subjects exemplify the quantitative logic of time's passing just as much as any other temporal being in the world. A phenomenology of time's passing provides an entryway into an ontological analysis of time as a form of worldly existence. That is, bracketing other metaphysical questions about the origin of time in the subject or the world, our experience gives us access to the phenomenon of time—access to the reality that time is. A phenomenological consideration of time thus provides further evidence for our more straightforwardly ontological account of time's passing. It will also ultimately motivate belief in time's reality despite the paradoxes involved in that ontological analysis.

With the chapter on sense-certainty (die sinnliche Gewissheit) in the Phenomenology of Spirit, Hegel's project of overcoming the difference between thinking and being, or knowing and truth, begins with the most abstract determination of knowing: an indexical pointing out of the this (das Diese). The failure to attain an identity of being and knowing in this exercise follows from the fact that pointing to something as this fails to articulate all the complexities of what it is. Because this form of knowing leaves so much unsaid given this non-identity, the phenomenological project progresses by further specifying the nature of what has been indexed. Accordingly, the this is further specified according to the determinations of the here (das Hier) and the now (das Itzt) in so far as they are implicated in the act of pointing to something. This turn to the here and the now more adequately articulates what was already at work in the indexical this. But these determinations likewise mire us in contradictions and inadequacies.

Because I am concerned solely with time, let us examine only the now. Hegel offers a simple thought experiment for demonstrating how attributing this with the now leads us to fail the phenomenological test of saying what we mean or overcoming the non-identity between thinking and the being that is thought. We can take a piece of paper and write ‘Now is Night’. We can return to the piece of paper the next day, at noon. Yet, when ‘we look again at the written truth we shall have to say that it has become stale [schaal]’ (PhG: 60/9: 64).Footnote ⁹ The now that is ‘proves itself to be, on the contrary, something that is not’ or was not supposed to be (PhG: 60/9: 64). While the now continues to be—I continue to look at the paper right now—, that to which the now refers has changed. In the act of gesturing to or uttering the now, ‘it has already ceased to be’ by becoming another now (PhG: 63/9: 67). The point of Hegel's thought experiment is not that we should attempt to look back at the paper as quickly as possible, as if the issue were merely an empirical test of our speed. Rather, there is a necessary temporal difference between writing ‘this is now’ and grasping its completed, written meaning since these are two distinct, successive acts. We never return to precisely the same now when we try to hold on to it.

While there is a sense in which we experience a living, extended present, and while Hegel recognizes that beings can in some respect remain self-identical over time, one would miss the point of his phenomenological exercise by appealing to a duration as a now that does not immediately become another. I might assert that the now to which I am referring with the paper is the whole night, valid over several hours; even if its truth becomes stale in the morning, I may return to the paper over the course of the night or even on another night to discover that its truth holds. I might assert that something enduring over some delineated period, which I consider an extended present, is present through it. However, the point of Hegel's analysis is that no duration is ever purely self-present or present at once, implicating a ceasing to be present or a not yet having become present within itself. Beyond clarifying how certain states of affairs fail to be true always, thus lacking the universality required for the complete identity of being and knowing, Hegel's phenomenological exercise demonstrates the inadequacy of identifying truth with an indexical that continuously changes, hence is not (not yet or no longer).

Hegel generalizes his thought experiment into the principle that the now, ‘just when it is’, ceases to be (PhG: 63/9: 67). I cannot locate a point at which the now simply is and continues to be just itself. Even when I attempt to point to a particular now right now, it is no longer precisely the same now that it has been when I was doing the pointing. It belongs to the very act of pointing out or attempting to fix the now, by there being a beginning and end to that activity, for there to be a difference preventing the now from being fully self-present or given at once. The now follows a logic of self-differing, meaning that it always already becomes other to itself as another now. The answer to the question of when the now is, assuming we are searching for a moment of pure presence, is that it is no longer (or, not yet). In this sense, it cannot be.

