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.
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.