On 11 Sep 2017, at 00:55, David Nyman wrote:
On 10 September 2017 at 18:24, Bruno Marchal <marc...@ulb.ac.be>
wrote:
On 09 Sep 2017, at 18:58, David Nyman wrote:
On 7 September 2017 at 10:03, Bruno Marchal <marc...@ulb.ac.be>
wrote:
On 06 Sep 2017, at 19:45, Brent Meeker wrote:
On 9/6/2017 7:35 AM, Bruno Marchal wrote:
Some physicists can be immaterialist, but still believe that the
fundamental reality is physical, a bit like Tegmark who remains
(despite he is willing to think differently) open to the idea
that the physical reality is a special mathematical structure
among all mathematical structures, for example. That is
problematical for pure mathematical reason: the notion of all
mathematical structures do not make much mathematical sense, but
it is of course problematic also with Mechanism, where the
physical reality becomes the border of the whole "computable
mathematics" (which is very tiny, as it is the tiny sigma_1 part
of arithmetic).
I think Tegmark has changed his opinion and now only champions all
computable universes.
Yes. The problem now, is that there are no computable physical
universes. Here he miss the first person indeterminacy in
arithmetic. He miss that any universal machine looking below its
substitution level is confronted to its infinity of implementations
in arithmetic. In fact, he remains somehow physicalist, and does
not seem aware of the computationalist mind-body problem.
Yes, it's quite surprising how elusive this absence of universes
seems to be in the context of mechanism. Old presuppositions
seemingly die very hard. Another elusive point is what Chalmers is
getting at with what he calls the Paradox of Phenomenal Judgement
. This is the problem of how what one might call an 'extensional
infrastructure' and any corresponding phenomenal reality are
seemingly able to 'refer' to each other. It's a big fly in the
ointment of physicalist theories of mind like panpsychism, although
it seems to be exceedingly difficult to point this out to
panpsychists in my experience. For example, if we consider a movie
being rendered on an LCD screen, nobody imagines that either the
pixels comprising the screen, or the action of the movie tracked or
carried by those pixels, either do, or in any way need to, refer to
each other. They are, in a sense, mutual epiphenomena. However, my
own utterances or judgements - standing in a general way for the
'extensional infrastructure' of my perceptions - and those
perceptions themselves, do indeed seem to need to cross-refer. It's
this cross-reference that is alluded to in Bp and p.
Hmm... Perhaps OK. There might be a problem with the "extensional
infrastructure" where I see an intensional one, and only the "body"
is the (relatively and indexically) extensional.
Yes, in this case I meant beliefs or judgments as they would
appear in bodily expression, e.g. utterances, and hence extensional.
I've been thinking about how this might play out very generally in
terms of the coincidence or intersection of action and perception
as generalisations of B and p. As you say, we assume at the outset
a knower in the guise of the universal or generic machine (i.e. a
number playing the role of 'processor' with respect to another
number).
You force me to be very precise. I assume only p, the true sigma_1
propositions. You can equate them with the computational states
attained by the, or a, universal dovetailing. I define the "believer-
knower-observer-feeler" by a universal number, mastering classical
first order logic, and (unlike what we need to assume for the
ontology) the induction axioms (on the sigma_1 sentences). The
believer can prove its own incompleteness and its "modesty", in the
conditional way.
So I assume elementary arithmetic; I prove the existence of the
universal number(s), then I define a notion of rational belief
"scientific belief", (Plotinus discursive reasoner) by Gödel's
(sigma_1 arithmetical) beweisbar Bp. That makes sense, due to
incompleteness which prevent provability to be a notion of knowledge.
Then incompleteness enforce the correct machine to distinguish the
nuances between p, Bp, Bp & p, Bp & Dt, Bp & Dt & p. Which
corresponds with Truth ("God", the One, Reality, ...), Belief
(theories, ideas), Knowledge (where ideas fits with Reality), and
the "material" version which encapsulate the idea of possibility and
non transitive alternative, which incompleteness offers on a plate:
consistency, Dt.
