2009/8/14 Bruno Marchal <marchal.domain.name.hidden>:
> Hi David,
> This is a nice post, but you are still putting the horse before the cart.
> Now I can see that you have not yet grasp the main UDA point. Hope you have
> no problem with being frank, and a bit undiplomatical, OK?
Don't worry Bruno, nothing pleases me more than discovering precisely
in what ways I am wrong! Having said this, I think you sometimes get
into a bit of trouble following me because of the way I structure my
arguments (my fault I'm sure). When I say something like "if we
assume x, then y follows" it doesn't mean that I'm saying that I
*believe* x or y; I'm just attempting to establish a position in order
to compare it with what I'm going to say next. Sorry if this is
already obvious to you, but I'll try to point to examples where
relevant.
> 1) A Turing machine is an idealised digital computer,
>
> No, Turing tried to capture the notion of a human computer, working with a
> pencil and paper.
> He tried to define mathematically what is human computable, and he is, with
> Post, and some other are the discoverer of a purely mathematical notion of
> computation, and this before the appearance of concrete computers. Computers
> have appeared after. Turing has played a role in that later appearance. A
> platonist could say those concrete beings are just pale approximation of the
> real thing. Later this statement will be made precise, but with the step 8,
> we just cannot invoke any physical things or physical reality.
> To be sure, the fact that computer have been discovered in math, before "in
> nature" is not an argument, yet it helps a lot to see that, especially for
> the grasp of the comp supervenience thesis. And that is the reason why I
> explain that absolutely fundamental mathematical discovery. Computation has
> nothing to do with physics at the start.
> Note that I abstract myself from the pioneer building of a computer by
> Babbage.
Thanks for this amplification.
> This has not been shown. But this follows from Church Thesis.
Thanks, I wasn't sure about this.
> and hence any
> other TM.
>
> What Turing has shown, is that there is a universal Turing machine, capable
> of simulating all Turing machines. Then that Universal machine can be shown
> to emulate all existing universal machine, and by Church Thesis: all
> universal (and particular) machines.
OK
> The meaning of 'emulation' here entails transforming
> precisely the same inputs into the precisely same outputs, given
> sufficient time.
>
> OK. But there is an intensional Church thesis, which can be deduced from
> Church thesis, saying that not only two universal systems can compute the
> same functions, but they can compute them in the same way (same algorithm).
OK
> 2) Insofar as the causal processes of physics are specifiable in the
> form of decidable (i.e. definitely stopping) functions, they are
> capable of finite computation on a TM - i.e. they are TM emulable.
> What this amounts to is that we can in principle use a TM to compute
> the evolution of any physical process given the appropriate
> transformation algorithm. Since we're dealing with QM this must
> entail various probabilistic aspects and I don't know what else: help
> here please. But the general sense is that the mathematics of physics
> could in principle be fully Turing-emulable.
>
> Step 08 forbids us to introduce anything physical. The reversal is done at
> that step. I guess you are right that it could be a better idea to do the
> step 8 before, but it is more difficult for most. Any way, computational
> supervenience is defined after step 8.
Now when you say "Step 8 forbids us to introduce anything physical" we
might have an example of 'taking things out of sequence'. In this
section I hadn't yet made the assumption of UDA-8. I was just setting
out what I understand with respect to the ordinary sense of the
physical as being mathematically describable in some way.
> Then we will discover that "Colin is right" no piece of matter should be Turing emulable > The mathematics of physics will have to escape the turing emulable. The apparent turing > emulability of the world around us, is a threat to indexical comp (the idea that "I am > machine"). Of course I disagree with Colin's reasoning where he deduce the non Turing > emulability of nature from the non emulability of mind. UDA deduces the non Turing- > emulability of matter from the non Turing-emulability of the mind. And the proof is > constructive. It redefines precisely what "matter" consists in.
Ah! So by 'the non Turing-emulability of matter' I take you to refer
to the example of Olympia: i.e. the argument that shows that
computation can't depend on the physicality of a TM. So it follows
that neither mind nor matter are 'emulable' by - in the strong sense
of being constituted by - a *physical* TM. Rather, the reverse is
true - both (including the now 'apparently physical TM') are
constituted by infinities of computations in a highly-specific
relation: i.e. the UD.
