The Modal Openness of the Future

There's a simple and valid argument for fatalism based on a proposition which most analytic philosophers would accept. The assumption is this

• There is an actual world, alpha, which contains a complete history. Unlike other merely possible worlds, alpha is the possible world that "obtains".

For the sake of argument I take this assumption for granted.

Now, fatalism can be understood as the doctrine that no events have an intermediate chance of occurring. By a 'chance' I mean a single-case objective probability. By an 'intermediate' chance I mean a value between zero and one. If the chance of an event is one, then it is unpreventable--it's guaranteed to happen. If the chance of an event is zero, then its non-occurrence is unpreventable--it's guaranteed not to happen. Fatalism simply says that, for any event, its chance of occurring is either zero or one.

Now, consider the actual world, alpha. This includes a complete history. Hence, for every possible event E, either alpha entails that E occurs, or alpha entails that E doesn't occur. If alpha entails that E occurs, then the chance of E's occurring given alpha equals one. If alpha entails that E does not occur, then the chance of E's occurring given alpha equals zero. Using CH() to represent the chance function, this means that for arbitrary E, either

1. CH(E | alpha) = 0, or
2. CH(E | alpha) = 1.

Now, what is the chance of alpha? That is, what is the chance that alpha obtains or that alpha is the case? Obviously, it's got to be one. In general, the chance that anything is the case has got to be either zero or one. Consider my sitting at time T. If it is the case that I sit at t, then the chance that I sit at T is one. It's too late to prevent it. Likewise, if it is the case that I stand at T, then the chance that I sit at T is zero. It's too late to bring it about that I sit at T. Thus, since alpha (in its entirety) obtains, and thus is the case, we get

3. CH(alpha) = 1.

But from 2 and 3 there follows

4. CH(E) = 1.

And from 1 and 3 there follows

5. CH(E) = 0.

Hence, E is not a future contingent. Since the argument holds for arbitrary E, fatalism is thereby established.

To avoid fatalism the initial assumption must be rejected. We must either deny that there is an actual world (i.e., we must deny that any possible world which includes a complete history obtains), or we must deny that possible worlds must include a complete history, in particular, a complete future history. Call that denial the modal openness of the future thesis. I maintain that the future is modally open. As contingencies are resolved, the modal changes. Things that were possible may not now be possible. Things that are necessary may not always have been necessary.

Three Models of Divine Sustaining

Theists believe that God is not only responsible for creating or bringing about (the initial state) of a world of concrete finite beings but also that God in some sense sustains those beings throughout their existence. But what does divine sustaining amount to? I'd like to identify three possible models of divine sustaining.

continuous creation: There is no fundamental difference between God's work in creating and sustaining. As long as creation endures, continuous activity on God's part efficaciously brings about the entire being of every existing created thing. This model is committed to an anti-conservation of created being principle: contingent beings cannot continue to exist, even for an instant, should God stop his sustaining activity.

infusion: There is a fundamental difference between God's work in creating and sustaining. Creating brings about the entire being of the creature. Sustaining does not. But sustaining is not mere conservation. It is a positive activity on God's part without which created things either (a) would gradually dissipate or (b) would not function optimally (even if they could persist indefinitely on their own), or (c) both. This model is committed to a limited conservation of created being principle: contingent beings can continue to exist for a time apart from divine sustaining, but they either cannot persist indefinitely or cannot function optimally apart from divine sustaining.

conservation: There is a fundamental difference between God's work in creating and sustaining. Creating brings about the entire being of the creature. Sustaining is merely God's refraining from annihilating a thing. This model posits a conservation of created being principle: things that exist automatically continue to exist unless something else destroys or annihilates them.

Now, I reject continuous creation because it seems to entail occasionalism (i.e., that the only genuine cause is God) and theological determinism. It renders creatures wholly passive with respect to God, in the same way that the image on the movie screen depends entirely at each moment on the light shining from the projector.

Either of the other two models are compatible with creaturely freedom, but one might worry that the conservation model is too passive on God's part. It seems to smack more of deism than theism.

The infusion model seems to me to strike the right sort of balance between continuous creation and mere conservation. It says that created things depend continuously on God not for the entirety of their being, but for either long-term existential stability and/or to be able to function at undiminished capacity. This allows creatures a limited independence of God, enough for creaturely freedom, without rendering divine sustaining a purely passive endeavor on God's part.