So the universal machine endowed with, say, a classical logical
instinct, is born with those quite different views on the universal
reality. Those views can be in conflict, or live at peace.
G* prove p <-> Bp <-> Bp & p <-> etc.
But G does not prove any of those equivalences. Sigma_1 truth, seen
as the set of all true arithmetical sigma_1 sentences is the same
set as the set of provable sigma_1 sentences.
The universal machine might know she is God, but she will never tell
you.
In turn you force me to be very imprecise! Or rather to try to
condense the detail of what you say above into a more approximate
form that can possibly be communicated and grasped more readily by
non-specialists. What I'm trying to articulate in very general
terms is that this schema extrapolates in some limit to the self-
selection (via the FPI) of those computations that track or carry
precise state changes that in turn appear in phenomenal terms as
particularised physical realities. It is this ineliminable and
undoubtable logical relation of the machine-knower's detailed and
ramified beliefs with their corresponding truth value (which is what
ultimately stands in place of those phenomenal realities) that is
then the golden key to avoiding the otherwise baffling reference
paradoxes I referred to.
That makes sense.
The computational duals enacted by such machines are then projected
to be elaborated to the point where they are tracking or carrying
the state changes of an extensional infrastructure equivalent to a
brain,
At the substitution level, but keep in mind that even the brain idea
is in our head. The fact that the physical would be a first person
plural structure, the notion of infrastructure leads quickly to
arithmetic.
Yes, I have that clearly in mind.
at whatever level turns out to be necessary for its stable emergence.
OK.
When I say 'equivalent to' I mean that this is what will appear,
from the phenomenal point-of-view of a knower, to be a brain.
It is when the "natural" born soul Bp & p learns to dissociate/
distinguish Bp and p. p kicks back.
Bp *is* the brain, the theory, still implemented, apparently, in
molecular biological language. It is the words which constitute
ourselves.
Yes.
Such state changes must, by assumption in some general but relevant
sense, be equivalent to what you call beliefs, or what Dennett
calls judgements, about perception.
OK. rational judgement, taking into account some reasonable
elementary beliefs like Kxy = x and Sxyz = xz(yz), or whatever which
makes you Church-Turing-Post-Kleene Universal.
But for knowledge, you need back the link with truth, and that is
given by Bp & p (which gives a new modal logical, say Kp = Bp & p,
we can show that Kp -> p, Kp -> KKp, etc. It is a logic of the
knowable.
For perception, you need a reality. by the completeness theorem,
that is equivalent with being consistent, so you need to add the Dt.
So perception (and qualia) are handled by the logic with "Dt" in
their definition. Let use R for that modality:
Rp = Bp & Dt, et W for Wp = Bp & Dt & p. R and W get separated along
the G/G* separation of justifiable rationally and true but not
justifiable (by the machine in question) rationally. That is useful
to distinguish quanta and qualia.
As in when I utter something like "I see a red apple", or for that
matter "I feel strongly about the current state of American
politics".
Yeah. I asked them to be an amoeba, but being a human was a bonus. I
do enjoy my little visit on the terrestrial plane, but yes, humans
are weird. (but I tend to think that it is in the family. All
universal machine are weird).
At this point, in order for us to persevere with the schema, we
grant that the p, heretofore provisionally referred to as true or
real by Bp in these cases, is that selfsame phenomenal reality
referred to by 'and p'. In doing this, we also grant retrospective
validity, or redemption, to the entire Wittgenstein ladder of
logical paraphernalia, emulated in computation, that we had been
ascending for just this purpose.
Maybe. The old Wittgenstein understood that belief and knowledge
might have the same referent but different intension. The young
Wittgenstein, well I don't know.
The question arises as to the 'substitution level' for all this.
All universal machines, and consequently all potential knowers,
Probably actual knower too, but in a highly "altered" dissociative
conscious state, but then more in the side of truth. It is Descartes
fixed point, and it is the consistency that we bet on, I guess
instinctively.
are formally equivalent.
They have a bigger common core than they thought, as the "creation/
dream" is in that core. you can, or not, identify them, like we
decide that the M-guy and the W-guy are the same H-guy.
