In the previous article in the C-theory series I have argued that time has two logical dimensions: the ‘timeline’ of causal succession of events and the ‘timeline’ of evental identity-formation. The first timeline corresponds to changes from one evental identity to another; the second timeline corresponds to changes in the identities of events. These two dimensions can be adequately defined within the theoretic limits of McTaggart’s (1908) model, whose A-series coordinates the historical dimension in terms of past, present and future, the B-series defines the sequence of evental succession in terms of before and after, and the C-series signifies order. In this and the next article I argue that neither the A-series nor the B-series are sufficient to construct a consistent model of temporality for being because change (a constitutive property of time) supervenes on the constitutive properties of being. Before tackling the question of supervenience I will examine some preliminary worries associated with A- and B- theories of time.
Numerous attempts have been made to account for the A-series in terms of the B-series and for the B-series in terms of the A-series in order to demonstrate superiority of one theoretic approach over the other. Mellor (1998), a leading proponent of the B-theory of time, defines the meaning of past, present and future according to the following B-theoretic formula:
‘<e> is past’ is true at any time <t> iff <e> is earlier than <t>
The proposed expression is problematic in view of McTaggart’s theory as it attempts to define the terms of a time series in terms of time per se – an impasse that McTaggart took pains to evince: “This explanation involves a vicious circle. For it assumes the existence of time in order to account for the way in which moments are past, present and future.” (1908, 468) In defence of Mellor, the alleged circularity is not necessarily vicious and can be (at least superficially) circumvented by assuming that does not signify time per se but, following Heidegger on ‘datability’ (1988, 262), an event standing-in as a temporal indexing reference:
‘<e> is past’ is true at any event <e’> iff <e> is earlier than <e’>
The preposition ‘at’ in the above statement signifies simultaneity, which can be expressed in strictly B-theoretic terms as ‘not before and not after’, but for simplicity I will assume that the notation ‘at’ signifies just that. Despite the adjustments the present formula is still too general to define the actual past, that is, the past which is immediately relative to the present moment of lived experience, since it allows us to assign the quality of being ‘now’ to any event in the B-series. The term ‘now’, which is assumed here to be synonymous with ‘the present’ of the A-theory, does not have a direct counterpart in the B-theory but, following Mellor (as reformulated above), can be expressed as follows:
‘<e> is present’ is true at any event <e’> iff <e> is at <e’>
The event <e> is thus defined as being present if and only if it is simultaneous with <e’>, but there is no indication whether the two events are simultaneous ‘now’. Mellor (1998, 5) suggests that <e’> can be made coincidental with the present by definition, but such a measure either conflicts with experience – by making the present arbitrary – or implicates a primitive element from the A-series and thus violates theoretic exclusivity of the B-theory. Without independent means of identifying the present there can be no purely B-theoretic account of change, because change takes place exclusively in the present; not in the generalised sense of something being present at an arbitrary time <t>, what is synonymous with simultaneity in general, but with the contextually unique consciousness of an event. Every statement based on the form ‘<e> is past’ is true at time <t> can be uttered exclusively in the present, including statements referring to the present memory of a past statement. In any case, the auxiliary verb <is> establishes the present condition associated with consciousness of an event, be it the present utterance of a statement or a memory thereof. According to Sellars:
“‘now’ is to be understood in terms of ‘is’, not ‘is’ in terms of ‘now’ construed as a basic demonstrative. Or, more accurately, this is the account of ‘now’ we must give if we are to construe our language as one in which the basic logical individuals are changeable things.” (Sellars 1962, 553)
In other words, the utterance is token-reflexive in the original sense of the term, as defined by Reichenbach:
“An act of thought is an event and, therefore, defines a position in time. If our experiences always take place within the frame of now that means that every act of thought defines a point of reference. We cannot escape the now because the attempt to escape constitutes an act of thought and, therefore, defines a now. (…) This fact is expressed in grammar by the rule that every proposition must contain a verb, that is, a token-reflexive sign indicating the time of the event of which one speaks; for the tense of the verb has a token-reflexive meaning.” (Reichenbach 1971, 270)
To assign the ‘now’ to an arbitrary event by definition would be as nonsensical as identifying myself with an arbitrary object by definition (a proposition which Mellor op. cit. explicitly denies), because insofar as the present is the temporal locus of being it is equivalent to the sense of ‘I am’: “What occurs now is any event that is contemporaneous with the moment when I speak; reduced to itself, the self-reference of the moment of speech is simply the tautology of the living present.” (Ricoeur 1992, 53) It follows that without the present there can be no ‘I’, or, for that matter, any identity. If, on the other hand, identity were assumed intuitively, by relying on the immanent presence of lived experience, such an assumption would exceed the scope of the B-theory. The absence of the primitive ‘present’ in the B-theory results in a seemingly paradoxical situation, where the events ordered in terms of before and after do not actually happen but are nonetheless asserted as existent. I therefore agree with McTaggart that without the primitive elements of the A-series there could be no consciousness of change, no possibility of transition from one event to another, no contextual unity, but only a series of discrete and eternally fixed events in a timeless universe.
