What if there is no tomorrow?

There are two parts of Aristotle’s theory that are hard to fit together.

First, we have Aristotle’s view of future contingents, on which

1. It is neither true nor false that tomorrow there will be a sea battle

but, of course:

2. It is true that tomorrow there will be a sea battle or no sea battle.

Of course, nothing rides on “tomorrow” in (1) and (2): any future metric interval of times will do. Thus:

3. It is true that in 86,400,000 milliseconds there will be a sea battle or not.

(Here I adopt the convention that “in x units” denotes the interval of time corresponding to the displayed number of significant digits in x. Thus, “in 86,400,000 ms” means “at a time between 86,399,999.5 (inclusive) and 86,400,000.5 (exclusive) ms from now.”)

Second, we have Aristotle’s view of time, on which time is infinitely divisible but not infinitely divided. Times correspond to what one might call happenings, the beginnings and ends of processes of change. Now which happenings there will be, and when they will fall with respect to metric time (say, 3.74 seconds after some other happening), is presumably something that is, or can be, contingent.

In particular, in a world full of contingency and with slow-moving processes of change, it is contingent whether there will be a time in 86,400,000 ms. But (3) entails that there will be such a time, since if there is no such time, then it is not true that anything will be the case in 86,400,000 ms, since there will be no such time.

Thus, Aristotle cannot uphold (3) in a world full of contingency and slow processes. Hence, (3) cannot be a matter of temporal logic, and thus neither can (2) be, since logic doesn’t care about the difference between days and milliseconds.

If we want to make the point in our world, we would need units smaller than milliseconds. Maybe Planck times will work.

Objection: Suppose that no moment of time will occur in exactly x₁ seconds, because x₁ falls between all the endpoints of processes of change. But perhaps we can still say what is happening in x₁ seconds. Thus, if there are x₀ < x₁ < x₂ such that x₀ seconds from now and x₂ seconds from now (imagine all this paragraph being said in one moment!) are both real moments of time, we can say things about what will happen in x₁ seconds. If I will be sitting in both x₀ and x₂ seconds, maybe I can say that I will be sitting in x₁ seconds. Similarly, if Themistocles is leading a sea battle in 86,399,999 ms and is leading a sea battle in 86,400,001 ms, then we can say that he is leading a sea battle in 86,400,000 ms, even though there is no moment of time then. And if he won’t lead a sea battle in either 86,399,999 ms or in 86,400,000 ms, neither will he lead one in 86,400,000 ms.

Response: Yes, but (3) is supposed to be true as a matter of logic. And it’s logically possible that Themistocles leads a sea battle in 86,399,999 ms but not in 86,400,001 ms, in which case if there will be no moment in 86,400,000 ms, we cannot meaningfully say if he will be leading a sea battle then or not. So we cannot save (3) as a matter of logic.

A possible solution: Perhaps Aristotle should just replace (2) with:

4. It is true that will be: no tomorrow or tomorrow a sea battle or tomorrow no sea battle.

I am a bit worried about the "will" attached to a “no tomorrow”. Maybe more on that later.

An attempt to define possible futures for open futurism

On all-false open future (AFOF), future contingent claims are all false. The standard way to define “Will p” is to say that p is true in all possible futures. But defining a possible future is difficult. Patrick Todd does it in terms of possible worlds apparantly of the classical sort—ones that have well-defined facts about how things are at all times. But such worlds are not in general possible given open future views—it is not possible to simultaneously have a fact about how contingent events go on all future days (assuming the future is infinite).

Here is an approach that maybe has some hope of working better for open future views. Take as primitive not classical possible worlds, but possible moments, ways that things could be purely at a time. Possible moments do not include facts about the past and future.

Now put a temporal ordering on the possible moments, where we say that m₁ is earlier than m₂ provided that it is possible to have had m₁ obtaining before m₂.

