The Principle of Bivalence and Tensed Truths in Possible Worlds

The Principle of Bivalence (PB) says, basically, that for any proposition P, either P or not-P.[1] That is, PB says P is either true or false. A possible world is something like a maximal description of propositions (like P) or else states of affairs (which of course contain propositions). This can seem like a problem for the Molinist who embraces an A-theory of time (more on that later), since, if a possible world W contains a maximal description of all propositions, this will include tensed propositions. An A-theory of time states that tensed-talk, like “He will do such-and-such,” or “She was there,” etc., all express real features of objective reality, and not merely subjective experiences. That is to say, A-theorists about time think that tensed-talk is all true, instead of a literally false but linguistically unavoidable heuristic (as on a B-theory). So what’s supposed to be the problem?

Well, if an A-theory is true, then descriptions of W are going to include tensed truths like “Jim will eat a hot dog in one hour.” But what sense does that make in W, which is a complete description of all propositions? It seems that proposition would be both true and false. “I know how to solve this,” you might think, “Just point out that ‘Jim will eat a hot dog in one hour,’ is a tenseless statement roughly equivalent to, ‘Jim eats the hot dog at time t+1h,’ where t is some specific time, and the +1h is meant to indicate the tenseless ‘later-than’ relation.” I think that’s a very correct account of what’s going on. But then notice it seems that, if Molinism is true, tensed statements don’t appear to be a part of possible worlds. We thus seem to have to jettison A-theory, Molinism, this particular account of possible worlds, or some combination. None of that seems appealing.

So how can we solve this? This is where PB comes in. The objecting argument above has assumed something like this is true:

It must be the case that one of the following is true in W:

1.     Jim will eat a hot dog in one hour.

or

2.     Jim will not eat a hot dog in one hour.

To see why this is fallacious, consider this proposition: “I still beat my wife.” According to PB, supposedly anyway, it must be that either one of the following is true:

3.     I still beat my wife.

4.     I do not still beat my wife.

But notice the problem? This implies: a) that you beat your wife, and b) that you have a wife. Perhaps it is the case that one or both of these conditions is unsatisfied. So do we say PB has gone wrong? Not at all. Instead, PB actually isn’t saying, necessarily, either (3) or (4). Instead, what is necessary is either (3) or

5.     It is not the case that I still beat my wife.

Now (5) can be asserted just in the case that: a) you no longer beat your wife, b) you did not ever beat your wife, or c) you do not have a wife. And from this it becomes apparent that (3) or (5) is the state of affairs that PB demands, not (3) or (4). And from this, it becomes apparent what our application will be. For it is not (1) or (2) that is being demanded by PB, but instead (1) or

6.     It is not the case that Jim will eat a hot dog in one hour.

Taken this way, PB demanding (1) or (6) means (6) can be asserted under the following conditions: a) Jim does not exist in W (that is, he is uninstantiated in W); b) that tensed statements are false; c) hot dogs do not exist in W. Let’s stipulate (a) and (c) are unsatisfied (that is, Jim and hot dogs are instantiated in W). So, (b) isn’t open to the Molinist who is an A-theorist, right? Wrong!

The Molinist can just employ William Lane Craig’s strategy of saying that time had a first moment, and, thus, God is timeless without the creation, and in time subsequent to it.[2] This means that, logically prior to the first moment of time, no tensed propositions were true; nothing like (1) would be true, (6) would instead. Then, propositions like (1) would become true (see that objective becoming, just like A-theory says?!) upon both: a) God’s actualizing the world, and b) the relevant time applying. So (1), for example, would still be false, until one hour prior to the state of affairs of Jim’s eating a hot dog.[3] Thus, it seems the Molinist can have his cake and eat it too, at least with respect to the A-theory, a first moment in time, and possible worlds semantics.

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[1] I am deliberately mixing this with the Law of Excluded Middle for simplicity; just take the not-propositions as affirming that the “false” side of the original proposition is true.

[2] William Lane Craig, “Timelessness and Omnitemporality,” Philosophia Christi, Vol. 2, No. 1 (2000:), 29-33.

[3] Interestingly, this type of proposition (1) can be false, become true, become false again, and then become true, because it’s not dependent on any specific hot dog; it is true just in case the state of affairs Jim’s eating a hot dog is true one hour from the point in time objectively considered.