On 01 Sep 2010, at 20:03, David Nyman wrote:
On 1 September 2010 09:21, Bruno Marchal <marc...@ulb.ac.be> wrote:
How does my experience of
dreaming of a tree connect to numbers? What is it that generates my
experience of a tree from the brutely existing substrate of numbers?
Well, from the true but non communicable part given by the self-
reference
logic of self-introspecting (ideally correct) programs (machine,
numbers,
theories ... words are used in a large sense here).
Rex's question excerpted above, and Bruno's response to it, seem to
relate directly to the topic I had in mind in my original post.
Speaking, as it were, somewhat in Bruno's rather "large" sense, the
"brutely existing substrate of numbers" might correspond to that
particular perspective on the Real which is characterised by
abstraction to what I called the pole of maximal fragmentation - i.e.
the role presumably occupied by the quantum field and its
manifestations in current physical theory. "The self-reference logic
of self-introspecting (ideally correct) programs (machine, numbers,
theories ...", would then be seen in the role of a combinatorial logic
operating over this domain - that occupied, in physical theory, by
whatever are supposed to be considered the fundamental relations
between "physical" ultimates.
The key subtlety then devolves on "the true but non communicable
part". This seems very difficult to state concisely. Perhaps what
makes it elusive is that first one has to appreciate that the
self-introspecting logic is (somehow) already capable of grasping that
certain of its beliefs have the characteristic of implying to the
believer, in a certain sense, the "metaphysical distinctness" of their
referents. To see this, let us consider "Logical-David" - i.e. that
aspect of David that is purely a manifestation of "self-introspecting
(ideally correct) programs". This Logical-David possesses - i.e. is
(partially) constituted by - certain self-referential beliefs that
mediate relations between "himself" and the "objects of his
experience". He is already, within the constraints of this purely
logical substrate, capable of demonstrating consistent commitment to
such beliefs, and to their putative referents; indeed this is what
motivates any communicable judgement or statement whatsoever that he
is capable of producing about them. There is something more, however.
There is something that already seems to him to transcend this purely
logical "substrate", something somehow metaphysically distinct, that
seems to arise from its peculiarly self-referencing character. It
seems somehow to be those very "objects of experience" themselves.
On reflection, however, Logical-David is (just) able to see that all
these considerations can still be confined within the constitutive
substrate of numbers and combinatorial logic. Or to put it another
way, as someone notoriously said, "he would say that, wouldn't he"?
Whatever this extra something might, or might not, be, he is incapable
of communicating it directly.
Yes. It is the truth as such that he cannot communicate. The third
person description can be confined in the combinatorials, but not the
truth. Like the truth of feeling to be the one reconstituted at here
or there in self-multipliation. A part of truth is livable, but non
communicable as such.
Consequently, purely "logically", he
must (just) concede that any such putative metaphysical distinctness
could still be, from a purely "logical" standpoint, chimerical.
No. G* extended properly G. There is two self-referential logics. The
true one, obeying G*, and the communicable part G.
The machine can expect that the same thing (truth) obeys different
logic (first person, third person). Incompleteness protects the
machine from confusing the views. If he takes G* minus G as
chimerical, he becomes inconsistent, or it lacks self correctness.
In
other words, it would appear that he cannot, with pure logic, rule out
the possibility - even to himself - of Logical-David being merely a
zombie.
No. Even the zombie can see that he cannot. That's why the self-
referentially correct machine cannot be a zombie.
And indeed, Logical-David is, precisely, such a zombie.
In a sense you are right. But such a third person describable "logical
david", is more akin to David's body, than David the (first) person,
which (by definition) is connected to the truth. You are confusing Bp,
and Bp & p. The third person self and the first person self.
Actually, in this somewhat etiolated form he really should be
considered more an intriguing interpretation of the
mathematico-logical substrate than a person, as it were, in his own
right
Can there be no escape from this seemingly doleful logic? Yes, if
there is *in fact* a David whose personal individuation is able to
transcend its merely logical embodiment.
That's what G* and its intensional variants offer on a plate.
And such transcendence
indeed implies a metaphysically distinct, direct grasp of certain
truths beyond their mere logical implication; some sort of personal
integration or synthesis - apotheosis, even - correlated with, but
irreducible to, any substrate considered in its purely
analytical-combinatorial aspect.
Exactly. You put things very well. But the G-G* separation makes
S4Grz1, the logic of the soul (Bp & p) a logical of a non formalisable
person. You cannot translate in the combinatorial or in term of
numbers the "p" of Bp & p. The soul has no name, no 3-descriptions,
from its point of view.
Yes, S4Grz, S4Grz1, X1, and X1* are quite remarkable, those logics
formalize the discourse of beings which are themselves NO
formalizable, nor even nameable by the machine, except by some
vindication like "could you please take care where you put your foot".
In short, for such transcendent
individuation to be the case, there must *actually exist* a
first-person David who is conscious,
David the soul. Again, you get it for the machine by the Theatetical
idea of defining the soul by the knower, and the knower by the
connection between the believer (a mechanical body) and God, or simply
Truth. It is the passage from G1 to S4Grz1. (the "1" has to be added
in the for the machine in the comp frame). It *is* the passage from Bp
to Bp & p. It is "p" (the truth of p) which is responsible for the non
formalizability.
as well as merely logically
possessed, of the objects of his experience.
