Saturday, February 27, 2016

Hilbert's Hotel

I recently ran a question by a brilliant philosopher:

I have two related metaphysical questions for you. These are temporal variations on Hilbert's Hotel. 

My question involves a hypothetical time-sharing/space-sharing arrangement. Would it be metaphysically possible for God to double (triple, quadruple, &c.) the human race without doubling the space it occupies.

Here's what I have in mind. To simplify the scenario, suppose the human race begins with a single breeding pair. Eventually, there are billions of people simultaneously living on planet earth. Let's call it human race A.

Suppose God moves that forward one second. Human race A now occupies the next second, thereby vacating the previous second. Having freed up the first moment in the temporal series, fills the prior, "empty" second with human race B. He duplicates the process he used for human race A (starting with a different breeding pair). Human race A is always one second ahead of human race B. Both groups occupy the same space a second apart. Human race B is always a second behind human race A. 

Assuming that's feasible, the same principle could be tripled, quadrupled, &c, in terms of split seconds or milliseconds, depending on how far you think time is divisible. 

Question, do you think there are theories of time and personal identity under which that scenario is metaphysically coherent? 

Related question: traditionally, the saints and the damned are separated by space (after the general resurrection). But, apropos the above, could they be separated by time?

Could both occupy planet earth (in the future), but be grouped such that one set is always a second behind the other? 

He wrote back and said "This seems quite coherent and unproblematic to me."

In subsequent discussions with a friend, added the following clarifications:

It's arguable that an actual concrete temporal infinite is possible. What's impossible is an incremental realization of an actual concrete temporal infinite. But if the timeline is instantiated as a given totality, then that's metaphysically feasible. 

i) Hilbert's Hotel is disanalogous insofar as it was meant to illustrate the counterintuitive implications of an actual infinite. 

However, I'm trading on different aspects of the thought-experiment:

ii) How to add people without adding space.

iii) The parallel between a spatial shift and a temporal shift.

In Hilbert's Hotel, even if all the rooms are full, yet because the hotel is infinite, you can always add new guests. A guest checks out of Room 1 and checks into Room 2. That frees up Room 1 for the new guest. And the guest in Room 2 switches to Room 3, and so on down the line. A domino effect.

If we conceive of a temporal series like a series of room (temporal units/increments/intervals), then can you have a similar shift? You advance the whole "row" of moments by a second. The moments were occupied by people. Now you've moved them one over, which vacates the preceding moment, which can now be occupied by a different set of people. 

By way of background, I was thinking about this on a recent walk. It was stimulated by the logistics of life in the world to come. Suppose you accept Warfield's view that between universal infant salvation and the postmillennial triumph of the Gospel, most of the human race will be saved. But would there be room for all of them on planet earth? So I was toying with a space-sharing arrangement.

Of course, Warfield's view represents a limiting case. Who knows what percentage of the human race will be saved. But it's interesting to explore various permutations.  

For background:

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