But do I not also experience presence as continuously present, as what is always now? While the now is always beyond me if I try to hold on to a particular moment of pure presence, am I not actively living in the present? Does the givenness of my experience not demand I recognize a difference between what is present for me and what is not as past or future? Must the now not be for its passing to occur ever—not just not yet or no longer, that is, never actually?

In the phenomenological exercise, the transitoriness of any moment does not articulate the entire experience of temporal presence. On the one hand, this transitoriness implies that the now has no purely self-identical being. On the other hand, Hegel claims, this transitoriness must itself be negated to ‘return to the first assertion, that the “Now” is’ (PhG: 63/9: 68). While the previous exercise attempts to retain the now as something immediate and simple (unmittlebares Einfaches)—that is, unmediated by any difference, being always and just the same—, it is rather ‘a movement which contains various moments’ (PhG: 64/9: 68). The now endures not because one can hold on to any particular moment but because presence is ‘something that is reflected into itself […] which, in its otherness, remains what it is: a Now which is an absolute plurality of Nows’ (PhG: 64/9: 68). The form of the now is preserved through the variegated contents pointed out by the many nows. As Hegel explains, it is ‘determined as a permanent and self-preserving Now through the fact that something else, viz. Day and Night, is not’, meaning ‘it is still just as simply Now as before, and in this simplicity is indifferent to what happens in it’ (PhG: 60/9: 65).

Because Hegel presents this phenomenological exercise in terms of the test of the adequacy of being and knowing, one may read this dialectic in terms of the contradictions of token-reflexives. Hegel is indeed concerned with whether indexicals stand the test of truth. But what might be missed with this focus on the gap between our utterance and its referent is that Hegel is also describing, in phenomenological terms, the very logic of time's passing. That is, this phenomenological analysis also develops an account of what time's passing is.Footnote ¹⁰

In the phenomenological exercise, Hegel conceives the now as both one and many ones. The form of the now is the self-same process of the present always being present. It is in this sense that Hegel means the now is simple or indifferent to what happens. Yet, the process or activity implicated by the form of the now is a transition in which any possibly delimited moment is negated into the next. In his logical discussion of quantity, Hegel explains that time is an ‘absolute coming-out-of-itself [Ausserichkommen], the generation of a one, of a point in time, a now which is immediately its coming-to-nothing and, again, the continuous coming-to-nothing of this vanishing’ (SL: 156/21: 178). The immediacy of the transition refers to the continuity of this process. The unity and continuity of time lie in how the temporal process ‘[goes]-out-of-self’ (Ausser-sich-gehen) as a ‘flowing [Strömen] that does not however pass over into opposition’, meaning that time is connected to more time—that the process of temporal self-differing continues without interruption (SL: 156/21: 178). In anticipation of Hegel's rejection of time modelled as a discrete magnitude composed of parts, I interpret the invocation of the point in terms of two principles: first, that any delineated point or part of this process marks not a pure or hermetic self-presence but a continuous self-differing; and second, that the process is differentiated and can therefore be described in terms of the many nows, as we have done above.

By distinguishing the many nows and the one form of the now, we distinguish between a continuously differentiated process and the presence of that process through its continuous differentiation as such. The many nows refer to the activity of continuous self-differing as what is itself present under the form of the now. The form of time, hence the presence of time as such, remains self-equal through that change. These many nows exclude or repel one another as unique moments while being attracted as equally now, continuing the being of the now under this one form. The experience of presence demands both principles following a quantitative logic.

Although Hegel's phenomenological discussion of time focuses on presence as such, the relationship between the self-same form of the now and the many nows may also be expressed in terms of the past and the future. In the Philosophy of Nature, in which he directly discusses time (and space) in terms of a quantitative logic, Hegel describes the present (Gegenwart) in terms of the passage from the not-being (Nichtsein) to the being (present) of the future (Zukunft) and from the being to the not-being (present) of the past (Vergangenheit). The present involves

Whereas a particular past or future moment is not-being or determined as no longer or not yet present, a particular moment of presence both is and is not, determined to be in so far as it has come to be and will perish. There are many particular nows excluding one another, continuously passing over into one another rather than being purely self-present. It belongs essentially to any particular moment of presence to cease to be, to be negated as the past of a future present.

