Tuesday, November 11, 2008

The semi-eternal itch

Let w be a world where there is only one finite being, George. George has always existed in w. Moreover, each day for George has been just like the previous. Each day, George is mildly happy overall—except he has a minor itch that he can't scratch. Let us suppose that the laws of nature in w are such that they allow one deviation from the endless cycle of repetition from day to day—the itch can disappear (and only in one way, at one particular time of day). After the itch disappears, each day will be mildly happy, and indeed happier than before, and each day, except the first post-itch day, will be just like the previous for George (George won't remember how many days it has been he has lost the itch), forever. Here is an intuition:

  1. It is better for George to have his itch disappear tomorrow than to have his itch disappear in a billion years.

But not all theories of time can do justice to this intuition. If time is relational (which also, I think, would imply that the B-theory holds), and we tell the details of the story right, then the world where the itch disappears today if the same as the world where the itch disappears in a billion years—both are worlds where there is an itch for an infinite number of years, and then there is no itch for another infinite number of years. Therefore, either time is not relational or else no situation like the above is possible. But the only good reason to think that no situation like the above is possible is if one thinks that there cannot be indiscernibles or one thinks that it is impossible to have existed for an infinite amount of time. Thus, either time is not relational or there cannot be indiscernible times or it is impossible to have existed for an infinite amount of time. Since I think time is relational, I conclude that either there cannot be indiscernible times or it is impossible to have existed for an infinite amount of time.

It's also not clear that presentism fits with (1). In both of the scenarios mentioned in (1), there is a present itch, and the future does not exist. So why should one of the scenarios be better than the other? If this argument, which I am less sure of, is right, then either presentism is false or it is impossible to have existed for an infinite amount of time.

It would be nice to do better than just getting disjunctive conclusions. For that, we'd need other arguments to rule out of more disjuncts.

5 comments:

Kyle said...

I'm not sure what you mean by an indiscernable time, could you explain a bit more.

Do you mean that if there were two worlds that matched this description they would in fact be indiscernable, so that there is really only one such world? This then makes the comparison impossible?

Gordon Knight said...

suppose you had a growing block view of time? Perhaps this view captures how it is that its better to stop the itch now (prevent its continuing?)???

Enigman said...

I think you are right to be less sure of the Presentistic version. At any time it is better to have the itch go away sooner rather than later.

Also, I wonder if there is an Eternalist version in which there are trivial variations between the days. We could have the second world shifted in such variations? That ought not to make any non-trivial difference, and yet according to our intuition it would.

Alexander R Pruss said...

Kyle:

Two times are indiscernible provided that the only differences between what is happening at the two times are in the numerical identity of the times and the items at the times (events, substances, accidents, whatever). Thus, t1 and t2 could be indiscernible if at both times there is exactly one person yawning, even though the yawnings would be numerically different, as long as they were yawning in exactly the same way. On the other hand, if at t1 there was exactly one person yawning, and at t2 there were at least two people yawning, the times would not be indiscernible.

GK:

Why should it matter whether the itch is stopped tomorrow or in a billion years on the growing block theory? In both cases, we don't stop the itch now, and the future continuation is unreal.

Enigman:

If one has trivial differences between days, I think the argument no longer works. Let's say that tomorrow George's nose is green, and the day after tomorrow it is mauve, and so on, so that on each day, the nose is a unique shade of color. Then George unproblematically has reason to ensure that on the day on which his nose is mauve, he is not itching, and so the relationalist eternalist can ignore the argument.

Enigman said...

Well, people can ignore what they want to ignore, of course; and indeed, it's not exactly the same argument, but it might rule out (if only as ad hoc) that resolution to your argument (leaving the rational relationalist eternalist with only the other one)? My reasoning was that if time is relational then if we make the colour on day n go to the colour on day n + m for any integer m, then we have actually made no change whatsoever (because the sequence is endless in both directions, and there are no other, intrinsic differences between the days).

The original intuition was that it is better for George to have his itch disappear tomorrow than to have his itch disappear in a billion years. The difference between those two is now expressible as the difference between the change occuring on the day when his nose has the colour it has on day n (that colour making that day nonidentical to any other day) and it occuring on the day when his nose has the colour it has on day n + m. That is, the original intuition is that there is such a difference. Of course, I may be wrong about one of those steps (my intuitions are no help to me here as they are presentistic:)