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Eddy Nahmias

Kadri and Terrance, this is really helpful. I need to think about it more, but it reminded me of a question that I can't find a good answer to, so maybe y'all can help. You seem to agree with the claim implicit but usually explicit in the definitions of determinism you cite--namely, that it is temporally asymmetric and that two possible worlds with the same laws are such that "they are not exactly alike through any stretch of time" (Lewis).

So, what do such definitions say about this simple law as applied to two possible worlds.
L of 'gravity': objects in this world move towards each other at a constant speed until they are touching, at which point they remain at rest (touching).

In W1 there are (only) two objects 1 meter apart at t1. By t2, they are touching and they remain that way for the rest of time.

In W2 there are (only) two objects (the exact same as the objects described in W1) 2 meters apart at t1. By t3, they are touching and they remain that way for the rest of time.

It seems to me that W1 and W2 have the same deterministic laws and that from t3 to eternity they are in the exact same state, but that from t1-t3 they are not identical.

Similar examples could be constructed with more complex universes and laws. Conway Game of Life examples can work this way too--different starting setups leading to exact same patterns, using same laws.

Am I missing something here?

tomkow

Eddy,
Thanks for the kind words!

What Lewis and we would say about your worlds is that a world governed by the "law of gravity" you describe is not fully Deterministic. A world can be deterministic going temporally forward but not going backward or vice versa. The W1 world pictured in our post is deterministic going backwards in time, but not forwards.

The law you give to your world W1 is deterministic going forward but not back. It allows for what Lewis calls "convergence". After the objects contact there is no distinguishing the futures of W1 and W2 and no way of telling how things got to be the way they are. Such laws and worlds are certainly possible, but not fully deterministic.

Philosophers often ignore temporally backward determinism but physicists rarely do. Physicists call the assumption that we may infer the past state of the universe from its present state, "The Principle of Conservation of Information". Leonard Susskind calls it a principle more fundamental than the Second Law of Thermodynamics. It's what the "Black Hole Wars" were about.

Note that all of this is separable from your question about whether or not W1 and W2 "have the same laws". I agree that W1 and W2 are described by the same laws. It is less clear to me that they are governed by them. To see why I say this you would have to read Computation, Laws and Supervenience but, in any case, this issue doesn't affect the point about determinism.

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