Possible Both
January 23, 2010 — 8:23

Author: Michael Almeida  Category: Uncategorized  Comments: 13

Lots of people have the modal intuition that there are infinitely many better and better worlds. I have it, for what it’s worth. I also have the intuition that there is a best possible world. Both seem possible, so both seem true. The good news is that we can have our cake and eat it, too. We can satisfy both intuitions.
Claim: If there are infinitely many better and better worlds, then there is (also) some best (unexceeded or unsurpassed) world.
Some assumptions. Let the overall intrinsic value of a world W be the sum of the intrinsic values of each temporal stage S of W. Let the intrinsic value of any stage S depend exclusively on the intrinsic facts in S. Finally, assume that for any non-overlapping stages S, S’ in any world W, the intrinsic facts in S do not logically entail the intrinsic facts in S’. Effectively, we are assuming–as seems reasonable–that God can terminate any world W at any temporal stage S of W.
How would the argument go that, even if there are infinitely many improving worlds, there must be a best world? For any arbitrarily chosen world Wn in the infinite sequence, there is a most valuable temporal stage Sn+ of Wn. A best stage S+ in W is a stage whose intrinsic value is positive and unexceeded by any other (overlapping or non-overlapping) stage in W. There is then a set B+ of the best stages of each world in the infinite sequence. We know that no temporal stage S of any world W entails any (non-overlapping) stage (recall that God can terminate W at any S). So we know that there is a world W+ composed of the stages in B+. The intrinsic value of W+ is itself unexceeded by the value of any world W in the infinite sequence (recall that the intrinsic value of any world W is the sum of the intrinsic value of its temporal stages). That concludes the proof.
So, if there are infinitely many improving worlds, there must be some world that is unexceeded in intrinsic value. There is then some best possible world.

Comments:
  • Ted Poston

    Hi Mike,
    Interesting post! Two quick questions: (1) what’s the justification for thinking that this method of aggregating the best segments of worlds produces an overall best result? Suppose there are infinitely many bad worlds whose best segments are not good. Then it looks like we need an argument that the aggregation method you use will yield a world of supreme value. For example, it looks like the aggregation method would include some segments that are worse than any segment of some other “almost best” world (I hope you can parse that!). (2) What if the temporal state that is ‘best’ for a world has no finite limit? What if there are several worlds like this (or, worse an infinite number of such worlds)?

    January 24, 2010 — 8:32
  • Mike Almeida

    Hi Ted,
    The idea in aggregating is that if S is a best stage of a world W, then S has positive value and there is no overlapping or non-overlapping stage S’of W that exceeds S in intrinsic value. So, I think I avoid the problem of bad worlds with all bad segments. Any best segment has to have positive value. I’m effectively taking the greatest on balance positive segments from each world, and leaving the remaining segments.
    Your second question is not easy to answer. Suppose we have a world W such that, for each segment S of W there is another (overlapping, I assume) segment S’ whose overall positive value is greater. In that case the best segment S or W is such that S = W. Let me know if I begged questions here.
    I’m talking about temporal segments, so it really matters where the positive value shows up in a world. A world in which positive value is fairly evenly distributed over temporal segments might be such that the overall best segment in that world is not so great. Worlds where positive value is concentrated in a few temporally contiguous segments will have a much more valuable overall best segment. Weirdly, the latter world might be much worse overall. The best world that I wind up with is going to be a big world and (I think) better than any possible multiverse. The multiverse approach doesn’t fly, anyway. But I just don’t know whether the best world will be much bigger than most worlds, at least in terms of moments of existence.

    January 24, 2010 — 8:59
  • Ted Poston

    I’m not sure I follow your response to my second question. Do that the best segment in a world will have finite duration? I wonder if it makes sense to think of a best segment as infinite in extent; e.g., something like a supreme event that stretches on and on (i.e., no finite part of which is better than the rest).
    Re the first question, what about its variant which perhaps I didn’t express clearly the first time. So there’s a world that has a best segment and it has positive value, but there’s another world (perhaps infinitely many) whose least good segment is far better than the first world’s best segment?
    Here’s another question about the aggregation method. Suppose the best segment of world 1–call it the Saints world–is where Reggie Bush runs for the winning touchdown in the NFC Championship game. And suppose the best segment of world 2–the Vikings world–is where Adrian Peterson runs for the winning touchdown in the NFC Championship game. What do you do about this problem?

