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.