J. M. E. McTaggart (1866-1925), a Cambridge metaphysician, introduced a distinction between three kinds of temporal series: A, B, and C.
The A Series: Past – now – future
The B Series: 43 BC – 2017 AD – 2067 AD
The C Series: Event 2 is between events 1 and 3, with 2060 years between 1 and 2, and 50 years between 2 and 3.
These three types of series correspond to three kinds of propositions:
A-propositions: Caesar lived 2060 years in the past. The first female US Presidency is in the future.
B-propositions: Caesar lived in 43 BC, Caesar lived before the American Civil War, the Civil War ended before WWI,
C-propositions: the Civil War occurred between the time of Caesar and the time of WWI.
We can use the distinction between A and B propositions to draw a distinction between kinds of facts:
A-facts: facts that are structurally isomorphic to A-propositions; facts including presentness, pastness or futurity as properties
B-fact: any fact that isn’t an A fact
Irreducible A-fact: A-facts that are not wholly grounded by B-facts.
Finally, we can distinguish two theories of time: A and B.
B Theory: all propositions are made true by B facts.
A Theory: some propositions are made true by irreducible A facts.
B Theorists either (i) deny the existence of A-propositions (insisting that all statements and thoughts have B-propositions as their content), (ii) insist that each A-proposition is made true at each moment by a B-fact, or (iii) insist that all A-facts are reducible (wholly grounded by) to B-facts. Option (iii) requires that the same event can be present, past, and future, treating the three A-facts as just three different guises of the same underlying B-fact.
Therefore, there are two key metaphysical differences between A and B Theories:
- Indexicalism (Egalitarianism) vs. Absolutism (Inegalitarianism)
- Real, non-perspectival passage of time itself vs. passage of time as an illusion.
B-propositions and facts have two corresponding essential characteristics: (i) they treat all times on a par, and (ii) they are themselves unchangeable in truth value (in the case of propositions) or in existence (in the case of facts). But these are in principle separable characteristics—there are at least two kinds of A-propositions and A-facts (three, if we count the kind of lacking both characteristics): those that depend on the existence of a unique present, and those that are changeable in truth-value/existence. So, there are at least three versions of the A-theory: a standard version, and two deviant versions:
- Standard A theory. There is a uniquely privileged present, and which time is present is changeable.
- Deviant A theory, type 1 (The Immobile Present). There is one, uniquely present moment of time, and its character as present is unchangeable.
- Deviant A theory, type 2 (The Moving Sidewalk). Presentness is a universal attribute of A moments, but nonetheless each A moment is in constant movement relative to the B series.
The Immobile Present has at least one weird and presumably unacceptable consequence: namely, it will have to be false that past events were ever present or future events will ever be present. MacTaggart would have argued that we cannot make sense of B-relations without a moving present.
The Moving Sidewalk has two sub-varieties, depending on whether we think of the future as linear or branching. The Branching Moving Sidewalk gives us a kind of temporal multiverse, in which every possibility is eventually actualized (with probability 1) by some A moment. It would result in something very like a generalization of the Many Minds interpretation of Everettian quantum mechanics (which we will discuss further in a later seminar).
The Linear Moving Sidewalk seems to imply a kind of logical fatalism: the future path of each A moment is pre-determined by the path taken by more advanced A moments.
What are the “A moments” that move through the B series on the Moving Sidewalk model? They could be Thomas’s acts of existence. We might suppose that my own present consciousness of the flow of time is tied to the movement of one particular act of existence. We’d also have to suppose that there are more advanced and retarded acts, each currently attached to me at different points in the B series. Does that mean that I exist many times over? In a way, but there’s room here for the Aristotelian to insist that the various modes of existence are analogically rather than univocally related to each other. My advanced self currently experiencing 2024 exists in a way that is only analogous to the way that my current Oct. 3, 2023 self exists.
Any A Theory other than the Immobile Present introduces a kind of meta-time or hyper-time. In addition to the ordinary dates in the B series (conventionally labeled by years, months, dates, and so on), there are datable events at a meta-level. In standard A theory, there is the event of the Present being located sometime in 2022. This event isn’t really an event in 2022 (like the midterm elections), but an event that occurs to 2022. However, it is easy to miss this distinction in standard A Theory, since that entails an isomorphism (1-1 correspondence) between meta-dates and ordinary dates. Each meta-date assigns the unique present to a unique B date.
This 1-1 correspondence breaks down in the case of the Moving Sidewalk models. Each meta-time corresponds to the coincidence of every act of existence with some B moment, and so no unique B moment is picked out as “the present.” The idea of meta-time is somewhat worrying, even for the standard A theory, since it raises the specter of an infinite regress of meta-meta-meta-…. times. If one level is too static, why isn’t the two-model still unacceptably static? The best A theoretic answer would be to insist that A-properties are metaphysically fundamental, and so-called “ordinary times” are all definable in A-terms.
The Moving Sidewalk model shares with other versions of the A theory one advantage over the B Theory: it can treat our experience of the passage of time as veridical, while all B Theories must count this experience as illusory. The A Theory forces us to treat one direction through time as uniquely privileged (the movement into the future, or the movement of the future toward us), as an order that can serve as the paradigm for all other orders (as Kant argues in the First Critique). This is more than just a matter of locating a kind of asymmetry in the temporal order. Even if we find a relation that is asymmetric, in other cases we can still order the relata in either direction, counting different things as ‘prior’ or ‘posterior’. Only in the case of time is only one order conceptually permissible.
B Theorists, especially Aristotelians, could argue that it is the directionality of causal powers and the subsequent teleological ordering of processes that gives us a real and un-discountable kind of priority of the earlier over the later. That seems right, but is it sufficient to explain why I must experience the times in my life in only one order? And can real causation be a relation between two eternal beings? Doesn’t it have to involve the coming-into-existence of some things (substances and accidents) and the going-into-nonexistence of others? Can the B Theory take these experiences as veridical? (More about this in section 5 below.)
One more advantage to the Moving Sidewalk model: it provides an answer to J. J. C. Smart’s challenge to the A Theory: how fast does time pass? The standard A Theory seems forced to say that the velocity is either undefined or necessarily fixed at 1 second/second, both of which seem to undermine the idea that this is ‘motion’ in any normal sense. However, in the Moving Sidewalk model, different acts of existence could be moving relative to the B series at different rates (they could, for example, be constantly accelerating as they move forward). Consequently, we can meaningfully measure the velocity of time now with the velocity of relatively retarded or advanced acts of existence.
The Analytic Thomist 