With the rather paradoxical expression that time is ‘the being which, in that it is, is not, and in that it is not, is’ (PN: §258), or that time is the contradictoriness of self-external being (PN: §258), meaning that its being (as present) must come no longer to be, Hegel rearticulates the phenomenological exercise of the many nows with these other temporalities. Although we may attempt to fix the now as something purely self-present, any moment of presence in fact ‘disappears into nothing’ (PN: §259R). Nevertheless, for Hegel, the very form of these temporalities—the past as what has been, the future as what will be, and the present as what now is—itself always is, as what the concept of time always implies (PN: §259A).Footnote ¹¹

The logic of quantity, with its dialectic between the one and the many ones, is thus exemplified in presence as both the oneness of a self-same now, beyond whose form we do not move, and the multiplicity of many nows, never purely self-present in their continuous negation into the next. However, the question remains whether, despite the apparent adequacy of the logical dialectic to presence, the nature of temporal succession confounds this application of Hegel's logic and thus fails to resolve the paradox of presence. Let us turn more critically to the nature of time's magnitude, how its many ones belong as one, to investigate this question.

III. The discrete magnitude of time and its contradictions

In a remark discussing the applicability of quantity to time in the Science of Logic, Hegel warns that its quantitative form is not—or, rather, should not be—understood as composition by externally related and discretely enclosed units (SL: 156/21: 178). Likewise, in the Philosophy of Nature, Hegel warns against confusing time with its numerical measurement or modelling time off of number, as the ‘dead unity’ (todte Eins) arising ‘when the understanding paralyzes [time] and reduces its negativity to a unit’ (PN: 259R). While Hegel does not thereby deny the measurability of time by number,Footnote ¹² which he defines logically as an ‘absolutely determined quantum’ whose existence ‘excludes the existence of other ones’ (SL: 169/21: 194), he denies the conceptual adequacy of the discreteness of number to the continuous nature of temporal succession. Yet, despite the phenomenological reflection on the self-differing of the many nows, Hegel does not develop arguments against the model of time as a discrete magnitude. In this section, I take on this task in Hegelian terms.

We may understand the problem of temporal magnitude in terms of the passing from one now to the next, that is, how a series of nows is possible but still now. We may also understand it in terms of the formation of a more encompassing extension or duration from this passing series.

Let us first defend with a reductio the premise that, if time is a successive series, any discrete quantum or unit of time must be extended, hence internally differentiated with a before and after. If a quantum lacked this internal differentiation, it would be instead a simple, unextended point. It is easy enough to see why time cannot pass successively or form a temporal magnitude if composed thusly.Footnote ¹³ An unextended point cannot share a limit with another.Footnote ¹⁴ Because an unextended point is internally undifferentiated, thus without even potentially differentiated parts, there would be no extremity at which a limit between two points would be shared. The points would meet as whole with whole and therefore would lack contact as distinct points. If the magnitude were composed of these simple points all the way down, it could not form over time given this collapse into indistinction. The points could form a magnitude only by following each other successively, hence by taking time, but would then imply inner differentiation or extension. An unextended point of time takes no time by definition, thus contradicting this proposal.

Nor, following Hegel's logical critique of a void between ones as an abstract negativity, can the passing of time be explained if a void existed between unextended points. A void between times would be either nothing at all, hence nothing preventing the points from collapsing into indistinction, or have an extension of its own, contradicting its temporal indifferentiation as the supposed negation of time's positive being. Moreover, as an extension, the void would itself be internally differentiated with a before and after, contradicting the premise that the temporal magnitude is composed solely of unextended points.