    January 24, 2010 — 13:22
  • Mike Almeida

    Nice questions!
    I wonder if it makes sense to think of a best segment as infinite in extent; e.g., something like a supreme event that stretches on and on (i.e., no finite part of which is better than the rest)
    If the world W is infinite in duration, there is on my account a segment of that world that is just equal in duration to W. I don’t see any problem offhand. Maybe I’m missing something. Why not let segments be infinite in duration?
    So there’s a world that has a best segment and it has positive value, but there’s another world (perhaps infinitely many) whose least good segment is far better than the first world’s best segment?
    This is all good, I think. I want every best segment of every world. Those best segments will vary a lot in value.
    Suppose the best segment of world 1–call it the Saints world–is where Reggie Bush runs for the winning touchdown in the NFC Championship game. And suppose the best segment of world 2–the Vikings world–is where Adrian Peterson runs for the winning touchdown in the NFC Championship game.
    Yes, there will be these odd outcomes, but it does not affect the argument given the assumptions. The best world will include both segments. Those segments have an intrinsic value that depends on intrinsic facts of those segments alone. So, the picture of the best world agggregated in this way is a picture of a disjointed world. But it need not appear disjointed to those in the world. We have effectively partial-worlds running one after another, and not necessarily otherwise related to other partial-worlds composing the best world. Given the assumptions on intrinsic value, this will be the (or a) best world, even if odd from our point of view.
    It does suggest another idea I’ve considered running. For any temporal segment S of any world W, it is possible that God actualizes a segment S’ whose value is as great as S. The segments that God actualizes in this way need not have the disjointed appearence of the best world I’ve beed describing, and it too will be a best world.

    January 24, 2010 — 15:28
  • That’s a really interesting construction.
    But I have some doubts:
    1. The total value of a world is not equal to the intrinsic values of the stages. The reason for that is a lot of intrinsically valuable states are such that their value is not subsumed in the intrinsic values of stages. Knowledge is valuable. But whether it is the case at t that I know p will often depend on what happens at times other than t (the most obvious scenario is that p concerns something happening at another time, and then whether the belief that p is true depends on what happens at the other stage). Diachronic variety is valuable, but whether a world exhibits diachronic variety or not is not something one can read off the intrinsic values of the stages. Likewise, much of the value in human relationships is through-and-through diachronic. Think about the value of faithfully holding on to a commitment over many years, for instance.
    2. The logical independence of stages seems to exclude some options. For instance, take cases of divine prophecy of the future or divine revelation of the past.
    3. The resulting world is a world where a sceptical hypothesis about memory is true. In particular, it does not seem that memories will typically be correct, and even those that happen to be correct, won’t typically be caused in the right way. Thus, it is a world where people know very little about the past, and most of what they think they know about the past just isn’t so. That seems significantly disvaluable.
    4. It’s unclear what the causal relations between stages would be. But it seems that the value of a state often depends on how the state is located in the causal nexus. The value of my receiving a present depends on the cause of my receiving it (and that will include the identity and intentions of the giver).
    5. Overall value depends on the order between stages. A life of growth in virtue is more valuable than a life of decay in virtue, even if we can run a stage-by-stage correspondence between the two lives, and the corresponding stages have equal intrinsic value.

    January 25, 2010 — 13:15
  • Mike Almeida

    The total value of a world is not equal to the intrinsic values of the stages.
    That’s true only if some form of Moore’s organic unities is true. But do you know any form of organic unities thesis that is (likely) true?

    January 26, 2010 — 8:10
  • Robb

    “For any arbitrarily chosen world Wn in the infinite sequence, there is a most valuable temporal stage Sn+ of Wn.”
    This assumption seems to have no basis. There could, for example, be a world in which each temporal stage is better than the previous one. If this world is temporally infinite, there is no best stage.
    Also, the construction of B+ leaves open the possibility of temporal gaps: when we put all the Sn+ together, there might be “seams” between them that are unfilled.

    January 26, 2010 — 10:58
  • Mike Almeida

    This assumption seems to have no basis. There could, for example, be a world in which each temporal stage is better than the previous one. If this world is temporally infinite, there is no best stage.
    What I say is this,
    For any arbitrarily chosen world Wn in the infinite sequence, there is a most valuable temporal stage Sn+ of Wn. A best stage S+ in W is a stage whose intrinsic value is positive and unexceeded by any other (overlapping or non-overlapping) stage in W.
    The world W you are describing does have a best stage. That stage S = W. That is, the only stage S of W whose intrinsic value is unexceeded by any other overlapping or non-overlapping stage is the stage identical to the world itself.
    Also, the construction of B+ leaves open the possibility of temporal gaps: when we put all the Sn+ together, there might be “seams” between them that are unfilled.
    B+ is a set, not a world.