On the basis of the above, I can perhaps see why you say "The apparent
turing emulability of the world around us, is a threat to indexical
comp (the idea that "I am machine")", if one were to take
'emulability' in the strong sense above, since we would now seem to
have a contradiction of some sort. But - and I stress I mean outside
of the UDA framework - I have been accustomed to understand
'emulation' in the sense of a mathematical model of the evolution of
physical systems, not an ontological reversal with what-is-emulated -
hence this post. Why would the 'Turing emulability' of nature in this
weaker sense constitute a threat to comp?
> 3) Now we get into more controversial territory.
>
> Really? I don't think so. Difficult, not yet very well known, and rather
> subtle, no doubt.
> But I don't think there is anything controversial. Nobody told me that.
I think the ordinary English usage of 'controversial' is that there is
considerable disagreement - of which this list demonstrates ample
proof! It doesn't imply that it is wrong. But I didn't mean to
offend.
> Bruno has shown (at
> least I agree with him on this) that for the mind to be regarded as a
> computation,
>
> The wording is a bit dangerous. All I know after UDA is that my state of
> mind at time and place (x,t) has to be linked to an infinity of computations
> going through that state, and that my next state, from my first person point
> of view is indeterminate on the set of all those computations.
Yes, I'll avoid saying "a computation".
> essentially everything else must also be regarded in the
> same light: IOW our ontology is to be understood entirely from the
> perspective of numbers and their relations.
>
> True, but this excludes quickly that it can be conceived a priori as
> computations. Immaterial relation between numbers, sure, but not necessarily
> computable relation. Cf the first person indeterminacy.
>
> This is not universally
> accepted, but more on this in the next section.
>
> This is not universally understood, nor really studied. But it is understood
> quickly or slowly when studied. To my knowledge.
When I make a gesture to one side of the argument (i.e. the simple
fact that they don't - in fact - accept it) the other side objects!
But I understand your frustration.
> Suffice it to say
> that on this basis we would appear to have a situation where the
> appropriate set of computations could be regarded not as mere
> 'emulation', but in fact *as real as it gets*. But this of course
> also renders 'stuffy matter' irrelevant to the case: it's got to be
> numbers all the way down.
>
> No. With the first person indeterminacy it would be more correct to say that
> it's got to be number all the way up.
Yes, I nearly said 'all the way up'.
> It makes the comp immaterial
> appearance of "stuffy matter" infinitely complex and non turing emulable, a
> priori. I suspect you have not yet really see the role of UDA1-6 in the
> step-7.
Ah, this is a key point, I suspect. Now, in my pre-UDA ("beam me up
Scotty") way of thinking about it, I saw that teleportation could be
coherent only if consciousness was seen in terms of a movable
viewpoint within some larger context, not as consisting in a
'thing-in-itself' - hence the a priori 1-person indeterminacy.
Consequently this also implied that the brain - matter itself - must
be seen somehow in this way too, but I was unable to say how. Anyway,
now I see the Star Trek part as UDA1-6. UDA-7 introduces the UD
itself, and from this, that "comp "stuffy" matter has to be made by a
infinite sum of infinite computations including infinities of white
rabbits-computations".
UDA-8 crucially shows - finally - that the computations cannot
themselves supervene on stuffy matter - i.e. the 'stuffy TM' one
previously assumed they were running on. So the overall picture
derived from this is that both the first person and the appearance of
matter are complex - and, in any specific instance, a priori
indeterminate - emergents from this infinite blizzard of computation;
hence 'individual instances' of minds and bodies can't be regarded as
'isolated computations'. Is this is what you mean when you say that
matter is "non turing emulable, a priori"?
> 4) If we don't accept 3) then we can keep stuffy matter,
>
> We can't by step 8;
Surely we can if we're willing to drop the computational theory of
mind? Note that I say this later on (another sequencing problem).
> but by the whole UDA 'stuffy matter" does no more make
> sense at all.
Yes, but my point was that one isn't forced to accept the UDA, as long
as one is equally willing to give up the computational theory of mind.
Faced with the UDA, I suspect many non-specialists might well see
that as preferable to relinquishing their grasp on stuffy matter. I'm
not making claims about the correctness of positions here, I'm just
contrasting them.
The comp "stuffy" matter has to be made by a infinite sum of
> infinite computations including infinities of white rabbits-computations.
> The apparent computability of the physical laws *is* a problem for the
> indexical computationalist.