A strict B-theory inevitably results in infinite regress associated with the question of evental positioning of the present:
<e> is present if <e> is simultaneous with <e’> and <e’> is present; <e’> is present if <e’> is simultaneous with <e”> and <e”> is present…
Without the A-theoretic truth-maker associated with consciousness of an event there would be no possibility of evental correlation between multiple observers, no temporal nexus upon the plane of being and therefore no simultaneity or communication. The B-theory indeed does require knowledge of the present and Mellor (1998, 47) concedes that “we cannot do without A-beliefs”, but that implies that the B-series alone does not satisfy the practical demands of lived experience.
Another problem faced by the B-theoretic account of change is the lack of ontological continuity. Granted that “change needs identity as well as difference” (Mellor 1998, 89), the difference between ‘before’ and ‘after’ is not synonymous with change unless it applies to the same, enduring identity, but since there is no formal continuity of being in the B-theory there is no way of determining whether consecutive differences apply to the same identity. Since I intend to focus on the question of the ontological structure of change in the next article I will not pursue this matter any further here, but will instead proceed to consider the merits of the A-theory.
The main objection to the A-theoretic account of time is its lack of native evental order: an event which belongs to the past or to the future has no strict A-theoretic priority or antecedence with respect to any other past or future event, respectively. Furthermore, it is not at all evident that the future is after the past, because we do not perceive, remember or imagine the past as past, or the future as future, but only as the present thought of a nominally past or future event: “we never directly experience future or past events, nor do we ever perceive a passing of events into the present from the future, or their departure out of the present.” (Ingthorsson 2013) On the other hand, we do experience temporal order in terms of ‘before’ and ‘after’ because these are the two defining limits inherent to the very meaning of change, and therefore of experience. Statements which assert that an event ‘will be present’ or ‘was future’ actually involve both A- and B-series, because any non-present tensed expressions derive from the B-series: ‘will be’ is equivalent to ‘ the present’, while ‘was’ is equivalent to ‘ the present’. Were we to remain adamant to interpret tensed expressions as strictly A-theoretic by formulating them as ‘of the future’ and ‘of the past’, we would end up with a duplicitous set of temporal propositions in the same sentence, for example, ‘will be present’ would become ‘of the future of the present’, or, taking the logical reduction even further, ‘of the not-present of the present’. Tensed expressions must therefore be disassociated from the A-series in order to avoid duplicitous and possibly contradictory combinations of tensed propositions. The problematic application of tensed expressions to the A-series has been emphasised in (Mellor, 1998, 73) by formulating statements containing two or more tensed propositions stacked together, for example: ‘e will have been present’.
