Truthmakers, presentism and indeterminacy

In my ‘Truthmaking for Presentists’ paper, I end up defending the following 2 theses:

1) Truths concerning what was or will be the case are grounded by the presently existing world instantiating a distributional property – I’ll call it a world history – that says how it is across time.
2) The asymmetry of fixity – that the past is fixed and the future is open – is to be explained as follows: there is a non-empty non-singleton set, S, of candidate world histories, such that it’s determinate that exactly one of them is instantiated by the present world but not determinate of any member of S that it is instantiated by the present world. The candidate properties ‘agree’ on how the past was and ‘disagree’ on how the future will be, which is why propositions concerning the past are fixed whilst those concerning the future are unsettled.

This raises a bunch of questions: What makes it the case that the present candidates for being our world’s world history are the present candidates for being our world’s world history? What change in being has there been between yesterday and now that accounts for the fact that there are fewer candidate world histories? What is the difference in being between our world and a world whose past is like ours but which has a less open future? What makes it true that it’s determinate that a member of S is the world history of our world? What makes it true that it’s indeterminate of any particular member of S that it is the world history of our world?

These questions raise issues concerning how the truthmaker theorist should deal with propositions of the form ‘(In)determinately, p’, which I’ve been thinking about recently.

There are two broad approaches to answering these questions. On the first approach, propositions of the form ‘Determinately, p’ or ‘It’s indeterminate whether p’ get treated just like any other. On this view, there will be some truthmaker for ‘Determinately, p’, some thing which can’t exist and p not be determinately true, and some truthmaker for ‘It’s indeterminate whether p’, some thing which can’t exist and p have a determinate truth-value.

This approach will, perhaps, be favoured by those who hold that there is no gap between truth and determinate truth. On this view, it’s safe to simply identify the truthmaker for ‘determinately, p’ with the truthmaker for p: all God has to do to make p a determinate truth is to make p true, so any thing that makes p true will make it true that p is determinately true. On this view, indeterminacy leads to a truth-value gap, and so a truthmaker for ‘It’s indeterminate whether p’ can be thought of simply as something whose existence necessarily excludes the existence both of any truthmaker for p and any truthmaker for not-p.

I, however, hold that there is a gap between truth and determinate truth. More has to happen for the world to be such that p is determinately true than that p is true. If truth doesn’t entail determinate truth, what more is needed of ontology to make p determinately true than is needed to make it merely true? I reject the answer that says there must be an additional truthmaker for ‘Determinately, p’: rather, I say that the truthmaker for p must simply be a determinate existent rather than a mere existent.

If God wants to make sure that p is not only true but determinately true, He doesn’t need to add another entity to the world, in addition to the truthmaker for p, that will make it true that p is determinately true. Rather, all He needs to do to ensure that p is not merely true but determinately true is ensure that the truthmaker for p not only exists but determinately exists, (or at least that it’s determinate that a truthmaker for p exists – He needn’t make it determinate of a particular truthmaker for p that it exists). If God wants to make a world where p is indeterminate, He should create a world where it’s indeterminate whether a truthmaker for p or a truthmaker for not-p exists. And if He wants to create a world where p is true but indeterminate, He should create a world where there is a truthmaker for p but where it doesn’t determinately exist (and nor is it determinate that there is any truthmaker for p).

The idea is that propositions expressed by sentences involving the determinacy or indeterminacy operators don’t themselves get matched up to possible truthmakers. Rather, the ‘(in)determinacy free’ propositions that are their constituents get matched up to possible truthmakers, and the ‘(in)determinacy involving’ propositions get their truth-value bases on whether those truthmakers determinately exist, determinately don’t exist, exist but don’t determinately exist, or don’t exist but don’t determinately not exist.

Traditionally, the truthmaker theorist thinks that in order to fix exactly what is true, God simply has to decide what to create. On the view under offer, this isn’t quite right. Deciding what to create fixes the truth-value of the ‘(in)determinacy free’ propositions; but to further fix the truth-values of the ‘(in)determinacy involving’ propositions, God has to do one more thing: decide which of the things He’s decided to create are to exist determinately and which are to exist but not determinately exist., and decide which of the things He’s decided not to create are to determinately not exist and which are to not exist but not determinately not exist. Once He’s done that, he’ll have settled everything there is to settle.

Let’s return to the questions we asked earlier regarding the candidate world histories. Presumably, what would make it true that H is the world history of our world would be the state of affairs of our world instantiating H. In the normal run of things – when we’re not dealing with indeterminacy – explanation can stop here; we don’t have to admit an additional entity to make it true that the state of affairs of our world instantiating H exists: the state of affairs itself makes that true. Everything makes true the fact that it itself exists, so once we’ve reached the facts concerning what truthmakers exist, we’ve reached the level of facts where explanation comes to a halt.

