Thursday, June 7, 2012

Punishment, time, and a poor objection to identity after fission

It is a truism that the punishment should follow the crime. Thus, even if you know with enough certainty for court conviction that Smith will commit a crime, that is not enough for punishment.

But we need a qualifier. Punishment only needs to follow the crime in internal time. Smith builds a time machine while in prison and travels to 160 million BC. Now, there is a small police outpost in 160M BC, protecting time-traveling scientists from nefarious time travelers, and there is a small jail. It turns out that backwards time travel is much cheaper than forwards time travel (at any decent speed, measured in the ratio of external to internal time). To send Smith back to his time would be prohibitively expensive. There would be no injustice in jailing him in the year 160M BC, notwithstanding his protestations that he hasn't committed any crimes yet. For that's only true according to external time, since by his internal past, he had committed crimes.

Now, consider an apparent case of a person fissioning, say due to a Star Trek transporter malfunction. I used to argue that it is not tenable to suppose that the result of that is a single bilocated person on the grounds that it would be then be appropriate to punish the person in one location for what their copy in the other location did, which seems absurd. But I now think this argument is mistaken. For on the hypothesis that the person comes to be bilocated, we should now think of the person's internal time as having different branches corresponding to each location (this can best be seen by noting that we can run twin paradoxes between them). But then it is false that the person in location A can be justly punished at t2 for what the person in location B had done at an earlier time t1. For punishment should follow the crime in internal time. But since the two internal timelines are parallel, what B did is neither earlier than, nor simultaneous with, nor later than the punishment of A—there is no comparison between these internal times. Of course the external time of the punishment is later than the external time of the crime, but that is irrelevant. If parents took a 14-year-old Hitler for a time-travel excursion to our time, it would be wrong for us to now punish the young Hitler for the crime he had committed in the 1930s, since those crimes would not be earlier than the punishment in his internal time.

So while there might be objections to identity-after-fission, the punishment objection is not very strong.

One qualifier: It would not be wrong to set things up so that the punishment would be simultaneous with the crime, as long as the crime caused the punishment in the right way. So where I say that the punishment should follow the crime, I should include the possibility that the two are internally simultaneous, but with the crime explanatorily prior.

6 comments:

jessriedel said...

For physicists, "proper time" and "coordinate time" are the more appropriate choices rather than "internal" and "external time". It's probably worth at least mentioning at the beginning of the discussion.

Alexander R Pruss said...

Proper time and coordinate time may only make sense in the case of worlds whose spacetime structure is something like that given by the theory of relativity. But we want to be able to talk about punishment, fission and the like in worlds where physics is completely different.

Moreover, proper time is defined along a worldline with no spatial extension. But a typical substance, like you or I, is spatially extended, and hence does not seem to define a unique worldline. The internal time of a substance, then, might not match up with proper time along any particular worldline. In fact, it could be that a really long extended substance--think of a living worm that's a light-year long--is such that there is no timelike worldline wholly contained within it (just think of the different ways that one amputate and transplant long sections of such a substance).

jessriedel said...

If you're not assuming that the physical laws are close enough to general relativity such that the notions of proper and coordinate time are obvious, then I have no idea what you would mean by internal time and external time. Can you give me an example of a universe with new physics where internal/external time is not the same as (the obvious generalization of) proper/coordinate time and yet I can still apply my human moral intuitions concerning internal/external time?

With regards to your second paragraph, I don't know how you could define a morally-significant internal time for such a worm. If we look on short enough time scales, the human brain has significant spatial extent (so that different areas of the brain are isolated except by the slow electrical signals being exchanged). And don't know what it would mean for this brain to behave immorally on such timescales. Any action attributable to this brain would be smeared out over a timescale long enough to treat the brain as a point particle.

In short, I think the idea of keeping the terminology general vs. contingent on relativity is misleading, because you haven't said anything that would apply to a more general situation.

Alexander R Pruss said...

"Can you give me an example of a universe with new physics where internal/external time is not the same as (the obvious generalization of) proper/coordinate time and yet I can still apply my human moral intuitions concerning internal/external time?"

Take something like the universe of Leibniz's monadology. The world consists of a number of aspatial monads, in each of which there is a causal ordering on states. The causal ordering on states grounds the internal time ordering, and if there are enough appropriate regularities in the states, we can get some sort of a natural metric in that time ordering. That's internal time. But the substances also interact causally, so that the state of one substance can be a partial cause of the state of another substance (Leibniz has a reductive story about this causation, and the story I am telling works both with his own story, as well as with a more robust causal notions.) This allows us to induce relations between the time sequences of the different monads, say by stipulating that if state A of monad x partly causes state B of monad y, then A is not later than B. If there are enough regularities in these, they may suffice to generate some sort of aggregate external time. There will probably be multiple ways of doing this, none of them canonical, but I don't care, since my point is that it's the internal, not the external, time that matters to me.

