In the previous article in the C-theory series I have argued that McTaggart’s A-series and B-series fail to provide a complete and consistent description of time, but A- and B-theorists could still have a way out. In this article I conclusively reject the possibility of defining time in terms of A-series and/or B-series and I begin formulating the C-theory of time.
McTaggart maintained that we cannot define time in terms of past, present and future while also defining these as properties of events at different times, as that would amount to circular reasoning: a definition of time in terms of time. All we can justifiably claim is that an event is either past, or present, or future, and not, for example, that the present event becomes a past event, because becoming implies time which is yet to be defined. This gives rise to the question whether any future event, present event and past event can be justifiably regarded as the same event. Clearly there is an ontological difference between an event which is imagined as the future, remembered as the past, and one which is experienced as the present, notwithstanding all these scenarios being associated with the same nominal identity. When we objectify an event with an identity E, we are actually conflating the event of thinking of E as an anticipation of its occurrence, the event of perceiving E as it happens, and the event of remembering E as it has happened, each event involving an entirely different perspective on E.
The thesis that every event possesses contradictory qualities of being past, present and future suggests that McTaggart (1908, 468) may have regarded temporal relations between objects as of-the-same-kind as temporal relations between events, but there is a critical difference between objects and events: objects endure through change on a particular timeline; events are the change on that timeline. We can talk about object-histories and therefore about events only if we maintain that differentiation: “Histories have no historical significance in themselves but only in reference to the continuously existing entities which are the bearers of these functions.”(Ricoeur 1984, 205). No event can posses the combination of temporal qualities of being past, present and future unless it endures in time, but when we refer to an event as something enduring we implicitly ascribe object-identity to a duration between two reference states in the life-sequence of an object. A consistent reading of the A-series must not therefore enumerate temporal qualities of events per se but only the temporal status of constitutive states of a particular object. According to Broad,
“The change of events cannot be treated like the changes of things. (…) The changes of things are changes in Time; but the change of events or of moments from future, through present, to past, is a change of Time. We can hardly expect to reduce changes of Time to changes in Time, since Time would then need another Time to change in…”(Broad 1923, 64-65)
It is evident that neither the A-series nor the B-series can differentiate between particular objects but only between events, because identities and relations cannot be defined solely in terms of temporal tokens. Consequently, if the model of temporality is to remain consistent, all elements in the A-series or the B-series must refer to events of the same object rather than to events in general: “For it is not only a matter of being certain that we are speaking of the same thing, but also that we can identify several occurrences of the thing as the same.” (Ricoeur 1992, 32). By imposing the above restriction we ensure that the series remain homogeneous, that is, composed only of elements of the same kind, avoiding thereby the paradox that was interpreted by McTaggart as a proof of unreality of time. Let us now consider implications of declaring the first two series object-specific.
An object is said to be the same object only if it endures through change and over a duration, what presupposes and consolidates its past, present and future under one identity, but the same object must also be able to accommodate constitutive transformations, that is, it must exhibit a plurality of internal states and external relations that can be ordered in terms of before and after. Without change there would be no indexing references with which to delimit different points in time, and therefore no events. A genuinely singular, isolated ‘object’ which, by definition, is not engaged in any external relations cannot be said to endure in time; it is not even an object. Consequently, for change to be conceivable there must be a plurality of interrelated objects providing the context (situation) wherein a relationship between that which is measured and the measure of change could be established. The model of duration must therefore incorporate information identifying the relevant situations and the objects making up those situations. “The ‘laws’ of temporality determine not only a general sequence of before and after but also what comes before and what after.”(Lauer 1965, 115)
We are led to the same conclusion by following the argument from supervenience. It is a defining property of supervenience that change in supervening properties must correspond to change in base properties. If time is real because it supervenes on the constitutive properties of being then time-realists owe an explanation how change in the temporal properties is determined by change in the non-temporal properties of objects, and then, how could objects that are constitutively different be identical in their supervening, temporal properties. If, on the other hand, time does not supervene on the constitutive properties of objects and is not like any object in the world then it is unclear how it could be consistently counted as a real element of the world. Proponents of the A- and B-theories may respond that while temporal properties do supervene on non-temporal constitutive properties of being, no two real objects are ever identical in either constitutive or temporal properties – every object is a result of a unique constitutive sequence and thus can be also uniquely located in the temporal sequence. Alternatively, they may respond that temporal properties do not supervene on the constitutive properties of being but are themselves constitutive of objects. I argue, against the first response, that information about constitutive states is not contained in either the A-series or the B-series, therefore it does not formally establish a link between constitutive and temporal properties; against the second response, the same things cannot both be made of time and change in time, at least not without knowing how temporal and non-temporal constitutive properties of multiple objects are related. In both cases we must turn toward the C-series as the last remaining facility for defining a system of constitutive and temporal relations.