Cahn on Ockhamist Semantics

By 'Ockhamist semantics' ('Ockhamism' for short) I mean the thesis that what's true at a time about other times depends entirely on what occurs at those other times. Thus, if a coin is flipped at T and lands heads at T*, then Ockhamism implies that "The coin will land heads at T*" was true at T, even if (suppose the coin is heavily biased toward landing tails) it was very improbable at T that the coin would land heads at T*.

I think Ockhamism is false, but a lot of philosophers accept it. When asked to give an argument for Ockhamism, they have a standard response. Suppose a person makes a bet that the Red Sox will win the next World Series, and suppose that when the next World Series comes around and the final out is called, the Red Sox are indeed the champions. Wouldn't it be appropriate to say to the person who made the bet, asks the Ockhamist, "Gee, you were right when you said that the Red Sox were going to win"?

Now, this isn't a compelling argument. That we often talk as if something is or was the case doesn't come close to proving that it is or was the case, or even that we believe that it is or was the case. For example, we often speak of the sun's rising and setting, but no educated person today would take that at face value. Still, I'll grant that the Ockhamist's argument has a force. The anti-Ockhamist does have a legitimate burden to explain away our practice of retrospectively attributioning truth (or seeming to do so). But I'm going to set that aside. I've recently begun rereading Stephen Cahn's classic Fate, Logic, and Time (Ridgeview Publishing, 1967) and noticed, in a footnote (p. 36), a retort to the Ockhamist argument:

Consider a man who bets that horse A will win a particular race. After the race is over and horse B has won, the man who bet on horse A is told that at the time he placed his bet it was true that horse B would win the race. Would not the man immediately suspect that the race was fixed? The winner of a bet is the man whose prediction becomes true, not the man whose prediction was true. (my emphasis)

This strikes me as exactly right. If, as of the time the bet was placed, horses A and B were neither guaranteed to win nor guaranteed to lose, then nothing that exists as of that time suffices to make it true that horse B will win the race. So why think it was true then that horse B would win? And if we do suppose that it was true then, doesn't this commit us to there having then been a truthmaker sufficient to make it true then that horse B will win? And if that's the case, then how could we still regard horse B's winning as having been a future contingent rather than as something antecedently "fixed"? A proposition is true at a time if and only if it would be true simpliciter were that time present. But as of the time the bet was placed, nothing that obtained simpliciter sufficed to make it true simpliciter that "Horse B will win" was true then. Hence, "Horse B will win" was not true then, or so it seems clear to me. What we should say, as Cahn suggests, is that "Horse B wins" became true when horse B won. It wasn't true previously.

On a Misguided Application of Excluded Middle

Many discussions of logical fatalism and of the compatibility of divine foreknowledge and future contingency turn on the question of whether propositions about future contingents are true in advance. More exactly, they raise questions about whether any 'will' or 'does' propositions about events which have an intermediate chance of occurring (i.e., a current single-case objective probability greater than zero and less than one) are true. One common argument contends that the 'open future' position, which denies that any propositions about future contingents are now true, leads to a denial of the law of excluded middle (LEM). For example, in a recent collection, David Hunt writes (p. 276):

Either I will call my mother tomorrow, or I won't call my mother tomorrow. One or the other of these statements about the future must be true. The principle that either a given statement or its denial is true is called the "Law of Excluded Middle."

According to Hunt, LEM necessitates that some propositions about future contingents are true. But he's simply mistaken if he thinks his example gives us a clear instance of LEM. It doesn't, and it's easy to show this.

LEM states that, for all propositions P, either P or its denial, Not-P, is the case. This can be given either a truth-functional or a supervaluationist reading.

• Truth-functional LEM: For all P, either P is true or Not-P is true.
• Supervaluationist LEM: For all P, 'either P or Not-P' is true.

In general, though, the point behind LEM (on either reading) is that P and Not-P are mutually exclusive and jointly exhaustive. Between them, they completely exhaust logical space. Every possible scenario is one in which one of those two holds, and no possible scenario is one in which both hold.

But Hunt's example doesn't correspond to either reading of LEM. To show this we need only describe a logically possible scenario in which neither (1) 'Hunt calls his mother tomorrow' nor (2) 'Hunt does not call his mother tomorrow' obtains. Here's one: Hunt doesn't exist. In that case, Hunt isn't around either to call his mother or to refrain from calling his mother. So neither (1) nor (2) is true. (Compare with 'The present king of France is bald' and 'The present king of France is not bald'. Neither of those is true if there is no present king of France.)

