Hi Jesse,

On 15 May 2009, at 06:32, Jesse Mazer wrote:
>
>
> >Maudlin shows that you can reduce almost arbitrarily the amount of  
> physical activity for running any computation, and keep their  
> computational genuineness through the use of inert material. So the  
> isomorphism you introduce vanish on the original Olympia (Pre- 
> olympia).
>
> >Olympia *is*  "Pre-Olympia" + Klara (the inert (for the computation  
> PI) machinery needed for the counterfactuals) OK? Olympia run the  
> computation PI.
>
>
>
> But what do you mean when you say the isomorphism vanishes? Do you  
> mean that the causal structure of pre-Olympia would *not* be  
> isomorphic to the causal structure of the original Turing machine  
> that pre-Olympia was supposed to imitate (according to the  
> definition of causal structure in terms of logical relations between  
> propositions about the system's state at different moments)?


Yes. When I assume physical supervenience, for the benefit of the  
refutation. Olympia, relatively to me, implements Alice (or PI), Pre- 
Olypia does not. I would say yes to a doctor if he gives me an Olympia  
brain, no if he gives me pre-Olympia! That is what I mean by the  
vansihing of the "causal" isomorphism. Of course my goal, when I say  
yes to the doctor, is to preserve my consciousness, and my ability to  
manifest it in the "normal" (most probable) histories. My  
consciousness is already in "plato heaven", so what I need "here" are  
the right dispositional devices.



> If so, that would mean that regular Olympia (pre-Olympia + Klara)  
> wouldn't have a causal structure isomorphic to the Turing machine  
> either, since I was defining causal structure solely in terms of  
> propositions about events that *do* occur in the system's history,  
> meaning the extra counterfactual conditions provided by Klara are  
> irrelevant to Olympia's causal structure, so Olympia's causal  
> structure would be the same as pre-Olympia's.


Right. But Maudlin manages to show that Olympia can have an empty  
causal structure, and that you have to say yes to the doctor when he  
proposes to substitute your brain by nothing. Personally I conceive  
propositions only in a net of related propositions by theories or  
models. The causal structure is mainly given by axioms and inference  
or computation rules, or by a (mathematical) semantics (model). You  
can't separate a proposition from other propositions like you can't  
separate a number from the other numbers.
I guess you would say that the movie-graph (the movie of the filmed  
active boolean graph corresponding to Alice's dream) would vehiculate  
Alice's dream. I can agree if you call the causal structure the  
computation corresponding to the local events lending to that graph,  
but then you have abandon the "real time" physical supervenience  
thesis already (or comp).
It is a very subtle and complex point here, we can go back on this  
later.



>
> If that's the case, why can't we postulate that consciousness  
> supervenes on causal structure, since causal structure is after all  
> part of the physical world?


The point is that you can realize any computation with any causal  
structure in that sense. Maudlin's construction explains well that the  
Klaras, or the *material* for the counterfactuals are a read herring  
as far as giving a role in the logical relations describing a  
computation. And not just the material one! Any choice of a particular  
universal system cannot work, you have to take them all. You can then  
choose the simplest one (+ and *) to retrieve those who define  
observable realities from the point of view of universal machines.




> In fact one could say that physics is *only* concerned with  
> "causality" in the sense of lawlike relations between propositions  
> about observations, since the laws of physics tell us nothing about  
> what particles or fields or wavefunctions "really are", only about  
> how they interact with one another and how they can be used to  
> predict the outcomes measurements. So if we say consciousness  
> supervenes on causal structure, then Olympia would not qualify as an  
> instantiation of the observer-moments that the original Turing  
> machine instantiated, in much the same way that a lookup table  
> wouldn't qualify.


I don't see that at all. Olympia is just a "crazy" implementation of  
an algorithm, but it is correct on all inputs. Its resemblance with a  
look-up table is local, finite, and does not change Olympia's  
semantics. If such a change makes a change, I would no more say yes to  
a doctor. My consciousness would depend on the nature of the  
implementation.



>
> I don't have a problem with the idea that a giant lookup table is  
> just a sort of "zombie",

Look-up table contains the counterfactuals. I am not sure that a giant  
look-up up table can be considered as a zombie. The problem is that  
such a look-up table would be gigantic and hard to address. Also, its  
origin, relatively to me, would need a strange "history". But if that  
exist I could say yes to a doctor providing me with that lookup table.  
Very practical: let us look what I am answering to Jesse today :)



> since after all the way you'd create a lookup table for a given  
> algorithmic mind would be to run a huge series of actual simulations  
> of that mind with all possible inputs, creating a huge archive of  
> "recordings" so that later if anyone supplies the lookup table with  
> a given input, the table just looks up the recording of the occasion  
> in which the original simulated mind was supplied with that exact  
> input in the past, and plays it back. Why should merely replaying a  
> recording of something that happened to a simulated observer in the  
> past contribute to the measure of that observer-moment? I don't  
> believe that playing a videotape of me being happy or sad in the  
> past will increase the measure of happy or sad observer-moments  
> involving me, after all.


Unless in some story you survive during a period. The problem of the  
lookup table is that to manage the counterfactual it has to run all  
your future as well. The problem comes from the physical supervenience  
only. You try to select one notion of causality, when with comp  
consciousness supervene on all notion of all relatively probable  
notions of causality.