    January 26, 2010 — 11:14
  • Mike:
    What is the organic unities thesis?
    It seems as obvious as anything that knowledge is intrinsically better than justified false belief.

    January 26, 2010 — 12:29
  • Having looked it up, I see. 🙂
    Here is a thesis that seems plausible:
    1. Two things can have exactly the same parts in the same respective intrinsic states, but differ in overall intrinsic value.
    Here’s one case. Imagine a beautiful statue made of wooden blocks in w1 and a random heap of the same blocks in w2. Same parts, same intrinsic states, but different values of the whole in virtue of the arrangement.
    All I need for my argument is (1). The organic unities thesis is a slightly different claim than (1):
    2. Two things can have exactly the same parts with the exact same respective intrinsic values, but differ in overall intrinsic value.
    One might think that (1) entails (2). But that is only true if the following thesis is true:
    3. If x has intrinsic value V, then having value V is an intrinsic property of x.
    I am inclined to think that (3) is false and (1) is true, and I have no view about (2), though (2) seems somewhat plausible.
    I suspect that what makes (3) seem plausible is a confusion between two senses of “intrinsic”.
    A counterexample to (3) is knowledge. I have the intrinsic value of being a knower of the fact that the universe is billions of years old. But my being such a knower is not an intrinsic property of me–it depends on the content of the knowledge being true.
    In any case, I think all I need to argue against you is (1).

    January 26, 2010 — 15:05
  • Russ Dumke

    Mike, it’s not clear to me if you are selecting the best stages from some worlds or the best stages from every world. In any case, this begs the question of the criterion that we use to determine what is “best.”
    In either case, however, I have a worry. Consider S1 from W1, which has the property that abortion is moral. Now consider S2 from W2 in which abortion is immoral. You mentioned above that the best world you envisage is a set, not a world (which, as an aside, seems to weaken its status metaphysically or epistemologically). This yields two difficulties: 1) the set you posit contains an axiological inconsistency, or 2) the criterion we use to select the best stages allows some axiological inconsistencies. On this basis, we can infer that the moral status of the best possible world is suspect, given that the that axiological set includes the moral set. We may then question whether the best possible world is in fact the best. We can conceive of one (perhaps we might more accurately say we can conceive the construction of one) that has all the best-making properties of your best possible world, and in addition is axiologically consistent and therefore quite possibly morally superior.

    January 26, 2010 — 21:32
  • Mike Almeida

    it’s not clear to me if you are selecting the best stages from some worlds or the best stages from every world. In any case, this begs the question of the criterion that we use to determine what is “best.”
    I’m selecting the best stages from every world that has a best stage in the sense defined. I’m conceding that some worlds might not have a best stage as I am using the phrase.
    Now consider S2 from W2 in which abortion is immoral. You mentioned above that the best world you envisage is a set, not a world (which, as an aside, seems to weaken its status metaphysically or epistemologically).
    No, I said that B+ is a set. W+ which is formed from B+ is a world–a best possible world. Since we have God existing in every possible world, I assume that the same moral standard obtains in each world. It is also necessary to the assumption that we have an infinite series of improving worlds. They must be improving relative to some shared standard.

    January 27, 2010 — 8:55
  • Mike Almeida

    1. Two things can have exactly the same parts in the same respective intrinsic states, but differ in overall intrinsic value. Here’s one case. Imagine a beautiful statue made of wooden blocks in w1 and a random heap of the same blocks in w2. Same parts, same intrinsic states, but different values of the whole in virtue of the arrangement.
    Surely, my position does not commit me to the absurd claim that the value of a universe is equal to the sum of the value of it’s most basic constituents. That’s an incredibly silly position. I obviously wouldn’t say that the value of David is equal to the sum of the values of the smallest particles composing Daivd (assuming there are smallest particles).
    My postion is that the intrinsic value of a world W is equal to the sum of the intrinsic values of the stages of W. The most valuable stages in worlds vary in temporal dimension: a possible world in which nothing occurs but a single Bach concerto, and whose duration is precisely that long would likely include one valuable stage S such that S = W.

    January 27, 2010 — 9:13