Hunt might respond by suggesting that we should read (2) as (2*) 'It is not the case that Hunt calls his mother tomorrow'. On that reading we do indeed have an instance of LEM with (1) and (2*). But a new problem arises: (2*) isn't about a future contingent. It is true right now simply in virtue of the fact that tomorrow hasn't happen yet. Hence its current truth doesn't depend on anything future. What's more, its truth doesn't depend on Hunt's existence, the existence of his mother, or even the existence of any created thing whatsoever. Of course, if tomorrow Hunt should call his mother, (2*) will then have become false. But that in no way licenses the inference that it is now false.

In sum, either we have a choice between propositions about future contingents, but LEM fails to apply, or LEM applies, but we are no longer forced to choose between two propositions about future contingents. Either way, Hunt's argument has zero force against the open future position.

Theism and Truthmaking

Trenton Merricks claims that truthmakers must be what truths are "about" in some unarticulated sense of "about". He then argues against truthmaker-type principles by claiming that there are truths of various sorts for which his undefined aboutness criterion cannot be met.

In two of my last three posts I have criticized Merricks for leaving this vital piece of his argument undefined, and in my last post, I sought to rectify matters by presenting a criterion of aboutness for truthmakers:

A truth is "about" one of its truthmakers in the relevant sense if and only if (a) there exists something such that (b) full acquaintance with that thing and only that thing would enable one to know with certainty that the truth in question is true.

Now, I'm pretty sure that Merricks would reject my criterion, but until he shows me why its wrong I'm going to stick by it. What I want to argue in this post is that if one accepts my criterion of aboutness and if one accepts the necessary existence of an essentially omniscient God (as Merricks does), then Merricks' main objection against truthmaker principles (that there are truths which are not about any truthmakers) fails. In particular, I consider negative existentials and truths about the past.

Negative Existentials
It is true that there are no hobbits. In virtue of what could this be true? Merricks considers the suggestion that the entire physical universe might make this true, but he argues against that suggestion. For one thing, it doesn't suffice unless we posit a totality state of affairs, e.g., there being nothing more. Otherwise we could simply add a hobbit (and maybe a few other things) on top of the physical universe. But in that case the physical universe as it stands would not necessitate the truth of 'there are no hobbits' and so would not suffice to make it true. One wonders, though, what this totality state of affairs is supposed to consist in. It seems rather suspicious. Merrick's chief objection, though, is simply to claim that 'there are no hobbits' is not relevantly about the physical universe.

I think Merrick's is right that the physical universe by itself will not suffice without a totality state of affairs. And I agree that such a state of affairs looks unacceptably suspicious. But I don't think he's considered a plausible alternative truthmaker, one the existence of which he himself would seem to be committed to in virtue of being a theist, namely, God's having a hobbit-free experience of creation. No extra totality state is needed here because God's essential omniscience takes care of that. Nor could any theist reasonably dismiss this as unacceptably suspicious. And, moreover, by my aboutness criterion, this is a truthmaker for 'there are no hobbits' - thus, if we were fully acquainted with God's experience of creation, we would be able to know with certainty that that proposition is true.

Truths about the Past
Merricks, like myself, is a presentism, someone who believes that only what exists now exists simpliciter. A common objection against presentism is that it lacks the resources to supply truthmakers for truths about the past. Merricks accepts the objection but denies its force. He claims that truths about the past are relevantly about any presently existing things. And he argues that presentism is more plausible than any truthmaker principles, hence if the two conflict, it is the truthmaker principles that must go.

Against Merricks, I deny that there is any conflict between presentism and truthmaker principles. In a recently published paper, "Presentism, Truthmakers, and God" (available on my website), I argue in detail that God's memories can supply truthmakers for truths about the past. Moreover, God's memories satisfy my aboutness criterion - thus, if we were fully acquainted with God's memories, we would be able to know with certainty that, say, 'Caesar crossed the Rubicon' is true.

I think similar options are available for the other alleged problem-cases that Merricks considers. Moral: If you're a theist, don't bracket your theism when doing metaphysics. If God exists, he should be metaphysically relevant to (nearly) everything else.

