1) A Turing machine is an idealised digital computer, based on a tape
(memory device) of potentially infinite length, that has been shown to
be capable of emulating any type of digital computer, and hence any
other TM. The meaning of 'emulation' here entails transforming
precisely the same inputs into the precisely same outputs, given
sufficient time. In effect, digitally 'emulating' a computation is
conceptually indistinguishable from the computation itself; or to put
it another way, computation is deemed to be invariant under emulation.
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.
3) Now we get into more controversial territory. Bruno has shown (at
least I agree with him on this) that for the mind to be regarded as 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. This is not universally
accepted, but more on this in the next section. 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.
4) If we don't accept 3) then we can keep stuffy matter, but at the
cost of losing the digital computational model of both mind and body.
Not everyone agrees with that radical assessment, I know; 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. The stuffiness doesn't of course mean that the evolution of
physical systems can't in principle be specified algorithmically, and
'emulated' on a TM if that is possible; we still have mathematics as a
model of stuff and its relations. 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.
5) We might call 3 the numerical (necessary) model, and 4 the stuffy
(contingent) model of reality - but of course I don't insist on this.
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. And I think this has something to do with what Colin is
getting at: if your model is stuffy, then no amount of
digital-numerical emulation is ever going to get you anything stuffy
that you didn't have before. A physical-stuffy TM doing any amount of
whatever kind of computation-emulation remains just a physical-stuffy
TM, and a fortiori *not* transmogrified into the stuff whose causal
structure it happens to be computing.
Now of course this stricture wouldn't necessarily apply to model 3).
But the 'comp' that Colin claims to refute is, I suspect, not this but
stuffy-comp - i.e. the comp based on stuff rather than numbers, that
Olympia, in her lazy but decisive way, dismisses as ephemeral. This
is also the comp that I have argued against, but I don't intend this
merely to be a re-statement of my prejudices. I know that Colin isn't
precisely a proponent of model 3) nor model 4), arguing strenuously
for a distinctive alternative; so it would be interesting (certainly
for me) if he'd care to characterise precisely how it diverges from or
extends the foregoing stuffy-numerical dichotomy.
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?
David
Colin's recent interesting (not to say impassioned!) posts have - yet
again - made me realise the fundamental weakness of my grasp of some
of the discussions that involve Turing emulation - or emulability - on
the list. So I offer myself once more as lead ignoramus in
stimulating some feedback on this issue . Anyway, here's what I think
I know already (and I beg you patience in advance for the
inaccuracies):
1) A Turing machine is an idealised digital computer,
based on a tape
(memory device) of potentially infinite length,
that has been shown to
be capable of emulating any type of digital computer,
and hence any
other TM.
The meaning of 'emulation' here entails transforming
precisely the same inputs into the precisely same outputs, given
sufficient time.
In effect, digitally 'emulating' a computation is
conceptually indistinguishable from the computation itself; or to put
it another way, computation is deemed to be invariant under emulation.
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.
3) Now we get into more controversial territory.
Bruno has shown (at
least I agree with him on this) that for the mind to be regarded as 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.
This is not universally
accepted, but more on this in the next section.
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.
4) If we don't accept 3) then we can keep stuffy matter,
but at the
cost of losing the digital computational model of both mind and body.
Not everyone agrees with that radical assessment, I know;
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.
The stuffiness doesn't of course mean that the evolution of
physical systems can't in principle be specified algorithmically,
and
'emulated' on a TM if that is possible; we still have mathematics as a
model of stuff and its relations.
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.
5) We might call 3 the numerical (necessary) model, and 4 the stuffy
(contingent) model of reality -
but of course I don't insist on this.
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.
And I think this has something to do with what Colin is
getting at: if your model is stuffy, then no amount of
digital-numerical emulation is ever going to get you anything stuffy
that you didn't have before. A physical-stuffy TM doing any amount of
whatever kind of computation-emulation remains just a physical-stuffy
TM, and a fortiori *not* transmogrified into the stuff whose causal
structure it happens to be computing.
Now of course this stricture wouldn't necessarily apply to model 3).
But the 'comp' that Colin claims to refute is, I suspect, not this but
stuffy-comp - i.e. the comp based on stuff rather than numbers, that
Olympia, in her lazy but decisive way, dismisses as ephemeral. This
is also the comp that I have argued against, but I don't intend this
merely to be a re-statement of my prejudices. I know that Colin isn't
precisely a proponent of model 3) nor model 4), arguing strenuously
for a distinctive alternative; so it would be interesting (certainly
for me) if he'd care to characterise precisely how it diverges from or
extends the foregoing stuffy-numerical dichotomy.
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?
The appearance of the continuum is a consequence of comp. If digital
or constructive physics is possible, then by UDA comp if false. Of
course digital physics entails trivially comp. So digital physics is
inconsistent (with or without comp).
> It can
> only be approximated digitally.
Yes. Comp explains this, I mean the "can only", in the best case.
Today there are still too much non computable white rabbits. So,
strictly speaking, it is an open problem.
> QM supposes true randomness, which
> Turing machines can't produce.
Well, here too comp explains the randomnes, by the (hopefully plural)
first person indeterminacy. QM randomness is just the randomness due
to our self-multiplication (or differentiation) in the many-dreams.
> Again it may just be a matter of
> "sufficient approximation", but the idea of a multiverse and
> "everything-happens" assumes real numbers.
Comp forces this to be true.
>
>> 5) We might call 3 the numerical (necessary) model, and 4 the stuffy
>> (contingent) model of reality - but of course I don't insist on this.
>> 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. And I think this has something to do with what Colin is
>> getting at: if your model is stuffy, then no amount of
>> digital-numerical emulation is ever going to get you anything stuffy
>> that you didn't have before. A physical-stuffy TM doing any amount
>> of
>> whatever kind of computation-emulation remains just a physical-stuffy
>> TM, and a fortiori *not* transmogrified into the stuff whose causal
>> structure it happens to be computing.
>>
>
> I can look at it either way. A sufficiently detailed, accurate and
> predictive numerical model is as good as the stuff it models. But
> also
> a sufficiently accurate, detailed and predictive stuffy model is as
> good
> as the consciousness it models.
The stuffy model works for consciousness only if consciousness is a
actually infinite stuffy thing itself, making indexical comp false.
But you told us that you still don't follow step-8, so I am not
astonished by this reply. More explanations will be given.
Bruno
>
> 2009/8/14 Brent Meeker <meek...@dslextreme.com>:
>
>> A good summary, David. However, there are some other possibilities.
>> Physics as now conceived is based on real and complex numbers. It can
>> only be approximated digitally. QM supposes true randomness, which
>> Turing machines can't produce. Again it may just be a matter of
>> "sufficient approximation", but the idea of a multiverse and
>> "everything-happens" assumes real numbers.
>
> But the possibility of 'mathematical ontology' would remain a
> possibility for physics, even if it turned out that we needed an
> alternative to the digital TM as the 'computational substrate'?
Not at all. With comp, the basic "level" has to be any universal
system. (N,+,*) of combinators or JAVA, whatever. Quantum like stuffy
bricks have to emerge from the inside first person indeterminacy. The
proble of comp is that such a stuff is a priori not digitally
emulable. The quantum computer is a threat to comp! That is why I have
developed AUDA, it shows that universal machine have a highly non
trivial epistemology and physics, so that hope remains to save comp by
providing the comp explanation of the origin of the apparent quantum
waves.
>
>
>> A sufficiently detailed, accurate and
>> predictive numerical model is as good as the stuff it models
>
> And in terms of stuffy ontology, it would be a successful model - but
> you wouldn't expect to be able to build a house out of emulated
> bricks.
You are right, with comp. Stuffy bricks cannot be emulated by turing
machine, except perhaps by quantum one, but that has to be justified
from number and logic alone.
> By contrast, in terms of numerical ontology, a sufficiently
> complete 'model' would actually *constitute* the stuff it emulated
> (i.e. indicating the quite different force of 'emulation' in this
> case). Yes?
Only for the mind. Matter escapes computation, once we assume that
"we" are machine.
I think that you fail to take into account simultaneously UDA1-6,
UDA-7, and UDA-8. I know it is not easy.
>
>
>> But also a sufficiently accurate, detailed and predictive stuffy
>> model is as good
>> as the consciousness it models.
