Discrete time and Aristotle's argument for an infinite past

Aristotle had a famous argument that time had no beginning or end. In the case of beginnings, this argument caused immense philosophical suffering in the middle ages, since combined with the idea that time requires change it implies that the universe was eternal, contrary to the Jewish, Muslim and Christian that God created the universe a finite amount of time ago.

The argument is a reductio ad absurdum and can be put for instance like this:

1. Suppose t₀ is the beginning of time.

2. Before t₀ there is no time.

3. It is a contradiction to talk of what happened before the the beginning of time.

4. But if (1) is true, then (2) talks of what is before the beginning of time.

5. Contradiction!

It’s pretty easy to see what’s wrong with the argument. Claim (2) should be charitably read as:

• Not (before t₀ there is time).

Seen that way, (2) doesn’t talk about what happened before t₀, but is just a denial that there was any such thing as time-before-t₀.

It just struck me that a similar argument could be used to establish something that Aristotle himself rejects. Aristotle famously believed that time was discrete. But now argue:

6. Suppose t₀ and t₁ are two successive instants of time.

7. After t₀ and before t₁ there is no time.

8. It is a contradiction of what happened when there is no time.

9. But if (7) is true, then (7) talks of what is when there is no time.

10. Contradiction!

Again, the problem is the same. We should take (7) to deny that there is any such thing as time-after-t₀-and-before-t₁.

So Aristotle needed to choose between his preference for the discreteness of time and his argument for an infinite past.

Physicalism, consciousness and history

Many physicalists think that conscious states are partly constituted by historical features of the organism. For instance, they think that Davidson’s swampman (who is a molecule-by-molecule duplicate of Davidson randomly formed by lightning hitting a swamp) does not have conscious states, because swampman lacks the right history (on some views, one just needs a history of earlier life, and on others, one needs the millenia of evolutionary history).

I want to argue that probably all physicalists should agree that conscious states are partly constituted by historical features.

For if there is no historical component to the constitution of a conscious state, and physicalism is true, then conscious states are constituted by the simultaneous arrangement of spatially disparate parts of the brain. But consciousness is not relative to a reference frame, while simultaneity is.

Here’s another way to see the point. Suppose that conscious states are not even partly constituted by the past. Then, surely, they are also not even partly constituted by the past. In other words, conscious states are fully constituted by how things are on an infinitesimally thin time-slice. On that view, it would be possible for a human-like being, Alice, to exist only for an instant and to be conscious at that instant. But now imagine that in inertial reference frame F, Alice is a three-dimensional object that exists only at an instant. Then it turns out that in every other frame than F, Alice’s intersection with a simultaneity hyperplane is two-dimensional—but she also has a non-empty intersection with more than one simultaneity hyperplane. Consequently, in every frame other than F, Alice exists for more than an instant, but is two-dimensional at every time. A two-dimensional slice of a human brain can’t support consciousness, so in no frame other than F can Alice be conscious. But then consciousness is frame-relative, which is absurd.

Once we have established:

1. If physicalism is true, conscious states are partly constituted by historical features,

it is tempting to add:

2. Conscious states are not even partly constituted by historical features.

3. So, physicalism is not true.

But I am not very confident of (2).

Against divine temporalism

I stipulate that:

0. According to pure divine temporalism, God is a being in time without a timeless existence all of whose decisions are made at moments of time.

I will argue that on plausible assumtions divine temporalism is incompatible with divine creative libertarian freedom.

First, we need this:

1. If pure divine temporalism is true, time has no beginning in the sense that before every moment of time, there was an earlier moment.

This is because everyone agrees that God is eternal. If there were a moment that had no moment before it, then according to pure divine temporalism, that moment would be God’s first moment of existence, without any timeless existence prior to or beyond it, and that is just incompatible with divine eternity. At that first moment it would be correct to say that God has just appeared.

One might object by saying that the first moment has infinite duration, and so it was an infinitely long changeless state. This is difficult to understand. An infinitely long changeless state seems like a timeless state more than anything else. In any case, if the point is pressed, I will simply stipulate that I don’t allow for moments like that.

Now, add this:

2. Every contingent feature of creation not even partly due to creaturely indeterministic activity was decided on by God with God having had the possibility of deciding otherwise. (Divine creative libertarian freedom)

Next, add some plausible claims:

3. The fact N that there was a moment of time before which there were no stars obtains.

4. The fact N is a contingent feature of creation not even partly due to creaturely indeterministic activity.

5. There is no backwards causation.

6. Time is linearly ordered: for any distinct moments of time t₁ and t₂, one is earlier than the other.

Finally:

7. For a reductio ad absurdum, assume pure divine temporalism.

What do we have? Well, our assumptions imply that God at some time decided on N while yet having the possibility of deciding to the contrary. But prior to any past time t₁, the fact N was already in place. History by time t₁ already made it be the case that there was a time before which there were no stars. So if there is no backwards causation, at no past time t₁ did God have the possibility of making N not be true. It was always already too late! But divine creative libertarian freedom requires that possibility.

