In my dissertation, I defended a causal power account of modality on which something is possible just in case either it’s actual or something can bring about a causal chain leading to its being actual. I noted at the time that unless there is a necessary first cause, this leads to an odd infinite branching view on which any possible world matches our world exactly once you get far enough back, but nonetheless every individual event is contingent, because if you go back far enough, you get a causal power to generate something else in its place. Rejecting this branching view yields a cosmological argument for a necessary being. To my surprise when I went around giving talks on the account, I found that some atheists were willing to embrace the branching view. And since then Graham Oppy has defended it, and Schmid and Malpass have cleverly used it to attack certain cosmological arguments.
I want to note a curious, and somewhat unappealing, probabilistic feature of the backwards-infinite branching view. While it is essential to the view that it be through-and-through contingentist, assuming classical probabilities can be applied to the setup, then the further back you go on a view like that, the closer it gets to fatalism.
For let St be a proposition describing the total state of our world at time t. Let Qt be the conjunction of Su for all u ≤ t: this is the total present and past at t. Here is what I mean by saying that the further back you go, the closer you get to fatalism on the backwards-infinite branching view:
- limt→− ∞ P(Qt) = 1.
I.e., the further back we go, the less randomness there is. In our time, there are many sources of randomness, and as a result the current state of the world is extremely unlikely—it is unlikely that I would be typing this in precisely this way at precisely this time, it is unlikely that the die throws in casinos right now come out as they do, and so on. But as we go back in time, the randomness fades away, and things are more and more likely.
This is not a completely absurd consequence (see Appendix). But it is also a surprising prediction about the past, one that we would not expect in a world with physics similar to ours.
Proof of (1): Let tn be any decreasing sequence of times going to − ∞. Let Q be the infinite disjunction Qt1 ∨ Qt2 ∨ .... The backwards-infinite branching view tells us that Q is a necessary truth (because any possible world has Qt is true for t sufficiently low). Thus, P(Q) = 1. But now observe that Qt1 implies Qt2 implies Qt3 and so on. It follows from countable additivity that limn→∞ P(Qtn) = P(Q) = 1.
Appendix: Above, I said that the probabilistic thesis is not absurd. Here is a specific model. Imagine a particle that on day − n for n > 0 has probability 2−n of moving one meter to the left and probability 2n of moving one meter to the left, and otherwise it remains still. Suppose all these steps are independent. Then with probability one, there is a time before which the particle did not move (by the Borel-Cantelli lemma). We can coherently suppose that necessarily the particle was at position 0 if you go far enough back, and then the system models backwards-infinite branching. However, note an unappealing aspect of this model: the movement probabilities are time-dependent. The model does not seem to fit our laws of nature which are time-translation symmetric (which is why we have energy conservation by Noether’s theorem).
I gave a critique of this paper in Worldview Design, but I'll post it here. Maybe I'm not understanding branching actualism, because how I view it, it says that there is a necessarily existing infinite past.
ReplyDeleteI was reading some of Joe Schmid's and Alex Malpass's new paper called Branching Actualism and Cosmological Arguments. I will present a critique here.
First of all, I would like to point out that branching actualism supposes a necessary first cause of all contingent existence. So, the main point of cosmological arguments is supported by branching actualism. It wouldn't really bother a supporter of cosmological arguments if a response to them entails the conclusion that they were trying to argue for.
Second, we can get into the main arguments. The first section is about the Grim Reaper Paradox or GRP. The GRP is said to be impossible given an infinite past because everything in the past before a certain point is necessary, and so rearrangement principles can't apply. However, the GRP can be constructed without an infinite past. For example, it can be generated using an infinite amount of reapers activating in a finite amount of time, or an infinite amount of reapers in a line activating at once. These still support the conclusion of causal finitism, and if causal finitism is true, it is very implausible that the past is infinite. In fact, a causal powers account of possibility can further GRPs. For example, Pruss's argument in section 3.3.3 on pages 48-49 in Infinity, Causation, and Paradox on rearrangement. Each reaper is set to a non-paradoxical time, but each one also has the ability, or causal power, to set itself to a paradoxical time. Thus, on a causal powers account of possibility, the non-paradoxical story would entail the possibility of the paradoxical story.