>
> If we take 'sufficiently' to the limit I suppose I must agree. But as
> before, in terms of stuffy ontology, any digital emulation - if that's
> what we're still discussing - is a model, not the stuff modelled, and
> hence wouldn't meet any such criterion of sufficiency. If we accept
> for the sake of argument a stuffy TM as equivalent to a stuffy brain,
> then what we're asked to accept here is that - although emulated
> bricks are no good for stuffy house building - stuffy neurons are just
> great for stuffy brain building. But why isn't a stuffy TM running a
> computation just a stuffy TM running a computation: WYSIWYG isn't it?
You are dismissing the first person indeterminacy. A stuffy TM can run
a computation. But if a consciousness is attached to that computation,
it is automatically attached to an infinity of immaterial and relative
computations as well, and from the perspective of that consciousness,
it entails that if the person (with consciousness) decide to look at
his stuffy neighborhood, below its comp-substitution, he will discover
the trace of that, a priori non turing emulable, infinities of
computations.
>
> And if that is so, then a stuffy brain running a computation is
> likewise just a stuffy brain running a computation: equally WYSIWYG.
> The only way you invoke consciousness in either case is by the
> straight a priori assumption: stuffy computation => consciousness.
> But according to lazy Olympia, going about computation in such a
> stuffy way reduces this assumption to an absurdity.
OK. And then UDA1-7 shows that any possible observable "stuffy" thing
is given by a probability/credibility measure on an infinity of
computations.
>
>
> Of course, in terms of numerical ontology, the assumption that
> computation => consciousness is equally a priori, but at least it's
> not absurd. In this case, brains, TMs - and bricks - share a
> computational ontology, so we can get building.
Hmm... Not really. The bricks become a priori beyond the computable.
Immaterial, like number relation, but non computable, like a
probability on a infinite, even continuous, realities made of infinite
computations.
>
>
> Reconsidering my recent statements in the light of this, I suspect I'm
> trying to eat my cake and have it (an old tendency) - but this might
> be OK. It still seems to me that the a priori ontological assumption
> of choice is some fundamental conjunction of self-access +
> self-relativisation: i.e.the One, I guess.
Here we are back on our little theological divergence. I may insist
you take a look on the Plotinus paper. The ONE is really arithmetical
truth before any notion of self is yet defined. Once a notion of self
appears, truth degenerate into provable provability and true
provability (G and G*, the eterrestrial intellect and the divine
intellect), which will degenerate into the universal self/soul (the
God of the eastern). And this one, due to tension with the intellect,
will fall, and that fall generate the non Turing emulable stuffy
matter. Then the soul will try to go back to the ONE. Except that this
temporal image is a bit a simplification. In a sense the fall and the
coming back are the same arithmetical process. "The ONE see the
falling souls, and the souls see their rise to the ONE. Same
arithmetical truth, but from different points of view.
> Stuff and consciousness -
> which I suspect to be a spurious dichotomy - get collapsed into this.
> But given self-relativisation in the context of self-access, you can
> follow the math in either 'stuffy' or 'computational' directions till
> you get where you need to be, and like others I suspect this will play
> out according as we discover the relative derivation of persons <=>
> things. As before, perhaps this is a no-more-neutral-than-necessary
> monism, and I guess it leaves the question of emulation as model or
> reality to be settled empirically.
With comp, reality is definitely not Turing emulable. If we discover a
computable theory of reality, then we will know that we cannot say yes
to the doctor, we will have to abandon the comp hyp.
Bruno
Quentin, your post is simpler to answer, so I do it no, but then I
have to do some works.
On 14 Aug 2009, at 12:16, Quentin Anciaux wrote:
>
> 2009/8/14 Bruno Marchal <mar...@ulb.ac.be>:
>>
>>
>> On 14 Aug 2009, at 03:18, David Nyman wrote:
>>
>>>
>>> 2009/8/14 Brent Meeker <meek...@dslextreme.com>:
>>>> A sufficiently detailed, accurate and
>>>> predictive numerical model is as good as the stuff it models
>>>
>>> And in terms of stuffy ontology, it would be a successful model -
>>> but
>>> you wouldn't expect to be able to build a house out of emulated
>>> bricks.
>>
>> You are right, with comp. Stuffy bricks cannot be emulated by turing
>> machine, except perhaps by quantum one, but that has to be justified
>> from number and logic alone.
>>
>
> Well, as a quantum computer can be simulated by a classical one (a
> quantum computer can't compute what a classical computer can't)... it
> will just be order of magnitude slower for the classical computer. So
> I don't understand the 'perhaps by quantum one'.
Because stuffy bricks, with comp, have to been recovered from the
physics extracted from comp, infinite statistics on infinite
computations) and this one predict some amount of indeterminacy which
is or is not covered by quantum computations. This is an open problem
(*the* open problem, partially solved by the 4th and 5th AUDA-
hypostases).
>
>
>
>>
>>> Stuff and consciousness -
>>> which I suspect to be a spurious dichotomy - get collapsed into
>>> this.
>>> But given self-relativisation in the context of self-access, you can
>>> follow the math in either 'stuffy' or 'computational' directions
>>> till
>>> you get where you need to be, and like others I suspect this will
>>> play
>>> out according as we discover the relative derivation of persons <=>
>>> things. As before, perhaps this is a no-more-neutral-than-necessary
>>> monism, and I guess it leaves the question of emulation as model or
>>> reality to be settled empirically.
>>
>> With comp, reality is definitely not Turing emulable. If we
>> discover a
>> computable theory of reality, then we will know that we cannot say
>> yes
>> to the doctor, we will have to abandon the comp hyp.
>
> I don't understand this either, if reality is computable, obviously
> our consciousness is too.
You are right. Reality is turing emulable ====> our consciousness is
Turing emulable (obvious).
But we have: our consciousness is Turing emulable ===> physical
reality is NOT a priori Turing emulable (by UDA-7-8)
From this it follows that: Reality is turing emulable ====> Reality
is NOT turing emulable.
This entails that: Reality is NOT turing emulable. With or without comp.
The prospect that reality is described by a quantum computation is not
yet ruled out, because the non computable part of reality could still
be only the first person indeterminacy. The non computable feature
would be the "geographic" one, like finding oneself in Washington
instead of Moscow after a self-duplication experiment.
Best,
Bruno
I understand they have to be recovered from all computations... but
what I'm asking is how a quantum computation could cover more than a
classical one ? it would violate the church-turing thesis.
Ok, but if you come up with a computable theory of reality you can't
invoke UDA to disprove it (as UDA would have been disproved from the
fact there is a computable theory of reality). So your objections is
correct only if UDA is true... but if UDA is true, you can't come up
with a computable theory of reality hence you never come to the
contradiction.
So, either there is a computable theory of reality then UDA is false
(not COMP), or UDA is true and there isn't a computable theory of
reality, you can't have both. But you can't use an argument that is
already disproven to disprove the theory.
> This entails that: Reality is NOT turing emulable. With or without comp.
>
> The prospect that reality is described by a quantum computation is not
> yet ruled out, because the non computable part of reality could still
> be only the first person indeterminacy. The non computable feature
> would be the "geographic" one, like finding oneself in Washington
> instead of Moscow after a self-duplication experiment.
>
>
> Best,
>
> Bruno
>
>
>
> http://iridia.ulb.ac.be/~marchal/
>
Regards,
Quentin
> A good summary, David. However, there are some other possibilities.
> Physics as now conceived is based on real and complex numbers. It can
> only be approximated digitally. QM supposes true randomness, which
> Turing machines can't produce.
As Bruno said, a branching algorithm can produce true randomness from
the perspective of the embedded observer.
--
Stathis Papaioannou
You are of course right about Turing. He was thinking of human computation. But he was
preceded by some real computers, notably those of Charles Babbage.
As an aside, when I was in college I worked during summers for a geophysical research
company in Texas. I calculated subsurface distances from sonic echo records. My
official job title was "Computer".
But don't you start with the hypothesis that saying yes to the doctor continues your mind?
Are you contemplating that the brain may do something that is not computable or only
that the world is not computable?
I don't care where stuffy matter comes from, but whatever the TOE is, I want it to recover
stuffy matter because that allows it to connect to all the science we have based on stuffy
matter.
