On 17 May 2017, at 14:08, David Nyman wrote:
On 17 May 2017 11:27 a.m., "Bruno Marchal" <marc...@ulb.ac.be> wrote:
On 17 May 2017, at 12:06, David Nyman wrote:
On 17 May 2017 8:06 a.m., "Bruno Marchal" <marc...@ulb.ac.be> wrote:
On 16 May 2017, at 17:34, David Nyman wrote:
On 16 May 2017 at 08:07, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 15 May 2017, at 22:44, David Nyman wrote:
On 15 May 2017 at 15:56, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 15 May 2017, at 12:38, David Nyman wrote:
I've been thinking a bit about physical supervenience in the
computationalist context and have come to the conclusion that I
don't really understand it. So let's consider CT + YD. YD means
accepting the replacement of all or part of my brain with a
digital prosthesis. Now, whatever theory the doctor may
vouchsafe me with respect to the function of this device, the
replacement will FAPP be, in the first (and last) instance, a
physical one. IOW after the procedure some are all of my
neurological function will be have been replaced by digital
componentry (presumably some species of logic gates) that
putatively (sufficiently) faithfully mirrors the function of the
biology that has been replaced. From any extrinsic perspective,
all that will have happened (assuming the success of the
procedure) is that the net physical behaviour of my generic
brain will have been preserved to the required extent. Notice
that there is no necessary reference to computation per se so
far, however much we may wish to appeal to it in explicating
what is "actually" supposed to have occurred.
OK. For example, you might have accepted a transplant of each
individual neurons, by pig neuron. But, even here, some implicit
computationalism is used, in case you agree that the new neurons
keep the same finitely describable functions. If, not, the very
idea of that transplant tends to be irrational. You might accept
pig's neurons because you believe that pig neurons are as much
divine than human one, to give an example.
Agreed
In a minimal sense supervenience will have been satisfied, in
that my behaviour will continue to covary systematically with
the net physical action of my generic brain, but there is no
necessary reference to computation in this.
Careful, because the surgeon might need to explain you why pig's
neuron can be judged to have the right functional properties, and
if such explanation is possible in finite time, some mechanist
assumption is used.
OK
And indeed if the proposition of CTM were simply based on YD
alone, there would seem to be no further criteria to satisfy.
However, with the additional assumption of CT, it would still
seem necessary to make a further step towards explicating the
relation between the above mentioned net physical action and the
relevant spectrum of computation deemed to underlie both it and
the (perceptually) substantial terms in which it is subjectively
made manifest. The use of the word "net" in the above is
noteworthy as a little reflection will remind us that, no matter
how many "layers" of software are in principle being implemented
on a given hardware, the only relevant observable consequence is
their net physical effect, which may be rendered entirely
minimal, or even be approximated adventitiously.
It has been asserted that "physics" emerges epistemologically as
a consequence of the net perceptual integration (aka the
psychology) of an infinity of digital machines. We can say this
because of the formal equivalence of the class of such machines.
This in effect equates, in a certain relevant sense, to their
having a single such psychology, or monopsychism, albeit one
that must be highly compartmentalised by programming and the
contents of memory. In this sense, it may be possible to
analogise this monopsychic perceptual position as akin to that
of a multitasking OS running on a single "processor". There are
at least two aspects to the physics of which we speak. The most
obvious aspect is the observed behaviour of any physical system
under study, which must always be rendered in terms of the net
change in some set of concrete perceptual markers (e.g. the
classic needle and dial). The second aspect is however
unobservable in principle and consists of an abstract set of
transition rules between physical states (assumed to be finitely
computable, according to CTM) between observations. For present
purposes, we may perhaps consider these rules to be represented
by the wave equation which describes the unitary evolution of
physical states.
... or some digital approximation. (to avoid some non-digital
mechanism hypothesis, à-la Penrose).
OK
A question now occurs to me. On the foregoing presuppositions,
are we to suppose that the computations representing the
abstract unitary transition "rules" of the wavefunction (i.e.
the second, abstract, part above) are *the selfsame ones* that,
(under an alternative but putatively compatible logical
interpretation) are supposed also to explicate the concrete
perceptions in terms of which the observations (i.e. the first,
perceptual, part) are made?