Third, we can move to the contingency argument. The response says that there could exist a necessary infinite causal chain that doesn't need an explanation. But this just supports the contingency argument already. The conclusion of the contingency argument is that there is a necessarily concrete thing. So, the response just affirms the conclusion.
Fourth, we have the modal argument from beginnings or MAB. Schmid and Malpass suggest a premise that they say would entail the impossibility of the beginning of contingency. The premise is that possibly, contingency obtains past-infinitely. But this is clearly false given branching actualism, for if contingency obtained past-infinitely, then there would always be a point in a world's history in which it would differ from another world. But that goes against branching actualism, because branching actualism says there is a segment in time that is shared by all worlds and is necessarily existent. If contingency never began to obtain, there would be no necessary starting point for the possible worlds to branch off from, so branching actualism would be false.
Finally, I want to make a few notes about branching actualism that includes a temporal section of reality as its starting point. It would be strange to suppose a necessarily existent past infinite regress. This would multiply the necessary things to infinity, which seems implausible. It would also introduce the epistemic possibility that we have not started branching yet, and that also seems implausible. As for the temporal part being finite, that would violate the causal principle, which is plausible as well. These are not really full-blown arguments, but just notes of consideration.
Another potential issue with branching actualism is how it seems to be about how objects in A concrete world go back to a certain point in time - all possible ways a certain world COULD have developed are rooted in the causal powers of the objects that existed in the past in that world.
ReplyDeleteBut the existence of those objects itself isn't necessary - nothing about any one object or collection of objects makes their existence necessary. A similar conclusion can be reached by considering whether or not ALL possible objects do indeed exist - if they don't, then this further supports the contingency of objects in our world in general. If ALL possible objects do exist in concrete reality, then this would require that the existence of ALL logically possible object categories is necessary, which seems very unlikely.
Plus, this commits any atheistic branching actualists to holding that the existence of many objects - at least one per kind or category or even species of object - is necessary, maybe even the things we currently experience. Which seems very counterintuitive to the fact our minds don't perceive or cognise any of them as being actually strictly necessary.
This comment has been removed by the author.
ReplyDeleteI doubt (1). I think the proof fails because you may not have countable additivity.
ReplyDeleteExample: Assume past-infinite discrete time. Suppose that at each time, there are two possible states, A and B. Each state either persists to the next time (with probability 1/2) or switches to the other (with probability 1/2). A branching world model (as I understand it) would take the possible histories to be those that agreed with the actual history up to some time at or before the present.
It’s not clear that it makes sense to assign probabilities to these histories at all. But if you do, you must say that all possible histories up to the present, including the actual one, have equal probability. [Any possible history matches the actual history up to some time. If this time is N intervals before the present, then, conditional on the common initial segment, both the actual history and the possible one have probability 2^(-N). So unconditionally, they have equal probability, which must be at most 2^(-N).] There are an infinite number of possible histories, so this common probability can be at most infinitesimal.
The reasoning also shows each history up to N units before the present has a common probability that is 2^N times the probability of each history to the present. But 2^N times zero or infinitesimal is still zero or infinitesimal, contrary to (1).
Another thought: the possible histories to the present are countable, so this would in effect be a fair infinite lottery, with all the usual issues that go with that.
Fascinating post, Alex! Super glad you checked out the article -- it's always nice seeing my work serve those (like you) who influenced my philosophical development in wonderful ways. I may offer thoughts later, I may not; I'm currently in quite a deal of discomfort from knee surgery.
ReplyDeleteIn between my hourly exercises, though, I was able to compose a response to Alithea, which I'll paste here for those interested :)
Alithea: “First of all, I would like to point out that branching actualism supposes a necessary first cause of all contingent existence.”