Brent
>Colin is correct for saying bodies
> cannot be computable, but this follows from the mind being "computable",
> in the "yes doctor" sense, not from the scientist mind being non computable.
>
>
>
>>
>> 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).
>
>
>> 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.
> makes, it is the big hard point, any notion of stuffiness, irrelevant*
> for physical objects too*.
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 rathersubtle, 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 (atleast I agree with him on this) that for the mind to be regarded as acomputation,The wording is a bit dangerous. All I know after UDA is that my state ofmind at time and place (x,t) has to be linked to an infinity of computationsgoing through that state, and that my next state, from my first person pointof 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 thesame light: IOW our ontology is to be understood entirely from theperspective of numbers and their relations.True, but this excludes quickly that it can be conceived a priori ascomputations. Immaterial relation between numbers, sure, but not necessarilycomputable relation. Cf the first person indeterminacy.This is not universallyaccepted, but more on this in the next section.This is not universally understood, nor really studied. But it is understoodquickly 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 saythat on this basis we would appear to have a situation where theappropriate set of computations could be regarded not as mere'emulation', but in fact *as real as it gets*. But this of coursealso renders 'stuffy matter' irrelevant to the case: it's got to benumbers all the way down.No. With the first person indeterminacy it would be more correct to say thatit's got to be number all the way up.
Yes, I nearly said 'all the way up'.It makes the comp immaterialappearance of "stuffy matter" infinitely complex and non turing emulable, apriori. I suspect you have not yet really see the role of UDA1-6 in thestep-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 makesense 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 ofinfinite computations including infinities of white rabbits-computations.The apparent computability of the physical laws *is* a problem for theindexical computationalist.but at thecost of losing the digital computational model of both mind and body.Most want introduce a stuffy matter because they believe they can savecomputation 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 ofunderstanding 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 eventhose who don't concur presumably do hold that everything that happensfinally supervenes on something stuffy as its ontological and causalbasis, and that numbers and their relations serve merely to modelthis.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 ofphysical 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 anyway 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 digitalemulation of a physical system can - as a mere structure of numbers -be considered the 'real thing': it's got to be stuffy all the waydown.Well, with comp+physicalism. But this is inconsistent, at theepistemological 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 theemulability or otherwise of physics, we may sometimes lose sight ofwhether we are interpreting in terms of numerical or stuffyontologies.But "stuffy" or just primitively physical, after UDA has no more anymeaning.
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 thedistinction between numerical 3) and stuffy 4) to be cogent with*specific* respect to the significance and possible application of theconcept of 'emulation' in each case?You don't yet have grasped the UDA yet. It makesthe stuffy things not justuseless for having computations and relative emulation, but it makes, it isthe big hard point, any notion of stuffiness, irrelevant for physicalobjects 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 nochange in consciousness, and can't have any relation with what we observe innature
On the basis of the comp theory of mind-body: yes, definitely, no question.
We will come back on this.
I love Babbage.
>
> As an aside, when I was in college I worked during summers for a
> geophysical research
> company in Texas. I calculated subsurface distances from sonic
> echo records. My
> official job title was "Computer".
It is still an open problem for me if, for the english speaker,
computer really means automatically universal computer, or does it
means also some non universal device. In french we have the term
"ordinateur", but it has the connotation of big monumental machine.
People said "PC" today. The universal thing can take many shapes and
have many names.
Yes.
> Are you contemplating that the brain may do something that is not
> computable or only
> that the world is not computable?
Both. Below my substitution level. My histories does not care.
I am sure it will, or comp will appear to be false, and then UDA gives
a tool to measure the degree of non-computationalism. Don't worry, we
have to be very near the big one to escape the stuffy world.
Look at this in this way: may be it is because I like the stuffy stuff
so much that I want to assoir it on something more solid than
observations and guesses.
Bruno
Because stuffy bricks, with comp, have to been recovered from thephysics extracted from comp, infinite statistics on infinitecomputations) and this one predict some amount of indeterminacy whichis or is not covered by quantum computations. This is an open problem(*the* open problem, partially solved by the 4th and 5th AUDA-hypostases).
I understand they have to be recovered from all computations... but
what I'm asking is how a quantum computation could cover more than a
classical one ? it would violate the church-turing thesis.
You are right. Reality is turing emulable ====> our consciousness isTuring emulable (obvious).But we have: our consciousness is Turing emulable ===> physicalreality is NOT a priori Turing emulable (by UDA-7-8)From this it follows that: Reality is turing emulable ====> Realityis NOT turing emulable.
Ok, but if you come up with a computable theory of reality you can't
invoke UDA to disprove it (as UDA would have been disproved from the
fact there is a computable theory of reality).
So your objections is
correct only if UDA is true... but if UDA is true, you can't come up
with a computable theory of reality hence you never come to the
contradiction.
So, either there is a computable theory of reality then UDA is false
(not COMP),
or UDA is true and there isn't a computable theory of
reality, you can't have both. But you can't use an argument that is
already disproven to disprove the theory.
>
>
>
> On 14 Aug, 09:48, Bruno Marchal <marc...@ulb.ac.be> wrote:
>
>> You are dismissing the first person indeterminacy. A stuffy TM can
>> run
>> a computation. But if a consciousness is attached to that
>> computation,
>> it is automatically attached to an infinity of immaterial and
>> relative
>> computations as well,
>
> There's your Platonism.
Not mine. The one which follows from the comp assumption, if UDA is
valid.
> If nothing immaterial exists (NB "nothing",
> I don't make exceptions for just a few pixies or juse a few numbers)
> there is nothiign for a cosnc. to attach itself to except a propbably
> small, probabuily singular set of stuiffy brains and computers.
I can understand how easy for a materialist it is, to conceive at
first sight, that numbers and mathematical objects are convenient
fiction realized as space-time material configuration, perhaps of
brains.
But those space-time configuration are themselves described by
mathematical functions far more complex that the numbers described or
explain. This leads to major difficulties, even before approaching the
consciousness problem.
This shows that a purely physicalist explanation of numbers could lead
to difficulties. But the same for a description of any piece of
material things, by just that token.
So, I am not sure that physicist can be said to have solved the
"matter" problem either, and some physicists are already open,
independently of comp, to the idea that physical objects are relative
mathematical (immaterial) objects. Which of course are "no material".
Wheeler, Tegmark, for example.
But then with comp, you are yourself an immaterial object, of the kind
person, like the lobian machine. You own a body, or you borrow it to
your neighborhood, and "you" as an immaterial pattern can become
stable only by being multiplied in infinities of coherent similar
histories, which eventually the physicists begin to talk about
(multiverse).
I tend to believe in many immaterial things. Some are absolutely real
(I think) like the natural numbers.
Some may be seen as absolutely real, or just as useful fiction: it
changes nothing. This is the case for the negative number, the
rational, a large part of the algebraic and topological, and analytical.
Some are both absolutely real, and physically real, they live in
"platonia", and then can come back on earth: they have a relatively
concrete existence. For example, the games of chess, the computers,
the animals, and the persons. But the concreteness is relative, the
'I' coupled with the chessboard is an abstract couple following
normality conditions (that QM provides, but comp not yet).
Some could have an even more trivial sense of absolute existence, and
a case could be made they don't exist, even in Platonia, like the
unicorns, perhaps, and the squared circles (hopefully).
Each branch of math has its own notion of existence, and with comp, we
have a lot choice, for the ontic part, but usually I take
arithmetical existence, if only because this is taught in school, and
its enough to justified the existence of the universal numbers, and
either they dreams (if "yes doctor") or at least their discourse on
their dreams (if you say no the doctor and decide to qualify those
machines are "inexistent zombies").
There is a sense to say those universal machines do not exist, but it
happens that they don't have the cognitive abilities to know that, and
for them, in-existence does not make sense.
And for a mathematicans, they exists in a very strong sense, which is
that, by accepting Church Thesis, they can prove the existence of
universal digital (mathematical) machine from 0, succession, addition
and multiplication.
Both amoebas colony (human cells), and engineers are implementing some
of them everyday in our neighborhood, as we can guess.