If the discrete quanta composing a temporal magnitude were instead extended, their own extension would be either quantized or continuous. Contradictions arise in either case. On the one hand, if the quanta of time were themselves quantized, the quanta of those quanta would be either quantized or continuous in turn. If quanta were quantized all the way down, meaning that each quantum must include its own quanta, ad infinitum, there would be an infinity of quantized parts in any quantum. Because any quantum would be internally differentiated with its own quanta, each of which is completed over time for that greater quantum to be completed, its successive formation would depend on an actual infinity of parts. But an actual infinity cannot be formed successively; we cannot begin to add parts, thus posit a first part, and achieve a collection of parts beyond all finitude. The impossibility of completing the required infinite renders all quanta of time inconceivable. Moreover, the very idea of having a beginning to this addition is contradictory, as any quantum would be extended and thus inconceivable in its own having-been-formed; an actually infinitely small quantum, or a smallest given amount, is a contradiction in terms since any determinate amount could always be smaller. Another argument against an actual infinity, which applies to both forming and completed quanta, also involves the problem of the non-zero extension of any quantum. However small the quantum may be, only a finite number of non-zero quanta would be required to fill another finite quantum. On the other hand, if quanta were internally continuous at any point in the regress of parts, time would not be fundamentally composed of discrete quanta. It would instead be a continuous magnitude.

One might retort that quanta can be continuous in themselves but absolutely bounded at their extremities, hence that the magnitude would remain discrete. But returning to Hegel, we find a problem with the absolute boundedness of temporal quanta in general. In the Science of Logic, following his analysis of magnitude, Hegel describes the logical category of quantum in terms of a plurality of many self-referring (auf such beziehende), enclosing (umschliessende), and other-excluding (anderes ausschliessende) units (SL: 168/21: 194). Because they are enclosed and other-excluding, any quantum is initially conceived as ‘indifferent with respect to its limit, and hence with respect to other quanta and its “beyond” [Jenseits]’ (SL: 190/21: 219). Hegel criticizes the quantized representation of continuous (and even discrete) magnitudes when these units are thus abstracted from their connection in a greater whole. Any quantum delineated as part of the quantitative process is in fact ‘continuous with this beyond; it consists precisely in being the other of itself, external to itself’ (SL: 191/21: 221). So, when quanta are delineated on a continuous magnitude, any one is immediately determined by another one sharing its limit, not absolutely separated from it.

Hegel's criticism of the abstractness of the logic of quantum applies to time. A quantum of time indifferent to its limit with another cannot be made intelligible; a limit must be shared immediately between them if time passes. We will soon examine the contradictions implied by this shared limit, particularly in terms of presence. For now, let us explain why a temporal limit would be conceived thusly. Between distinct quanta, a limit taking no time would pass immediately into another limit taking no time, meaning they would lack any real temporal difference as time passes. An unextended point could not hermetically separate these times because it has no distinct extremities at which they do not touch. Appealing to an intermediary void alongside or without such a point proves once again futile. If the void were nothing at all, the quanta would share a limit. If it were temporally extended, contradicting its temporal indifferentiation as the negation of time, the transition between quanta would take time. Not only would the problem of positing an immediate or shared limit between times remain; that time would likewise face the dilemma of being quantized or continuous, reproducing the contradictions above.

These ontological considerations confirm Hegel's phenomenological analysis of the now. A series of discrete units cannot be purely self-present as the present. We must think a change internal to those units and between them to explain time's passing. There must be a part of the quantized presence that is before and another after relative to that before. The quanta will have already included a past moment within itself that is no longer present or a future moment that is not yet present. That problem is irreducible up to the reduction of presence to a discrete, unextended point, which we have seen likewise fails to explain time's passing.

IV. The continuous magnitude of time and its contradictions

If time cannot be modelled as a discrete magnitude, it must be a continuous magnitude. As Hegel explains, ‘space, time, matter, and so on, are continuous magnitudes in that they are repulsions from themselves, each a flowing forth out of itself which is not, however, a going over, or a relating, to a qualitatively other’ (SL: 166/21: 190). Although Hegel is also wont to characterize time (and space) as both continuous and discrete,Footnote ¹⁵ we have examined how discreteness applies to a continuous magnitude in logical terms. Likewise, the discreteness of an extension of time lies in its infinite potential for delimitation—the ‘absolute possibility that the one may be posited in [time] anywhere’ (SL: 166/21: 190)—which does not contradict its homogeneity or make it into actually discrete units. Let us examine Hegel's account of presence given time's continuous magnitude. We will again understand the problem of magnitude in terms of a series of successive nows, that is, how time can pass from one to the next but still now, but also, following Hegel and our need to address the past and future, in terms of a durational extension formed from that series. Although it is again necessary to move beyond the word of Hegel's text, I argue that two interpretations of presence, as an extension and as an unextended limit, engender contradictions.

