At 11:50 09/03/04 +1100, Russell Standish wrote:
Yes, in your thesis you often talk about survival under replacement of a digital brain (cerveau digital). Digital simply means "operates with 1s and 0s". Since any analogue value can be represented arbitrarily accurately by a digital signal, this doesn't seem much of a stretch.
Except that the processing is also digitalized, making things a little less trivial.
In your chapter 1, you refer to a "machine universelle digitale, c'est a dire un ordinateur". The English word computer, which is the literal translation of ordinateur, can refer to an analogue computer, which is merely a device for performing computations - it needn't even be Turing complete.
Not really. Ordinateur means really (in french) "*universal* computer". If not universal we say "calculateur" (and that one can be analog indeed).
The fact that you used the word "universelle" previous does imply Turing completeness, but not that it is equivalent to a Turing machine. After all, I might be concerned if there was some noncomputable part of the brain that was not captured by a Turing machine, but could be built into a digital machine of some kind (eg by accurate copying of the physical layout of the brain).
In that case you would be simulable by a computer at *some* level. COMP asks only that, mainly.
Now I noticed you used the word "indexical". What does this mean? (I tend to skip over terms I don't understand, in the hope that I understand the gist of the argument).
Indexical is an adjective which applies to word like "me", "now", "here" ... I did use "indexical" in "Conscience et Mecanisme", but I don't use it any more. It is implicit in the "Yes Doctor" part of comp where it is supposed that it is *you* who says "yes" to the doctor.
Anyway, the upshot of this was that I assumed that COMP was in fact more general that computationalism. In fact I believe the first half of your thesis (chapters 1-4) indeed still hold for this more general interpretation of COMP (namely the necessity for subjective indeterminism etc).
Yes. The comp hyp can be weakened. I have not try to prove the most general theorem.
True computationalism is perhaps only required for the later sections where you invoke Thaetus's (is that the correct translation of Theetete?) theories of knowledge (connaissance). For here, you need Goedel's theorem, which is applicable in the case of Turing machines.
I don't think so. What *is* true is that when I interview the universal machine (through the logic G and G*) I do choose "computationalist universal machine". Such machine believes in the use of classical logic in arithmetic, etc. BTW Goedel theorems apply to a lot more than simple digital machine, in particular it applies to machine with oracle(s).
I agree one can simulate the Schroedinger equation of QM (albeit with irrelevant exponential slowdown). However, mapping this back to your "YD" postulate, this involves the doctor swapping the entire universe, not just your brain. Perhaps you mean that one of the options the doctor has is to upload you into a well crafted digital simulation (by a Turing machine even) of you and your complete environment (a la Matrix).
This is why in the new version of the argument including those I send to the list sometimes ago I explicitely add the "NEURO" hypothesis (the hypothesis that the brain is in the skull), but then I explicitly show how the NEURO hyp. is eliminated once the Universal Dovetetailer is introduced. After all the DU will generates the many state of my brain whatever it is, if one accept just the fact that we are Turing-emulable.
Reminds me of the option Arthur Dent was presented with by the pandimensional beings (aka mice) when they wanted to mince his brain to extract the question for which the answer was '42'.
(And this reminds me that string theorists seems to succeed toward getting a reversible theory of black hole. See the nice "economist" summary. There is a link to an abstract from Mathur's paper with outline of the paper.) http://www.economist.com/printedition/displayStory.cfm?Story_ID=2478180