The original declaration of McTaggart’s C-series as simply an ‘order’ does not explicitly stipulate ontological structure but is intelligible only if understood in terms of a plurality of ordered and therefore related elements. If the C-series is to remain a proper series in its own right it must not be regarded as a temporal order, that is, as an order of events already in time, but as an order of atemporal elements constituting the relational structure within which temporality could become meaningful not as a condition of order but as its logical consequence. “The events must not only be registered within the chronological framework of their original occurrence but narrated as well, that is to say, revealed as possessing a structure, an order of meaning, that they do not possess as a mere sequence.”(White 1987, 5) This condition can be achieved by stipulating a constitutive order that would reflect the logical hierarchy of constitutive relations in a system of objects (a world). Such a logical hierarchy, according to McTaggart, could follow the logic of assembly of parts fractionally derived from the whole: a mereological hierarchy. “The parts of such a whole will necessarily have some relations to each other, and the fact that it has these related parts is what I mean by its having internal structure.”(McTaggart 1921, 181) This nicely dovetails with McTaggart’s definition of the C-series: “Of any two terms in the C series, one is included in the other, which includes the first, and by means of these relations all the terms can be arranged in one definite order.”(McTaggart 1927, 240) For example, one cannot quarter a circle until the circle is first defined on a plane, what presupposes definition of a plane as a section of space. Similarly, a cart can come into being only after invention of the wheel because the concept of a cart already incorporates that of the wheel, while every natural process inevitably implicates the entire constitutive order of nature: “all that exists, both substances and characteristics, are bound together in one system of extrinsic determination.”(McTaggart 1921, 151) I propose the following, informal definition of the C-structure of a world:
C-structure: an ontological hierarchy of a world, where every order of constitutive states of an object (C-series) is related to other constitutive orders, so that every change in a property of an object can be ‘measured’ in terms of constitutive changes in other objects.
The basic element of the C-series is a state of some relational property P (C-state-P) in the constitutive sequence of an object, which not only relates to the constitutive conditions in the same sequence but, more fundamentally, is defined by relations with other objects. Since every state in the constitutive sequence is logically conditional on some other state, the sequence is intrinsically directional and object-specific, doing all the ordering work of the B-series but also relating to other objects in the same world (I take being in-a-world as the sense of being an object). A basic C-structure undergoing constitutive change can be modelled as follows:
The positional C-series for the point a is fully, but so far uninterestingly, determined by the logical relation of ontological equivalence of points a, b, c, d belonging in a world abcd and by their positions relative to a, that is, by differences on the positional dimensions. Since all points (objects) are ontologically related (co-exist) in the C-structure there can be no ambiguity about temporal relations between their states, but before incorporating biaxial temporality into the model I will address some phenomenological worries about the present moment. I will attend to this task in the next article.
- Broad, C. D. Scientific Thought. London: Kegan Paul, Trench, Trubner & Co., 1923.
- Lauer, Quentin. Phenomenology: Its Genesis and Prospect. New York: Harper & Row, 1965.
- McTaggart, J. Ellis. The Nature of Existence (Volume I). Cambridge: Cambridge University Press, 1921.
- —. The Nature of Existence (Volume II). Cambridge: Cambridge University Press, 1927.
- McTaggart, J. Ellis. “The Unreality of Time.” Mind, 1908: 457-474.
- Ricoeur, Paul. Oneself as Another. Chicago: The University of Chicago Press, 1992.
- —. Time and Narrative (Volume 1). Chicago: The University of Chicago Press, 1984.
- White, Hayden. The Content of the Form. Baltimore: The Johns Hopkins University Press, 1987.