An account of presence as an extended, continuous magnitude falls into the contradictions we have already demonstrated in terms of discrete quanta. It does not matter whether we conceive a given duration as continuous or discrete: as an extension, a magnitude of time is never purely self-present because it includes a before and after within itself. By conceiving presence as an extension, we fail to explain a present that is not already as the past or yet to be as the future; yet, the passing of time must be occurring now, not no longer or not yet.

Although Hegel does not explicitly describe temporal points or limits as unextended in the Phenomenology of Spirit, the Philosophy of Nature, or the Science of Logic, the contradictions implied by an extension of pure self-presence leave us only with this option. Following this interpretation, as opposed to the potential limitation of any hypothetically given temporal extension, the now as unextended limit must be actual for time to pass. However, the challenge lies in explaining how the present can be an unextended limit in the first place. Following the phenomenological analysis of the now, the transition from future to past must be always happening and always differentiated in its happening as many nows. How might we reconcile the unextended nature of the now with the passing of time as a continuous magnitude, and hence a differentiated activity?

A temporal limit is, Hegel claims, quantitative. In the Science of Logic, Hegel distinguishes between the concept of qualitative limit as ‘completed, elapsed, and therefore of not continuing’ or ‘interrupted’ and quantitative limit as ‘self-surpassing’ (SL: 199/21: 230). Whereas qualitative limit reflects ‘a popular determination which sense-representation easily lets pass for a limit’, with delineated parts sharing a boundary to which each is indifferent, quantitative limit is ‘self-sublating being-for-itself’ or continuing into otherness (SL: 199–200/21: 230–31). Let us consider two ways in which time's passing might be explained in these terms.Footnote ¹⁶

The first possibility for conceiving this limit is with the now as itself the actively self-differentiating principle of time. That is, the always present limit would itself be the source of time's passing. But that unextended limit could do nothing to pass continuously or form a time series. It is inconceivable for time to pass as an unextended point or series of points, as we have argued above. An unextended point of time takes no time. It would therefore lack time's actively self-surpassing character. And if we imagine it to take time, we contradict its unextended nature. The now cannot take time without implicating a before and after within itself, hence determining it as an extension rather than the unextended limit it is meant to be. Although we have described the now as engaged in a continuous self-differing, we face insoluble contradictions if the passing of time requires that its principle be the now as an unextended limit.

The second possibility for conceiving this limit is as that through or from which a temporal magnitude passes. In general, whatever principle is determined as active, the unextended now would be immediately connected to any magnitude it limits. Indeed, the claim that an unextended limit or point would be hermetically separated from that magnitude fails for the reasons we have discussed above, namely requiring a void that collapses into nothingness or itself becomes a magnitude. Hence, two magnitudes divided by an unextended now would share it as their limit; paradoxically, this limit must be neither past nor future precisely by marking their transition.Footnote ¹⁷ With these general points in mind, might the continuous magnitude of time, conceived as the sole principle of time's passing, be ontologically co-primordial with the inert, unextended limit of the now? We might imagine this model of time like water running through a faucet, albeit if this faucet were unextended and the water were past and future time.Footnote ¹⁸

