>> 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 
>> prevent
>> 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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