It happens that the wave function *is* computable, so this will
follow if the Hamiltonian itself is computable. Now, it is not
too much difficult to build (mathematically) a non computable
hamiltonian. There is no evidence this exists in "nature", but
logically, computationalism can be false (and in that case, a
digital substitution will no more work a priori, or just by pure
chance, of "just" by the will of some supernatural or non-Turing
emulable entity).
If this were the case, we could indeed say that perception
supervened both on computation (under one interpretation) and
observed physical action (under a different but compatible one).
The problem will be: what do you mean by "physical action"? Human
perception can depend crucially on physical actions, but physical
actions might (and have to) emerge from arithmetic.
What I mean by physical action in this context is
(approximately) the conjunction of observed relations between
concrete perceptual objects and an abstract set of "fundamental"
transition rules in terms of which these relations can be both
formulated and predicted.
I am not sure I understand in this context what you mean by
perceptual object.
Is it brought by a program, or by an infinity of programs?
Is it something computable, or is it recoverable by the first
person indeterminacy?
I mean an object *of* perception (like the apple I see). So it
is related to the p of Bp & p. Recoverable by the FPI I guess.
Hence what I term above "the relation between concrete perceptual
objects" is how correspondence with the facts is primarily
established, whether that be a reading on a dial or the
abstraction of the intuitive arithmetical notion of 2 from two
objects, or from the symbol "2" for that matter. In my view, that
is. What happens next is a separate matter.
OK.
I think that you agree that we are conscious during dreams. In
that case perception comes from random inputs to the cortex made
by the cerebral stem (in Hobson theory), and the feeling that we
perceive things is build up by the brain. few people would say
that this is a perception.
I would though.
OK? Fair enough, and that answers Brent persistent use of the
environment.
However, in this case there is no necessary relation with a
consistent covariant externality.
I might have lost the line. The question is: is there such a
consistent covariant externality?
I was a little too quick above. What I meant was that in
dreaming we are likely to be deluded about any "external
reality" we are experiencing because it will tend to be
largely an artefact of the perceptual apparatus. That doesn't of
course mean that the functioning of that apparatus, or of the
organism as a whole, is by that token disconnected from the
(more correct) externality associated with the "waking" (or more
correct dreaming) state.
OK. I would say that a dream is "more correct" when its relative
measure is closer to 1. It is more "normal" in the Gaussian sense.
The delusion comes to a stop when we realize that there is no
"external reality" except for the "arithmetical reality". That
would be like the "enlighten state", and/or perhaps death.
The point being made is that we have to justify it from
arithmetic. The "p" in Bp & p is an arithmetical proposition.
Yes of course, assuming comp. To be a little shorter in my
remarks, I don't always say this explicitly, but on the basis that
comp is being assumed in the argument you can rely on that being
my meaning.
Rather, the perception is an artefact of the perceptual apparatus
in semi-isolation from its normal input channels.
This is correct if "normal" means high probability coming from the
infinitely many input channels. Those comes from the infinitely
many universal numbers with oracles competing below our
substitution level.
Agreed. Of course that's what normal or typical has to mean in
this context.
Is this compatibility in effect what is meant by Bp (i.e. the
communicable "belief in", or procedural commitment to, a finite
set of rules)
Technically, we need an infinite set of rules or axioms. But that
is a detail. We can generate UD* wilth a finite set of rules, but
each observer created in UD*, once Löbian, use infinite set of
rules in general (but that is a recursive set, so we staty in the
mechanist frame).
If you want, []p, or Bp, is all what your brain does when you see
an apple say.
Yes.
You could translate Bp by "I dream of an apple". Then an
observation is when the dream fits some reality. Bp & p becomes
"I dream of an apple" and there is an apple. The relation between
both []p and p will be statistical, hoping the measure that we
get from S4Grz1 (in this case) will work.
Yes again. My use of the expression "procedural commitment
to a finite set of rules" is meant to imply that belief, in this
context, is to be taken to refer to much more than, say, a merely
verbal expression. Rather it implies the commitment of an entire
organism to this set of procedures.
and also p (i.e. the "true", or directly incommunicable,
correspondence between perceptual facts) implied by that belief?
Well, implied by the belief, when we restrict ourself to correct
machine.
