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

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 eachother.

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.