On 26 May 2017, at 21:51, David Nyman wrote:
On 26 May 2017 at 18:32, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 26 May 2017, at 14:04, David Nyman wrote:
where that elusive internal space (which we seek in vain in
extrinsically-completed models such as physics tout court)
Here we might differ, and you might be more mechanist than me (!).
We could have used a notion of physical truth, instead of
arithmetical truth. What the UDA shows is that this requires to
abandon mechanism. But if we get evidence that consciousness
reduces the wave, or that QM is false, then we might reasonably
consider that a physical reality exists ontologically, and well, in
that case we must find a non computationalist theory of mind, which
of course, in that case, will rely on the physical notion of truth.
It is an open problem if we can use or not the same hypostases with
non-arithmetical modal boxes. G and G* remains correct for a vast
class of non mechanical entities.
Well, I think, with your help, that I've reached an elementary
understanding (or at least a better intuition) of what you mean by
arithmetical truth and its possible application in the resolution
of the mind-body problem.
Arithmetical truth is easy, although its use is more delicate. It is
easy, and it is taught in primary school (here = 6 to 12 years old).
The complexity is only in metamathematics (mathematical logic). It
comes from the fact that we cannot define a predicate of truth, V,
such that a machine could prove
p <-> V("p") (which is the least we can ask for a truth
predicate).
If that existed, by Gödel diagonal lemma, we could find a
proposition k such that the machine will prove k <-> ~V(k), and so
the machine would prove both k <-> V(k), and k <-> ~V(k), and
eventually conclude k <-> ~k, and be inconsistent. That is of course
the Epimenides paradox.
Yes, so on pain of inconsistency, not everything the machine can
say can definitely be provably true (or false).
In a way ascertainable by the machine, or the entity under
consideration. OK.
If you and me believe that PA is arithmetically sound (like all
mathematicians believe), and if PA proves X, then you and me can say
that it is provably true, but PA cannot. PA can say X, but cannot say
true('X'). PA can express "I know X" in the sense of proving
'Beweisbar('X') & X, but not in the sense "beweisbar('X') & true('X').
(The predicate ~V would also exist, and the diagonal lemma says that
for all predicate P the machine can find a solution to the formula x
<-> P(x), that is, can find a sentence k such that the machine will
prove k <-> P(k).
But we can define truth predicate on restricted set of sentences.
Necessarily so, it would seem.
Yes, but it is not completely obvious.
And we can use richer theories. In set theory, it is easy to define
the arithmetical truth. Of course, in the background we use the
notion of set-theoretical truth, which, if we would define it would
requires strong infinity axiom (ZF + kappa exists) for example.
Arithmetical truth is the simplest notion of all definition of
truth. "AxP(x)" is true simply means that P(n) is true whatever n
is. It is the infinite or:
P(0) v P(1) v P(2), v P(3), etc.
The amazing thing, alreadu apparent in Post 1922 and Gödel 1931, but
quite clarified since, is that
1) we can describe the complete functioning of any universal (and
non universal) system in the arithmetical language, but, and that is
the key, in virtue of the true-ness of the relation between the
numbers, the computations are not just describe in arithmetic, but
they are emulated.
In effect, they are actioned.
OK. In the out-of-time manner of the block-mindscape, in virtue of the
true realtion existing in the number relation. It is there that many
confuse:
the number s(0),
the Gödel number of s(0),
the Gödel number of the Gödel number of s(0), which plays very
different role, all important, when we translate UDA in arithmetic.
Of course, this needs a good familiarity with the understanding of the
difference between language, theories, and truth (models).
I know you and some other have well understood this, but not all
here seems to have grasped that quite important distinction, between
truth, theories and languages. Also, I am sure you forget to apply
this sometimes, see below. I think you don't take mechanism
seriously enough. (as working hypothesis of course).
Oh dear. But I've looked below and I'm not sure where I'm going
wrong :(
May be I have just misunderstood some proposition you made.
But what might be a corresponding notion of physical truth? Is it
just Brent's insistence on a completed instrumental account of
neurocognition in terms of physical action?
Brent defines truth by physical truth. It is OK, but cannot work
with mechanism (uda, etc.)
But then you say below there is no physical truth, only physical
modes. But perhaps you mean only assuming mechanism. If one doesn't
assume this, what then is physical truth?
A primitive thing. It is then assumed at the start. To be sure, this
is never done. But logically, assuming non mechanism, someone can do
that. Implicitly, the metaphysical natiuralist does that all the time.
In applied physics, we do that by simple pointing.
No politician would refuse a project to go on the moon by saying that
"moon" is not well defined. But when doing metaphysics, we have to be
clear on such things.
But such an account would not even address the provenance of the
perceptual facts in terms of which that very action appeared to us.
Could that be sufficient to justify the inference that perception
was a "physical truth", as opposed to merely being effectively
eliminated?