This is untrue and evinces a misunderstanding of branching actualism. According to branching actualism, each possible world shares some history with the actual world. For each possible world w, w shares some history H with the actual world. This does not entail that there is some history H that is shared by every possible world, i.e., that there is some necessarily existing initial segment that is shared by all worlds. That is a quantifier shift fallacy, which is a formally invalid inference; from ∀w∃H[…], it does not follow that ∃H∀w[…].
One way for branching actualism to be true while there is no necessary first cause(s) of all contingent existence is precisely if the past is infinite and populated purely by contingent causes. In that case, each possible world may diverge from the actual world at some point — thereby satisfying branching actualism — and yet there is no necessary first cause of all contingent existence. So it is simply untrue that branching actualism supposes a necessary first cause of all existence.
Alithea: “So, the main point of cosmological arguments is supported by branching actualism. It wouldn't really bother a supporter of cosmological arguments if a response to them entails the conclusion that they were trying to argue for.”
But again, this just evinces a misunderstanding of branching actualism.
Alithea: “Second, we can get into the main arguments. The first section is about the Grim Reaper Paradox or GRP. The GRP is said to be impossible given an infinite past because everything in the past before a certain point is necessary, and so rearrangement principles can't apply.”
This mischaracterizes the argument in the paper. Nowhere did we say that everything in the past before a certain point is necessary. We also didn’t argue that “the GRP is impossible given an infinite past”. Instead, we argued that the patchwork principle upon which the GR Kalam relies, in its Koonsian manifestation, is false if branching actualism is true.
Alithea: “However, the GRP can be constructed without an infinite past.”
Nowhere did the article deny this. In fact, the article recognizes this point in footnote 7. Importantly, though, the fact that GRP can be constructed without an infinite past is irrelevant to the actual point of the criticism in the article. Even if the GRP can be constructed without an infinite past, it remains true that the patchwork principle underlying the Koonsian GR Kalam — namely, PInf — is false under branching actualism (with a caveat about non-spatial initial regions of the actual world that we explore in the paper, of course). That was our sole point.
Alithea: “For example, it can be generated using an infinite amount of reapers activating in a finite amount of time, or an infinite amount of reapers in a line activating at once. These still support the conclusion of causal finitism, and if causal finitism is true, it is very implausible that the past is infinite.”
Once again, this doesn’t actually engage our point. Our point was solely that the patchwork principle underlying the GR Kalam in its Koonsian variety is false under branching actualism. (And also, if Alithea is curious, I argue that these paradoxes don’t lend support to causal finitism in several videos. See, e.g., my Kalam playlist here: https://www.youtube.com/watch?v=ZTDbUE83JyI&list=PLxRhaLyXxXkZzH2YffI32ViTZ73Tu8jSR&pp=gAQB )
Contd. in another comment!
Contd., pt. 2/3
ReplyDeleteAlithea: “In fact, a causal powers account of possibility can further GRPs. For example, Pruss's argument in section 3.3.3 on pages 48-49 in Infinity, Causation, and Paradox on rearrangement. Each reaper is set to a non-paradoxical time, but each one also has the ability, or causal power, to set itself to a paradoxical time. Thus, on a causal powers account of possibility, the non-paradoxical story would entail the possibility of the paradoxical story.
Merely from the fact that each individual reaper has the power to set its own time to a particular time in the original, paradoxical story — and hence, per the powers-based view of modality, each individual reaper is such that its time is possibly set to the time in the original, paradoxical story — it doesn’t thereby follow that it’s possible that *all* the reapers jointly do so. That’s a formally logically invalid inference from ‘each reaper possibly has F’ [for the relevant predicate F] to ‘possibly, all the reapers have F’. But this is formally invalid; from a wide scope universal quantifier concatenated with a narrow scope possibility operator, a corresponding formula with a wide scope possibility operator concatenated with a narrow scope universal quantifier does not follow. Consider: each day of the week is such that, possibly, I was born on that day of the week; but it doesn’t follow that it’s possible that I was born on all the days of the week (together, i.e., Mon AND Tues AND Wed AND Thurs AND Fri etc.). And a powers view of modality only licenses the former, not the latter, since only the former corresponds to doling out possibilities where there are relevant powers. (More specifically: because each individual reaper has the power to set its time to a particular time in the original paradox, the powers view of modality implies that each reaper is such that, possibly, that reaper’s time *is* a particular time in the original paradox. But we can only infer, using a powers view of modality, that it’s possible for ALL of reapers to JOINTLY set their times as they’re set in the original paradox if something has the causal power of bringing it about that ALL of the reapers are JOINTLY set in that way. But, of course, nothing has that power, since that would require having a power to bring about a contradiction, and nothing has the power to bring about a contradiction.)