For a possible moment m, define:

• open m-world: a maximal set of possible moments including m such that (a) all moments in the set other than m are earlier or later than m and (b) the subset of moments earlier than m is totally ordered

• possible history: a maximal totally ordered set of possible moments

• possible future: a possible history that contains m.

Exactly one possible moment is currently actual. Then:

• possible future: a possible future of the currently actual moment.

Now consider the problem of entailment on AFOF. The problem is this. Intutiively, that I will freely mow my lawn entails that I will mow my lawn, but does not entail that I will eat my lawn. However, since on AFOF “I will freely mow my lawn” is necessarily false—it is false at every possible moment, since “will” claims concerning future contingent claims are always false—both entailments have necessarily false antecedents and hence are trivially true.

Given a set S of moments and a moment m ∈ S, any sentence of Prior’s (or Brand’s) temporal logic can be evaluated for truth at (S,m). We can now define two modalities:

• p is OW-necessary: p is true at (W,m) for every open m-world W

• p is PH-necessary: p is true at (H,m) for every possible history H that contains m.

And now we have two entailments: p OW/PH-entails q if and only if the material conditional p → q is OW/PH-necessary.

Then that I will freely mow my lawn is OW-impossible, but PH-possible, and that I will freely mow my lawn OW-entails that I will eat my lawn, but does not PH-entail it. The open futurist can now say that our intuitive concept of entailment, in temporal contexts, corresponds to PH-entailment rather than OW-entailment.

I think this is helpful to the open futurist, but still has a serious problem. Consider the sentence “I will mow or I will not-mow.” On AFOF, this is false. But it is true at every possible history. Hence, it is PH-necessary. Thus, PH-necessity does not satisfy the T-axiom. Thus PH-entailment is such that a truth can PH-entail a falsehood. For instance, since “I will mow or I will not-mow” is PH-necessary, it is PH-entailed by every tautology.

On trivalent logics, if "I will mow or I will not-mow" is neither true nor false, we have a similar problem: a truth PH-entails a non-truth.

There are is a more technical problem on some metaphysical views. Suppose that it is contingent whether time continues past a certain moment. For instance, suppose there is no God and empty time is impossible, and there is a particle which can indeterministically cease to exist, and the world contains just that particle, so at any time it is possible that time is the last—the particle can pop out of existence. Oddly, because of the maximality condition on possible histories, there is no possible future where the particle pops out of existence.

I wonder if there is a better way to define entailment and possible futures that works with open future views.

Possible futures

Given a time t and a world w, possible or not, say that w is t-possible if and only if there is a possible world w_t that matches w in all atemporal respects as well as with respect to all that happens up to and including time t. For instance, a world just like ours but where in 2027 a square circle appears is 2026-possible but not 2028-possible.

Here is an interesting and initially plausible metaphysical thesis:

1. The world w is possible iff it is t-possible for every finite time t.

But (1) seems false. For imagine this:

2. On the first day of creation God creates you and promises you that on some future
   day a butterfly will be created ex nihilo. God never makes any other promises. God never makes butterflies. And nothing else relevant happens.

I assume God’s promises are unbreakable. The world described by (2) seems to be t-possible for every finite time t. For the fact that no butterfly has come into existence by time t does not falsify God’s promise that one day a butterfly will be created. But of course the world described by (2) is impossible.

(It’s interesting that I can’t think of a non-theistic counterexample to (1).)

So what? Well, here is one applicaiton. Amy Seymour in a nice paper responding to an argument of mine writes about the following proposition about situation where there are infinitely many coin tosses in heaven, one per day:

3. After every heads result, there is another heads result.

She says: “The open futurist can affirm that this propositional content has a nearly certain general probability because almost every possible future is one in which this occurs.” But in doing so, Seymour is helping herself to the idea of a “possible future”, and that is a problematic idea for an open futurist. Intuitively:

4. A possible future is one such that it is possible that it is true that it obtains.

But the open futurist cannot say that, since in the case of contingent futures, there can be no truth about its obtaining. The next attempt at accounting for a possible future may be to say:

5. A future is possible provided it will be true that it is possible that it obtains.

But that doesn’t work, either, since any future with infinitely many coin tosses (spaced out one per day) is such that at any time in the future, it is still not true that it is possible that it obtains, since its obtaining still depends on the then-still-future coin tosses. The last option I can think of is:

6. A future is possible provided that for every future time t it is t-possible.

But that fails for exactly the same reason that the t-possibility of worlds story fails.