The first challenge to such a model of time concerns the reality of past and future time. If we accept Hegel's account of temporal change, the magnitudes of past and future time cannot exist in the same sense as they have existed or will exist. For Hegel, what no longer exists really passed through the present but is posited as not-being similarly to what will happen—but not yet—in the future. What exists in the past and future is ‘negative’, actually present only in subjective representation in memory or anticipation (hope, fear) of what is to come (PN: §259, §259R). Nevertheless, in another sense, for Hegel, whatever presently exists arises from the past and is pregnant (trächtig) with the future (PN: §259A); any particular now could not be that particular now except in so far as it is determined in the time series in relation to past and future time. That is, there are always a past and future in relation to the present. So, for the sake of argument, without engaging further complications or paradoxes, let us consider the possibility that past or (more controversially assuming temporal unidirectionality) future magnitudes are real in so far as they ground the present. Whether these non-present magnitudes, alone or together, could be the agents of time's passing is the question at hand.Footnote ¹⁹

There are at least two contradictions associated with attributing the past or the future with an activity allowing them to pass through an unextended now—contradictions to which Hegel's analysis of quantity provides no clear response. First, assuming time actually passes, we attribute past and future with reality in the present, meaning that the activity is itself neither past nor future. It bears repeating that time's passing cannot always only have been or will be—there would never be any actual passing—but must occur at some present. The proposal at hand is that the presence of time's passing belongs to past or future magnitudes, rather than the unextended limit of presence, but these are thus not present. This proposal implies a blatant contradiction. Second, it remains unclear how a continuous, extended magnitude can pass through or from an unextended limit if its continuity excludes composition by unextended points at which that passage is localizable.Footnote ²⁰ If a temporal magnitude passes through this unextended limit, must it not be fully describable in terms of a series of unextended moments that have been or will be present? If past and future pass through the now, yet the now is unextended and thus no constitutive part of their extension, how could their extension be attributed as a whole to it?Footnote ²¹ This proposal fails to explain how the now can be unextended yet is through time's passing, as that to which all temporal existence is attributed as having been or will having been present. The now would always be without being that at which anything temporally enduring exists.

We have again failed to explain presence in relation to time's passing. Following our failures to think time as either discrete or continuous, any reconciliation seems to be foreclosed. The paradox of presence has not been resolved with Hegel's quantitative logic.

V. The irresolvable paradox of presence

Although time exemplifies a quantitative logic, contradictions arise with the non-identity between the analysis of logical relations, abstracted from the concept of time, and the phenomenon of time. For example, the logical one is limited, not itself a limit. In contrast, after revealing the contradictions of conceiving it as an extension, we confront the now as a limit, albeit only to discover more contradictions. In addition, the logical relations between the many ones are intelligibly immediate or continuous in that the unfolding of the determinations of any one brings forth or implies another. In contrast, we have discussed the contradictions involved in thinking a transition between many unextended nows and also between extended magnitudes united by an unextended now. And these examples of divergence emerge from a more fundamental one. The one and many ones of Hegel's logic do not imply the uniquely temporal determinations of a transition from not-being to being and vice-versa, despite some almost inevitable temporal metaphorics in the logical analysis. Whereas the logical relations between the one and many ones do not involve the passing of what does not yet exist or no longer exists in relation to what now exists, time does. All our contradictions stem from this.

The question remains whether Hegel thinks that he has given a conceptually adequate account of presence by thinking the one and the many of time in quantitative terms. There is certainly no evidence to the contrary. Indeed, he nowhere discusses further contradictions in his account or the non-identity between logic and time. This is not to say that Hegel must have been unaware of these problems, only that he gives us no indication that he finds his resolution irresolvably contradictory or as a challenge to the conceivability of time.

Nevertheless, bracketing what Hegel might have remarked about our argument, there are two options available to the Hegelian who admits it, that is, that time implies contradictions and cannot be conceived otherwise to evade them. The first is to accept the contradictoriness of time but deny its philosophical significance due to the inherently contradictory nature of all reality. One might point to Hegel's emphasizing that contradictions pervade all thought and all reality to claim our paradox mundane. In his very discussion of quantity, we find a critique of Kant's ‘excessive tenderness for the world to keep contradiction away from it’ (SL: 201/21: 232). Why be concerned about the contradictions of time in particular?

