Ken G
Gold Member
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Yes, and if a convincing case can be argued for an equation along the lines of
M = Ps <--> Pr,
I think it would be even more interesting if the relation was something more akin to
P(M) = Ps <--> Pr,
where P means "the projection onto the physical." It would not be necessary for P to be invertible, so the physicalist claim that
M = P-1(Ps <--> Pr)
does not necessarily logically follow.
It is apparent that changes in the Ps <--> Pr interaction correlate with changes in M, and can be viewed as causal of changes in M because the detection of causality is one of the main properties of the P operation. However, if E signifies the evolution operator, involved in making some change, we still cannot say
E[M] = P-1(E[Ps <--> Pr]),
as that requires not only that P is invertible, but also that it commutes with E. Instead, what we can say is
E[P([M])] = E[Ps <--> Pr].
If we assert that EP = PE' as our definition of E', then we have
P(E'[M]) = E[Ps <--> Pr],
and this is the fundamental equation that systems-type neurologists study. But note we must wonder to what extent P is invertible, and to what extent P commutes with E. If neither holds, we have a particularly interesting situation.
M = Ps <--> Pr,
I think it would be even more interesting if the relation was something more akin to
P(M) = Ps <--> Pr,
where P means "the projection onto the physical." It would not be necessary for P to be invertible, so the physicalist claim that
M = P-1(Ps <--> Pr)
does not necessarily logically follow.
It is apparent that changes in the Ps <--> Pr interaction correlate with changes in M, and can be viewed as causal of changes in M because the detection of causality is one of the main properties of the P operation. However, if E signifies the evolution operator, involved in making some change, we still cannot say
E[M] = P-1(E[Ps <--> Pr]),
as that requires not only that P is invertible, but also that it commutes with E. Instead, what we can say is
E[P([M])] = E[Ps <--> Pr].
If we assert that EP = PE' as our definition of E', then we have
P(E'[M]) = E[Ps <--> Pr],
and this is the fundamental equation that systems-type neurologists study. But note we must wonder to what extent P is invertible, and to what extent P commutes with E. If neither holds, we have a particularly interesting situation.