Of course.We are not, in the first instance, dealing with
delusions.
The theory explains that this is a not constructive act. We just
never know if we are awake. We can know that we are dreaming, but
we can't know that we are awake.
Correct. But we can at least commit ourselves to the belief
(i.e. trust, or as you would have it, bet) that we are dreaming
extremely consistently and pervasively. And if that be so the
distinction between that dreaming and reality becomes otiose.
Keep in mind that "p" is a proposition of arithmetic.
Ultimately, yes.
In some sense. In other sense: we start from arithmetic, and the
(sigma_1) p behave or should behave like physical propositions,
when we take the views (Bp & p, Bp & Dt, Bp & Dt & p) into
account. physics is ultimate in that sense: it needs the
statistics on the arithmetical computations.
I think that once one accepts that physics appears as a
consequence of the machine-psychological reversal, then physics
and computation reach a kind of virtuous explanatory circularity,
as Brent often points out. One hand washes the other, as the
Russians say.
OK. I think this is what can be derived mathematically from the
"bisimulation between G and Z (or between G1* and Z1*, ...). But we
don't have this with the S4Grz1, or with X1*. One russian hand is
bigger and deeper than the other. My image is that the physical is
somehow the clothes, or the border of the universal mind (the mind
of the "virgin" Löbian machine, or perhaps already the universal
machine in general. You are trying to use intuition at the place
where I prefer to use the counter-intuitive logic of self-
reference. It is OK, as long as we don't get a contradiction with
the math.
Yes, I may have reached a little too far in the desire to find
common ground with Brent. As my most recent comments elsewhere
imply, although physics and computation are inextricably entangled
in an explanatory embrace as a consequence of the reversal, exactly
what each can be taken as explaining is not precisely coequal.
Physical explanation is situated within the domain of appearance
(alternatively, what is observable or open to interpretation).
Consequently it can be taken as explaining net transformations in
those appearances. Computational explanation seeks to give an
account of how, why and from whose point of view those appearances
come to exist, to the extent that such an account can be rendered.
To that extent, the abstract or mathematical component of physics
is itself computational (insofar as its predicted transformations
are finitely computable), but its observable component cannot be so
considered without becoming poisoned by intractable ambiguities.
Exactly. I might try to add some possible mathematical precision,
but I need to think a bit on this. Later. Up to now, the B of Bp & p
is interpreted by its computational rendering, but "B" is really
provability, and not computation. Up to here, that absence of
distinction works well (indeed for a very deep and subtle reason
related to Mechanism), but for the precision I want to add, I will
need to make the distinction.
Are you, and others, OK with those facts:
RA cannot prove the consistency of RA. PA cannot prove the
consistency of PA, etc.
But:
PA can prove the consistency of RA.
Now the key fact which I intend to use is that RA can prove that PA
can prove the consistency of RA. In fact RA can prove also that F
can prove the consistency of PA, and of RA.
Despite this RA cannot be convinced that those facts prove its own
consistency (by incompleteness).
Interesting. I think I get your point to the extent that computable
is a claim about the formal definability of procedure itself (which
IIRC was the goal of Turing's original paper OCN). Provable is by
contrast a truth claim: IOW something or other is being shown (i.e.
with respect to some point of view) to be the case, i.e. to
correspond to some set of (perspectival) facts. So on this account
RA itself is not in a position by itself to command such a view of
the facts of its own consistency, but it can nevertheless grasp
logically that PA is in a position to do so.
As a (very) rough and partial analogy, if I am on deck, and you are
observing me from aloft, I can grasp that you are in a position to
command an entire domain of such personally "unprovable" facts about
me, despite my not being in a position to access them. Such
personally unprovable facts might also bear directly on questions of
my own consistency, for example if I were forced to rely on them in
some crucial sense. Say you offered from your superior perspective
to "be my eyes" in guiding my survival through some risky
predicament below. I might choose to trust that guidance under
hazard despite being in no position to prove independently the
correctness of such a critical viewpoint. So in such a situation I
might be unable to be unambiguously convinced of my own consistency
but nonetheless choose to trust in it implicitly in order to promote
my survival.
