I recently posted a comment in reply to Russell on the topic of
supervenience, but it may have got lost in the recent posting confusion.
Anyway, I append it again below, slightly amended for comprehension in
isolation. The comments bear on physical supervenience and on whether
consciousness could be said to supervene on UD*.

1) Any coherent notion ​that particular states of consciousness supervene
uniquely on a specific physical object​ ​*qua computatio​*​ is effectively​
​poisoned by ​ambiguity with respect to how ​that object ​​can​ ​variously
​be parsed as implementing computation​​​.​ Nevertheless one could still
say, in the case of a suitable observable such as a brain, that
consciousness supervened, in the straightforward sense of covariance, on
its observed physical transitions. In this case there would be no necessary
further entailment to those transitions instantiating a computation. Indeed
this is in effect a direct implication of the comp theory itself. The claim
is that conscious states "in fact" supervene on computation, in the sense
both of covariance and fundamental explanatory relation. But at the same
time those states *must appear* to supervene, in a brutely covariant but no
longer strictly computational sense, on observed physical transitions. So
it would seem then that the implicit "theory-of-mind of observable physics"
will always appear in the form of an identity relation realised in terms of
physical action. In this sense the two theories (or more properly a duality
of the same general theory) are not strictly incompatible, but they rely on
two different explanatory relationships, which in fine must be
commensurable for the comp theory to be viable.

2) Whether or not consciousness supervenes on the dovetailer ​I think bears
on a separate ambiguity. Of course particular conscious states cannot be
understood as supervening on the dovetailer's trace as a whole because it
is by definition unchanging. Consequently there is no possibility here of
covariance.​ ISTM then that the interpretative ambiguity is that a
principle for 'singling out' particular programs and their associated
conscious states has not been made explicit. When first one then another
particular set of such correlations is successively 'selected' from the
trace as a whole then we can indeed intuit a covariance. When the implicit
selection changes, there is deemed to be a corresponding change in the
'states' of both consciousness and computation. In Bruno's work IIUC the
initial selection is simply that we start from a particular state in which
we are interested and progress by computational relations to the various
continuations. One of the reasons I like Hoyle's heuristic as a pedagogical
device is that it makes a serialisation of such 'selections' explicit and
it may consequently be easier to intuit what is supposed to be changing.

David

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