Events and the unreality of time

When I think about McTaggart’s famous argument against the A-theory of time—the theory that it is an objective fact about the universe what time it is—I sometimes feel like it’s just a confusion but sometimes I feel like I am on the very edge of getting it, and that there is something to the argument. When I try to capture the latter feeling in an argument that actually has a chance of being sound, I find it slipping away from me.

So for the nth time in my life, let me try again to make something of McTaggart style arguments. Last night I gave a talk at University of North Texas. When I gave the talk, it was present, and afterwards it became past, and every second that talk is receding another second into the past, becoming more and more past, “older and older” we might say. There is something odd about this, however, since the talk doesn’t exist now. Something that no longer exists can’t change anymore. So how can the talk recede into the further past, how can it become older and older?

Well, we do have a tool for making sense of this. Things that no longer exist can’t really change, but they can have Cambridge change, change relative to something else. Suppose a racehorse is eventually forgotten after its death. The horse isn’t, of course, really changing, but there is real change elsewhere.

More generally, we learn from McTaggart that events can’t really change, but can only change relative to real change in something other than events. The reasoning above shows that events can’t really change in their A-determinations. And they can’t change in their intrinsic non-temporal features, as McTaggart rightly insists: it is eternally true that my talk was about God and mathematics; all the flaws in the talk eternally obtain; etc. So if events can’t really change, but only relatively to real change elsewhere, and yet all of reality is just events, then there is no change.

But reality isn’t just events, and in addition to events changing there is the possibility for enduring entities to change. Here’s perhaps the simplest way to make the story go. The universe is an enduring entity that continually gets older. My talk, then, recedes into the past in virtue of the universe ever becoming older than it was when I gave the talk. (If one is skeptical, as I am, that there is such an entity as the universe, one can give a more complex story about a succession of substances becoming older and older.)

Can one run any version of the McTaggart argument against a theory on which fundamental change consists in a substance’s changing rather than in the change of events? I am not sure, but at the moment I don’t see how. If a person changes from young to old, we have two events: their youth A and their old age B. But we can now say that neither A nor B changes fundamentally: A recedes into the past because of the person’s (or the universe’s) growing old.

If this line of thought is right, then we do learn something from McTaggart: an A-theorist should not locate fundamental change in events, but in enduring objects.

A problem with Special Relativity Theory for perdurantists

There seems to be a problem for the conjunction of Special Relativity and perdurantism.  Maybe this is a standard problem that has a standard solution? Let's say that being bent is an intrinsic property. Perdurantists of the sort I am interested in think that Socrates is bent at a time in virtue of an instantaneous temporal part of him being bent (I think the argument can be made to work with thin but not instantaneous parts, but it's a little more complicated). Therefore:

1. x is bent at t only if the temporal part of x at t is bent simpliciter.

The following also seems like something perdurantists should say:

2. x is bent simpliciter only if every temporal part of x is bent simpliciter.

Now, we need to add some premises about the interaction of Special Relativity and time.

3. There is a one-to-one correspondence between times and maximal spacelike hypersurfaces such that one exists at a time if and only if one at least partly occupies the corresponding hypersurface.

Given a time t, let H(t) be the corresponding maximal spacelike hypersurface. And if h is a maximal spacelike hypersurface, then let T(h) be the corresponding time. Write P(x,t) for the temporal part of x at t. Then:

4. P(x,t) is wholly contained within H(t) and if z is a spacetime point in H(t) and within x, then z is within P(x,t)

and, plausibly:

5. If a point within x is within a maximal spacelike hypersurface h, then P(x,T(h)) exists.

Now suppose we have Special Relativity, so we're in a Minkowski spacetime. Then:

6. For any point z in spacetime, there are three maximal spacelike hypersurfaces h₁, h₂ and h₃ whose intersection contains no points other than z.

Add this obvious premise:

7. No object wholly contained within a single spacetime point is bent simpliciter.

Finally, for a reductio, suppose:

8. x is an object that is bent at t.

Choose a point z within P(x,t) and choose three spacelike hypersurfaces h₁, h₂ and h₃ whose intersection contains z and only z (by 6). Now define the following sequence of objects, which exist by 4 and 5:

• x₁=P(x,t)
• x₂=P(x₁,T(h₁))
• x₃=P(x₂,T(h₂))
• x₄=P(x₃,T(h₃))

Observe that x₄ is wholly contained in the intersection of the three hypersurfaces h₁, h₂ and h₃, and hence:

9. x₄ is wholly at z.
10. It is not the case that x₄ is bent simpliciter.