Bruno
>
> 2009/8/16 Bruno Marchal <mar...@ulb.ac.be>:
>>
>> On 14 Aug 2009, at 12:58, Quentin Anciaux wrote:
>>
>>> 2009/8/14 Bruno Marchal <mar...@ulb.ac.be>:
>>>>
>>>> Because stuffy bricks, with comp, have to been recovered from the
>>>>
>>>> physics extracted from comp, infinite statistics on infinite
>>>>
>>>> computations) and this one predict some amount of indeterminacy
>>>> which
>>>>
>>>> is or is not covered by quantum computations. This is an open
>>>> problem
>>>>
>>>> (*the* open problem, partially solved by the 4th and 5th AUDA-
>>>>
>>>> hypostases).
>>
>>
>>> I understand they have to be recovered from all computations... but
>>> what I'm asking is how a quantum computation could cover more than a
>>> classical one ? it would violate the church-turing thesis.
>>
>> A quantum computation does not violate Church-turing thesis,
>> because it
>> cannot compute more than a classical machine.
>> But, a quantum computation covers simultaneously big numbers of
>> classical
>> computations.
>
> Ok but as this could be done on classical machine an order of
> magnitude slower I don't see how it is relevant.
It is an evidence wich confirms the sort of reality we can expect with
comp. below our substitution level we should have evidence of more
than one computation acting in parallel.
>
>> The problem of comp today, is that a priori, the "comp
>> computation", seems
>> to cover much more classical histories than we can with quantum
>> computers.
>
> I don't understand what you mean here ?
Comp predicts that any miece of observable matter "does not exist
primitively" but emerge from a first person view on an infinity of
identical (with respect to the level of description) but dissimilar
(below that level) computations. They relative proportion dtemined the
way we have to quantify the 1-indterminacy. Just remember how the step
seven works. You are in front of a UD which never stop. To predict
your next experience accirately, a priori you have to run the whole
UD, so as to measure the right relative frequencies. In reality, no
such runhas to be done, because the first person is not aware on any
of the UD delays, and that is why "nature" does automatically, in
appearance, what would take an infinite time, if we would search for
such an accuracy. But then why is the physical world so much
computable in appearance. Matter has become the phenomenon that we
have to explain without any recourse of theories based on observable
matter.
It is really the step seven, and we are doing again in detail, so
don't worry if it is still unclear.
>
>> According to what we can say today from the 3th, 4th, and 5th
>> hypostases,
>> (which describe matter) the math are still to hard to say if we the
>> comp-computations, as seen from insides covers less, or more, or
>> the same,
>> histories with the right relative proportions.
>
> I'm sorry but here too.
The UD* run all quantum computation going through my state, and a
priori much more other computations.
>
>>>>
>>>> You are right. Reality is turing emulable ====> our consciousness
>>>> is
>>>>
>>>> Turing emulable (obvious).
>>>>
>>>> But we have: our consciousness is Turing emulable ===> physical
>>>>
>>>> reality is NOT a priori Turing emulable (by UDA-7-8)
>>>>
>>>> From this it follows that: Reality is turing emulable ====>
>>>> Reality
>>>>
>>>> is NOT turing emulable.
>>>>
>>> Ok, but if you come up with a computable theory of reality you can't
>>> invoke UDA to disprove it (as UDA would have been disproved from the
>>> fact there is a computable theory of reality).
>>
>> I am not sure I understand.
>> UDA is a reasoning showing that comp => reality is not computable
>> (roughly
>> speaking).
>> UDA is valid, or not valid. But that's another discussion.
>
> If UDA is not valid, you don't get the contradiction (I'm not saying
> the argument (UDA) is invalid, I'm saying that you could not deduce
> the contradiction if UDA is invalid because the contradiction only
> arises if UDA is valid). If you come up with a computable theory of
> reality, either UDA is invalid or the computable theory of reality is
> invalid. But you can't use UDA to say the computable theory of reality
> is invalid if UDA is invalid.
Of course. Unless someone find another proof which is valid.
In case someone would find a flaw in the UDA.
But this you can say for all theorems.
>
>> So if someone rational believes in a computable reality, it has to
>> abandon
>> comp.
>> (if p -> q, then ~q -> ~p).
>> But now, with comp, it should be obvious that reality is not
>> computable, if
>> only because, roughly speaking reality is arithmetical truth, which
>> indeed
>> vastly extends the realm of the computable.
>
> I'm ok with that... but obvious I couldn't say it is, there could be
> rules which restrict to something vastly smaller than arithmetical
> truth... not that I believe it.
I doubt it too. I mean how to make such restriction, without making
more or less than a universal machine. We will come back on this.
>
>> So, with comp, it became astonishing that the physical reality,
>> which is a
>> sort of universal border of the ignorance of all universal machine,
>> looks so
>> much computational.
>> Thus QM, with its local and sharable indeterminacies is a relief
>> for the one
>> who hope comp to be true (like the day before saying yes to a
>> doctor).
>>
>>> So your objections is
>>> correct only if UDA is true... but if UDA is true, you can't come up
>>> with a computable theory of reality hence you never come to the
>>> contradiction.
>>
>> comp => Reality is not computable (UDA)
>> thus
>> Reality is Computable = > ~comp (contraposition)
>> But
>> Reality is Computable = > Comp (to emulate me, emulate Reality if
>> necessary)
>> So Reality is computable => (comp and ~comp) a contradiction.
>> So reality is not computable. In all circumstance.
>
> No, not in all circumstance, only if UDA is valid.
I was supposing UDA is valid. But when you present an argument,
usually you don't have to assume the reasoning valid to pursue. If the
reasoning is non valid, people (intersted) have to point on where the
argument if not valid.
In AUDA, do you think we have to assuming Turing, Gödel, Church,
Kleene to be valid?
If UDA is not valid, all what I say should be abandoned. Well actually
you can recover a part of the theory by postulating Pytahgoreanism at
the start (What Peter seems to believe): the assumption that there is
nothing but numbers (with +, and *). But no need to do that, unless
you feel an error remains in UDA. Of course *you* can think like that
only when you are personally convinced by UDA, or by some other
argument.
Bruno
>
> On Fri, Aug 14, 2009 at 10:03:41PM +0200, Bruno Marchal wrote:
>> Look at this in this way: may be it is because I like the stuffy
>> stuff
>> so much that I want to assoir it on something more solid than
>
> ^^ seat? - "base" perhaps.
Thanks Russell. Now, I was thinking some french words here and there
can be tolerated, and that it would only make my prose looking
snobbish. But then I guess I was wrong, right? Or does it look too
much snobbish?
Best,
Bruno
> Without Platonism, there is no UD since it is not observable within
> physical space. So the UDA is based on Plat., not the other way
> round.
Are you saying that without platonism, the square root of 2 does not
exist? Prime number does not exist? That mathematical existence is a
meaningless notion?
Mathematics would be a physical illusion?
But physics use mathematics, would that not make physics illusory or
circular?
> It's a perfectly consistent assumption. THere is no
> disproof of materialism that doesn't beg the quesiton by
> assuming immaterialism
Well, I do believe in the natural numbers, and I do believe in their
immateriality (the number seven is not made of quantum field, or
waves, or particle).
So either you tell me that you don't believe in the number seven, or
that you have a theory in which the number seven is explained in
materialist term, without assuming numbers in that theory.
>> This leads to major difficulties, even before approaching the
>> consciousness problem.
>
> Such as?
Explaining number with physical notions,
and explaining, even partially, physical notions with the use numbers.
> You arguments here are based on the idea
> that primary matter needs to be given a
> purely mathematical expression. That in turn
> is based on an assumption of Platonism. If
> Platonism is false and materialism true,
> one would *expect* mathematical explanation
> to run out at some point. Your "difficulty" is a
> *prediction* of materialism , and therefore a
> successfor materailism
Not at all. Cf the "even partially" in my sentence just above.
>> and some physicists are already open,
>> independently of comp, to the idea that physical objects are relative
>> mathematical (immaterial) objects. Which of course are "no material".
>> Wheeler, Tegmark, for example.
>
> They have a consisent set of assumptions. So do
> their materialist oponents. You can't get an "is true"
> out of a "might be true"
Well the movie graph conclusion is that materialism is not consistent,
unless it opt for eliminativism of persons and/or non computationalism.
>> I tend to believe in many immaterial things. Some are absolutely real
>> (I think) like the natural numbers.
>
> There's your Platonism again. Believe what you like, but don'
> call it proof.
