The Future and What Might Have Been – Rachael Briggs (Stanford) and Graeme A Forbes (Kent)
Abstract:
We develop a partial account of the ‘nomological package’ – a set of categories comprising laws, counterfactuals, chances, and dispositions – tailor-made for the Growing-Block view. We begin with the framework given in Briggs and Forbes (2012), and, taking laws as primitive, we show that the Growing-Block view has the resources to provide an account of possibility, chances and counterfactuals, that links our account of modality to their account of tense.
Full paper here.
Because the papers are works in progress, they have been password protected. To register for the conference, and get the password, please contact Graeme A Forbes at G.A.Forbes@kent.ac.uk
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Great stuff! Here re two questions:
1. 1a So if the laws are deterministic the Growing Block collapses into Eternalism?
1b Where do you get the measure on branches from? Quantum Theory?
2 Here is an argument against identifying degrees of truth with chances.
If there are indeterminate states then various propositions have degrees of truth between 0 and 1.
It is conceivable (indeed I hold it is true) that the past is indeterminate at the very small scale. If it is conceivable then there are propositions now about the past that now have degree of truth between 0 and 1 (e,g just where the electron was before it went through the two slits , in a cases in which we are just about to observe which it went through.) We can assign an epistemic probability to it’s being just about to go through slit 1 but not a chance.
Likewise it is conceivable that the laws are deterministic but the Big Bang was itself indeterminate. In that case we might wonder about the degree of truth of ‘The Big Bang’s initial state determined that we all came to exist’. But is it a matter of chance?
Author
1a) No. This is something we address explicitly in our earlier paper. Unlike McCall’s view, we can have a single feasible future without it ceasing to be a Growing-Block. It’s just a Growing-Block that will grow in a very predictable way.
1b) Rachael will be better placed to answer this than me, but I think the answer is that the measure will be based on the laws. If the laws are laws of quantum theory, then yes, it will be from those. One of the things we don’t do in this paper is explain what logical form stochastic ersatz laws will take, but it it is those that give us the feasible extensions of a timeline.
Good questions, Peter!
1a) As Graeme says, no. Our Growing-Block view is committed to the existence of a lot of past stuff, about which there is only one complete and consistent story, and also a handful of complete and consistent stories about how the future might go. What qualifies something as a story about how the future might go (as opposed to just a story about how some other scenario might have gone) is the past stuff. This is true even if the handful of stories about the future is small enough to contain only one story.
1b) I think the measure will have to be based on the laws. Actually, I think that not all probability measures derived from our best scientific theories will count: the deterministic probabilities discussed here by Jenann Ismael won’t. But any probabilities that can be slotted into the theory should come from indeterministic laws.
2) As I said in the previous paragraph, not all probabilities will measure degrees of truth: subjective probabilities won’t; epistemic probabilities won’t; even some physical probabilities won’t. Something can have {subjective, epistemic, deterministic physical} probability between 0 and 1, but also have a truth value. If there are indeterministic chances, those measure degrees of truth, and if past events have indeterministic chances, then they have degrees of truth between 0 and 1. That said, I’m inclined to deny both the antecedent and the consequent (on the supposition that the Growing-Block Theory is true): I don’t think that past events have indeterministic chances, and I don’t think they have degrees of truth between 0 and 1.
You might worry whether I can reconcile my (Growing-Blocker’s) claim that past events are not chancy with quantum mechanics, and that’s definitely something I’ll need to think more about! (Oliver Pooley is going to help us out with relativity soon, at least!)
Thanks! Some clarificatory questions:
pp. 7/8 seem like they touch on central issues so I’d like to understand better what’s going on there. Not sure how to understand the ‘all every’ and ‘all no’ in LT and NLT. They seem to be the same principle?
p. 32 I thought that the persistence debate was about the persistence of objects, not of events (if events persist too)?
On the amended definition of enduring from t to t*, should there be a clause ‘there is something wholly present at t*’? But if that’s put in, and ‘is’ is meant to be present-tensed (presumably the point of amending the original definition), doesn’t that suggest that the only things that endure(d) are things that endure(d) up until the present?
Author
Thanks, pp.7/8 you definately seem to have caught a typo there – LT and NLT appear to be the same, and that isn’t right.
p.32. Thanks. You are right, we (I) formulated that sloppily. We certainly don’t want to say that past things persist in a different way to present things. We should probably formulate that disjunctively:
If x endures from t to t* then there is something that was wholly present at t,
and either there was something wholly present at t* which is identical to the thing that was wholly present
at t, or, if t* is succeeded by no times, then the thing at t* is wholly present and is identical to the thing that was wholly present at t.