But in the above context, where it is indeterminate which member of S is the world history of our world, it must be indeterminate what state of affairs exists. Suppose S just has two members: H1 and H2. Then here are three truths:

1) It is indeterminate whether H1 is the world history of our world
2) It is indeterminate whether H2 is the world history of our world
3) It is determinate that exactly one of H1 and H2 is the world history of our world

The truth of (1) – (3) entail the truth of (4) – (6) below:

4) It is indeterminate whether the state of affairs of our world instantiating H1 exists
5) It is indeterminate whether the state of affairs of our world instantiating H2 exists
6) It is determinate that exactly one of the state of affairs of our world instantiating H1 or the state of affairs of our world instantiating H2 exists.

On the approach I rejected, we now need truthmakers for (4) – (6). I suggest abandoning this approach. Intuitively, the difference in being between a world in which (4) is true and a world in which it is false is simply the difference in the status this state of affairs has in both worlds: in one it has determinate existence, in the other it lacks determinate existence (without going so far as to have determinate non-existence). Doesn’t that sound like difference in being enough? Why should we feel the need to postulate something outside of this state of affairs that exists at one world and accounts for the state of affairs’ determinate existence and which doesn’t exist at the world where the state of affairs does not determinately exist?

On the view I advocate, there are no truthmakers for (4) – (6). (4) – (6) are brute truths; explanation comes to a halt here. If p is indeterminately true then what grounds this is that it is indeterminate whether a truthmaker for p exists; but that it is indeterminate that such a truthmaker exists is not itself something that demands a truthmaker.

Is this revisionary? It’s not clear to me that it is, and I certainly think that it’s in the spirit of truthmaker theory. Truthmaker theory just is a theory about what truths are brute. The only brute truths, says the truthmaker theorist, are truths about what there is: explanation only comes to an end when we reach the ontological inventory. Now, if there’s no indeterminacy in the world, then it’s natural to characterise such truths as all being of the form ‘X (the Xs) exist(s)’. But if it can be indeterminate what exists, then it’s not clear why ‘It is indeterminate whether Y exists’ should be grounded in some truth of the form ‘X exists’: there is a perfectly good sense in which ‘It is indeterminate whether Y exists’ is about what there is, and hence is exactly the kind of truth that truthmaker theory allows us to take as brute. ‘It is indeterminate whether Y exists’ is not about how Y is, it’s about whether Y is: it belongs with ‘Y exists’ and not with ‘Y is F’, in that it is a truth simply about what should go on the ontological inventory and not a truth about how the things that are on the ontological inventory are. To put this another way: being indeterminately existent is no more a property than being existent, and so attributing indeterminate existence to an entity is no more to say something about how that entity is than attributing existence to it: both attributions are to do with whether the entity is, not how it is, and so if one can acceptably be taken as brute, so can the other.

The truthmaker theorist is fond of theological metaphors: all God has to do to fix what is true is to fix what exists. I agree. And if He wants to make a proposition p determinately true he will make sure to make the corresponding portion of ontology that makes p true determinately existent (or at least make it determinate that there is a corresponding bit of ontology), whereas if He wants to make it indeterminate whether p is true, He will make it indeterminate whether that portion (or indeed, any such portion) of ontology exists. He does not need to thereby add more ontology to the world to make it true that this portion of ontology determinately or indeterminately exists: His fixing that it determinately or indeterminately exists is part of His fixing what there is.

Consider two presentist worlds, wc and wo. Since they are presentist worlds, they consist of one time only: call it t. But both worlds are such that they will last for exactly one more instant after t and haven’t existed before t. Both worlds will be such that they have lasted for two instants, then. They both contain one entity, a, which exists throughout the duration of the world; which is just to say that a exists at t and that it will persist into the next instant. At t, the first instant of each world (the present instant), a is F. In wc (the closed world), it is settled at t that a will remain F in the second instant. In wo (the open world), it is unsettled at t whether a will remain F in the second instant or whether a will cease to be F.

What does God have to do to make wc? He has to take a and the distributional property of being F and then (in the next instant) F and put them together in the state of affairs of a having this distributional property: call it SC. He then has to make this state of affairs a determinate existent. Were wc actual, it would be true that a will be F, and this would be made true by SC; furthermore, in this closed world, a’s future is settled: it is determinately true that a will be F, and the truth of this is secured by the fact that SC doesn’t just exist but rather exists determinately.

Making wo is a little more complicated for God. As a first step, He’ll need the distributional property of being F and then (in the next instant) not-F, and the state of affairs (call it SO) of a having this property. He then needs to decree that it is determinate that exactly one of SC or SO exists, but that it is indeterminate that SC exists and indeterminate that SO exists. This suffices to ensure that, were wo actual, it would be open what will happen to a: it will be determinate that a is F (since it’s determinate that a truthmaker for ‘a is F’ exists, since it’s determinate that one or other of SC and SO exist, and the existence of either will make it true that a is F), but it will be determinate whether or not a will be F in the future (since it’s indeterminate whether there’s a truthmaker for ‘a will be F’, since one of the candidate world histories would make that true and the other won’t).