> And Olympia seems to be somewhat similar to a lookup table in that  
> the only way to construct "her" would be to have already run the  
> regular Turing machine program that she is supposed to emulate, so  
> that you know in advance the order that the Turing machine's read/ 
> write head visits different cells, and then you can rearrange the  
> positions of those cells so Olympia will visit them in the correct  
> order just by going from one cell to the next in line over and over  
> again.
>
> So: why can't the idea of consciousness supervening on causal  
> structure be a possible strategy for avoiding the problem you talk  
> about in step 8 of your UDA argument (if I am understanding it  
> correctly), namely the idea that even if there was a physical  
> universe it wouldn't be able to tell us anything about the measure  
> of different computations? If we talk about the causal structure of  
> a given computation, why can't we look at how frequently sets of  
> physical events with an isomorphic causal structure occur in the  
> physical universe, and derive a measure on physical implementations  
> of computations in this way?

Because any consciousness will be attached to any "causal structure"  
in your sense. Your propositional interpretation of the causal  
structure needs the counterfactuals and all the conditional theorems  
in the theories which defines your "true and probable" theorem. If you  
want to singularize consciousness through the choice of a particular  
machine, this one will have to be actually infinite.


> Not that I personally would favor this approach to a philosophical  
> "theory of everything", but would you say it isn't even a coherent  
> possibility?

I don't think so, for the reason allude above.


>
>
> Are you saying that a notion similar to my definition of "causal  
> structure" is already made use of in the areas of mathematics you're  
> talking about, or when you say "the history of a particular Turing  
> machine computation" are you talking about something unrelated to my  
> definition of the computation's causal structure?



You should give a more precise definition of what you mean by "causal  
structure". If you postulate a physical world (or any particular  
universal machine) and define causality the truth of some propositions  
(theorems, conjecture) I can follow you only insofar that you realize  
we have to justify the "physicals laws from an average based on that".





>
> I also wonder if anything similar to this notion of causal structure  
> could be found in category theory, since in some layman's summaries  
> I've read that category theory defines mathematics in a purely  
> relational way, where any mathematical object (or proposition?) is  
> defined entirely in its relationships to other objects.


You are right. Category provides genuine information about those  
things. But it is an investment, and it is a bit labyrinthine. Also,  
in computer-land, most objects are only partially defined, and it is  
hard to just find the "good" morphism in between objects. The very  
fact that you mention category theory, which has nothing physical per  
se, for your causal structure, makes me think that you don't take too  
much seriously that such causality has to be based on a notion of  
substance, or primary matter. That's all what the movie-graph try to  
convey.




>
> When you say "that approach", are you talking specifically about  
> looking at isomorphisms between 1) logical relations among  
> propositions about arithmetic, and 2) logical relations among  
> propositions about the history of a Turing machine computation?


Always proposition about numbers.  (or combinators, etc.). Remember  
that we can translate the logical metamathematics in term of relations  
between numbers.



> Or were you saying that UDA takes an approach that is similar in  
> some broader fashion?


UDA was originally just an argument to explain that the mind-body  
problem is not yet solved, and that assuming comp, it can be pertially  
reduce in the problem of justifying physics from computer science/ 
number theory. What you ask me could depend of what you mean by  
"causal structure". Should such a structure defined in term of physics  
or in term of logic+number (or logic+combinators, etc.).


> since I'm suggesting some kind of absolute measure on all causal  
> structures, and if you identify particular causal structures with  
> OMs that would correspond to the ASSA, but you have said that your  
> approach only uses the RSSA.
>
>
> >There is no absolute measure on all "causal structures" , still  
> less on OM, right! I would ba an ants or a bacteria in two seconds!
>
> I guess it would depend on how the measure was defined.

Sure. that is what I like with comp, the measure is immediately  
relative and indexically defined. that is why we can, and are forced,  
to use the logic of self-reference at some point.



> It might not just be in terms of the numerical frequency that a  
> given causal structure appears in the world, but also in terms of  
> things like how many other causal structures "remember" that causal  
> structure in some sense (contain detailed information about it).  
> That could perhaps give a measure which was biased towards more  
> complex causal structures like human minds even though ants are much  
> more common numerically.


You are right. It is a reason for being a bit skeptical about  
"absolute measure" here.




> Well, I didn't mean to sugest that your ideas are vague, only that  
> my own notions of a connection between causal structure and measure  
> were rather ill-defined...


OK.  I would be pleased if you try to define causal structure, or just  
tell me if it is based on physics. Even accepting the primacy of  
physics, it is a complex notion. Comp get rid of it, or "relegate" it  
at the higher epistemological level, like consciousness,  
responsibility, free will, etc. The proposition that machine x on y  
will output z, can be defined entirely in term of addition and  
multiplication of numbers, with the usual logic. Even much less thanks  
to Matiyazevitch.



> there'd be a lot more math I'd need to learn if I wanted to  
> seriously try to develop these ideas, or to really understand the  
> details of your own ideas. By the way, do you have a bibliography  
> somewhere of books you think someone could use to self-teach  
> themselves enough math to understand the details of your AUDA  
> argument?


I think that Günther has put some biblio in the everything list  
documentation (look for AUDA). Two excellent books are the Boolos,  
Burgess and Jeffrey book, and the book by Epstein and Carnielli. They  
give the most genuine, with respect to UDA-7 and AUDA, balance of  
logic and theoretical computer science.
For AUDA and the logic of self-reference, Boolos 1979, Boolos 1993,  
and Smorynski 1985 are very good. Or look at the reference of my  
french thesis:
http://iridia.ulb.ac.be/~marchal/lillethesis/these/node79.html#SECTION001300000000000000000

On Gödel and Mechanism: Webb 1980 is the best published book.

I must go; no time for adding typo errors today!

Best,

Bruno


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




--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To post to this group, send email to everything-list@googlegroups.com
To unsubscribe from this group, send email to 
everything-list+unsubscr...@googlegroups.com
For more options, visit this group at 
http://groups.google.com/group/everything-list?hl=en
-~----------~----~----~----~------~----~------~--~---

Reply via email to