Of course this particular intuition pump is more than likely to
prove somewhat leaky :(
It makes concrete sense, but eventually, it leads to the most used
theory in the applied human science: the boss is right. But that
theory has its advantage in all crucial and time scheduled situation,
like with the military: you can't discuss an order, the enemy would
swallow you before you get to the conclusion. We need, in some
resource limited circumstances, to trust the eye of the other. Human
evolution and history benefits a lot from that.
This can be compared with I can emulate Einstein's brain, without
being able to understand anything said by Einstein during that
emulation.
Although crucially I can grasp that, from some perspective, there is
an Einstein who is indeed saying something.
Absolutely. The points is that it is not you. Even if you could
mentally simulate Einstein's brain in real time, it would still be
Einstein who does the thinking, and Einstein would be conscious. Your
own consciousness would not change, except for the mental, but simple,
task to imitate a brain of another person. When a A computer run a
program, he does not become that program. That was also Searles' main
mistake in his chinese-room argument. If I can emulate the brain of a
chinese person, I might fake to be chinese, but I don't become a guy
who know chinese. I might do a conference in chinese, without
understanding anything "I" would say. But the chinese guy I am
emulating would be conscious and would do that conference, through me,
so to speak.
Similarly, When RA proves that ZF proves the consistency of RA, RA
might not, and actually will not, understand it. But ZF, will, and
this by being enabled by RA.
It is good to keep in mind that computation (and simulation) are
absolute notions, they do not depend on which formal system enable(s)
them. But provability is a relative notion. The Bp is already a point
of view. Computations are just a "real" absolute part of the
arithmetical reality. Provable(p) is real only for this or that
machine/number.
Of course, were a maximally lazy creator to content itself with
devising the UD widget, it could thereby invoke both all possible
emulations and their associated understandings without the
possibility of anticipating any consequence whatsoever. We, its
creatures, by contrast can grasp the consequential existence of
points of view within which such understandings can be situated.
Exactly. And that situation is a relative notion, and the first person
is somehow associated to the many arithmetical relations enacting each
of them, and the logic relating them.
I probably read you too much quickly. My only worry was that you took
the reference to an external physical reality too much seriously, a
bit like Brent seems to do sometimes. Note that Brent is mostly
correct, but what he inferred from that is not always correct. We can
refer to physics and physical implementations, and environments, but
we can't invoke them to explain why consciousness would be produced by
a brain, still less that brain exist "really".
I understand finally why you did put "quotes" on "external reality".
Your argument seems entirely comp-valid now :)
Bruno
David
This is important to understand that "provable" is very different
from computable/simulable.
OK? (More on this later)
Bruno
David
Even sigma_1 arithmetic. It asserts the existence of state, or of
an halting computation, or a number. The physical appears only
for Bp & p (with p sigma_1), or better, with Bp & ~B~p & p.
Yes.
If this were indeed the case, then the indispensable
characteristic of the necessary physics (i.e. the second,
abstract, part) that would permit it to be singled out
perceptually from the dross of the computational Babel in this
way would it be sufficiently "robust" in the relevant sense.
That robustness would consist firstly in the capacity to
stabilise the emulation of an (ultimately monopsychic) class of
perceptual machines. And secondly in that the necessary machine
psychology would supervene on common computational transition
rules resulting in a (sufficiently) consistent covariance with a
concrete externality as perceived by those selfsame machines.
That would single out a universal machine, but below our
substitution level, we need to single it out of the infinitely
many universal machine which compete to provide your next state.
OK?
Yes. IIUC, this would be determined by the predominance of
(relatively) highly stable,
Yes, but not just the predominance. the logical structure imposed
by the views might play a role in weighing the computations as
seen by a subject.
Yes of course. In fact IMO the relevant predominance is that of
the narrative consistency, pervasiveness and stability imposed *by
that very logical structure*. So what would have to predominate,
for this view to be plausible, is the net monopsychic effect of a
relatively pervasive remembering (literally "putting together") of
those compelling and consistent personal narratives. This may be
conceived as the "positive" pole of a sort of subjective
ambiguity, whose "negative" antipole is an at least equally
pervasive forgetfulness and cancelling out of consequence, to the
effective relative exclusion of the myriad competing subjectively
pathological fragments. My rough analogy in this case, you may
recall, was akin to having your attention totally riveted by a
very compelling and coherent speaker standing very close to you.