Alithea: “Third, we can move to the contingency argument. The response says that there could exist a necessary infinite causal chain that doesn't need an explanation. But this just supports the contingency argument already. The conclusion of the contingency argument is that there is a necessarily concrete thing. So, the response just affirms the conclusion.”
Once again, this mischaracterizes the article. Nowhere in the article do we say that there could exist a necessary infinite causal chain. (And also, nowhere do we say that it doesn’t need an explanation. We only say that the chain falls outside the scope of the relevant restricted PSR and hence, solely by using that PSR, we cannot infer that it needs an explanation. This is different from saying it doesn’t need an explanation.) Instead, we said that it’s not possible for the *entire* chain to be *globally* different (even though each individual member of the chain may possibly be different). So each particular thing, on this model, would exist contingently, even though it is necessary that there are some contingent things stretching throughout an infinite past. It is false, then, that we affirm the conclusion; in fact, our point denies it! Our point is that even though each individual thing is contingent in the relevant model (and hence there is no object which necessary exists), under branching actualism it can still be the case that, necessarily, there are some contingent things.
This comment has been removed by the author.
ReplyDelete
ReplyDeleteMajesty of Reason, if we have an infinite branching past where all things contingently exist it seems that something is still left unexplained. Each individual thing may have an explanation for its existence but it seems that there is no explanation for why there is any existence in the whole infinite chain. It seems that a good way to explain why there is any existence at all would be to say that there is something that by its nature either includes existence or just is existence. But now it seems that we have a necessary being again.
Trevor, I'm actually sympathetic with that view; my favored model of reality probably includes either one or more necessarily existent concrete objects. Still, though, I like to see how far I can push views, and that's what I'll do here! In short, I think the proponent of the all-contingent infinite past branching actualist view -- call it the ACIPBA view (an absurd name, I know...) -- will say that they have an explanation ready to hand of why there's any (contingent) existence at all: namely, it is metaphysically necessary that there be (contingent) existence [equivalently: there being *no* (contingent) existence is metaphysically impossible]. This, after all, falls out of their theory of modality together with their view of the extent of the past. Maybe this is unsatisfactory in some way; or maybe it cites facts themselves in need of explanation; I'm not convinced that this is so, but I'm quite open to being convinced!
ReplyDelete"Maybe this is unsatisfactory in some way; or maybe it cites facts themselves in need of explanation; I'm not convinced that this is so, but I'm quite open to being convinced!"
ReplyDeleteI can't speak for Trevor but it seems unsatisfactory to me because it violates the principle of contradiction. How can any thing––let alone existence––be metahysically necessary and not necessary "(contingent)" at the same time?
This comment has been removed by the author.
ReplyDeleteZoe:
ReplyDeleteThe following two claims are different:
(1) Necessarily, some contingent things or other exist.
(2) Some contingent things exist necessarily.
MOR's claim is that proponents of ACIPBA will affirm (1), not that they will affirm (2). But only (2) leads to a contradiction. (1) might be false (I find it *deeply* implausible myself), but it isn't outright contradictory.
James:
DeleteWhy do you think 1 is deeply implasible?
Thanks James, I see your point.
ReplyDeleteBut doesn't MOR's "[equivalently: there being *no* (contingent) existence is metaphysically impossible]" strengthen his claim such that it is more like (2) than (1)?