Events do persist, I think. But many people think that events have temporal parts, and perdure. But presentists (especially Trenton Merricks) may find the persitence conditions of events tricky. It seems plausible to me that events and objects both persist but in different ways. Possibly processes (whatever they are) persist in yet another way. I need to read Joseph’s paper properly, now it’s up, so I can see what he says about events.
Hi Natalja,
Thanks for picking up on these things.
Graeme has helpfully stepped in to answer your page 32 question, and he can blame me for the sloppy proofreading on pages 7-8.
On pages 7-8, the formal version of (LT) is correct, and the informal gloss should say:
“For every time e1, there is a time e2 which is later than e1.”
The formal version of (NLT) should be (LT) with a negation sign within the scope of the universal quantifier, and outside the scope of everything else. So the tex should say:
$$Pi e_1 \neg \Sigma e_2 L(e_1 e_2)$$
And the informal gloss should say:
“For no time e1 is there a time e2 which is later than e1.”
The bigger idea is that there are a sentence counts as true in our books as long as it’s guaranteed to become true, and as false as long as it’s guaranteed to become false, even if the thing that intuitively looks most like its truthmaker (or falsemaker) hasn’t yet come into existence.
Ok thanks…
I see now why there is no collapse of Growing Block to Block theory if determinism holds, but let me try to develop my second question a little more.
There are various ‘probability’ distributions associated with a quantum state ( distributins for position momentum etc.)Assume these have the right mathematical properties for probabilities. They may also be interpreted as specifying indeterminate values. One problem with interpreting them as chances is that the associated chances are for IDEALIZED observations.Another problem is that if thee were no observations or other ‘collapses of the wave packet’ (due to interaction with measuring devices) there would be no propensity to come to have more precise values.
Author
I’m no quantum mechanic, so can I ask a clarificatory question?
Is this problem a distinct problem from worries about metaphysical indeterminacy due to vagueness?
Some people think that there is no fact about whether something is a heap or not. We might need to accommodate metaphysical indeterminacy for such cases anyway. Are there problems peculiar to quantum states, or are the problems similar to cases of metaphysical indeterminacy due to vagueness?
I will let Peter speak for himself, but it looks like there are problems peculiar to quantum states. In the vague case, there’s not really a problem about logically combining different features of things. If I can use my supervaluationist model to evaluate both the claim “this sand makes a heap” and the claim “this sand is red”, I can also use it to evaluate the claim “this sand makes a heap, and is red”. In quantum mechanics, I can often assign probabilities to individual propositions, but not to any logical combinations of propositions. In the paper and my comments, I assumed the Growing-Block theorist was committed to one big probability distribution over a bunch of points where all propositions had truth values; I take it that Peter is worried about that.
Also, people can blame me rather than Graeme for deficiencies in this part of the paper. I’m not a quantum mechanic either, but I can tinker with the laser in the physics lab until I break it!
Hi Peter,
If I’ve got the first part of your follow-up right, you’re asking: what does the Briggs-Forbes theory when we have probability distributions for each variable we might choose to measure (position, momentum, etc.), but can’t have a joint probability distribution for all the variables? There seems to be no one thing that deserves the name of the chance distribution.
I think the way to interpret the probability distributions for position and momentum as somehow conditional–they’re the distributions that will operate if the appropriate measurement is made. So if it’s now inevitable that a measurement of position will be made, and a measurement of momentum won’t be, then the position distribution is the chance distribution. If what kind of measurement will be made is itself a chancy matter, then there’s some chance that a position measurement will be made turn out thus-and-so, some chance that a position measurement will be made and turn out in some other way, and some chance of various outcomes in which position won’t be measured and momentum will (in which case there will just be no answer to the question of how the position measurement turned out). I think that on this way of thinking, if it’s guaranteed that a measurement won’t occur, then propositions about its outcome will not have chances or truth values.
I’m not sure what to say if the measurement might occur, but might not. Questions which presuppose that it will have some outcome or other. If it’s chancy whether somebody will have children, then it’s not clear what to say about the claim that their first child will be named Sam–because there’s a chance that that claim suffers from some kind of presupposition failure. Does that sound like a reasonable start?
I’m not sure I’ve understood your point about idealized observations–is this a version of the Cartwright-style idea that our models, with their laws and chances, are technically false of the actual world? Or did you have something else in mind?
Thanks Rachel
I am not really worried about the joint probability distribution : i just asked my question in terms that did not presuppose there was one. (I think the problem of the joint distribution dissolves in the quantum field theory.)
So you take the probability as conditional on an idealized measurement being made. . I take it as a measure of indeterminacy (due I think to many possible worlds having equal claim to be actual.) My objection to the conditional probability of idealized measurement is that this is too complicated unless there is an underlying theory not stated in terms of ‘probabilities’. But if I am right then we have two candidates for degrees of truth, indeterminacy and chance.
Peter