More on Merricks on Truthmaking

I've now finishing my re-reading of Trenton Merricks' book Truth and Ontology and I'm still quite unconvinced by his contention that what's true does not depend on what exists in any substantive way. A couple posts ago I noted my main reasons for dissatisfaction with Merricks' arguments:

1. He loads down truthmaker principles, which affirm a substantive dependence of truth on being, with extraneous commitments.

Most significantly, he takes the raison d'etre of such principles to be that of catching all sorts of metaphysical "cheaters"--those who either (a) try to have their truths on the cheap, without paying an appropriate metaphysical price, or (b) invoke "suspicious" properties to do their truthmaking work. I deny that these concerns are fundamental to truthmaker principles. Such principles are merely attempts to articulate the driving intuition behind correspondence theories of truth, namely, that truth depends on being in a substantive way and, therefore, that there must be some being corresponding to any given truth that "makes" that truth true. What properties count as "suspicious" is to be determined not by truthmaker principles but by explanatory considerations (e.g., Are such properties merely "ad hoc", or do we have independent reasons for positing them? Can they plausibly be regarded as primitives, or can they be cashed out in some explanatorily informative way?)

2. He never carefully defines the crucial notion of "aboutness" upon which his major arguments depend.

Merricks insists that truths can only be made true by what those truths are "about". He then argues that for many types of truths there are no existing things that those truths are "about", from which he concludes that truthmaker principles are false. It is clear that the notion of "aboutness" is crucial to this argumentative strategy, and it is surprising that a philosopher of Merricks' calibre doesn't define it carefully. In fact, he explicitly declines to give an analysis (pp. 33-34) and relies, instead, on a handful of examples (e.g., pp. 28-29) which indicate only that "aboutness" has something to do with relevance. Here's one such example:

[Y]our thumb fails to be a genuine truthmaker for FLT [Fermat's Last Theorem]. . . . Even though your thumb's existence necessitates FLT's truth, FLT is not about your thumb. (p. 27)

I'll grant that a thumb is not a truthmaker for FLT. And I'll grant that a thumb's inadequacy as a truthmaker for FLT can be explained, to a first approximation, by the observation that FLT is not relevantly "about" a thumb. But Merricks needs to go a lot further than that. If he wants to refute truthmaker principles (and he does) then he needs to give an analysis of what the relevant "aboutness" relation is. Were he to provide such an analysis, of course, fans of truthmaker principles could subject it to scrutiny. Leaving the notion nebulous allows Merricks to rest his argument on impressionistic declarations that this or that type of truth isn't relevantly "about" any existing thing. He thus arrives at his conclusions by a certain amount of theft over honest toil.

In the rest of this post I'm going to help Merricks out a bit by clarifying the relevant sense in which truthmakers must be what truths are "about".

First, we need to distinguish between connotative and denotative senses of "about". In the connotative sense, to speak "about" (say) FLT is to say something about the content of the theorem. This requires some understanding of what the theorem means. But I can say, "I heard that some dude proved FLT a few years ago" and thereby talk "about" FLT without having any clue what FLT stands for. That's a strictly denotative sense of "about". Now, truthmaker principles are metaphysical, not epistemological in nature. They require that there exists something in virtue of which a truth is true, but they don't require us to know what that something is. Hence, the relevant sense of "aboutness" is denotative, not connotative.

Second, truthmakers must relevantly necessitate their truths. What that means is not simply that it must be impossible that the truthmaker exist and the truth in question fail to be true. Your thumb, after all, necessitates FLT in that sense. No, it must also be the case that the truth in question could be derived from knowledge of the truthmaker. In other words, if (hypothetically) someone were fully acquainted with a putative truthmaker and only that truthmaker, would that person thereby know with certainty that the truth in question is true? Your thumb is not a truthmaker for FLT because someone acquainted only with your thumb (however fully) would not thereby know FLT.

I claim that the above two points are all there is to the relevant "aboutness" relation. A truth is "about" one of its truthmakers in the relevant sense if and only if (a) there exists something such that (b) full acquaintance with that thing and only that thing would enable one to know with certainty that the truth in question is true.

Merricks, undoubtedly would want to insist on further constraints, at which we could have a healthy debate about them. My complaint is that he should have gone at least as far as I have here, and he could easily have done so.