I guess I'm still unsatisfied because if MOR only affirms (1) the "or other" of your claim disputes his reply to Alithea. But his reply to Alithea and the quoted alternative formula for his claim together suggest he meant your (2).
Zoe:
ReplyDeleteIf (1) is true, then it is metaphysically impossible for there to be no contingent beings. This is simply equivalent to saying that it is necessary that some contingent things or other exist. MOR's claim just requires (1).
Ian:
ReplyDeleteThere are perfectly sensible countably additive probabilities for some backwards-infinite histories -- but not for ones coming from the branching model in question.
To avoid worries about infinities, suppose time is discrete and consider a particle engaging in a random walk on a discrete circle, i.e., points 0,1,2,...,N-1, wrapping around so that to the left of 0 is N-1 and to the right of N-1 is 0. At time n, the particle makes a random transition to the left or to the right with equal probability, independent of the transition at any other time. At any time n, the unconditional probabilities of the particle are uniformly distributed over the N points. This is perfectly coherent as a countably additive probability--just think of a standard random walk, and reverse time.
Majesty of Reason, It seems like one of the motivations for the branching actualism view is the belief that all facts about what is actual or possible depend on things and their natures or causal powers. The proponent of ACIPBA may be able to say that it is metaphysically necessary that some contingent things must exist but it seems that this fact should be explained by some thing and its powers. However I am not sure that any of the contingent things explain why it is necessary that some contingent thing or other must exist. But perhaps the proponent of ACIPBA can just say that the fact that there must be some contingent things is a sort of brute fact. I just personally feel that explanations in terms of the essences or natures of things are much more satisfactory than brute facts.
ReplyDeleteTrevor:
ReplyDeleteWhat makes it necessary on ACIPBA that there are (tenseless) contingent things is that no entity that ever exists has (tenseless) the power to prevent there from being (tenseless) contingent beings. Why? This is simple: because on the theory all beings are contingent, and no being has the power to prevent its own existence!
BTW, what I find most problematic about ACIPBA is that it seems intuitively obvious that there is a possible world where there have always been fox-like beings.
Alex:
ReplyDeleteDisagree. The reasoning I gave for my model applies equally to these models. (I exclude N=2, which gives deterministic alternation of states 0 and 1.) Note that for my model too, the probabilities at any time are just fine, 1/2 for A and 1/2 for B. It’s the histories that don’t have countably additive probabilities. And (1) is a statement about histories.
As in my model, all possible histories must have the same probability. [Same reasoning: Any possible complete history must agree with the actual history on some initial segment. Suppose they agree up to time K before the present. Then, conditional on the common segment, both the actual history and the possible history have probability 2^(-K). (Note that, conditional on the initial segment, sequences of states correspond uniquely with sequences of steps. This is why I have to exclude N=2, for which they don’t.) So unconditionally, they must have the same probability.] As in my model, there are countably many possible histories. So, as in my model, the common probability must be at most infinitesimal, and the probabilities won’t be countable additive over histories. As in my model, the probability of a history up to time K before the present is 2^K times the at most infinitesimal probability of a full history. This is at most infinitesimal, contrary to (1).
You could complicate the maths with unequal left and right transition probabilities. Or with a general finite state (ergodic, non-periodic) Markov model. But I don’t think it would change the conclusion.
Dr. Pruss, it does seem like that would explain why there are contingent things. I wonder if ACIPBA would work on a more Thomistic metaphysics? It seems that if we accept the essence existence distinction and that existence must be passed down in a per se chain then merely contingent things could not be the ultimate explanation of anything’s existence. Of course Thomistic metaphysics are more controversial to many but it may provide a better answer to this ACIPBA view if one accepts Thomism.
ReplyDeleteM. Rifat Algan:
ReplyDeleteWell, one reason is just that I have a very strong intuition that it's metaphysically possible for there to be no contingent things. This seems to follow from some very plausible assumptions; for instance, Barbara Vetter notes that "the possibility, for each contingent object, that it does not exist, together with what we might call a principle of independence—that the non-existence of contingent objects can never force other contingent object into existence—yields the global possibility that none of the actual contingent objects exist" (Potentiality: From Dispositions to Modality, p. 275).
