Time as a transition from a whole which is constitutable by each of many sets of parts to the set of parts that generates the shortest path?

Question

Summary:

• Any entity E which is constituted by extrinsically indiscernible parts A and B remains extrinsically the same, in all stages of the change, even if A changes to B and B to A (concurrently).

• More generally, an entity E which is constitutable by a set of parts {A, B} as well as another set of parts {C, D} remains extrinsically indiscernible even if A changes to C and B to D and vice versa.

• Accordingly, (McTaggart's) B-series may be described as consisting of multiple sequences with different beginnings (sets of parts) which are alternating and therefore are non-simultaneous but all constituting/causing the same whole (or equivalently simultaneous and indiscernible wholes).

• If causal is the flow of constitution (parts-to-whole direction), there are multiple causal routes each from any of the sets of parts to the whole. Thus, it seems appropriate to suggest that temporal is the flow of de-constitution (whole-to-parts) -- time as the transition from a whole which is constitutable by each of many sets of parts to the set of parts that generates the shortest path.

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SEP article on "Change and Inconsistency" discusses the notion that change involves some sort of Inconsistency. There seems to be a sense in which such an inconsistency is minimal: the entities (say E) that are constituted by parts undergoing change are to remain extrinsically unchanged during and after the change. It means that A changes to B if and only if

• B changes to A concurrently,
• A and B are extrinsically indiscernible (have identical constitutional roles)
• and for all entities E if A is a part of E, then B is a part of E.

If we take into account the stage during the change as well not just before and after the change, A changes to B if and only if

• there are C and D such that A changes to C before changing to B and B changes to D before changing to A, and that the whole constituted by A and B is extrinsically indiscernible from the whole constituted by C and D,
• and for all entities E if A is a part of E, then B is part of E and if C is a part of E, then D is a part of E.

The entity E before the change (constituted or caused by A and B) is extrinsically indiscernible from E during the change (constituted or caused by C and D) and after the change (constituted or caused by B and A).

If we translate this structure into the language of something like McTaggart's B-series, both pairs (A, B) and (C, D) are in the block "before" the block containing the entity E (since the pairs both cause E independently) but do NOT occur at the same time. However, the entity E caused by the first pair and that by the second pair are extrinsically indiscernible as if both effects occur at the same time regardless of which pair is at work at any given time. Thus, B-series may be described as consisting of multiple sequences with different non-simultaneous alternating beginnings (sets of parts) all converging to the same end (or equivalently, to simultaneous and indiscernible wholes).

if causal is the flow of constitution (parts-to-whole direction), there are multiple causal routes from each of the sets of parts to the whole. This may be described as the source of inconsistency. It seems that some consistency is gained if there is a shortest temporal path from the end of the b-series to its beginning (more precisely, one of its beginnings). That is to suggest that temporal is the flow of de-constitution (whole-to-parts) -- the transition from a whole which is constitutable by each of many sets of parts to the set of parts that generates the shortest path. This also seem to implicate that the temporal flow must deploy a different causal mechanism than the one operating in the causal routes.

(it is worth noting that in that (a, b) and (c, d) are "before" e in the b-series, "before" does not mean "earlier than").

In the context of the Laplacian universe (initial conditions + deterministic laws) this formulation is equivalent to the case in which the initial conditions are only critically determined at the beginning of time, enough to set off the temporal process, and are further determined (crystallized) towards the end of time, as causal routes are excluded from the set of candidates for the shortest path.

Answer 1

Quite the sophisticated question. I suspect there aren't a lot of people on this forum who speak McTaggert fluently and fewer who understand the mathematical physics of relativity and QM well enough to integrate it into a philosophical theory. I'm certainly not one of them, however, I recognize the prima facie validity of the question so maybe we can't tease from the SEP's article on Time something that resembles a response.

Let's see. The pith of your claim seems to be:

B-series may be described as consisting of multiple sequences with different non-simultaneous alternating beginnings (sets of parts) all converging to the same end (or equivalently, to simultaneous and indiscernible wholes). As a result, time may be thought as the transition from the end to a beginning which gives rise to the shortest path of the transition.

You clearly accept time as an anti-realist, and are discussing the topology of time (SEP) by exploring what seems to be B-series time relations that are defined as permutations of parts which are presumed extrinsically indiscernible. The way I read your question, you want to know if it makes sense to interpret time as the shortest path of permutations through this topology, to which I would say yes. In fact, it seems to my unschooled mind that you are describing a light cone for the following reasons:

1. Clearly the extrinsically indiscernibility implicitly invokes the concept of the observer who exists in the present.
2. Changes are events in the cone that are temporally ordered, and potentially physically distant from the observer.
3. You draw a distinction between causal flow and temporal flow, and that would be served by the distinction between the temporal axis and the world line of your entity and its constituents.
4. The indiscernibility of change serves as the generalization of specific changes that would be described by actual coordinates in Minkowski space allowing you to bind a set of possible worlds that might allow you to address the inherent unpredictability that arises from quantum uncertainty.
5. Your attempt to use a straight line to collapse the permutations of B-series sequences would be like combining intervals on the temporal axis to create a single interval that realizes a continuum.
6. Since you are looking to use observation as the starting point to work backwards to initial conditions, the past as part of the light cone is an actual calculation from that extends out from the present.

So, on the whole, I would guess yes. What you say is sensible since it seems to comport both with McTaggert's notion of B-series for characterizing time, and with models that mathematical physics provides to understand space-time. But, I'm not really well-versed in either so I'm just speculating hoping to spark an insight for you.