In my next post, I'm going to use my "aboutness" criterion and show that on metaphysical assumptions that Merricks accepts, there are truthmakers for all of the truths for which he says there aren't any.

Gratuitous Evil and Divine Providence

I'm really happy right now because a paper of mine ("Gratuitous Evil and Divine Providence") was just accepted at Religious Studies. In my experience, at least, the turnaround at that journal is phenomenally fast. This is the second paper I've submitted there. On both I received an acceptance notice within a week or less.

I'll post a digital version of the paper to my website once I've sent the final version off to the journal. Here's the abstract:

Discussions of the evidential argument from evil generally pay little attention to how different models of divine providence constrain the theist’s options for response. After describing four models of providence and discussing theistic strategies for responding to the evidential argument, I articulate and defend a definition of “gratuitous evil” that renders the theological premise of the argument uncontroversial for theists. This forces theists to focus their fire on the evidential premise, enabling us to compare models of providence with respect to how plausibly they can resist it. I then give an assessment of the four models, concluding that theists are better off vis-à-vis the evidential argument if they reject meticulous providence.

UPDATE (7/20/09): The penultimate draft of the paper is now available on my website.

Merricks on Truthmaking

I've recently been rereading Trenton Merrick's book Truth and Ontology (Oxford, 2007) in which he argues against the substantive dependence of truth on being. Thus, he rejects theses like

• TM - Every truth has a truthmaker, a parcel of reality the existence of which necessitates, and thereby grounds, that truth.
• TSB - Truth supervenes on being. I.e., every possible difference in truth corresponds to a possible difference in reality (i.e., in what things exist and in what properties have and/or what relations they stand in), and vice-versa.
• Correspondence theory of truth - A proposition (or truth-bearer) is true iff what it represents is the case (i.e., iff reality is as the proposition depicts).

Merricks' strategy is to saddle the above theses with as much baggage as he can, thereby imposing steep restrictions on what an adequate theory of substantive dependence would have to look like, and then arguing that such theories fail to satisfy those restrictions.

His favorite restrictions are (1) that it is the purpose of theses like TM and TSB to "catch cheaters" by criticizing (a) those who fail to endorse an ontology robust enough to ground or necessitate the truths they feel free to invoke, and (b) those who try to discharge their grounding obligations by positing "suspicious" properties; and (2) that substantive grounds for truths must consists of what those truths are "about", in some rather loosely defined sense of that term.

For example, Merricks argues (ch. 6) that presentism (the theory that whatever exists simpliciter exists now) is true, that it violates TM and TSB, and therefore, that TM and TSB should be rejected. While he discusses some attempts by presentists to satisfy the demands of TM and TSB, Merricks rejects these either because they trade in "suspicious" properties or because they violate the "aboutness" constraint.

I'm not persuaded by Merricks. In part, that's because I think he's wrong that a purpose of TM and TSB is to catch cheaters of the second sort, namely, those who invoke allegedly "suspicious" properties. (All things equal, we ought to try to avoid "suspicious" properties where possible, but it's not TM and TSB's job to say what those properties are.) Also, I don't think he's nearly clear enough on the relevant sense of "aboutness". He admits it has something to do with "relevance", but apart from a handful of examples that he claims to find intuitive, he nowhere defines the notion.

Still, it is a fair question what someone like myself who is partial to TM and TSB should say about the truthmakers or the supervenience base for various kinds of truths. In particular, necessary truths, general truths, modal truths, negative existentials, counterfactuals, and metaphysical theses like presentism, actualism, and nominalism have all been thought to raise serious problems for TM and TSB. In the next few posts, I'm going to look at some of these problem cases and argue that they are less worrisome for theists than they might be for those of different metaphysical persuasions.

I Made the List

of 100+ living philosophers of religion.

Back to Blogging

I haven't done much in the way of blogging for the past several months. In large part this is because my energies have been focused on being a father to my now 18-month old daughter and on finishing several papers that I've been working on. Now that my desk is starting to clear up, I'm going to resume blogging again.

I don't promise to blog regularly. Blogging is something I do when I have spare time. It's not something I want to get absorbed into. So when I feel like I'm spending too much time at it, I'll back off again for a while. We'll see how it goes.

I'll put up a post sometime tomorrow with thoughts on truthmaking, theism, and modality. Right now, however, I've got to go home and spend time with my wonderful wife and daughter.