Here is one way out: Deny classical theism, say that God is in time, and insist that God has to act at t in order to create something ex nihilo at t. But God, being perfect, can’t make a promise unless he has a way of ensuring the promise to come true. But how can God make sure that he will one day create the butterfly? After all, on any future day, God is free not to create it then. Now, if God promised to create a butterfly by some specific date, then God could be sure that he would follow through, since if he hadn’t done so prior to the specified date, he would be morally obligated to do so on that day, and being perfect he would do so. So since God can’t ensure the promise will come true, he can’t make the promise. (Couldn’t God resolve to create the butterfly on some specific day? On non-classical theism, maybe yes, but the act of resolving violates the clause “nothing else relevant happens” in (2).)

This way out doesn’t work for classical theism, where God is timeless and simple. For given timelessness, God can timelessly issue the promise and “simultaneously” timelessly make a butterfly appear on (say) day 18, without God being intrinsically any different for it. So I think the classical theist has reason to deny (1), and hence has no account of “possible futures” that is compatible with open futurism, and thus probably has to deny open futurism. Which is unsurprising—most classical theists do deny open futurism.

Eternalism and future non-existence

I go back and forth on whether this is a strong argument against eternalism:

1. Given eternalism, it is guaranteed to be eternally the case that one exists simpliciter, even if one’s existence comes to an end.

2. Given eternalism, one’s existence coming to an end is just finitude in the forwards temporal direction.

3. If it is guaranteed to be eternally the case that one exists simpliciter, finitude in the forwards temporal direction would not be something to be dreaded.

4. So, given eternalism, one’s existence coming to an end would not be something to be dreaded. (1–3)

5. One’s existence coming to an end would be something to be dreaded.

6. So, eternalism is false. (4–5)

(As a theist, I think our existence does not come to an end. Hence the hypothetical “would” in (5).)

The intuition behind (3) is that finitude in the forwards temporal direction, given that one exists simpliciter, is akin to finitude in the backwards temporal direction or along a spatial axis, and these are clearly not to be dreaded.

But, on reflection, I think the eternalist can make very good sense of the appropriate attitudes to an end of existence. Consider this: If I were threatened with amputation of the part of me below the head—i.e., with being reduced to a head in a life-support tank—that would be something to be dreaded. It would be something to be dreaded, because the kind of functioning that is natural to human beings requires the below-the-head portion of the body. On the other hand, we could imagine sessile aliens that are very much like human heads, and there is nothing dreadful about the life of these aliens. These aliens’ lack of the below-the-head functioning normal humans enjoy would not be a deprivation.

Thus, human flourishing has spatial requirements: we require all of our body to fully flourish. Similarly, human flourishing has a robust temporal requirement: it requires an eternal future. This is because of the nature of human flourishing. Plausibly, human flourishing has a drive to infinity, requiring endless growth knowledge of reality and relationship with others. (This is probably not the whole story, but it will do for this post.) But our flourishing does not require spatial unlimitedness—on the contrary, there is a maximum size along each spatial axis such that a human being that is too big along that axis is not a fully flourishing human being.

We are four-dimensional beings, and we require a specific four-dimensional shape to flourish: a shape that is not too small and not too large in the three spatial directions and that is infinite in the forwards temporal direction. A finite future is a terrible truncation.