Personal identity is a matter of personal choice, but the humans are
still at the stage "personal identity is a matter of the boss is
right".
Happiness is far simpler than humans think, but when we live in a
world where people tolerate government using religion and/or
science, you can't really leave the dark era.
Consequently we cannot know which of an infinity of such machines
is immediately associated with any given moment of our phenomenal
reality.
Ah! OK. You were talking of the "infrastructure" of the implemented
many computations. Yes, below the substitution level, we met the
FPI, and that is treated by the restriction to sigma_1, and the
adding of "Dt".
However, the 'yes doctor' assumption is that at some level the
computations that track or carry the formal equivalent of a brain
must be substitutable by a suitable digital prosthesis, at least in
principle. At the very least, we must assume that an atom-for-atom
substitution of a physical brain, as presumably occurs naturally
through time, would preserve phenomenal reality without significant
error.
Yes. No more change than the tiny contingent events. What I say
would be more difficult to prove on *arbitrary* analog machines, but
still hold for large class of such machine.
The question also arises as to the possibility of a tractable
'search function' for anything corresponding to the above states of
affairs within the Babel-like infinities of the computational plenum.
I think the UD does that.
Yes, as I go on to say below.
I tell you know a theorem I mention in "Conscience et Mécanisme".
The speed-up theorem, a version of a theorem by Blum and Marquez. It
applies to a generalisation of creative set (universal machine), the
subcreative set. But so universal, and subuniversal, machine have
not better interpreter, and on all inputs, modulo a finite number of
exceptions, they are infinitely speedable. That too, could play a
role in the winning measure process.
In the terrestrial plane, our ways to explore will be enhanced by
quantum computing, but that will not violate the "Turing barrier",
or endangered the "Gödel's miracle". It is the closure of the set of
partial computable function for the diagnalization which makes me
feel that arithmetic, seen intensionally is more explanatively close
than physics.
No such function can be both tractable and extrinsic. We are
relying here on filtration by internal self-identification; this is
(obviously, I would suggest) not a bug, but a feature.
I think so.
The observed robustness and tightness of constraint on the
'extensional' component thus isolated would also seem to render
both Bp and p in a certain sense as 'canonical' of their type.
These two considerations in tandem are extremely suggestive of a
step-change in explanatory style and stand in stark contrast to the
situation with the alphabetic Library of Babel which lacks both of
them and is consequently intractable and haphazard in the extreme.
Computer science, (and thus arithmetic) provides a theory of mind. A
rather conservative one. For the laws of thought, consult George
Boole. For the laws of mind, consult George Boolos, 1979 and 1993.
The "little baby God", the universal machine is a type of God
mentioned by some Jewish and Muslim Theologians, some centuries ago.
The god that you better should not name because it multiples when
named. It is also a bit like in the TAO, where the first thing you
learn is that "the TAO which has a Name is not the TAO". But then,
you learn that that type of God can be named, after all. And you
learn the result, It multiplies and get many names. In fact it is
how the ONE transforms into the MANY, somehow. Universal numbers are
like that. Once Church called it lambda calculus, you get Turing
machine, LISP, algol, game-of-life, c++, etc. They are equivalent
in computability ability, but have already quite different
personalities. We (the humans) are constrained by geometrical and
dimensional considerations, like if the key words was "don't break
the symmetries" (like when eating the Snark!).
I think the problem extensional/intensional for the infrastructure
(machine, brain genome, number, ...) is solved. It is relative, but
for the first person views the phenomenology is confronted to a
continuum, at least a random oracle, on the set of locally
undistinguishable histories. There is a notion of physical bottom,
albeit non primary, but deducible from the existence of a
substitution level.
Yes, this is also the way I've come to think about it. It's so
weird, though.
Eventually, this saves fundamental physics from disappearing entirely
into geography/history. It introduces a non primary "primary matter
phenomenology". The physical is an unavoidable aspect of (arithmetic)
reality for all incarnation of all (universal) machine/number. With
the empirical method, we can't distinguish contingencies and laws in
the physical domain. We can only pray!
Bruno
David
Bruno
David
Bruno
Brent
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