Objection 1: The fact N does not actually obtain. We live in a sequential multiverse and before every time there were already stars in our universe or another.

Response: In that case, let S be the following contingent feature of creation: it was always the case that there already had been at least one star. I.e., for any past time t, there was a time t′ < t at which there had already had been at least one star. And an argument similar to the above goes through with S in place of N. At any past time, it was already too late to make S true, because history at that time was sufficient to make it be the case that prior to every time there was a star.

Objection 2: Fact N is made true by an infinite conjunction of facts such as that in year n there were no stars, in year n − 1 there were no stars, in year n − 2 there were no stars, and God unproblematically makes each of these facts true while having the power not to make it true.

Response: This objection is basically a rejection of (2). It says that some facts (even among the ones that aren’t due to creaturely indeterminism) aren’t freely decided on by God, but are instead consequences of other facts freely decided on by God. This reminds one of the Principle of Double Effect: God need not intend all the consequences of what he intends. He intends N_n, there not being stars in year n, as well as N_n − 1, and N_n − 2, and so on, but doesn’t intend their joint consequence N. I think this is a powerful objection. I don’t want to rule out the possibility of such a thing. But N is a morally unproblematic and structurally central part of the arrangement of reality. It seems very plausible that even if we reject (2) in general, we should accept it in the special case of morally unproblematic and structurally central parts of the arrangement of reality. Otherwise, God isn’t really in charge of creation.

Is the past changing all the time?

The past is unchangeable. But if the A-theory is true, then past events constantly objectively get older and older. That seems to be a kind of objective change. So, the A-theory is false.

Approximate truth and the very recent past

Suppose I say that Jim yelled in delight at 12:31. But in fact he did so at 12:32. Then I said something false but approximately true.

Now, suppose that I hear Jim giving a loud yell of delight about 300 meters away. While I am listening to that yell, I think that Jim is yelling. But in the last second of my hearing, Jim is no longer yelling, but the sound waves are still traveling to me. No big deal. My belief that Jim is yelling is false, but approximately true. Or so I want to say.

And it’s important to say something like this, for it allows us to preserve the idea that our sense give us approximate truth. The case of sound from 300 meters away is particularly strong, but the point goes through in all our sensation, as none of it travels faster than the speed of light. Now, granted, often when we become aware of a stimulus, our sensory organs are still undergoing it. But nonetheless it is strictly speaking false to say that this very part of the stimulus that we are now aware of is in fact going on. So our senses seem to lead us slightly astray. But at most very slightly. It is approximately true that this part of the stimulus is going on now, because it is in fact going on a fraction of a second earlier. Or, perhaps, it is a part of our common sense knowledge of the world that the data of the senses is only meant as an approximation to the truth, and so there is no straying at all.

Now imagine that I say that Jim actually yelled in delight at 12:31, but he was actually completely silent all day, although in a very nearby possible world he did yell in delight at 12:31. Then what I said is not approximately true. In ordinary contexts, the modal difference between the actual and the merely possible vitiates approximate truth, no matter how nearby the merely possible world is.

So now on to one of my hobby horses: presentism. If presentism is true, then the difference between what is happening now and what happened earlier is relevantly like the difference between the actual and the possible. In both cases, it is a difference between a neat and clean predication and a predication in the scope of a modal operator, pastly or possibly, respectively. If this is right, then if presentism is true, I cannot say what I said about its being approximately true that Jim is yelling if Jim has actually stopped. That difference is a very deep modal difference. That the time when Jim is yelling is in a nearby past no more suffices for the approximate truth of “Jim is yelling now” than that Jim is yelling in a nearby possible world is enough for the approximate truth of “Jim is actually yelling”. The ontological gulf between the actual and the possible is vast; so would be the ontological gulf between the present and the past if presentism were true.

Thus, the presentist cannot say that the senses tend to deliver approximate truth.

Objection: We know to correct the data of the senses for the delay.

Response: We know. But that's a recent development.

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".

Why can't the past change?

If you're a B-theorist, it is no puzzle that the past can't change. It can't change because we are always in the same world, and so neither the past, nor the present nor the future can change. Today, let us suppose (I think correctly) that it is the case that on Wednesday it was raining. Could it tomorrow be the case that it wasn't raining on Wednesday? Not at all—for the very same world, the very same events, that make propositions true today is the one that we evaluate against tomorrow. The fact that the past can't change, thus, is a matter of mere logic—it just follows from the truth conditions for sentences.