Now not every animal is like humans. Brute animals do not require an eternal future to be fully flourishing: they can achieve complete flourishing in a finite life, say because the lack the drive to the infinite that humans have. If we were like that, it would not be appropriate for us to dread future non-existence. Not being inclined to dread future non-existence is hard for us to imagine, because the drive to the infinite arises from such deep features of our nature. But philosophically, it makes perfect sense to think that there could be beings that can complete their flourishing in a finite compass.

The eternalist’s seeing a future end of existence of a human as a terrible truncation, but as not necessarily a terrible truncation in a non-human, seems very compelling. On the other hand, I think it is harder for a presentist to make sense of the difference here. Future non-existence seems really bad, because future non-existence on presentism would imply that eventually one will not exist simpliciter, and that seems dreadful. But the dreadfulness of this seems to have to do with the value of existence simpliciter, and not with our nature. Thus, we may have a story as to why it would make sense for a presentist to dread an end to existence, but that story proves too much: for that story would apply even if the presentist were the kind of non-human that doesn’t need an infinite future for flourishing.

Presentism and counting future sufferings

I find it hard to see why on presentism or growing block theory it’s a bad thing that I will suffer, given that the suffering is unreal. Perhaps, though, the presentist or growing blocker can say that is a primitive fact that it is bad for me that a bad thing will happen to me.

But there is now a second problem for the presentist. Suppose I am comparing two states of affairs:

1. Alice will suffer for an hour in 10 hours.
2. Bob will suffer for an hour in 5 hours and again for an hour in 15 hours.

Other things being equal, Alice is better off than Bob. But why?

The eternalist can say:

1. There are more one-hour bouts of suffering for Bob than for Alice.

Maybe the growing blocker can say:

2. It will be the case in 16 hours that there are more bouts of suffering for Bob than for Alice.

(I feel that this doesn’t quite explain why it’s B is twice as bad, given that the difference between B and A shouldn’t be grounded in what happens in 16 hours, but nevermind that for this post.)

But what about the presentist? Let’s suppose preentism is true. We might now try to explain our comparative judgment by future-tensing (1):

3. There will be more bouts of suffering for Bob than for Alice.

But what does that mean? Our best account of “There are more Xs than Ys” is that the set of Xs is bigger than the set of Ys. But given presentism, the set of Bob’s future bouts of suffering is no bigger than the set of Alice’s future bouts of suffering, because if presentism is true, then both sets are empty as there are no future bouts of suffering. So (3) cannot just mean that there are more future bouts of suffering for Bob than for Alice. Perhaps it means that:

4. It will be the case that the set of Bob’s bouts of suffering is larger than the set of Alice’s.

This is true. In 5.5 hours, there will presently be one bout of suffering for Bob and none for Alice, so it will then be the case that the set of Bob’s bouts of suffering is larger than the set of Alice’s. But while it is true, it is similarly true that:

5. It will be the case that the set of Alice’s bouts of suffering is larger than the set of Bob’s.

For in 10.5 hours, there will presently be one bout for Alice and none for Bob. If we read (3) as (4), then, we have to likewise say that there will be more bouts of suffering for Alice than for Bob, and so we don’t have an explanation of why Alice is better off.

Perhaps, though, instead of counting bouts of suffering, the presentist can count intervals of time during which there is suffering. For instance:

6. The set of hour-long periods of time during which Bob is suffering is bigger than the set of hour-long periods of time during which Alice is suffering.

Notice that the times here need to be something like abstract ersatz times. For the presentist does not think there are any future real concrete times, and so if the periods were real and concrete, the two sets in (6) would be both empty.

And now we have a puzzle. How can fact (6), which is just a fact about sets of abstract ersatz times, explain the fact about how Bob is (or is going to be) worse off than Alice? I can see how a comparative fact about sets of sufferings might make Bob worse off than Alice. But a comparative fact about sets of abstract times should not. It is true that (6) entails that Bob is worse off than Alice. But (6) isn’t the explanation of why.