Given that the theorem is "comp => platonism", and given that I am
open to the idea that comp could be correct, I am of course open to
the idea that Platonism may be correct.
But again, I don't need platonism (non-physicalism) to be an
arithmetical realist, like all classical mathematicians. This is
explicit in the assumption. The non physicalism and general
immaterialism is a consequence of the movie graph argument. What is
wrong with it?
> It changes everything. If the UD is a useful ficiton, I cannot be a
> programme running on it, any more than I can book a flight to Narnia.
Would you say that the 1000^1000th base ten decimal of PI is a fiction?
>> There is a sense to say those universal machines do not exist, but it
>> happens that they don't have the cognitive abilities to know that,
>> and
>> for them, in-existence does not make sense.
>
> If they don't exist, they don't exist. You don't have the
> rigourous mathematical argument you think
> you have, you have some baroque Chuang-Tzu metaphysics.
I do like Chuang-tzu, and I can see the relation between comp and
Chuang-tzu, although it is more clear with Lao-Tzu, as you may see in
"Conscience et Mécanisme", where an explicit correspondence is
suggested.
So, what you tell me is that you don't believe in *any* form of
mathematical existence.
So you reject arithmetical realism, and thus you reject comp.
Arithmetical realism is needed to give a sense to Church thesis, which
is part of comp.
Some posts ago, you seem to accept arithmetical realism, so I am no
more sure of your position.
Bruno
>
> On 17 Aug, 08:43, Bruno Marchal <marc...@ulb.ac.be> wrote:
>
>> Good intuition David. I think that at some point you are too much
>> precise, so that I can refer only to the interview of the Universal
>> Machine, and you may agree with her, perhaps by making some
>> vocabulary
>> adjustments.
>
> Thanks Bruno. How might I take part in such an interview?
I am not sure what do you mean exactly.
Today, the concrete universal machines are still very primitive, if
not already too much enslaved (full of non universal programs).
So the existing "interview" is still part of mathematical logic
exclusively. It is known today as the logic of provability, or the
logic of consistency, or the logic of self-reference.
The notion of self-reference is the natural third person notion of
self-reference as defined by Gödel in his 1931 paper. It applies to
very general notions of self-referential entity, not just machine. But
I I limit myself on correct machines.
May be you could study the second part of the sane04 paper, and help
yourself with an introductory book on the subject like the book by
Raymond Smullyan "Forever Undecided", but you may need some taste in
logic.
Textbooks exist like Boolos 1979 (which has been reedited), Boolos
1993, and Smorynski 1985. You will find the reference in my Lille PhD
thesis. Those books assumed some knowledge of mathematical logic. Good
books are Elliot Mendelson (many editions), or the book by Boolos,
Burgess and Jeffrey.
Have you follow the seventh step series, or the older but recent UDA
and MGA threads? I am actually explaining the math from scratch needed
to understand the seventh step, which is the step where the Universal
Dovetailer appears.
The understanding of the notion of Universal Dovetailer requires the
notion Universal machine, which requires the notion of computable
functions, which requires the notion of functions and related
elementary set theory.
UDA shows this: "if I am a machine" then "correct physical prediction
= a sum on self-consistent extensions".
This transforms a part of the mind body problem into a tremendously
hard mathematical body problem.
That was the goal: to show that the comp hyp reduces, if only
partially, the mind body problem into a computer science/mathematical
logico problem.
Now at first sight you get an infinite sum of infinite things, so it
could seem UDA is just a refutation of comp.
Now UDA shows *and illustrate* that machines which introspect
themselves can see that physics is the head, so to speak. So instead
of using computer science to look at the sum on self-consistent
extension, it is simpler, conceptually to directly study what a
correct universal machine can see by introspecting herself. We know
she must see the "physics" in her "head", OK? And that is what Gödel
did for correct machines known by logicians as (sufficiently rich)
axiomatic theories. This has given the logic of self-reference.
I give an exemple: Gödel shows that (arithmetical or above) axiomatic
theories can talk (prove) propositions about themselves. The
"themselves" is a third person self-reference, so that the machine is
talking in the manner of a scientific about her body, in a third
person way.
Examples
- An incompleteness theorem: it asserts that the correct machine
machine cannot prove its own consistency (own based on that third
person self-reference). This can be written ~B(~Bf) (it is not
provable that the false is not provable).
- *the* incompleteness theorem: if "I" am consistent then "I" cannot
prove "my" own consistency ("I", and "me" = 3-self).
This can be written ~Bf -> ~B(~Bf ). First person reference are more
tricky to define, and requires Theaetetus.
Now, some machine believes this, they believes in the natural numbers.
For example, they believe in Ex (x = 0), (it exists a number x equal
to the 0). and also, they believe in Ex (x = s(0)), i.e. it exists a
number x equal to the 0), and so one with s(s(0)), s(s(s(0))), etc.
But they believe also in all the induction formula:
[p(0) and Ax(p(x) -> p(s(x))] -> Ax p(x)
I translate (read the colonne vertically):
p(0) the property p is true for zero
and and
Ax for all number x we have that
(p(x) -> p(s(x)) the truth of p for x entails the truth of p for the
successor of x
-> all what precedes entails the truth of what follows
The induction formula gives an enormous power of probability. To
believe in addition and multiplication makes you already universal. To
believe in addition, multiplication and in the induction formula makes
you Löbian, and this makes you know, in a sense, that you are
universal. At the propositional level the logic has been axiomatized
soundly and completely by Solovay, and with the mathematical decor
(the so called normal modal logic) they are entirely characterized by
the formula B(Bp->p)->Bp. A formula related to a theorem by Löb.
Oops I must go. We were beginning the AUDA. It could be premature,
given that we are just at the seventh step of UDA in another thread.
Let me be short and hopefully not too much discouraging. If you want
to take part in the interview, you have to learn theoretical computer
science, math and logic. You may have an opportunity, given that I
like to teach those matter especially when people are motivated by
deep questions.
Bruno
I think of numbers as part of our descriptive models. We (along with our evolution)
invented them). Mathematical existence is only meaningful in the sense that some
mathematical object follows from axioms. Descriptions are not illusory if they model
something in reality. The number 2 models pairs of things in the world, but a model is
not the thing. Pairing things by similarity or function or color is done by abstracting
away the particularities.
Brent
I agree in a sense. There is the allowance of a primariness, i.e. some things exist and
some don't, that is irreducible and perhaps mysterious. It is not asserted, but it is
accepted that however good one's models are at making accurate predictions one can never
know if they are really real or just good models.
Does Bruno assume arithmetic is really real or just a really good model, and can the
difference be known? And what if his theory is empirically falsified, as he says it could
be? Will that suddenly change arithmetic to fiction?
If you can't settle for less than certain knowledge - then you will end up like Rex, with
none at all.
>
> And are you making any explicit assumption about the relation between
> this "primary matter" and qualia/first-person experience? If not, then I
> don't see why it wouldn't be logically possible to have a universe with
> primary matter but no qualia (all living beings would be zombies), or
> qualia but no primary matter (and if you admit this possibility, then
> why shouldn't we believe this is exactly the type of universe we live in?)
I don't have any model in which there would be qualia but no matter. Most models of the
world suppose there were no qualia prior to a billion years ago. For me it's not a
question of logical possibility, but nomological possibility.
Brent
No less, but some more. Compare the concept that chemistry gives rise to life. As we
have come to understand life we see that it has lots of sub-processes and there are
different kinds suited to different environments. We can manipulate some aspects of life,
e.g. genetic engineering. So we did get more than just certain chemical processes give
rise to life in virtue of being the processes they are. The very concept of life is now
seen to be a fuzzy abstraction with no definite meaning.
Brent
>
>
>
> On 17 Aug, 11:17, Bruno Marchal <marc...@ulb.ac.be> wrote:
>> On 17 Aug 2009, at 11:11, 1Z wrote:
>>
>>> Without Platonism, there is no UD since it is not observable within
>>> physical space. So the UDA is based on Plat., not the other way
>>> round.
>>
>> Are you saying that without platonism, the square root of 2 does not
>> exist?
>
> Yes, the square root of two has no ontological existence.
All what matters with comp is that things like the square root of 2
has a notion of existence independent of "me".
>
>> Prime number does not exist?
