Abstract
In his seminal work, McTaggart (Mind 17(68):457–484, 1908; The nature of existence, Cambridge University Press, Cambridge, 1927) dismissed the possibility of understanding the B-Relations (earlier than, simultaneity, and later than) as irreducibly temporal relations, and with it dismissing the B-Theory of time, which assumes the reality of irreducible B-relations. Instead, he thought they were mere constructions from irreducible A-determinations (pastness, presentness, and futurity) and timeless ordering relations (his C-Relations). However, since, philosophers have almost universally dismissed his dismissal of irreducible B-relations. This paper argues that McTaggart was correct to dismiss the possibility of B-relations, and that would be B-theorists should be C-theorists and its concomitant commitment to the unreality of time. I do this by first elaborating C-Theory, noting that B-relations appear indiscernible from C-relations on close examination. This establishes an onus on B-theorists to distinguish B-relations from C-relations by elaborating the distinctively temporal character of the former. I then present a problem for the possibility of accommodating temporal character in B-relations. Following this, I question from whence derives our sense of the temporal character that purportedly resides in the irreducible B-relations. Finally, I extend the challenge against irreducible B-relations to a series of irreducible abstract temporal relations—so called Ersatz-B-Relations—modelled on them.
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Notes
Yagisawa (2009, p. 52) makes a similar point.
Michael Dummett was also making this point when he wrote: ‘To say that time is unreal is to say that we apprehend relations between events or properties of objects as temporal when they are not really temporal at all. We have therefore to conceive of these events or objects as standing to one another in some non-temporal relation which we mistake for the temporal one’ (1960, p. 503).
Thanks to an anonymous referee for this journal for raising the following objection.
Whereby the subscript of a moment Gn indicates the quantity of green objects at that moment.
Though there is much debate about how these two theses ought to be refined, Brock and Mares’ characterisation should suffice for current purposes.
A referee for this journal has encouraged me to make the case that the geometry of Minkowski Spacetime, that underlies relativistic physics, supports C-theory, rather than B-theory, despite being a common case of appeal by B-theorists (cf. Mellor 1998, Ch. 5, §§. 5–6; Mozersky 2000; Sider 2001, Ch. 2, §. 4). Firstly, I should note that my case for preferring C-theory over B-theory does not rely on relativistic physics, and is certainly not diminished by relativistic physics. But I think that the referee may be right in their suggestion that Minkowski Spacetime suggests C-theory, rather than B-theory. In particular, B-theorists commonly speak of B-relations being relative to inertial reference frames. However, though it is sometimes helpful to imagine such relative (to an inertial reference frame) temporal orderings of things, spread out across a Euclidean space, that presentation is strictly inaccurate, since such relative temporal orderings are not features of the Minkowski Spacetime, but rather constructions out of the Minkowski Spacetime. This is why Tim Maudlin wrote:
It is commonly said that in Relativity, the notion of simultaneity is relative to an observer or to a state of motion. We can see the grain of truth in this characterization, but perhaps it also does as much harm as good. The key claim of Relativity is the nonexistence of simultaneity as a real physical relation among events (2012, p. 92).
If this is the correct way of understanding Minkowski Spacetime, where there are only “spacetime” relations, and no “purely spatial” nor “purely temporal” relations, then I think the referee is indeed correct in suggesting that relativistic physics lends its support to C-theory rather than B-theory. The constructions of the relative (to an inertial reference frame) temporal orderings would be mere conventions in the sense suggested by Dummett in the passage quoted above.
A referee for this journal has enquired about the bearing that this preliminary discussion of internal and external relations has on the accommodation problem that I develop throughout Sect. 2. Though they would be right to think that the problem could be developed without reference to that distinction, I believe that the distinction helps to focus on what it is about B-relations that makes accommodating their temporal character so problematic. Furthermore, by situating the accommodation problem as a special case of a more general problem, I believe that I strengthen the case through the analogies, with similarly problematic theories, that the general problem allows me to draw.
We would not want to say that those properties inherit their character from further higher-order properties, since that would start an infinite regress where the source of character is constantly deferred.
I exclude simultaneity here because I assume it is characterised by a lack of temporal character (see Sect. 1).
Note that the act of experiencing isn’t necessarily an act of attending, since we may be unaware of some aspects of the experience. Think, for example, of how we sometimes attend to things, before unnoticed, when reflecting back on old experiences.
For an elucidation of what real metaphysical change consists in, see Robert Pezet (Pezet 2017a, §3).
Note, that experiential presentism does not obviously require full-blown Presentism—the thesis that all and only present things exist. For instance, with respect to the Moving-Spotlight Theory, Bradford Skow (2015, Ch. 10 and §12.2) develops a version whereby things are only conscious, alive, and otherwise “causally active”, when present, whilst Ross Cameron (2015, Ch. 4) defends the more extreme view (which Skow also toys with) that all recognisable characteristics of things change when the thing’s particular age ceases to be present. Similarly, Peter Forrest (2004, 2006) and Graeme Forbes (2010, Ch. 3, 2016) defend a version of Growing-Block Theory where conscious experience is restricted to the present. These views would all be versions of experiential presentism, if not full-blown presentism—though there are doubts whether such accounts of time are coherent at all, given that they are all committed to the doubtful claim that there are past/future events which are never present (cf. Pezet 2017b).
There is no obvious reason why a growing-block theorist cannot also accept an irreducible ersatz-B-series, perhaps to offer some form of surrogate for the absence of a future reality on their theory. Though I know of no instances where this development has been attempted.
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