Here I am assuming, with Kant and possibly Aristotle, that time is defined by causal ordering.

"If we look on short enough time scales, the human brain has significant spatial extent"

Good point: That may yield a reason to think that the brain is not the same as the mind.

It could be that the substantial form of the worm (and worms, like all other living things, have substantial forms, which we can also call "souls") has its own time sequence, and that time sequence is what yields the inner time of the substance.

Or it could be that the talk of "internal time" is anyway in the end just a vague approximation to more complex statements about the nexus of internal causal relationships, which is all the more reason not to talk about proper time.


It's also not clear that talk of proper time will make good sense of some time travel scenarios. Suppose that Sam comes into existence at coordinate time 2, with respect to some set of coordinates. He then lives over the coordinate time interval [2,3). But he doesn't quite reach coordinate time 3--instead, he then jumps back to coordinate time 1. Then he continues to live over the coordinate time interval [1,2), and is so located that the limit of his position as coordinate time approaches 2 from below is equal to the position he had when he came into existence at coordinate time 1. But then as the time interval [1,2) ends, he travels forward to coordinate time 3, precisely to the location he left from, and lives for ever from then on.

Suppose, too, that Sam is pointlike.

Then despite the time travel, Sam's life traces a continuous timelike worldline. Proper time would then seem to be time along that worldline. Thus, the proper time corresponding to coordinate time 1.5 would be prior to the proper time corresponding t the coordinate time 2.5. But the internal time corresponding to coordinate time 1.5 is after the internal time corresponding to coordinate time 2.5, since he (internally) first lived through the interval [2,3) of coordinate time and (internally) then lived through the interval [1,2), and (internally) then finally through the interval [3,infinity).

I am using "internal time" to generalize David Lewis's notion of "subjective time". (Objects, like clocks, that have no subjectivity can have an internal time.)

jessriedel said...

"That may yield a reason to think that the brain is not the same as the mind."

I don't see how. My evidence for the mind being subsumed by the brain may not be ironclad, but it certainly is stronger than the evidence for there being a sensible notion of morality on timescales much shorter than those on which a person can think.

"Suppose that Sam comes into existence at coordinate time 2..."

World lines are (the equivalence class of) functions from the real line to the spacetime manifold (where equivalence is defined by a monotonic reparameterization of the real line). World lines are not just 1-dimensional subsets of manifolds. In particular, they are ordered.

Proper time for a world line is then determined by the metric, which gives a preferred parameterization of the world line (up to affine transformations) which is perfectly compatible with the piecewise world line you described for Sam.

This is just semantics, of course.

Alexander R Pruss said...

"My evidence for the mind being subsumed by the brain may not be ironclad, but it certainly is stronger than the evidence for there being a sensible notion of morality on timescales much shorter than those on which a person can think."

Inter alia, I was thinking of the idea of something like a transcendental unity of apperception--that there needs to be an absolute notion of simultaneity among mental events. But I am actually sceptical of transcendental unity of apperception, so I don't endorse that line of thought.

Another kind of worry is that taking the mind to be spatially extended may result in a tiny bit of vagueness about some moral matters, such as questions whether you acquired a certain duty. But I don't believe fundamental facts are subject to vagueness, and I think some moral facts are fundamental. So now the question is whether those moral facts about which there would be vagueness were the mind spatially extended are fundamental. I don't know.

"World lines are (the equivalence class of) functions from the real line to the spacetime manifold"

Fair enough if that's how you want to define world lines.

One interesting thing about identifying internal time with proper time in this way is that it does not allow what seems to be a logical possibility: that your and my worldlines be always coincident but that I be continuously time-traveling forward at a year of coordinate time per second of internal time, while you are continuously time-traveling forward at one second of coordinate time per second of internal time. For then our world-lines will be in the same equivalence class, and there would be no way to capture using proper time the idea that we're time-traveling at different rates.

It would also be tricky to understand internal time as proper time in the case of a person who time-travels in a really weird way, say whose position in coordinate time, as a function of internal time, is nowhere differentiable, or worse. I am not sure that's possible, though: I don't myself think time is an actual continuum.

Here's another time-travel possibility that's hard to account for in terms of proper time: you stay still at a single coordinate time for an extended period of internal time. It's going to be tough to use proper time to quantify "how long you spent at that coordinate time".

Now it's far from obvious that these are genuine metaphysical possibilities. But it's not much more obvious that any kind of time travel is a metaphysical possibility. :-)