>
> Yes, prime numbers have no ontological existence
I guess you make a "material" ontological commitment. One of my goal
is to explain, notably with the comp hyp, that a term like matter has
no referent. This would explain why physicist never use such
ontological commitment explicitly.
To say that matter exists simply is a non rational act of the type
"don't ask". UDA makes just this precise by reudcing the mind body
problem to a body problem.
>
>> That mathematical existence is a
>> meaningless notion?
>
> Sense but no refence. Mathematical statements have
> truth values but do not refere to anything outside the
> formal system.
Then they have no truth value. What you say is formalism, and this has
been explicitly refuted by mathematical logicians.
We know, mainly by the work of Gödel that the truth about numbers
extends what can be justified in ANY effective formal systems (and non
effective one are not really "formal").
But I know that there are still some formalists in the neighborhood,
and that is why I make explicit the assumption of arithmetical
realism. It is the assumption that the structure (N, +, x) is well
defined, despite we can't define it effectively.
>
>> Mathematics would be a physical illusion?
>
> A referentless formal game, distinguished from fiction
> only by its rigour and generality
You evacuate the whole approach of semantics by Tarski and Quine. I
will not insist on this because I will explain with some detail why
Church thesis necessitate arithmetical realism, and why this leads
directly to the incompleteness and the discovery that arithmetical
truth cannot be captured by any effective formal system. The formalist
position in math is no more tenable.
>
>> But physics use mathematics, would that not make physics illusory or
>> circular?
>
> No, because it uses mathematics empirically. The same
> language that can be used to write fiction can be used to
> write history. The difference is in how it used. not in the langauge
> itself
I don't see any difference in the use of analytical tools in physics
and in number theory. The distribution of the prime numbers is
objective, and this is the only type of independent objectivity needed
in the reasoning. Nothing more.
>
>>> It's a perfectly consistent assumption. THere is no
>>> disproof of materialism that doesn't beg the quesiton by
>>> assuming immaterialism
>>
>> Well, I do believe in the natural numbers, and I do believe in their
>> immateriality (the number seven is not made of quantum field, or
>> waves, or particle).
>
> Then you are a Platonist, and you argument is based
> on Platonism.
I believe that the truth of arithmetical statement having the shape
"ExP(x)" is independent of me, and you and the physical universe (if
that exists).
You can call that Platonism, if you want, but this is not obviously
"anti-physicalist". Non-physicalism is the conclusion of a reasoning
(UDA).
Given that Plato's conception of reality is closer to the conclusion,
I prefer to use the expression "Arithmetical realism" for this (banal)
assumption, and Platonism or non-physicalism for the conclusion. But
that is only a vocabulary problem.
>
>> So either you tell me that you don't believe in the number seven, or
>> that you have a theory in which the number seven is explained in
>> materialist term, without assuming numbers in that theory.
>
> The latter.
Show it. I know an attempt toward "science without number" by Hartree
Field (wrong spelling?), but I found it poorly convincing. Most
physicists accept the objectivity of numbers. Even more so with the
attempt to marry GR and QM.
>
>>>> This leads to major difficulties, even before approaching the
>>>> consciousness problem.
>>
>>> Such as?
>>
>> Explaining number with physical notions,
>> and explaining, even partially, physical notions with the use
>> numbers.
>
> That is just a repetition of the claim that there
> are problems. You have not in the least explained what
> the problems are.
UDA is such an explanation. AUDA gives a constructive path toward a
solution.
I am not even sure of that, but given the fuzziness of the notion of
"primitive matter", why not. May be God created it in 6 days, or the
big bang in zero seconds.
I always felt that taking notion of matter, or consciousness, for
granted, is a creationist-like move on the type "don't ask". UDA shows
that we have to ask more precisely when we assume that personal
consciousness can be invariant for the change of implementations done
below the substitution level.
> Moreover, the movie graph doesn;t prove
> what you say it does since it involves an illegitimate move from
> "minimal physical basis" to "no physical basis".
It goes explicitly to "no physical activity" in the MGA3 thread. But
MGA2 is enough, due to the "qua computatio" condition in the "yes
doctor" hypothesis. I guessed that your problem is in the
understanding of UDA step-8.
>
>>>> I tend to believe in many immaterial things. Some are absolutely
>>>> real
>>>> (I think) like the natural numbers.
>>
>>> There's your Platonism again. Believe what you like, but don'
>>> call it proof.
>>
>> Given that the theorem is "comp => platonism", and given that I am
>> open to the idea that comp could be correct, I am of course open to
>> the idea that Platonism may be correct.
>
> The theorem is platonism=>UD, UD=comp=>immaterialism
I am glad you see this. All what I have to do is convince you that
formalism does not work for arithmetic and mathematical computer
science.
>
>> But again, I don't need platonism (non-physicalism) to be an
>> arithmetical realist, like all classical mathematicians.
>
> Yes you do. The UD doesn't exist physically. If it doesn't
> exist non-physically either, it doesn't exist, and I am not
> a programme running on it.
Because you don't believe in anything non physical. But this comes
from your "formalist" position which does no more make sense after
Gödel. Each formal system, and machine, miss almost all arithmetical
truth.
>
>> This is
>> explicit in the assumption. The non physicalism and general
>> immaterialism is a consequence of the movie graph argument. What is
>> wrong with it?
>
>
> The movie graph doesn;t prove
> what you say it does since it involves an illegitimate move from
> "minimal physical basis" to "no physical basis".
See MGA3. Actually the contradiction appears, in the movie graph, even
when the whole physical activity is still there, but is no more
corresponding to any computation. This is a subtle point, no doubt,
and it asks for an understanding of the computational supervenience
thesis, which I am explaining in the "seven step series" thread.
>
>>> It changes everything. If the UD is a useful ficiton, I cannot be a
>>> programme running on it, any more than I can book a flight to
>>> Narnia.
>>
>> Would you say that the 1000^1000th base ten decimal of PI is a
>> fiction?
>
> Yes. I don't beleive in *any* pixies, not a single one.
All what I need is that the statement "the 1000^1000th base ten
decimal of PI is even" is true or false independently of the
existence of me, the planet earth or the physical universe (if that
exists).
>
>>>> There is a sense to say those universal machines do not exist,
>>>> but it
>>>> happens that they don't have the cognitive abilities to know that,
>>>> and
>>>> for them, in-existence does not make sense.
>>
>>> If they don't exist, they don't exist. You don't have the
>>> rigourous mathematical argument you think
>>> you have, you have some baroque Chuang-Tzu metaphysics.
>>
>> I do like Chuang-tzu, and I can see the relation between comp and
>> Chuang-tzu, although it is more clear with Lao-Tzu, as you may see in
>> "Conscience et Mécanisme", where an explicit correspondence is
>> suggested.
>
>> So, what you tell me is that you don't believe in *any* form of
>> mathematical existence.
>
> Not in any, and not in any pixies either.
>
>> So you reject arithmetical realism, and thus you reject comp.
>
> The computaitonal Theory of Mind has no implications about Platonism.
Comp is based on the notion of digitalness, which needs Church thesis.
I will explain in detail why Church thesis needs arithmetical realism.
I think that you are confusing everyone by switching "arithmetical
realism" with "Platonism". If you call "Platonism" what I call
"Arithmetical realism", I will put the result in the following way:
comp => non physicalism. It leads to a reduction of the mind-body
problem to the search of an explanation of stable beliefs in matter,
without matter. AUDA provides the explanation, yet not the physical
theory (but still the logic of physical propositions). It explains the
appearance of "many worlds" below the substitution level.
>
> You may of course mean something else by "comp".....
>
>> Arithmetical realism is needed to give a sense to Church thesis,
>> which
>> is part of comp.
>
> if AR is as claim abotu the immateial existence of numbers it does
> not.
> Not even remotely.
AR is a claim that number exists independently of my body and soul.
Number are immaterial, by definition. You don't need a theory of
matter to explain what numbers are. On the contrary, all book which
talk on matter assumes them more or less explicitly.
>
>> Some posts ago, you seem to accept arithmetical realism, so I am no
>> more sure of your position.
>
> I may have assented to the *truth* of some propositions...
> but truth is not existence. At least, the claim that
> truth=existence is extraordinary and metaphysical...
Mathematical existence = truth of existential mathematical statement.
The number seven exists independently of me, is equivalent with the
statement that the truth of the mathematical statement Ex(x =
s(s(s(s(s(s(s(0)))))))) is true independently of me.
