>> My idea was rather that the instantiations would not correspond to
>> numbers in the first place
> But that would violate the comp assumption.
No, you still misunderstand me ;-) not correspond in the sense of
non-existing, not in the sense of existing but not number.
>> - that is why the aliens could destroy the
>> machine (it follows from 3-det that something _had_ to happen to
>> successor states which wouldn't correspond to numbers).
> But machines are secondary. The "physical machines" are pattern
> emerging in the mind of persons themselves emerging from the relation
> between numbers. I don't see how aliens could manage a machine not to
> have successors.
The idea was that the numbers encode moments which don't have successors
(the guy who transports), that's why there exist alien-OMs encoded in
numbers which destroy all the machines (if we assume that arithmetic is
> If a successor state requires something impossible, *that* successor
> state will be impossible, but it does not mean there will not be other
> successor states, indeed, for mind corresponding on machine's state, a
> continuum of successor states exists.
This is the issue at stake: from what do you gather that all machine
states have a continuum of successor states (the aleph_0/aleph_1 is not
at issue now; it suffices to say: at least one successor state)?
After all, there are halting computations.
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