Our best explanation of why Bob is worse off than Alice is, thus, (1). But the presentist can’t accept (1). So, presentism is probably false.

An open future precludes present motion

1. Whether an arrow is moving now depends on where it will be in the future.
2. If the future is open, there is no fact about where the arrow will be in the future.
3. If if whether p depends on how A is, and there is no fact about how A is, then it is not a fact that p.
4. So, if the future is open, no arrow is moving now.

Premise 1 is the most controversial one. Suppose that an arrow has been flying for half a second. There are two metaphysically possible worlds. In the first, it continues moving as usual. In the second, its motion instantly reverses after this moment, so that this moment is the furthest point in its flight. In the second world there is no more reason to say that the present moment is the last moment of forward motion than to say that it is the first moment of backward motion. So we shouldn't say the arrow is moving forward in the second world.

Hence there are worlds that differ on whether the arrow moves now and yet that differ only in the future positions of the arrow. That gives us reason to accept 1.

Premise 2 is particularly clear given theism: God can miraculously relocate the arrow if he so chooses. But I think premise 2 is going to be plausible on other views, too.

The importance of the future

It would be bad for me to permanently cease to exist in five minutes. But why? Suppose first a metaphysics of time on which there is no future, namely Growing Block or Presentism. On such a metaphysics there is no such thing as my future life, so how could it be bad for there to be a cessation of it?

Since the only tenable alternative to Growing Block and Presentism is Eternalism, the view that the past and future are real (oddly, there are no Futurists who think the future is real but deny the reality of the past), Eternalism is true.

Now, given Eternalism, we have a choice for three visions of our persistence through time. On one vision, Exdurantism, we are instantaneous stages that do not persist through time at all—at most we have temporal counterparts at other times. This does not fit with the intuition of my radical incompleteness should I cease to exist in five minutes. The second vision is Endurantism: I am wholly present at each time at which I exist. But then if the present moment is real, and eternally will be real, and I wholly exist at this present moment, then the intuition about the deep incompleteness I would have were my existence to permanently end in five minutes is undercut. So that can't be right either.

What remains is a family of views on which we are strung out four-dimensionally. The most common member of the family is Perdurantism: I am four-dimensional but have three-dimensional stages localized at times. A less common view is that I am four-dimensional, but not divided up into stages. Both of these views do justice to the idea that my existence is deeply incomplete, in something like the way it would be if I were missing an arm, should I cease to exist in five minutes.

As far back as I thought much about time (probably going back to age 10) I was an Eternalist. Until a couple of years ago, I was an Endurantist. Then I started being unsure whether Endurantism or a stageless four-dimensional view is right. The above argument strongly pushes me towards a four-dimensional view, and since I don't believe in stages, a stageless one.

Moreover, the above may help with a puzzle I used to have, which was how a B-Theorist should think about the badness of impending evils (especially death). How can a B-Theorist make sense of the badness of being closer and closer to something bad? But that may primarily be a problem for the Endurantist, since the Endurantist thinks we are three-dimensional beings wholly located in the here and now (as well as in the there and later, of course).

Antipastism

Antipastism would be the view that the past is unreal, but both the present and the future are. I asked my six-year-old son whether he thought the past was real. He was quite sure it wasn't. One of his reasons was that we can't get there. I then asked him if he thought the future was real. He was quite unsure either way. In other words, he vaccilated between presentism and antipastism.
This is interesting, because if presentists feel a pull away from their theory, I would expect that it would often be towards an open future view on which the past is real but the future is not.
Anyway, one can take my son's reasoning and formalize it into a plausibilistic argument:

1. If you can get somewhere, it's probably real.
2. You can get to the future. (It's easy, just wait a moment.)
3. So the future is probably real.

In an earlier post, I called antipastism "Shrinking Block".

A quick argument against Open Future views

Open Future views hold that if p is a proposition making a contingent claim about the future, then p is not true (on some versions, p lacks truth value, and on other versions, p is false).

