I interpreted your experiment as a setup where P tests the truth of a
statement
and R tests the operation of P. In this case all we have is a series of
time delayed outputs.

If R is a true reliability test (see Reliability Testing below) then we have
some
problems implementing the experiment.

The first problem is that all tests must check Experience at the same time
(t=0), this might be difficult but not impossible.

The second problem is that reliability testing with an unreliable process is
flawed from the outset because you can only know that Experience at t=0 is
true if the reliability of the test (reliability Pn) is already known, in
other words, if P is unreliable
the experiment is pointless. If P is unreliable then given enough instances
of P
we must always end up with the same answer: 'either experience does not
exist
or the test is unreliable'.

Cathy:
I'm afraid I may have confused things slightly by using the word "reliable",
which has a technical meaning of "consistent".  But I wasn't talking about
whether P was reliable in this technical sense, but in the non-technical
sense of whether we could rely on P -- in other words, I was talking about
whether P is accurate as well as consistent.  Your reliability test, for
example, will fail to terminate if Experience does not exist but P is
consistently inaccurate.  And even if your reliability test does find an
inconsistent output from P, you might have to wait an infinitely long time
before it does it.

Of course, you could always determine whether P is accurate to some
arbitrary level of confidence, but you could never be absolutely certain
that P is accurate.  And it's absolute certainty which is the issue here --
we can be absolutely certain that we have subjective states, but it is
difficult if not impossible to see how any physiological system could
produce this kind of certainty.

I think you are quite right to see this as an analog of the Halting Problem.
It appears that our minds are capable of determing something which would
require a Turing machine to run for an infinite amount of time.  And that
was really the point of the exercise.

Cathy

[Catherine Reason]