### 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:

- 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.
- 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.
- 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.

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.

## 6 Comments:

This relates to the points I made below. As I understand, you are saying (1) That it is perfectly possible that truths at one time can be totally uncorrelated with truths at another time. I.e. it is theoretically or logically possible that x can be true or false on Wednesday without anything having to be true or false on Thursday. Logically possible, of course, for in reality there must be causal connections between times that also connect the truths - e.g. moon and sun in this position today = truth of eclipse tomorrow. However (2) you also claim that if it is true on Wednesday that there will be a sea-battle on Thursday, then the 'truth on Wednesday' is a truth for Wednesday (and not just Thursday). This is because the truth 'obtains for that time' i.e. Wednesday, as well as obtaining for Thursday.

My reply is the same. We can signify now (Wednesday) that there will be a sea battle tomorrow. The truth now, for Wednesday, is that something is *now* being signified, not that something tomorrow is *now* true. And I use his argument again, that to signify (now) now that it is the case *now* that you will be white at a, signifies more than to signify now that you *will be* white at a. All that is required is that it is possible to signify at some other time what is signified now (when the seabattle occurs) by "a sea battle is happening".

Thanks for you comments, Ocham.

First, I don't claim here that truths at one time can be totally uncorrelated with truths at another time. Whether this is true depends on accessibility relations among times. I don't take a stand on that issue in this post.

As for it's being true on Wednesday that there will be a sea battle on Thursday, this implies that "there is a sea battle" is true on Thursday. But it obviously doesn't imply that "there will be a sea battle" is true on Thursday.

You say,

"We can signify now (Wednesday) that there will be a sea battle tomorrow. The truth now, for Wednesday, is that something is *now* being signified, not that something tomorrow is *now* true."Your unexplained distinction between "now" and "*now*" is confusing to me. Perhaps you can elaborate.

I put the asterix in the wrong place. The distinction is between 'signifying now that A will be the case' and 'its being the case now that A will be the case'.

I agree the first is true, i.e. 'now' qualifies 'signifying'. I don't agree that 'now' qualifies the present existence of a truthmaker

Regarding the post: If other times exist, how does truth at a time depend on what's the case at that time? I don't see how that would be true unless presentism were true. I'm not sure I'm really following you here.

Hi Ian,

Even if times other than T exist, I deny that it's analytically true that those times are mirrored at T. Perhaps other times are like other universes on the many universes hypothesis - causally and spatio-temporally isolated from each other. In other words, I don't think that truth accessibility relations among times (or 'truth-value links') can be had for free. They incur substantive metaphysical commitments, or so I claim.

If we're talking about the future, though, it can't fail to be spatiotemporally related to us (although I'm not really sure why that's supposed to be relevant anyway). So again, I'm not really sure what's going on here.

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