I think we are perhaps close to a point where we could slightly
disagree. I can still make some sense of Brent's proposition, and of
physicalism, by assuming a physical universe, as starting
hypothesis. The price is to abandon mechanism. That will make
everything a bit magical, but it can be consistent, and worst, true.
Yes, but what's true about a physical universe that could be
invoked (or inferred, pace Brent) to explain consciousness of it?
I might have answer this already? If not please bring the question back.
better say no to the doctor, in that case. This would need things
like kappa, or even more complex set-theoretical objects. Eventually
it is like Ptolemeaus epycicle, and with mechanism, literal
invisible horses, but time consuming horses to describe when doing
the prediction. Today that remains possible, and that is why I try
to propose a test.
Do you mean YD? That's some test! Mind you, partial brain
prostheses are almost upon us.
I suspect, in the end, that any viable notion of physical truth
would inevitably collapse, under analysis, to mechanism and
consequently to arithmetical truth. And so the argument will begin
again ;)
The physical truth, with mechanism, is the truth about the (measure
on) the computations which "continues" you in arithmetic, as seen
from some internal points of view.
OK
using G, we can described it roughly but precisely by Bp & Dt & p,
with p computable (sigma).
In Plotinus-like terms, arithmetical truth is the One. the only
thing you need to believe in, or understand.
OK again. And as I remarked recently (although you haven't
commented yet) the body is perhaps what allows the symmetry of that
One to be broken, at least in terms of the points of view.
Yes. Like the consciousness of the guy who open the door in
Washington, after a WM-duplication, breaks the 3p symmetry of the (3p)
protocol.
(of course it is a physical body, but a relative representation among
infinitely many, in the real "global" case, "in front of the
"immaterial UD").
But that is a semantical reality. it is know that the arithmetical
truth cannot be axiomatize completely by any reasonable/effective
theory. We cannot "really" define it ourselves, but like
consciousness, we have quickly a good intuitive grasp on it. We
don't complain when our kids learns that prime numbers exists, even
an infinity of them.
That is what I sum up by p. It is the sentence asserted by a machine
(or not, here there is the nuance which, if misunderstood paved the
road to the theological trap). Indeed, with mechanism, p will be
sigma. And for the sigma proposition we have G* proves p <-> []p. So
God becomes the universal turing machine! Blaspheme!
Well, the machine becomes the universal experiencer, the
monopsychic, multiply-amnesic "solus ipse". Is that God?
It is the inner God, but with computationalism at the meta-level, it
is God from God's point of view, but the machine cannot know that.
That is why some prayer, to God, remains unavoidable for the YD.
ISTM that an aspect of God must also somehow be implicated in
arithmetic itself which, as the fons et origo of the supremely
creative widget, is the sole assumptive ontology for everything that
follows.
Yes, but once Mechanism is assumed, we are free to assume only the
sigma1 arithmetical truth. That is why the *theory* can assume only
RA. But for the semantic, it is easier to keep the whole (non
effective) arithmetic---the structure (N, 0, + ,*), even if we decide
to put it in the machine epistemology.
Not really, because the correct machine will just stay mute on []p -
> p.
With mechanism, we don't go out of the much more tiny, computable
(cf the universal dovetailer, the "splashed universal Turing
machine) sigma truth. The usual Arithmetical truth can also be
relegate to the imagination of the universal numbers.
So, we have the truth,
p
and we have the modal nuances, literally enforced by incompleteness,
as the Löbian machine already know:
Bp The justfiable (G1 and G1*)
Bp & p The knowable (S4Grz1)
and the two matters of the neoplatonists:
Bp & Dt intelligible matter (sharable quanta and
piece of classical and quantum bits) The observable (Z1 and Z1*)
Bp & Dt & p (sensible matter (unsharable qualia,
undescribable by any bits in any language) The sensible (X1 and X1*)
Thee modes split, by inheriting the G/G* split. Note that the
decidability of G is inherited on all modes, including G*.
The splitting gives interesting corona (G* \ G, Z1* \ Z1, X1* \ X1).
Some quantum logics appears in S4Grz1, Z1*, X1*.
So, if you want, there is only one notion of fundamental truth
assumed (ontologically).( (sigma) arithmetical truth). All the rest
are imposed as self-referential modalities, by incompleteness (which
belongs to the arithmetical truth) on the self-referentially correct
universal number, relatively to each others.
Which I called, rather vaguely in answer to Brent,
(epistemological) generalisations of arithmetical truth (meaning
only that they added no new entities or relations to the assumptive
ontology)
All right. Not even PA's induction axioms. Despite we will interview
PA, when mimicked by RA.
The physical truth is one way "arithmetic" looks at itself. It is
first person plural, because we share the "measure one", in the "&
Dt" modalities, although this has not yet been completely clarified.
Yes, I've just said that in response to Brent's remarks about the
point-of-view invariance of physical observables.
OK.
To put is more bluntly: there is no physical truth. Only some true
physical mode.