>
> but at the
> cost of losing the digital computational model of both mind and body.
>
> Most want introduce a stuffy matter because they believe they can save
> computation for both mind and body.
Yes, but I agree with you that this doesn't work.
> Not everyone agrees with that radical assessment, I know;
>
> Who disagree? It is not a question to agree or not. It is a question of
> understanding or not (or to find a mistake).
Whoa! It's a fact that not everyone agrees. This is obviously true,
because when I don't say this, the ones that don't, start disagreeing!
Your point is that disagreement isn't refutation (or even
understanding).
> but even
> those who don't concur presumably do hold that everything that happens
> finally supervenes on something stuffy as its ontological and causal
> basis, and that numbers and their relations serve merely to model
> this.
>
> That is comp, before UDA, before the necessary reversal.
The reversal is necessary only to save the computational theory of mind, surely?
> The stuffiness doesn't of course mean that the evolution of
> physical systems can't in principle be specified algorithmically,
>
> Comp-stuffiness *is* a priori not algorithmic.
Yes, but I was referring here to matter in the stuffy sense, precisely
to *contrast* it with the comp sense. IOW mathematics is still
"unreasonably effective" even if it turns out that comp doesn't go
through as a TOE.
> and
> 'emulated' on a TM if that is possible; we still have mathematics as a
> model of stuff and its relations.
>
> UDA entails there is no stuff at all. No stuff capable of justifying in any
> way the observation of stuff.
Yes, of course, I know this! This is what makes me think you have a
problem with the way I present the argument in stages. I was trying
to characterise the stuffy model in its own terms (with the caveat
that IMO this entails abandoning the comp theory of mind), as well as
comp (however inadequately) also in its own terms. I just get
confused when you interpolate comp objections when I'm not saying
anything about comp.
> But it does entail that no digital
> emulation of a physical system can - as a mere structure of numbers -
> be considered the 'real thing': it's got to be stuffy all the way
> down.
>
> Well, with comp+physicalism. But this is inconsistent, at the
> epistemological level.
Yes, but there's no reason to claim that comp is necessarily the
*only* theory of mind. Physicalism itself isn't necessarily
inconsistent at the epistemological level, but it does need a
different theory of mind - IMO.
> Rather, it seems to me that in our various discussions on the
> emulability or otherwise of physics, we may sometimes lose sight of
> whether we are interpreting in terms of numerical or stuffy
> ontologies.
>
> But "stuffy" or just primitively physical, after UDA has no more any
> meaning.
Again, surely only on the basis that a stuffy theory still hangs on to
comp as a theory of mind? Can't we escape the UDA in this way, even
in principle?
> Be that as it may, the punchline is: do we find this analysis of the
> distinction between numerical 3) and stuffy 4) to be cogent with
> *specific* respect to the significance and possible application of the
> concept of 'emulation' in each case?
>
> You don't yet have grasped the UDA yet. It makes
> the stuffy things not just
> useless for having computations and relative emulation, but it makes, it is
> the big hard point, any notion of stuffiness, irrelevant for physical
> objects too.
Well, I'm always willing to stand corrected, but I had hoped in my
post on Olympia to show you finally that I had indeed grasped
*exactly* this point. My questions in this post about emulation were
really directed to clarifying the stuffy-ontology position, as a
result of the debate with Colin: i.e. what does emulation mean in a
stuffy context? The common sense view is that - if stuff is primitive
- emulation can only be a 3-description. However, if numbers are
primitive, then in principle mathematical structures - in very special
relation, as you argue - actually *constitute* reality, not just
describe it.
I think what muddies the waters all the time is the physicalist
assumption that 'immaterial computation' can still be claimed account
for the mind on the basis of a stuffy ontology. Without this, we
would have more or less the simple dichotomy I propose: i.e.
stuffy-ontology => stuffy stuff + stuffy mind; or comp-ontology =>
comp stuff + comp mind. Each side could then argue against the
other's position, but at least without laying claim to each other's
'stuff'!
> There is just no stuff available. Even if we introduce it, it makes no
> change in consciousness, and can't have any relation with what we observe in
> nature
On the basis of the comp theory of mind-body: yes, definitely, no question.
David
We will come back on this.
> Bruno
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
> >
>
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Received on Fri Aug 14 2009 - 17:05:29 PDT