Alethic Openness and Bivalence (Part 2 of 2)

By | May 20, 2014

In my previous post I briefly presented a reason, one having to do with the need to avoid fatalism and accommodate future contingency, for thinking that the future is alethically open, or such that there is no complete, true, linear story of the future.  I then noted that we can make sense of alethic openness by supposing that the members of the relevant class of propositions about future contingents are either (a) all false, or (b) neither true nor false. I left off in the middle of considering reasons for preferring (a) over (b) and vice-versa. I now resume that discussion.

Please note that I am not here defending the thesis that the future is alethically open. Rather, I am merely trying to adjudicate between

  1. IF the future is alethically open THEN (a).
    and
  2. IF the future is alethically open THEN (b).

The first thing we should do is specify more precisely the “relevant” class of propositions. There are two important distinctions to be made. One concern the form of the propositions. The other concerns what the propositions are¬†about.

Concerning form, some propositions about the future represent it¬†as determinate with respect to whether a given event occurs. Let’s call these determinate future propositions (DFPs).¬†For example, both <A sea battle (will/will not) occur tomorrow> and <A sea battle (does occur/does not occur) tomorrow> represent tomorrow as determinate with respect to whether a sea battle then occurs. In contrast, other propositions represent the future as indeterminate with respect to whether a given event occurs. Let’s call these¬†indeterminate future propositions (IFPs).¬†For example, both <A sea battle may occur tomorrow> and <A sea battle will probably occur tomorrow> leave open the possibility that a sea battle does¬†not occur tomorrow. (a) and (b) are to be understood as theses about DFPs, not IFPs.But they do not concern all DFPs. This is where the second distinction comes in.

Concerning aboutness, the relevant class of DFPs are those that are¬†about future contingent events. By an¬†event¬†I mean a concrete temporal occurrence. Events can stand in temporal relations (before, during, after), have durations (one day, one week, one year, etc.), and have both relative (yesterday, today, tomorrow) and absolute (Monday, May 19, 2014) temporal locations. A¬†future contingent¬†event is one¬†that¬†is undetermined¬†in relation to its¬†explanatory¬†antecedents. If the explanatory antecedents of an event do not determine the event, then they are compatible both with the events’ occurrence¬†and its non-occurrence. Finally,¬†a propositions is¬†about a future contingent event.

Let’s call DFPs that are about future contingent events¬†determinate future¬†contingent propositions (DFCPs).¬†(a) and (b) are to be understood as theses about DFCPs, not DFPs in general.

With the relevant propositions now demarcated, I now resume the discussion of (a) versus (b).

The main argument for (a) over (b) is that (b) requires denying two highly intuitive (but not incontestable) principles, namely, bivalence‚ÄĒthe thesis that each proposition is either true or, if not true, then false‚ÄĒand the¬†law of excluded middle, the thesis that, for all propositions p, either p is true or not-p is true.

The main argument for (b) over (a) is that some pairs of DFCPs seem to be contradictory. Since, by definition, two contradictory propositions cannot both be true and cannot both be false, if some pairs of DFCPs are contradictory, then it cannot be the case, as (a) alleges, that all such propositions are false.

It is the second type of argument I want to focus on here. In my previous post I sketched a version of such an argument. It was perhaps, needlessly complex, as it invoked a very subtle distinction between tensed and¬†tense-neutral propositions. I’m not sure that the distinction matters in this context, though it is important for the metaphysics of time. Readers not interested in the distinction are invited to¬†skip the next paragraph.

Excursus on ¬†tensed vs. tense-neutral propositions. Tense-neutral propositions represent matters from an absolute¬†or, if you will, “God’s eye” perspective as opposed to the¬†temporally situated perspective characteristic of tensed propositions. For example, if we read <Alan is¬†sitting at his computer> as a present-tense proposition, then it has the sense of “Alan is now sitting at his computer” and is true just in case Alan is now sitting at his computer.¬†But if we¬†read this¬†tense-neutrally then it merely has the sense of “Alan sits at his computer” and is true just is case reality includes Alan sitting at his computer, regardless of whether this is the case now,¬†at some other time, or even in some timeless manner.

So, why think that some pairs of DFCPs are contradictory? Consider first will/will not pairs of propositions like <Smith will attack Jones> and <Smith will not attack Jones>. These¬†may initially seem contradictory, but they aren’t. To show this it suffices to point out that the logical negation of <Smith will attack Jones> is <It is not the case that Smith will attack Jones> and that the latter is¬†not equivalent to <Smith will not attack Jones>. Why not? Because <Smith will not attack Jones> presupposes that Smith and Jones will both exist in the future, but¬†<It is not the case that Smith will attack Jones> could be true even if Smith and Jones will never exist and even if there is no future at all. Since they have different truth conditions, <It is not the case that Smith will attack Jones>¬†‚Ȇ¬†<Smith will not attack Jones>, and so the latter is not the contradictory of¬†<Smith will attack Jones>.

What about is/is not or does/does not pair of DFCPs? It may seem that <Smith is attacking¬†Jones> and <Smith is not attacking Jones> or <Smith does attack Jones> and <Smith does not attack Jones> are contradictory. After all, one might reasonably ask, if it isn’t the case that Smith is attacking Jones, then isn’t it the case that Smith is not attacking Jones. And if it isn’t the case that Smith is not attacking Jones, then isn’t it the case that Smith is attacking Jones?

But the same kind of reasoning as in the will/will not case shows that here too we don’t have contradictory pairs. To show this I’ll invoke a famous example of Bertrand Russell’s: <The present king of France is bald> and <The present king of France is not bald> are not contradictory. Both imply that there exists a present king of France, and so¬†both are false, as there is no such person. The logical contradictory of¬†<The present king of France is bald>, however, is¬†<It is not the case that the present king of France is bald>. This does¬†not assert that there is a present king of France and, in fact, it happens to be true. A similar analysis holds for all is/is not and does/does not pairs of propositions. Hence, no such pairs are contradictories. So the argument against (a) does not succeed.

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