But God’s job isn’t done yet. For suppose wo is actual. Once we wait an instant, we’ll be able to see whether a is F in the second instant of wo’s history, and this will reveal whether the proposition ‘a will be F’ was true at t. Suppose a does in fact remain F. In that case, a’s history in the two worlds is just the same: it’s just that in one world its history was open and in the other it was closed. At t in both worlds, what lies ahead in the future for a is the same: it’s just that in one world it is settled that this is what lies ahead for a, and in the other world it’s not settled that this is a’s future, because there are genuine alternatives that are not ruled out. So God needs to do one last thing to make wo: He needs to make SC exist. He just needs to be careful that in doing so He doesn’t make it determinately exist!

wo and wc, then, are exactly alike with respect to what ‘(in)determinacy free’ propositions are true, and differ solely with respect to the truth-value of propositions of the form ‘Determinately, p’ or ‘It is indeterminate whether p’. And this leads to exactly what you’d expect on the view under offer: they are exactly alike with respect to what exists, and differ only as to whether some of the things that exists determinately exist and whether some of the things that don’t exist determinately don’t exist. SC exists at both worlds and SO doesn’t exist at either world; but in wc SC is a determinate existent and SO a determinate non-existent, whereas in wo it’s neither determinately the case that SC exists or determinately the case that it doesn’t exist, and likewise for SO. On the other hand, a is a determinate existent at both worlds, and SX, the state of affairs of a having the distributional property being not-F and then (in the next instant) F, determinately doesn’t exist at both worlds.

So, I’d love any feedback on the above approach. I’d also really appreciate any thoughts on my response to the following potential objection.

Objection: “What you’re doing, basically, is allowing more truths as brute than simply those of the form ‘such-and-such exists’. You’re also allowing as brute truths of the form ‘Determinately, p’ or ‘Indeterminately, p’ provided that p is itself a truth of the form ‘such-and-such exists’. But if we’re allowed to do that with the determinacy operators, what’s the bar on doing that with temporal operators? That is, why can’t we allow as brute truths of the form ‘WAS, p’ or ‘WILL BE, p’, provided that p is itself a truth of the form ‘such-and-such exists’? If, when characterising what God has to do to fix what is the case, we’re allowed to say that He makes A a determinate existent and B an indeterminate existent, why are we not allowed to also say that He simply makes C a past existent, D a future existent, etc. There’s no privileged difference that will allow you to take truths of the form ‘Determinately, A exists’ as brute and not truths of the form ‘It will be the case in a year’s time that B exists’; but if we can take the latter as brute, there’s simply no truthmaker objection to presentism, and so all of the above is unnecessary.”

Reply: I think there is a privileged difference. ‘Determinately, such-and-such exists’ is about what there is in a way that ‘WAS, such-and-such exists’ is not – it’s just about what there was.

The temporal (and modal, for that matter) operators ‘point beyond’ themselves in a way that the determinacy operators don’t. When I modify ‘A exists’ with a temporal or modal operator, I’m attributing to A the same kind of existence as if I simply said ‘A exists’, but I’m attributing this kind of existence to A not in the circumstances of utterance but at some point removed from the circumstances of utterance: I’m saying that A has the bog-standard mode of existence – but it doesn’t have it here, it has it some distance along the temporal or modal dimension. By contrast, when I modify ‘A exists’ with a determinacy operator (by saying ‘Determinately, A exists’ or ‘It’s indeterminate whether A exists’) I’m making a claim about A’s existence in the circumstances of the utterance and instead modifying the mode of A’s existence.

To say that p is determinate or indeterminate is to say something about p’s status in our current circumstances, it’s not to ‘point beyond’ our current circumstances and say something about its status at circumstances removed from ours along some dimension in the way that we do when we say that p was or will be true, or that it could or must have been true. Determinate existence and not-determinate existence are types of existence a thing can have in the current circumstances; necessary or contingent existence, or temporary or eternal existence (e.g.), are not modes of existence – a necessary/eternal existent exists in the same way as a contingent/temporary existent, it just does so at every point across the modal/temporal dimension. Whereas when I say that something is a determinate existent, this is not to say (contra Akiba) that that thing exists at every point across some ‘precisificational’ dimension , but to say something about how it exists in our circumstances.

That’s why I think it’s acceptable for the truthmaker theorist to take as brute truths concerning what determinately exists or exists but not determinately, etc, but not truths concerning what will or did exist, or what could or must exist. Only the former are truths concerning what there is; the latter concern not what there is, but only what there was or will be, or what there could or must be, and hence must be grounded in facts concerning what there is.