Truth-at-T Depends on What Exists-at-T

In my previous post I made the following claim without argument: "for a proposition to be true now, what it represents as being the case must correspond to ... what is the case now." I'm now going to give that argument.

Every argument for any categorical conclusion requires some categorical assumptions which are not defended within the scope of that argument. Here are some of my assumptions:

1. Truth supervenes on being (TSB). This means that what is true depends on what exists for its being true. Moreover, every difference in truth corresponds to a difference in being, such that if anything that is true had not been true, then there would have been a corresponding difference in reality.
2. Correspondence theory of truth (CT). A proposition is true if and only if the state of affairs (STOA) that it represents obtains. In other words, a proposition p is true if and only if the STOA that would be posited were p asserted obtains.
   
3. It makes sense to speak of a proposition's being true at a time. This notion is compatible with, but does not entail, the idea that truth is temporally invariant.

I won't defend these claims here, though if pressed I might be willing to restrict (1) and (2) to contingent truths.

Now, the key to establishing my claim that what is true at a time depends on what is real or what exists at that time is to understand the notion of 'truth at a time'. I want to suggest that we should think about this notion in a manner analogous to the idea of 'truth at a world'.

In metaphysics, possible worlds are typically distinguished in terms of what is true 'at' them. Thus, worlds W and W* are distinct if and only if something is true at W that is not true at W*, or vice-versa. To consider what is true at a world is essentially to ask what would be true if that world were actual. Alternatively, since each world is actual from its own perspective, we can ask how things stand from the perspective of that world. Finally, what is true at one world may be reflected in what is true at another world. Whether this is so depends upon the accessibility relations that hold among the worlds in question. Thus, if p is true at W, and if W is accessible to W* (that is, if one can "see" W from the perspective of W*), then it is true at W* that p is true at W.

Analogously, 'truth at a time' means truth as judged from the perspective of a given time. By a 'time' I mean a complete time-slice of reality, an instantaneous world state. To determine what is true at a time we ask what would be true if that time were present. Alternatively, since each time is present from its own perspective, we can ask how things stand from the perspective of that time. If T is such that Caesar is ruling in Rome, then "Caesar is ruling in Rome" is true at T. If T* is such that Nero (and not Caesar) is ruling in Rome, then "Caesar is ruling in Rome" is false at T*. As with worlds, what is true at one time may be reflected in what is true at another time. Whether this is so depends upon the accessibility relations that hold among the times in question. Thus, if p is true at T, and if T is accessible to T* (that is, if one can "see" T from the perspective of T*), then it is true at T* that p is true at T. If, in addition, T* is earlier than, simultaneous with, or later than T, then accessibility may be expressed in terms of tense. Thus, if p is true at T, and if T is accessible to T*, and if T is earlier than T*, then it is true at T* that it was the case that p is true at T.

The thesis I set out to defend follows from what I have said above. Just as what is true at a world depends upon what obtains at that world, so also what is true at a time depends upon what obtains at that time. This neither precludes nor entails there being accessibility relations among times such that what is true at one time either has been or will be true at another time. Accordingly, it cannot be true now, for example, that there will be a sea battle tomorrow, unless this truth supervenes upon present reality. Depending on accessibility relations, however, it may be true now that it will (probably) be true tomorrow that there is a sea battle.