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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.

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.

Morteza
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  • In logic, and inconsistency is when your premises lead to both P and ~P for some proposition P. I don't think the problem you are suggesting leads to an inconsistency. At most it leads to the observation that if something happens to switch parts, it may not be possible to be able to tell just from examining the whole and parts at a later time. – David Gudeman Apr 14 '23 at 00:24
  • Is a brick constituted by two extrinsically indiscernible parts? – Boba Fit Apr 14 '23 at 00:25
  • @BobaFit, Perhaps not an ordinary brick. But when an electron and a positron collide, they annihilate, and so do other pairs of fundamental entities. I think this suggests an entity may be decomposed in multiple ways. – Morteza Apr 14 '23 at 01:25
  • @DavidGudeman, the inconsistency in question is related to something like this: an entity (event/state/...) has two different causes. Therefore, until it is determined which one, both causes are at work (P and ~P) but not at the same time (they alternate). – Morteza Apr 14 '23 at 01:35
  • @Morteza If you want to go there, you can take spin 1/2 particle and say that it can be prepared to be in a superposition of spin up and not spin up. We can even have that spin change over time in ways that alter the combination of spin up and not spin up we have. Is that related to what you have in mind? – Frank Apr 14 '23 at 02:19
  • @ Frank Exactly. In the context of Laplacean model (initial conditions plus deterministic laws) this is equivalent to say that initial conditions are only critically determined at the beginning only to set off the temporal process and are more completely determined only as time progresses. – Morteza Apr 14 '23 at 03:48
  • @Morteza I am not sure about "more completely determined only as time progresses" though - the case I was thinking about was just time evolution of a pure state for a two level quantum system, but the initial conditions would not "be more determined as time progresses"? – Frank Apr 14 '23 at 03:58
  • @Frank Actually what I meant was that once there is a new change in the system, the intial conditions are more fully determined. – Morteza Apr 14 '23 at 04:18
  • I have to say that I am struggling to understand the meaning and point of your question. Can I suggest that you provide an example to illustrate the meaning of your first sentence, and some explanation to justify the 'Thus' that begins the second? – Marco Ocram Apr 14 '23 at 06:52
  • @MarcoOcram I hope the following is helpful. The basic question is whether it makes sense to say that whatever inconsistency is involved in change has to be minimal. For instance, according to such a criterion, if A changes to B, then either B changes to A or, less trivially, there are C and D such that C changes to D, B to C, and D to A and that the pair A and B and the pair C and D constitute (cause) an entity E that always remains extrinsically indiscenible. A and B constitute E before the change and after the change. C and D constitute E during the change. – Morteza Apr 14 '23 at 11:18
  • @MarcoOcram if we translate this phenomenon into the language of B-series, both pairs are BEFORE the entity E (since they cuase E) but do NOT occur at the same time. The entity E caused by the first pair and that by the second pair are indiscernible, which means both effects occur at the same time regardless of which pair is at work – Morteza Apr 14 '23 at 11:20
  • I still cannot follow you. Your question and your subsequent comments are extremely ambiguous. It would be helpful if you could spell things out step by step, and illustrate your question with concrete examples. – Marco Ocram Apr 14 '23 at 14:06
  • In reality, how does x change into y and y change into x? Please give an example of what you have in mind here. – Marco Ocram Apr 14 '23 at 14:08
  • Once again. Is a brick constituted by extrinsically indiscernible parts? – Boba Fit Apr 16 '23 at 22:52
  • @Boba Fit, this is a shot at logical analysis, investigating a theoretical plausibility, not a phenomenological investigation, I must confess. – Morteza Apr 17 '23 at 00:07
  • @Boba fit, there is a sense in which one can say 0 is constituted by x and -x. The notion of interest is that some sort of _symmetry_ must be involved to minimize the inconsistency involved in change. – Morteza Apr 17 '23 at 00:27
  • I am afraid that your question does not make literal sense. I would like to engage with your idea, but in its current form your post is too ambiguous. Even your headline question is hopelessly vague. When you say that time 'goes' what do you mean? What is the 'whole' you are talking about? Do you mean the whole of time? etc etc. Please try rephrasing the question in plain unambiguous language. – Marco Ocram Apr 25 '23 at 06:06
  • @MarcoOcram Once I understand what the worst part of my presentation is, I will edit. 'goes' merely indicates time has a beginning and an end. The whole in question is what there is before the first temporal change. In other words, **if** there is a whole that constitutes the beginning of time and causes a temporal phenomenon, it must be the case that the final temporal effect (a privileged set of parts) causes the whole instantaneously, though the set is not the only one capable of doing so. Because the analysis is in some ways circular, I hope I am not trivializing your question. – Morteza Apr 25 '23 at 15:26

1 Answers1

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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.

J D
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  • This is a guess. If you want to try to clarify, hit me up. It's an interesting question. – J D Apr 17 '23 at 08:59
  • it would be very illuminating to figure out how considerations about QM and relativity (both of which I am mostly ignorant) bears on the discussion here. (6) is right on the point. But I have some hesitations about how to think of (5) and to less extent (1). – Morteza Apr 17 '23 at 15:08
  • The entry point to include notions like resence, simultaneity and time interval ... that I had in mind is temporal subdivision. All events are both before and after the first temporal change until some event is only before the change and some event only after, i.e., all events are present until some event is past (securing a place in the shortest path) and some event is future (the causal segment being excluded from the candidate paths). So there is a notion of ultimate presence (not the phenomenal one) that is realized at the end of time in the narrowest window of simultaneity. – Morteza Apr 17 '23 at 15:20
  • @Morteza: resence? Recents..? – CriglCragl May 24 '23 at 21:33
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    @CriglCragl I meant to say "present". – Morteza May 25 '23 at 02:28