Although we cannot develop an extensive analysis of Hegel's account of contradiction here, there is a difference in his philosophy between resolvable and irresolvable contradiction. In Hegelian terms, anything determinate can be put in contradictory terms despite being reconcilable in a common subject or some other respect. For example, the most basic contradiction pervading all determinate beings is that they are and are not, determinations that can be reconciled when we clarify the sense in which they are limited, thus how they are in one sense but are not in another, namely in having their limit transcended (or else containing a limit within).Footnote ²² Similarly, any meaningful logical judgment implies a contradiction between subject and predicate. The subject is but is not its predicate but can be both in different respects.Footnote ²³

While allowing for the intelligibility of such resolved contradictions, Hegel does not imply the truth of all contradictions, namely irresolvable ones rendering their subject unintelligible. Although contradiction is essential to the logical dialectic, so too is its sublation in a more encompassing truth or concept (SL: 745/12: 246). As Michael Inwood notes,Footnote ²⁴ Hegel also rejects contradictions in terms like ‘square circle’ or, to use Hegel's own example, ‘wooden iron’ (SL: 542/12: 45). Such irresolvable contradictions rightly appear to be, for Hegel, unintelligible and thus untrue.Footnote ²⁵ So, while Hegel might accept that the logical analysis of quantity and other aspects of worldly finitude imply resolvable or logically innocuous contradictions, the paradox of presence is such a threat and thus, I aver, unacceptable for reason—unacceptable, indeed, whatever else Hegel might say about contradiction. The rational inconceivability of time, a result of its unreconciled determinations, implies its impossibility or untruth.

The other possibility open to the Hegelian, the route of interpretation taken by McTaggart, would be to accept the contradictoriness of time but take that contradictoriness as an indication of time's unreality or, at least, its lack of full reality. McTaggart does not deny that, for Hegel, time appears but claims that this appearing must be somehow false or illusory for his system, having no true being due to its contradictoriness (albeit for other reasons than those we have discussed) (McTaggart Reference McTaggart1896: ¶¶141–42, 176). Interestingly, others characterize Hegel's interpretation of Zeno, for whom time proves unreal in our judgments about it despite the appearing of sensuous experience, in similar terms.Footnote ²⁶ In any case, according to this view, the failure of the logic of quantity to solve the paradox would be a mark not of a failure on Hegel's part but a simple reflection of its unreality. As such, there would be no ‘real’ paradox to be found.

However, the Hegelian who purports to resolve the contradiction by denying time's reality faces a serious rebuttal. Does denying the reality of time not contradictorily deny reality to something that appears, and thus is in its appearing?Footnote ²⁷ Hegel seems to address such a move at the beginning of his logical analysis of shine (Schein), criticizing sceptics who deny the reality of phenomenal appearing but nevertheless admit this appearing as an appearing, thus as something real (SL: 343/11: 246–47). The importance of our phenomenological consideration of time in its appearing is nowhere more evident than here. Our judgments are about this sensuous experience and the possibility of its appearing. It seems that we already admit its reality or being by addressing it in our judgments. In the phenomenological exercise of making our concepts adequate to the beings we seek to describe, presence is thought as both one and many ones, as both always present and a continuous self-differing. The paradox of temporal presence arises in our attempt to do justice to these two irreducible aspects of our experience; denying either of these aspects and their reconciliation would be abnegating the phenomenon of time's passing.

Although it extends beyond the scope of this article to develop a fully elaborated argument for the reality of time, this rebuttal engenders a series of difficult questions with which we will conclude. What does this paradox of presence indicate about the truth of our experience? If we cannot make sense of this experience without falling into contradiction, demonstrating its inconceivability, can it be real? If the tempting option for the philosopher is to expose experience as naïve, does experience not respond that it too must be explained in its very appearing? Would such an attitude toward the paradox of temporal presence not fail to address the very being of time's appearing in or as my experience? Must we not then confront this paradox as itself the truth of experience, thus of all temporal existence, despite having implied its impossibility? So long as time's passing is recognized as something, the paradox of presence cannot be so easily erased with the wave of a concept.