Now suppose you find out that at t₀, on an ordinary autumn morning in New York City, Bill Gates tossed down a million twenty-dollar bills from an airplane, each with a sticker attached saying: "Please take this. It's a gift from Bill Gates." You are then in a position to know the following fact:

1. At t₀+48hrs, at least one of the twenties is not be where it fell.

But if Open Future views are true, then you don't know this, unless you know something more about t₀. For if t₀ is somewhere in the last 48hrs, then (1) is a future contingent. Being a future contingent, you cannot know it. For the only propositions that can be known are ones that are true. But since you do know (1), Open Future views are false.

To put it differently: Oddly, if Open Future views hold, then whether you know (1) depends on whether t₀ was in the last 48hrs, or further back, regardless of further evidence. Thus, what inferences can be made from a fact depends on how far back that fact is. This is not very plausible.

Perception

With training, a tennis player can see where the ball coming towards her will strike the ground. Why not say this is genuine perception? That it takes training is irrelevant—most perceptions do. I guess the best reason to deny this is a perception is to require that a perception be caused by the perceived state of affairs. But now here is an interesting thing. This morning I saw a cow and I saw it as a cow. The causal criterion requires, then, that the cowness of the cow have caused my perception. And this requires an Aristotelian view of forms as causally efficacious. A Thus, it seems, either we can see the future or Aristelianism is true or we can't see any cow to be a cow. Maybe the causal criterion can be replaced with an explanatory one, though, which would weaken the Aristotelian conclusion while broadening the scope of what we can see.

[By the way, sorry for the typos in recent posts. They were typed mainly with vim over ssh on my Treo. I now have a Internet access on a device with a full-size keyboard, which should improve things.]

Knowledge of the future

It is sometimes claimed that our knowledge of the future is foggy and lacking in detail, that we know very little about the future, except in a general way. I will argue that if we discount eschatological considerations, we know a lot about the future, and with a lot of specificity. So, for now, let us discount eschatology. Then, I know that American history textbooks in the year 2040 covering the first decade of the 21st century will contain a statement entailing that GWB was elected in 2004.

I know that a record of this post will be available encoded in an operating or recoverable electronic form in 2015. Anything on this blog is currently found on at least dozens of hard drives, including yours, dear reader, if you're reading on a hard-drive based computer, and including hard drives in blogspot's servers, on my home server (both the main and the backup hard drive), etc. Granted, it may be that all this data will be overwritten, but it will still be recoverable if enough effort is put into recovery (see this story on recovery of data on a hard drive in the Columbia disaster). I also know this for a lot of other information on the Internet. I also know that at least one copy of the complete works of Shakespeare will survive to 2040.

In fact, if eschatology can be discounted, I submit that I know just about as many pieces of information about how things will be in the future as I do about how things were in the past. Of course there are many things I don't know about the future, just as there are many things I don't know about the past.

So why is it that we feel that the future is so much less known than the past? I want to offer two hypotheses. The first is that we have an awareness of eschatological possibilities, of the fact that we cannot really estimate the probability that, say, in one year God will step in and really change things heavily. I am not sure this hypothesis accounts for the phenomena, though. Non-religious people are also prone to feel that the future is less well known than the past. And I can probably modify at least some of my predictions so they take the eschaton into account. Instead of talking about history books, let's talk about knowledge: I know that some people will know in 2020 that GWB was elected in 2004 (these people might be in heaven, but that doesn't affect the claim). In fact, I know quite a lot about what people will know in 2020—just about every major widely known fact about the world as it is now will be known by somebody.[note 1]

My second hypothesis as to why we feel there is an asymmetry is that this is simply because so many of the things about the future which we want to know are unknown, while comparatively fewer things about the past which we want to know are unknown. The asymmetry, then, perhaps isn't in what we know about the future or past, but in what we want to know. There is a lot more unsatisfied desire in us to know the future than there is unsatisfied desire to know the past. Or at least so it is in our culture.