If you really believe that the number 7 has no existence at all, then
the UDA reasoning does not go through, but then you are abandoning
comp because you can no more give sense to digitalness. You can still
say "yes" to a doctor, but you have to refer to some analog material
object, and not accept that you survive "qua computatio". This plays a
role in step-8.
Bruno
>
>
>
> On 17 Aug, 14:46, Jesse Mazer <laserma...@hotmail.com> wrote:
>> 1Z wrote:
>>>> But those space-time configuration are themselves described by
>>>> mathematical functions far more complex that the numbers
>>>> described or
>>>> explain.
>
>> But what is this "primary matter"? If it is entirely divorced from
>> all the evidence from physics that various abstract mathematical
>> models of particles and fields can be used to make accurate
>> predictions about observed experimental results, then it becomes
>> something utterly mysterious and divorced from any of our empirical
>> experiences whatsoever (since all of our intuitions regarding
>> 'matter' are based solely on our empirical experiences with how it
>> *behaves* in the sensory realm, and the abstract mathematical
>> models give perfectly accurate predictions about this behavior).
>
> Primary matter is very much related to the fact that some theories of
> physics work and other do not. It won't tell you which ones work, but
> it will tell you why there is a difference. It solves the white rabbit
> problem.
QM mechanics solves mathematically the white rabbit problem. I do
agree with this, but to say it does this by invoking primitive matter
does not follow. On the contrary QM amplitude makes primitive matter
still more hard to figure out. Primitive matter is, up to now, a
metaphysical notion. Darwinian evolution can justify why we take
seriously the consistency of our neighborhood, and why we extrapolate
that consistency, but physicists does not, in their theories, ever
postulate *primitive* matter.
> We don't see logically consistent but otherwise bizarre
> universes because they are immaterial and non-existent--not matter
> instantiates
> that particualar amtehamtical structure.
Are you defending Bohm's Quantum Mechanics? The wave without particles
still act physically, indeed they have to do that for the quantum
disappearance of the white rabbits.
Bruno
Artithmetical theories model (in the physicists sense) the standard
model (in the logician sense) of arithmetic.
But you are right. Arithmetical truth is what our theories try to
model, always imperfectly, and necessarily so, as we know since Gödel.
Bruno
>>
>> What do you mean by "ontological existence"?
>
> Real in the Sense that I am Real.
What does that mean?
Do you mean "real in the sense that 1-I is real"? or
do you mean "real in the sense that 3-I is real"?
The 1-I reality (my consciousness) is undoubtable, and incommunicable
in any 3-ways.
The 3-I reality (my body, identity card, ...) is doubtable (I could be
dreaming) and communicable in 3-ways, yet always with interrogation
mark.
This makes a big difference.
Bruno
Any physcial theory is distinguished from an
Everythingis theory by maintaining the contingent existence of only
some
possible mathematical structures. That is a general statement that
is not affected by juggling one theory for another. I have further
defined PM in *terms* of such contingency.
>>
>> Each branch of math has its own notion of existence, and with comp,
>> we
>> have a lot choice, for the ontic part, but usually I take
>> arithmetical existence, if only because this is taught in school, and
>> its enough to justified the existence of the universal numbers, and
>> either they dreams (if "yes doctor") or at least their discourse on
>> their dreams (if you say no the doctor and decide to qualify those
>> machines are "inexistent zombies").
>
> Platonism is not taught in schools. You are conflatin
> existence with truth
Platonism is not taught in schools, I agree. But I have never said that.
I am not conflating existence with truth, I am conflating mathematical
existence with truth of existential arithmetical statements.
> mathematical stucture+matter gives you more to
> tackle the consciousness problem with than mathematical structure
> alone
The mind-body problem comes from the fact that we have not yet find
how to attach consciousness to matter. At least with comp, after UDA,
we know why.
> No. it is equivalent to the conjunction of that stament with
> "and the mathematicians Ex is a claim of ontological existence".
You are the one making that addition. So, again, show where in the
reasoning I would use that addition.
>
>> If you really believe that the number 7 has no existence at all, then
>> the UDA reasoning does not go through,
>
> at last!!!!!!!!!!!!!!!!!!!!!
Read or reread the SANE paper, I explicitly assume Arithmetical
Realism. This is hardly new. I really don't follow you.
UDA is an argument showing that comp (yes doctor + CT) => non
physicalism. (CT = Church thesis)
A weaker version of CT is provably equivalent with Ex(x = universal
number). It makes no sense without AR.
Bruno
I would say that giving-rise-to-conscious-perception = physical-existence. Roughly
speaking perceiving is being kicked back when you kick. It allows ostensive definition.
But I'm not sure this is the same as giving-rise-to-conscious-experience. Would it be
possible to have a stream of conscious experience with no perception, i.e. like a dream
about mathematics, but with no perceptions of the tokens we use to represent mathematical
concepts, i.e. a dream about the number two without any representation like "2" or "two"
or "{{}{{}}}"? I doubt it.
Brent
>>
>>
>>>> Some posts ago, you seem to accept arithmetical realism, so I am no
>>>> more sure of your position.
>>> I may have assented to the *truth* of some propositions...
>>> but truth is not existence. At least, the claim that
>>> truth=existence is extraordinary and metaphysical...
>>
>> Mathematical existence = truth of existential mathematical statement.
>>
>> The number seven exists independently of me, is equivalent with the
>> statement that the truth of the mathematical statement Ex(x =
>> s(s(s(s(s(s(s(0)))))))) is true independently of me.
>
> The above of course is a set of tokens symbolizing a set of
> cardinality eight.
Er, actually it symbolizes the number seven (it is a detail, but set
theory will never been formalized in my posts, except much later, for
giving another example of Lobian machine).
> The fact
> that it symbolizes something depends on humans interpreting it.
I would have used the usual humans notation "7".
So I was referring to any "interpretative machine" (computer,
universal number) which agrees on the usual first order axiom of
arithmetic, talking in first order language, together with the
supplementary symbols "s", 0, "x" and "+".
We fix the notation, and, in the case of such machine we fix the
semantic by the usual mathematical structure (N,+,x).
> This seems similar to the
> MGA and the idea that a rock computes every function.
I have already criticized this. Once sup-comp is accepted, the
computation exists in arithmetic and are given by well defined
relations among numbers, entirely defined with the language above, and
they have the usual interpretation in (N,+,x). But those relation will
define complex UD-like relationships describing relative observers in
relative environment/universal machine, like "Brent deciding to send a
mail", for example. Those internal interpretation will exist in a
sense which is not dependent of the choice of any interpretation or
even representation, once you assume the usual truth of the
arithmetical relations.
In comp, like in QM, a rock compute only in the sense that "it is made
of infinities of computations". Without comp, I have no clue of what a
rock is, except that QM seems to agree on the fact that it is made of
infinities of computations.
> They depend on being interpreted in
> some context or environment.
Right. The interpreter are given by the universal numbers, or
universal machine. This is a bit tricky to define shortly, and I
postpone it in the seven step series (but I am a bit buzy), so that
more can uderstand.
In the third person way: a computation is always defined relatively to
another universal number, or directly in term of number addition and
multiplication.
From the first person perspective we can only bet on the most
probable universal number, among an infinity of them.
> I'm happy to abstract them from their environment to get a
> manageable model.
But once the "model" is a number that the doctor will send on Mars,
where a reconstitution device has been build, you have to abstract
yourself from the environment, for awhile. Saying "yes doctor" *is* a
big theological step. Nobody should ever force you. The ethic of comp
is the right to say "no" to the doctor.
> I'm not so comfortable to say that that abstraction doesn't need the
> environment and is what is really real.
Yeah ... I am sorry. But let us not be driven by wishful thinking, and
if comp survives UDA, there is a sense in which matter becomes much
more solid and stable. Observable environment emerge statistically
from infinities of non temporal and non spatial computations/number
relations.
Including (universal) environment does not help, because the UD
generates them all (with their many variants), except some infinite
diagonal "garden of Eden" which are evacuated through the comp hyp.