Now:

11. x₁ is bent simpliciter. (By 1 and 8)
12. x₂ is bent simpliciter. (By 2 and 11)
13. x₃ is bent simpliciter. (By 2 and 12)
14. x₄ is bent simpliciter. (By 2 and 13)

Since 14 contradicts 10, we have a problem.  It seems the perdurantist cannot have any objects that are bent at any time in a Minkowski spacetime. This is a problem for the perdurantist. If I were a perdurantist, I'd deny 2, and maintain that an object can be bent simpliciter despite having temporal parts that are bent and temporal parts that are not bent. But I would not be comfortable with maintaining this. I would take this to increase the cost of perdurantism. What is ironic here is that it is often thought that endurantism is what has trouble with Relativity.

Identity theory of mind

Here is a quick, and no doubt well-known, argument that mental states are not token-token identical with brain states. The argument makes assumptions I reject, but they are assumptions that, I think, will be plausible to a materialist. The idea is this. It is possible to transfer my mind into a computer, while preserving at least some of my memories, and with my brain being totally destroyed in the process (I reject this myself, but I think the materialist should accept Strong AI, and her best bet for a theory of personal identity is some version of the memory theory, which should allow this). Were such a transfer to be made, then I would have some of the numerically same token mental states (e.g., a memory of a particular embarassing episode) as I do now. But if these mental state tokens are now identical with brain state tokens, then it follows that it is possible that some of my brain states can survive the destruction of my brain, without any miracle, just by means of technological manipulation. But no brain state token of the sort that is correlated with memories[note 1], can survive the destruction of the brain, perhaps barring a miracle.[note 2] Hence, the mental states are not identical with brain states.

Of course, one might try a four-dimensionalist solution, supposing some temporally extended entity that coincides with the brain state prior to the destruction of the brain and with the electronic state after the destruction of the brain. But that won't save identity theory—it will only yield the claim that the mental state is spatiotemporally coincident with a brain state, or constituted by the brain state, vel caetera.

Maybe, though, what the identity theorist needs to do is to disambiguate the notion of a "brain state". In one sense, a brain state is the state of the brain's being a certain way. Call that an "intrinsic brain state" (note: it may be somewhat relational—I am not worried about that issue). If identity theory is understood in this way, the above argument against the identity theory works (assuming materialism, etc.) But a different sense of "brain state" is: a state of the world which, right now, as a matter of fact obtains in virtue of how a brain is.

Thus, consider the following state S: Alex's brain being gray, or there being a war in France. State S now obtains in virtue of how my brain is. But state S obtained in 1940 in the absence of my brain, since I did not exist then; instead, it obtained in virtue of there being a war in France. The state S is now a brain state, though earlier it wasn't. Call such a thing a "jumpy brain state": it can jump in and out of heads.

The identity theorist who accepts the possibility of mind transfer had better not claim that mental state tokens are identical with intrinsic brain state tokens but rather must hold that they are identical with jumpy brain state tokens. Put that way, the identity theory is much tamer than one might have thought. In fact, it is not clear that it says anything beyond the claim that the present truthmakers for mental state attributions are brain states.

Also, consider this. Presumably, for any jumpy brain state S, there is an intrinsic brain state S*, which right now coincides with S, and which is such that S obtains in virtue of S*. Thus, corresponding to the jumpy state Alex's brain being gray, or there being a war in France, there is the intrinsic brain state Alex's brain being gray. There is now a sense in which our identity theory is not faithful to its founding intuition that mental states are the states that neuroscience studies. For neuroscience certainly does not study jumpy brain states (neuroscience as such is not about wars in France, or information on hard drives). Rather, neuroscience studies intrinsic brain states. The identity theorist's mental state is identical with some jumpy brain state S, but it is S* that neuroscience studies.

And so there is a sense in which the identity theory is a cheat, unless it is supplemented with a non-psychological theory of personal identity that bans mind transfer between brains and computers. But the latter supplementation will, I think, also ban AI, since if computers can be intelligent, minds can be transfered between computers (think of a networked computation—the data can move around the network freely), and it would be weird if they could be transfered between computers but not from a brain to an appropriately programmed computer. Moreover, once one bans AI, one has made a claim that intelligence requires a particular kind of physical substrate. And then it becomes difficult to justify the intuition that aliens with completely different biochemical constitution (even an electronic one—cf. the aliens in Retief's War) could have minds.