The Dust Hypothesis
Consider the following argument:
(1.) It doesn't matter what your mind is made of, as long as the functional relationships between your mental states and the inputs and outputs are right. A conscious person could be made of carbon-based molecules with an organic brain, or of silicon chips in a robot body, or of suitably complex magnetic iron structures. If a being dependably acts like a sophisticated, conscious, intelligent being, it is a sophisticated, conscious, intelligent being. (Searle would disagree with this, but it is the majority view in philosophy of mind and standard in fictional portrayals of android and alien intelligences.) Let's call each temporal slice of such a being a "cognitive state".
(2.) The cognitive states (or temporal slices) of people can be temporally or spatially distributed. If a being of the sort in (1) exists for only one second out of every ten, it is still a conscious, intelligent being, just one with temporal gaps in it -- gaps the being itself may not notice. Likewise, if the being is partly instantiated in Paris and partly in Rio, with the two parts in constant communication, reacting in a co-ordinated way to produce the right sort of behavior, that also does not deprive it of consciousness and intelligence. (Something like this is suggested by Dennett.)
(3.) Furthermore, the objective temporal order of cognitive states is irrelevant. If input 1 ("How are you?") is followed by cognitive states 2, 3, and 4, then by output 5 ("Better, now that you've stopped kicking me!"), it shouldn't matter if as measured by the objective time of the outside world, state 3 comes before state 2, as long as in terms of subjective time and cognitive sequence state 2 comes first. (Dennett, again, is useful here. It's a little tricky to figure out what subjective time and cognitive sequence are independent of objective temporal order; but the conclusion of the argument can be weakened to dispense with this premise if necessary.)
(4.) Also, actual connection to the outside world is irrelevant. You could still have the intelligence and consciousness you now in fact have if your cognitive states were instantiated in a brain in a vat. (Here we may be departing from Dennett; but even if, as Dennett's student Noe and others have argued, some environmental connections are essential to mindedness, we can probably still run the argument I'm interested in. We just turn it into brain-and-relevant-bit-of-the-environment in a vat. We could also dispense with certain "externally defined" mental states and still have an interesting version of the conclusion if necessary.)
(5.) If all this is true, it appears to invite the following conclusion: As long as somewhere in the universe, in some temporal order there exists a functional equivalent of each of your cognitive states, no matter where, in what material, or how grossly distributed over time and space, then there is a mental duplicate of you in existence.
(6.) Then, finally: In all the spatial and temporal vastness of the universe, each of your cognitive states will be instantiated somewhere other than your own brain, in vastly different times and locations.
(7.) So, there is a mental duplicate of you spread out across space and time.
(8.) And this generalizes: There are many, many such people; the universe (at least the complex bits of it) is permeated with them; they include many possible alternative versions of you; etc.
Call this the Dust Hypothesis, after science fiction writer Greg Egan's similar Dust Hypothesis in his book Permutation City.
Assuming the conclusion is absurd, the question is where to put on the brakes. My own inclination is either (1), following Searle, or (5), or (6). On 6: Perhaps the functional relationships necessary for sophisticated, conscious thought are so complex that even in the vast universe they would not be instantiated except in coherent, brain-like packages. But maybe that underestimates the vastness and complexity of the universe?
On (5): Perhaps actual causation between cognitive states is necessary to mentality and consciousness, not just the instantiation of those states with the right counterfactual and dispositional relationships. But I worry. Couldn't there be a mental being causally truncated on one end (brought suddenly into being by freak quantum accident, like Swampman), or on the other (destroyed suddenly by lightning), or both (thus existing for only a moment)? Or what if you have an idea due to stroke or quantum accident (and then maybe the idea vanishes for similar reasons)? Or suppose that you are destroyed and merely by chance a duplicate of you is simultaneously created elsewhere -- wouldn't there be a stream of mentality that transitioned from one to the other? (Could you tell? Would it matter deeply to you whether the duplicate came about by chance or design?) Then generalize. It's a complex issue, but for reasons like those, I'm inclined to think that the actual instantiation of dispositional and functional structures, even if they're not actually causally connected, is enough for interesting and subjectively continuous mentality (even if some externally defined states like genuine [as opposed to apparent] memory require actual causation). But then if we grant (1) and (6) and the others, we seem to be back to the Dust Hypothesis.