Thanks for that very nice summary. I let people think about it. We have discussed it a long time before on the Everything-list. A keyword to find that discussion in the everything list archive is "crackpot" as Jacques Mallah named the argument.
Good we can come back on this, because we didn't conclude our old discussion, and for the new people in the list, as for the for-list people, it is a quite important step to figure out that the UDA is a ``proof", not just an ``argument". Well, at least I think so. Also, thanks to Maudlin taking into account the necessity of the counterfactuals in the notion of computation, and thanks to another (more technical) paper by Hardegree, it is possible to use it to motivate some equivalent but technically different path toward an arithmetical quantum logic. I propose we talk on Hardegree later. But I give the reference of Hardegree for those who are impatient ;) (also, compare to many paper on quantum logic, this one is quite readable, and constitutes perhaps a nice introduction to quantum logic, and I would add, especially for Many-Wordlers. Hardegree shows that the most standard implication connective available in quantum logic is formally (at least) equivalent to a Stalnaker-Lewis notion of counterfactual. It is the David Lewis of "plurality of worlds" and "Counterfactuals". Two books which deserves some room on the shell of For-Lister and Everythingers, imo.
Also, I didn't knew but late David Lewis did write a paper on Everett (communicated to me by Adrien Barton). Alas, I have not yet find the time to read it.

Hardegree, G. M. (1976). The Conditional in Quantum Logic. In Suppes, P., editor, Logic and Probability in Quantum Mechanics, volume 78 of Synthese Library, pages 55-72. D. Reidel Publishing Company, Dordrecht-Holland.

Bruno

Le 13-mai-05, à 09:50, Brian Scurfield a écrit :

Bruno recently urged me to read up on Tim Maudlin's movie-graph argument
against the computational hypothesis. I did so. Here is my version of the
argument.
............................

According to the computational hypothesis, consciousness supervenes on brain
activity and the important level of organization in the brain is its
computational structure. So the same consciousness can supervene on two
different physical systems provided that they support the same computational
structure. For example, we could replace every neuron in your brain with a
functionally equivalent silicon chip and you would not notice the
difference.

Computational structure is an abstract concept. The machine table of a
Turing Machine does not specify any physical requirements and different
physical implementations of the same machine may not be comparable in terms
of the amount of physical activity each must engage in. We might enquire:
what is the minimal amount of physical activity that can support a given
computation, and, in particular, consciousness?

Consider that we have a physical Turing Machine that instantiates the
phenomenal state of a conscious observer. To do this, it starts with a
prepared tape and runs through a sequence of state changes, writing symbols
to the tape, and moving the read-write as it does so. It engages in a lot of
physical activity. By assumption, the phenomenal state supervenes on this
physical computational activity. Each time we run the machine we will get
the same phenomenal state.

Let's try to minimise the amount of computational activity that the Turing
Machine must engage in. We note that many possible pathways through the
machine state table are not used in our particular computation because
certain counterfactuals are not true. For example, on the first step, the
machine might actually go from S_0 to S_8 because the data location on the
tape contained 0. Had the tape contained a 1, it might have gone to S_10,
but this doesn't obtain because the 1 was not actually present.

So let's unravel the actual computational path taken by the machine when it
starts with the prepared tape. Here are the actual machine states and tape
locations at each step:

S_0 s_8 s_7 s_7 s_3 s_2 . . . s_1023
t_0 t_1 t_2 t_1 t_2 t_3 . . . t_2032

Re-label these as follows:

s_[0] s_[1] s_[2] s_[3] s_[4] s_[5] . . .s_[N]
t_[0] t_[1] t_[2] t_[3] t_[4] t_[5] . . .t_[N]

Note that t_[1] and t_[3] are the same tape location, namely t_1. Similarly,
t_[2] and t_[4] are both tape location t_2. These tape locations are
"multiply-located".

The tape locations t_[0], t[1], t[2], ..., can be arranged in physical
sequence provided that a mechanism is provided to link the multiply-located
locations. Thus t[1] and t[3] might be joined by a circuit that turns both
on when a 1 is written and both off when a 0 is written. Now when the
machine runs, it has to take account of the remapped tape locations when
computing what state to go into next. Nevertheless, the net-effect of all
this is that it just runs from left to right.

If the machine just runs from left to right, why bother computing the state
changes? We could just arrange for each tape location to turn on (1 = on) or
off (0 = off) when the read/write head arrives. For example, if t_[2] would
have been turned on in the original computation, then there would be a local
mechanism that turns that location on when the read/write head arrives (note
that t_[4] would also turn on because it is linked to t_[2]). The state
S_[i] is then defined to occur when the machine is at tape location t_[i]
(this machine therefore undergoes as many state changes as the original
machine). Now we have a machine that just moves from left to right
triggering tape locations. To make it even simpler, the read/write head can
be replaced by a armature that moves from left to right triggering tape
locations. We have a very lazy machine! It's name is Olympia.

What, then, is the physical activity on which the phenomenal state
supervenes? It cannot be in the activity of the armature moving from
left to right. That doesn't seem to have the required complexity. Is it in
the turning on and off of the tape locations as the armature moves?
Again that does not seem to have the required degree of complexity.

It might be objected that in stripping out the computational pathway that we
did, we have neglected all the other pathways that could have been executed
but never in fact were. But what difference do these pathways make? We could
construct similar left-right machines for each of these pathways. These
machines would be triggered when a counterfactual occurs at a tape location.
The triggering mechanism is simple. If, say, t_[3] was originally on just
prior to the arrival of the read/write head but is now in fact off, then we
can freeze the original machine and arrange for another left-right machine
to start from that tape location. This triggering and freezing can be done
using a simple local mechanism at t_[3].

For brevity, I have just sketched how the counterfactuals might be
implemented (see the original article for more detail). The point is that we
have implemented all this extra machinery for supporting counterfactuals,
but none of it is actually used during the original computation. It remains
silent and inactive. Olympia runs just as well without them. Does connecting
up all the counterfactual machinery make Olympia phenomenally aware? And
does disconnecting the machinery make her not phenomenally aware even though
exactly the same computation is taking place?

From the above, it would seem the following are inconsistent with each
other.

1. Your phenomenal state at a time is entirely determined by your brain
activity at the time.
2. For any phenomenal state of consciousness there exists some program, some
tape configuration, and some sequence of machine states that brings about
that phenomenal state on any physical machine capable of running the
program.
3. A physical system supports a phenomenal state if that the system can be
implemented as a Turing Machine performing some computation.

Maudlin's conclusion is that phenomenal states cannot supervene on physical
computational activity.

This, of course, is where Bruno and co. step in.
--------------------------------------


Notes:
1. Bruno Marchal independently discovered the movie-graph argument in 1988.
2. Maudlin considered a machine that used water troughs in place of tape
locations, but I really didn't want to inflict that kind of imagery on Bill!


Reference.

Maudlin, Tim (1989). Computation and Consciousness. Journal of Philosophy.
pp. 407-432.



http://iridia.ulb.ac.be/~marchal/

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