The thought then is that the competing babble of random fragments
emanating from a noisy surrounding environment cannot compete,
with any lasting consequence, relative to that repertoire of
powerful and consistently connected narratives.
pervasive and consistent relations between arbitrarily many
machine points of view. It is these characteristics that in
effect would extract the necessary first-person plural measure,
if this view of the matter is ultimately to succeed. As discussed
before, it would be necessary for pathological segments of
narrative (aka white rabbits) to mutually cancel or be swamped
(from the first-person perspective) in the monopsychic measure
struggle between forgetting and remembering. I don't know if the
various intuitive analogies I've sketched recently are any help
in thinking about this. I rather liked the one about the
compelling orator and the background of babble.
The conjunction of those rules and that observed externality
would then be what we call physics and the computational physics
so particularised would in effect be distinguished by its
intrinsic capacity for self-interpretation and self-observation.
Does this make sense and if it does, what in particular about
the computationalist assumptions or inferences make such a very
specific conjunction plausible?
Well, usually we start from computationalism (basically because
we have no other theory except for fairy tales). The conjunction
in Bp & p is added (by Theaetetus) because Socrates, like Gödel
for provability, destroys the link between Bp and p. Most people
would say that when we prove things (=when we justify things
rationally), it ought to be true. But Socrates said that some
people can be wrong in their reasoning, or can have false
premise, or that we could dream, etc.), and Gödel shows that no
correct machine can prove its own Bp -> p, nor its own Bp <-> (Bp
& p). We need faith all the time, in "real life", but we can
reason on simpler (but still Löbian) than us machine, and lift,
privately, the theology of that machine on us. But that is at our
risk and peril, all the times, and it becomes explicit with the
"yes doctor".
Yes, but I think there are important nuances with respect to
"true" that have frequently been missed in these conversations.
The first nuance is that there is a primary truth entailed by Bp
which is simply the perceptual "facts" it implies.
Bp -> p is true in the eye of God, but the machine cannot know that.
The machine cannot know that but the person implied by the
machine knows its primary truth beyond doubt.
OK. That is normally captured by the fact that for each p that the
machine can actually prove, Bp -> p will be provable
"trivially" (in classical and intuitionist logic, of you can prove
p, you can prove (<anything> -> p). Note that for a machine which
is unsound Bp & p can be actually false, in fact p can be false. It
is madness: case where we know something false. That does not exist
in my setting, because I limit myself to correct machine.
What can however be doubted is what exactly it refers to and what
action to take as a consequence.
Somehow p comes "first" (in a logical sense),
Yes, that's implied in a sense by what I said above.
then comes Bp, which is a bit like a window on reality.
It's also the actionable component of Bp & p.
Yes.
It is "p" as seen/believed by the subject, who can publicly share
"Bp",
Believed rather than seen, perhaps. IOW the action taken, as
remarked above.
Yes. In fact "seen" is ambiguous, but make sense in case the
physical measure exists. To see is just to believe/dream relatively
to a normal sheaf of computations.
but only hope for p, or hope in his own correctness.
Yes, it can hope that the direct perception of p (or IOW the
semantics implied by the syntax of Bp) won't lead it into mistaken
belief or action.
This, if you like, is simply the fact of the dream itself,
without any necessary entailment to a consistently covarying
externality. This, as mentioned above, can be considered an
ineliminable artefact of the perceptual apparatus. It is only
after this primary fact (i.e. the second nuance) that
considerations of consistent reference to such an externality can
be considered, and it is at this point that we can fall into
error and be deluded. As you say above, we can never be
absolutely sure what our dreams refer to, since the perceptual
apparatus must be substantially the same in all cases. Hence we
can only believe and act in good faith.
Don't hesitate to tell me if I missed your question. It might
help to keep in mind that there is no physical reality: only
dreams.
I think we agree.
I think too. We could differ only the intuition pump though,
perhaps. No problem, we need a lot of such pump, perhaps a
different one for each individuals.
All hands to the pumps ;)
:)
Bruno
David
Bruno
Knowing is when the dream are arithmetically true, and physical
observation is when the dream is arithmetically probable.
Immediate feeling is when the dream is probable and true.
Yup.
David
Bruno
David
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