Bruno
QM mechanics solves mathematically the white rabbit problem. I doagree with this, but to say it does this by invoking primitive matterdoes not follow. On the contrary QM amplitude makes primitive matterstill more hard to figure out. Primitive matter is, up to now, ametaphysical notion. Darwinian evolution can justify why we takeseriously the consistency of our neighborhood, and why we extrapolatethat consistency, but physicists does not, in their theories, everpostulate *primitive* matter.
Not explicitly, but physicists generally accept that some things happen and others don't;
not only in QM but in symmetry breaking.
>
>
>
> On 18 Aug, 11:25, Bruno Marchal <marc...@ulb.ac.be> wrote:
>> On 18 Aug 2009, at 10:55, Flammarion wrote:
>>
>>
>>
>>> Any physcial theory is distinguished from an
>>> Everythingis theory by maintaining the contingent existence of only
>>> some
>>> possible mathematical structures. That is a general statement that
>>> is not affected by juggling one theory for another. I have further
>>> defined PM in *terms* of such contingency.
>>
>> That is actually very nice, because it follows the Plato-Aristotle-
>> Plotinus definition of matter which I follow in AUDA.
>> And this is enough for showing we don't have to reify matter (nor
>> numbers).
>
> If you are not reifying anything. then there is nothing, hen there is
> no UD.
I think you have a magical conception of reality.
I don't need to reify number to believe in them.
I just need to play with them.
>
>> I don't see, indeed, how you can both define matter from contingent
>> structures and still pretend that matter is primitive.
>
> I am saying that material existence *is* contingent
> existence. It is not a structure of anything.
Plotinus says that too! Me too.
With church thesis this is can be made more precise in term of not-
computable or not-provable, or some relativizations.
>
>> Somehow you talk like you would be able to be *conscious* of the
>> existence of primitive matter.
>
> Well, at least I don't talk about immaterial machines dreaming each
> other.
In arithmetic, that happens all the time. More below.
>
>> All the Peter Jones which are generated by the UD, in the Tarski or
>> Fregean sense, (I don't care), will pretend that primitive matter
>> does
>> not exist, and if your argument goes through, for rational reason and
>> logic (and not by mystical apprehension), those immaterial Peter
>> Jones
>> will prove *correctly* that they are material, and this is a
>> contradiction.
>
> It's not a contradiction of materialism. If there are no immaterial
> PJ's, nothing is believed by them at all.
Once you say yes to the doctor, there are immaterial Peter Jones. All
your doppelganger emulating you, and being emulated at your level of
substitution and below relatively occuring in the proof of the Sigma_1
sentences of Robinson Arithmetic. (The arithmetical version of the UD).
>
>> So to save a role to matter, you will have to make your
>> "consciousness
>> of primitive matter" relying on some non computational feature.
>
> No. I just have to deny immaterial existence.
You have to deny the theorem of elementary arithmetic, which are used
by physicists (mostly through complex or trigonometric functions,
which reintroduce the natural numbers in the continuum).
> You keep confusing the
> idea
> that theoretical entities could hypothetcially have certain beliefs
> with the
> actual existence of those entities and beliefs.
You underestimate the dumbness of the DU, or sigma_1 arithmetic. It
contains the emulation of all the quantum states of the milky way,
with correct approximation of its neighborhood. It is hard to
recognize Peter Jones or Bruno Marchal from the huge relation and huge
numbers involved, in some emulations, but it is easy to prove there
exists, from the information the doctor got when scanning your brain.
In computations enough similar than our own most probable current one,
it is a "theorem" that those entities have such or such beliefs, and
behave in such and such ways, developing such and such discourses.
>
>> Note that if you accept "standard comp", you have to accept that
>> "Peter Jones is generated by the UD" makes sense, even if you cease
>> to
>> give referents to such "Peter Jones".
>
> False. Standard comp says nothing about Platonism or AR.
> I can give a Johnsonian refutation of the UD. I can't see it,
> no-one can see it, so it ain't there.
Standard comp says nothing about Plato's Platonism, but once you take
the digitalness seriously enough, and CT, it is just standard computer
science.
See "conscience & mécanisme" appendices for snapshot of a running
mathematical DU. It exists mathematically. But it can be implemented
"materially" , i.e. relatively to our most probable computations too.
>
>> Fregean sense is enough to see
>> that those Peter Jones would correctly (if you are correct) prove
>> that
>> they are material, when we know (reasoning outside the UD) than they
>> are not.
>
> So? That doesn't man I am wrong, because it doesn't mean I am in
> the UD. The fact that we can see that a BIV has false beliefs
> doesn't make us wrong
> about anything.
This is not the point. The point is that if you develop a correct
argumentation that you are material, and that what we "see" around us
is material, then the arithmetical P. Jone(s) will also find a correct
argumentation that *they* are material, and that what they see is
material. The problem is that if you are correct in "our physical
reality" their reasoning will be correct too, and false of course. But
then your reasoning has to be false too.
The only way to prevent this consists in saying that you are not
Turing-emulable, or that you just don't know if you are in the UD or
not. At this stage.
Then with step-8, you "know", relatively to the comp act of faith,
that you are already there. If you say yes to the doctor, you can bet,
from computer science that you are already in the (N,x,+) matrix.
>
>> Your argument should be non UD accessible, and thus non Turing
>> emulable.
>
> No, it just has to be right. The fact that a simulated me
> *would8 be wrong doesn't mean the real me *is* wrong.
But if you are correct in your reasoning, the simulated you has to be
correct to. It is the same reasoning.
Or you have a special sense making you know that you are the "real"
one, but either that special sense is Turing emulable and your
doppelganger inherit them, or it is not Turing emulable, and you
better should say "no" to the doctor, because you would loose that
sense.
>
>> If you feel being primitively material, just say "no" to the doctor.
>
> Why can't I just get a guarantee that he will re-incarnate me
> materially?
He will try.
> Even if matter doesn't exist, I won't lose out.
Note that I have never said that matter does not exist. I have no
doubt it exists. I am just saying that matter cannot be primitive,
assuming comp. Matter is more or less the border of the ignorance of
universal machines (to be short). There is a fundamental physics which
capture the invariant for all possible universal machine observation,
and the rest is geography-history. Assuming comp the consistent-
contingent obeys laws.
Bruno
I think you are right that the MGA is at the crux. But I don't know whether to regard it
as proving that computation need not be physically instantiated or as a reductio against
the "yes doctor" hypothesis. Saying yes to the doctor seems very straightforward when you
just think about the doctor replacing physical elements of your brain with functionally
similar elements made of silicon or straw or whatever. But then I reflect that I, with my
new head full of straw, must still interact with the world. So I have not been reduced to
computation unless the part of the world I interact with is also replaced by computational
elements (I think this problem is swept under the rug with the phrase "at the appropriate
level of substitution"). So suppose the doctor also emulates all the world that I will
ever interact with. Now it is not so clear that such an emulation is computable, but
suppose it is. Now my consciousness is entirely emulation - but it is also entirely in
another, emulated, world. In that world it is physically instantiated. So it has not
been shown that the emulation can be uninstantiated mathematics.
Brent
Download OpenOffice. It's free. It'll read .doc and .docx files and it will save in .doc
and .pdf (but it won't import .pdf).
Brent
"The first time Microsoft makes a product that doesn't suck will be when they make vacuum
cleaners."
Bruno Marchal wrote:This is not the point. The point is that if you develop a correctargumentation that you are material, and that what we "see" around usis material, then the arithmetical P. Jone(s) will also find a correctargumentation that *they* are material, and that what they see ismaterial. The problem is that if you are correct in "our physicalreality" their reasoning will be correct too, and false of course. Butthen your reasoning has to be false too.The only way to prevent this consists in saying that you are notTuring-emulable,
Why can't I just say I'm not Turing emulated? It seems that your argument uses MGA to
conclude that no physical instantaion is needed so Turing-emulable=Turing-emulated. It
seems that all you can conclude is one cannot *know* that they have a correct argument
showing they are material. But this is already well known from "brain in a vat" thought
experiments.
But if you are correct in your reasoning, the simulated you has to becorrect to. It is the same reasoning.Or you have a special sense making you know that you are the "real"one, but either that special sense is Turing emulable and yourdoppelganger inherit them, or it is not Turing emulable, and youbetter should say "no" to the doctor, because you would loose thatsense.
Or it is a relation to the rest of the world and you can say yes so long as the doctor
maintains your relations to the rest of the world - i.e. physically instantiates your
emulation.