If the proponent of ACIPBA is a naturalist (which I suspect virtually all of them are), then we also get some implausible results concerning laws of nature. So as Leftow notes, on a view like Graham Oppy's "there could not have been other natural laws... [nor] could there have been a different total amount of mass-energy" ("A naturalist cosmological argument," 325). I find that extremely implausible.
I also think that affirming the existence of a necessary being is the best way for branching actualists to validate S5 (Vetter and Samuel Kimpton-Nye have done interesting work on this front). But of course, if there is a necessary concrete being, then ACIPBA is false.
Thank you for your answer James.
DeleteI generally aggre with you about the intution.
But I have never seen other things that you wrote, I will think about them.
@James Reilly Do you know of any articles by Vetter & Nye that would be interesting in this regard? Relating to S5 proving a necessary being exists?
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteWesley:
ReplyDelete"Prove" is too strong; I think S5 gives the branching actualist REASON to accept a necessary being. Kimpton-Nye's paper "Can Hardcore Actualism Validate S5?" in Philosophy and Phenomenological Research is a good place to start. Vetter's book Potentiality: From Dispositions to Modality (OUP, 2015) is also useful.
I've argued in Section 8 of http://alexanderpruss.com/papers/LCA.html that a branching actualist view implies the following odd weak version of the PSR:
ReplyDelete(*) The PSR is true in every non-actual world w.
Now, the PSR entails the existence of a necessary being. So, branching actualism is committed to the following:
(**) Every world, with the possible exception of the actual one, has a necessary being.
Given S5 it follows that:
(***) Every world has a necessary being.
Actually, even if one is sceptical of S5, it would be very strange indeed to think that our world is the one and only unlucky world without a necessary being!
"Now, the PSR entails the existence of a necessary being. So, branching actualism is committed to the following"
DeleteBut according to brancing view that mentioned in the paper we can accept PSR Even if necessary being doesn't exist. So we can believe both PSR and we don't need to accept necessary being
What do you think Dr. Pruss
The conjunction of all the events in the infinite sequence of contingent events is not explained without a necessary being.
ReplyDeleteI think on their account, the candidate for an explanation is the giant disjunction Q. But the giant disjunction Q does not in fact explain any of its disjuncts.
This comment has been removed by the author.
ReplyDeleteBut on ACIPBA, it seems like they could say something like this: each individual event is explained by its immediate cause, and the entire series is metaphysically necessary (since on ACIPBA, it's not possible for all of history to have been different). So there's nothing left which stands in need of explanation. It isn't necessary to say that the disjunction itself explains its disjuncts, since each individual event has an explanation in terms of its immediate cause.
ReplyDeleteWhy we believe that entire series is metaphysically necessary?
DeleteThough there is a question about what exactly the necessary entity IS on this account. Schmid and Malpass say that the impossibility of an entirely different history affords a response to the contingency argument, but the details seem a bit fishy to me.
ReplyDeleteM. Rifat Algan:
ReplyDeleteI don't think we should. But for the proponent of ACIPBA, it's metaphysically impossible for the entire sequence to have been different. So if we accept a version of the PSR restricted to contingent facts, then it doesn't seem like the existence of the infinite series will stand in need of an explanation.
As I said, I think there are more than a few good reasons to reject ACIPBA. But it seems like its proponents could say something like the above as a means of avoiding the argument from contingency.
I don't see any reason for why we need to accept that it is metaphysically impossible the entire sequence to have been different.
DeleteWhy are they believe this?
This comment has been removed by the author.
ReplyDeleteM. Rifat Algan:
ReplyDeleteOn branching actualism, p is possible iff p is actual or there is something actual with the causal power to initiate a causal sequence leading up to p. If the sequence of contingent causes stretches back to infinity, then there has never been anything with the causal power to make it so that the entire sequence was different. So on ACIPBA, it's metaphysically impossible for the entire sequence to be different.