But what if you're an A-theorist? So, you think that things will be objectively different tomorrow. Indeed, you already do think that some things about Wednesday will objectively change. For instance, while today (Saturday) Wednesday is objectively three days in the past, tomorrow it will objectively recede one more day into the past. So in fact we already have a change, but a change that the A-theorist doesn't mind. (Though she should.)

In any case, logic alone doesn't do the job. One way to see this is that some A-theorists actually think the future changes. Thus, today, it is false that either I am at Mass on November 8 or that I am absent from Mass on November 8. But come November 8, this disjunction will be true. But the clever tricks that open futurists use to make sense of an open future could be used, equally well, to make sense of an open past. (The parallel holds for B-theory. The B-theorist is committed to the claim that the future cannot change. This sounds fatalistic, but we must distinguish the ability to change the future from the ability to affect the future.)

In the setting of my earlier post on A-theory, the claim that the past cannot change corresponds fairly closely (and in fact exactly, if we assume a closed past) to the claim that the earlier-than relation is transitive. If today, a world where it rains on Wednesday is is past, tomorrow that world will also be past. So in the setting of that post, the explanatory challenge to the A-theorist is why the earlier-than relation E is transitive. The A-theorist who takes E to be fundamental can only say that it is a brute fact that it is necessarily transitive.

There may be A-theorists who can meet the challenge, however. Suppose that you think that there is a TimeShift operator which shifts tensed propositions time-wise. Thus, if p is the proposition that it is sunny, TimeShift(+1 day, p) is the proposition that in a day it'll be sunny. Suppose, further, we take worlds to be maximal consistent collections of propositions, or maximally specific consistent propositions. Then the TimeShift operator can also operate on worlds, and we can define E(w₁,w₂) to hold iff there is a t<0 such that w₁=TimeShift(t,w₂). Then it really is a matter of simple logic that E is transitive, and we have a perfectly good explanation of why the past cannot change.

Note, however, that an open-futurist cannot take this explanation. For her, the fixeity of the past remains a surd.

If this is right, then Tom Crisp is mistaken in taking the earlier-than relation between abstract times (which are just worlds in my terminology) to be primitive. An A-theorist should not say it's primitive—it needs explaining. Or at least I remember him taking it to be primitive, but my memory isn't so good.

The changing past

A decade ago, the end of World War II was 54 years in the past. Right now, the end of World War II is 64 years in the past. If A-theory is true, these are genuine properties of WWII, and it has changed in respect of them. But something in the past cannot change. So A-theory is false.

The A-theorist's best answer to this argument is, I think, that this is a mere Cambridge change. A mere Cambridge change is when an object does not change in respect of intrinsic properties, but something else around it changes, which makes appropriate the application of a different predicate to it. The classic example is that x may grow shorter than y without changing in height—simply because y grew taller. The change in x was Cambridge and that in y was real.

A mere Cambridge of an object x change requires something else, a y, that really changes, where x's change consists in x having a description that makes reference to x's unchanged and y's changed qualities. Let us try to see how to do this for WWII.

Option 1: WWII has the unchanging property of ending in 1945. But 1945 has a changing property—it once was future, then was present, then was past, eventually being 54 years in the past, and now being 64 years in the past. So WWII, or WWII's end, undergoes a Cambridge change in virtue of 1945 (or a specific date in 1945) undergoing a real change. But the idea that 1945 should undergo a real change is at least a bit problematic, I think. It is plausible to say that 1945 is in the past, and so it shouldn't be able to really change. The alternative seems to be to makes times be something abstract—but the idea of abstract entities really changing is also troubling. So one would need to make 1945 be an enduring concrete entity. That's weird.

Option 2: WWII has the unchanging property of ending, say, 15,000,001,945 years after the beginning of the universe, but the universe has a changing age. When we say that WWII ended n years ago, we mean that the year that WWII ended, say 15,000,001,945 cosmic era, is equal to the age of the universe minus n. So, the end of WWII doesn't change, but the age of the universe does. This seems to work, but leads to further puzzles. What kind of an enduring entity is the universe? What is this property of age that so inexorably grows?

Option 3: WWII has the unchanging property of ending in 1945, but there is an objectively changing fact—the fact of which time is present. And in virtue of the latter changing fact, which does not consist in a change in any entity, 1945 undergoes Cambridge change. This view requires a relaxation of the account of Cambridge change—it doesn't require entities to change. (One might try to say that propositions reporting what time is present change in truth value. But that had better be true in virtue of something else.) I think the idea of change that does not happen in virtue of anything's changing is dubious.