OK but what about what you said above? I think I see that you must
intend this on the assumption of mechanism only. What physical truth
could be on any other assumption is presumably a different matter.
Yes, and with non-comp, you are free to say almost anything, as *from
a mechanist view*, this will always look like "God made it". You can
say that the physical reality are those potatoes on the table. The
problem is that physicalist sometime forget that [physics = the
fundamental science] is a metaphysical assumption which needs to be
made in a metaphysical theory. But they often use [physics = the
fundamental science] to avoid doing metaphysics. Like they can use
Mechanism to avoid the mind-body problem, but this kicks back.
Normally given by []p & Dt (& p). In my thesis I was wrong when
saying that S4Grz1, the logic of (Bp &p), p sigma, collapse. It did
not, which makes things even closer to Plotinus. The soul has
already a foot in Matter, somehow.
Well, surely without a connection to matter it would be
perceptually stranded in the unbroken symmetry of the One.
Except that S4Grz1 seems to broke the symmetry, even without matter.
But then I was wrong, matter does appear already.
The grz formula, in S4Grz(1) impose the Kripke relation to be
antisymmetrical. The (1), which comes from mechanism (made explicit in
arithmetic) restore a symmetry at the bottom of physics, that is the
reversibility of the fundamental physical laws (a good step toward
"unitary physics").
Note that the soul does not split along G/G*.
And therefore....?
The Divine Intellect, and the discursive man share the Soul. We are
the same person on Earth and in Heaven. That is not the case for the
observable and the sensible. Heaven and Earth obeys the same first
person quantum logic, but not in a sharable way. The outer-God does
not distinguish our particular soul and our universal soul, despite we
will feel different, for the observable and the sensible.
Hope this is not too much technical
!!
, but I needed to get the short answer: there is no physical truth,
only physical modes, which are uncertainty measure on accessible
continuation.
Yes, the Born "probabilities" (hopefully).
Yes!
What Aristotle called the physical universe, is only a map of our
most accessible continuations in arithmetic.
Indeed.
OK. I think that our difficulty remains only in the fact that I see
the Outer-God (the ONE) as 3p, where (and I think I see why) you would
prefer to consider it 0p, which I think is OK, but one step closer to
the blaspheme, the YD, without interrogation mark, assumes that the
doctor is a scientist, when he is really only a priest. Maybe I should
describe comp by CT + YD?. The "?" is not technically avoidable: it
requires a "religious" act of faith, and cannot be enforced to people
(and there is a problem with the kids, like in all religion, solvable
in practice by the "legal age" notion for deciding or not to ask the
kid's act of faith or not).
Bruno
David
Bruno
David
is equated with the truths, as distinct from the formal
procedures, of arithmetic. The strength of the logical models that
Bruno utilises in the machine interviews is then that they can be
characterised in this sense as "accessing truths". However, their
purely extrinsic formulation is in the relevant sense "incomplete"
in this regard. Their completion in that same sense is to be found
in the conjunction of an extrinsic formulation with an intrinsic
(reflexive) logic that is comprehensible only in terms of what the
subject thus modelled perceives to be true, i.e to correspond with
its perceptually-available "facts". The consequence is then that
consciousness is equated in this view with whatever is
perceptually true, in the first instance, for a given subject.
I mainly agree. I would use "intuit" for the Bp & p, and "perceive"
with the Bp & Dt (& p). But that is an old bad habit, perhaps, as I
thought that Bp & p collapse on p sigma. But that is not the case,
and Plotinus was right (!), the soul (Bp & p) has already a
intuition/perception of the physical reality).
Here we have the problem that we get three quantum logics, and thus
three physics. Normally Bp & p, with p sigma, is "heaven physics",
and Bp & Dt (& p), p sigma, is terrestrial physics. Normally Bp &
Dt gives the quanta, and Bp & Dt & p gives the qualia, but it is
slightly more complex than that, for technical reason.
Now, toy model or not, ISTM that there is surely something in the
foregoing that offers certain relevant conceptual footholds that
are unavailable in alternative schemas. It's also something that
can in principle be examined and tested rigorously even though it
is at present largely neglected and at a very early stage of
development. At least it seems to offer a way of avoiding the
equally unpalatable polarities I mentioned before - of brute
identity theory on the one hand, or the fruitless search for some
"internal" state of matter on the other. Either of these
alternatives has struck me for a long time as falling into the
category of "not even wrong".
OK. I agree, but I think that Brent's main mistake is that he is
oblivious that I show the existence of a problem with Mechanism,
and show that the problem can be translated in arithmetic, and that
it leads up to now to a theology, testable by the constraints it
put on the core of physics (indeed, we do get a quantum-like
logic). I show that Gödel's theorem is not only a chance for
mechanism by justifying the existence of the knower (Bp a p), but
Gödel's theorem justifies the existence of the matter appearances
as well, when p is sigma, and when we add the "probability" clause:
that is the "Dt".
Bruno
http://iridia.ulb.ac.be/~marchal/
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