Any evental ordering by means of secondary tensed expressions – in terms of being further in the past or nearer in the future – involves application of the B-series (Le Poidevin 2004). Consequently, if the A-series is to be retained as a primitive series in its own right it must not be considered as a temporally ordered series, but then it is clearly inadequate as a self-standing model of temporality. On the other hand, it cannot be dispensed with because it stipulates the present as the threshold between ‘not yet (and perhaps never)’ and ‘already (and once and for all)’, that is, it contains the temporal locus of change.
At this point it may seem that A- and B-series must be combined to account for temporal order, change and simultaneity, but I am yet to consider the question of duration. The B-theoretic model of duration may be expressed as follows: there are n events of type c after the event-a but before the event-b, so the period of time between a and b is n units of c. But such a model gives no indication whether the events being compared are temporally compatible. Problems could arise if, for example, the events of type c took place in a dream but a and b signified the event of falling asleep and the event of waking up, respectively. Clearly, duration cannot be determined according to a measure of temporally inconsistent or ontologically incompatible sets of references. Ultimately, even in a temporally consistent frame of reference there is no strictly B-theoretic way of defining duration for c-type events without falling prey to infinite regress.
Mellor (1998, 3) suggests another possible source of inconsistency, namely, the context of modern cosmology, where “simultaneity at a distance is relative to an arbitrary choice of reference frame”, but the assumption of simultaneity established between observers of ‘the same’ event may already be arbitrary at any distance and in any reference frame. Evental correlation among multiple observers certainly poses a problem that must not to be overlooked: if one observer experiences only the event-a, while the other experiences only the events c and b, the full temporal sequence a-c-b must be inferred by indirect means, for example, by referring to states of the same public clock which are deemed simultaneous with a, c and b. While symbolic conventions are employed to mediate temporal correlation between two or more observers, every such convention employs some constitutive order of relations as well as the criteria of ontological equivalence whereby it can be determined that both observers have in fact observed the same clock. The possibility of temporal miscorrelation between observers was indeed considered by McTaggart as evidence of the unreality of time.
The problem of evental correlation is not limited to the B-theory but applies to the A-theory also. The A-theoretic formula for duration can be expressed as follows: there are n events of type c in the future of the event a but in the past of the event b, so the period of time between a and b is n units of c. The assumption that events c are between a and b already presupposes evental order, and that, as noted earlier, is the domain of the B-theory: the intuitive convention that the future becomes the present becomes the past is B-theoretic. But without order there can be no configuring of a temporal narrative, and thus all past (or future) events are simply lumped together, temporally undifferentiated from one another if considered in strictly A-theoretic terms. Ultimately, similarly to the B-theory, there is no strictly A-theoretic way of defining duration for c-type events without infinite regress.
Considering the worries identified above it seems that a consistent model of temporality cannot be accomplished even by combining A-theoretic and B-theoretic properties, failing to account for duration and for a unified time across an integrated system of observers and objects, but A- and B-theorists may still have a way of avoiding these problems. In any case, we are yet to consider the third item in McTaggart’s argument against the reality of time, the C-series. I will attend to this task in the next article.
- Heidegger, Martin. The Basic Problems of Phenomenology. Bloomington: Indiana University Press, 1988.
- Ingthorsson, R. D. The Elusive Appearance of Time. In Johanssonian Investigations, by C. Svennerlind, J. Almäng and R. D. Ingthorsson, 304-316. Frankfurt: Ontos Verlag, 2013.
- Le Poidevin, R. A Puzzle Concerning Time Perception. Synthese, 2004: 109-142.
- McTaggart, J. Ellis. The Unreality of Time. Mind, 1908: 457-474.
- Mellor, D. H. Real Rime II. London: Routledge, 1998.
- Reichenbach, Hans. The Direction of Time. Berkeley: University of California Press, 1971.
- Ricoeur, Paul. Oneself as Another. Chicago: The University of Chicago Press, 1992.
- Sellars, Wilfrid. Time and the World Order. In Minnesota Studies in the Philosophy of Science, by Herbert Feigl and Grover Maxwell, 527-616. Minneapolis: University of Minnesota Press, 1962.