That's David-the-body, or the dynamical-believer machine. That's the
one described by G and G*.
And as to the truth of this - of course - only he would know.
As I said. You put *very well* the thing. You add the "truth" at the
right place, at an infinitesimal nuance I don't want to bother you
with now.
David (both of him)
You will end up 8 of you. Or 4 + 4.infinity, Oh! well, thare are many
ays to counts them. I say 8 for the 8 main intensional variant of
"third person belief":
p
Bp
Bp & p
Bp & Dp
Bp & Dp & p
I have underlined those variants who corresponds to non formalizable
beings. I have put in italic those who split in two, due to the G-G*
gap. So you can count: there are 8. Self-referential machine have to
live this that. They have already 8 quite different views on the
truth. [or 4 + 4.infinity, because you have all the variant with B^n p
& D^m p in place of Bp & Dp, and where B^5 p is BBBBBp ... ].
You have to study Gödel and Tarski theorem, or a result by Kaplan and
Montague, recasted in the Solovay logics. Smorynski wrote a paper "50
years of arithmetical self-reference", a rather long time ago. Boolos
1979 and 1993 consecrated a chapter to the "knower" (S4Grz). A student
and friend of mine has formalized Bp & Dp (the Z, Z1, Z* and Z1*)
logics, but the case for S4GRz1, and the X, X1, X*, X1* logics remains
unsolved. There are theorem prover for those logics, and so by an
indirect argument we know them formalizable, but no one has found the
axioms yet. Note that all those logic are non effectively soluble,
once extended at the modal predicate level.
The hypostases give a knowledge of the believer, the conscious knower,
the observer, the "feeler" each with they communicable and non
communicable part, from which you can derive, the observable, the non
observable, the feelable and the non feelable, well many things,
including quanta and qualia.
Weakness: hard mathematics.
Ask any question if you feel so. I am aware it is hard and ultra-
subtle stuff. Well, that is why only technics can handle those self-
references.
Bruno Marchal
On 31 Aug 2010, at 19:36, Rex Allen wrote:
On Mon, Aug 30, 2010 at 11:11 AM, Bruno Marchal
<marc...@ulb.ac.be> wrote:
So "idealist accidentalism"...the view that what exists is
mental, and
that there is no underlying process that explains or governs this
existence.
If idealist accidentalism is correct then there is no theory at
all.
Well, I'd have to hear your definition of "theory" and what the
conditions are for its existence.
The existence of a theory is usually not the object of the theory,
but of a
metatheory.
In some case the metatheory can itself be an object of the theory.
For
example zoologists are animal (but botanist are not plant). Since
Gödel we
know that the theory "Peano Arithmetic" can be studied "in" Peano
arithmetic. And monist philosophies makes mandatory that the theory
and/or
the theoretican has to belong to the collection of objects or
phenomena of
the theory. Physicists do obey to the laws of gravitation for
example. A
physicist of masse m will attract a physicist of mass M with a force
proportional to mM/(square of the distance between two physicists).
of
course that force is negligible compared to the natural repulsion
that a
physicist can or cannot have for a colleague ...
So obviously something exists...my conscious experience of this
moment.
That is obvious for you. I have to postulate it.
Unless you postulate we are the same person?
I can agree with that, at some level, but you waould not refer to
"this
moment". I am not sure what you mean by "moment" with idealist
accidentalism
(IA).
This experience is a multifaceted thing...in that there are
many "things" I am conscious of in this moment.
But this is true of dreams as well. I am conscious of many things
in
a dream, but those aren't things that exist outside or independently
of the dream.
In which theory. Such a sentence seems to assume a lot, if only to
make some
sense. If IA is correct, words like "world", "outside" refer to what?
So what accounts for the dream? Numbers?
In the theory "digital mechanism", aka "computationnalism", we can
argue for
this, indeed.
How does my experience of
dreaming of a tree connect to numbers? What is it that generates my
experience of a tree from the brutely existing substrate of numbers?
Well, from the true but non communicable part given by the self-
reference
logic of self-introspecting (ideally correct) programs (machine,
numbers,
theories ... words are used in a large sense here).
Why should numbers give rise to my dream experience of a tree?
Obviously I can use numbers to represent the tree...in the sense
that
I can use saved numerical measurements to "re-present" the tree to
my
self...if I can remember how to interpret the measurements. And I'm
even willing to grant that I can use numbers to represent my
experience of the tree. But representation is just the re-
presenting
of something to your conscious experience, which is not at all the
same as explaining the fact of that experience.
The fact of experience is given by the true fixed point of the
representation, like a map of the USA, when situated in the USA
will have a
representing point superposed on the real point.
But idealist accidentalism is a theory (even if vague)
So there is no theory, and there is one theory.
So 0 = 1.
Contradiction.
So idealist accidentalism is refuted.
I think you should have your logician license revoked...
I will not insist on that littel reasoning. Was just trying to
shortly
points that IA makes little sense for me.
You may save it by insisting that idealist accidentalism is not a
theory.
It
would be a mere philosophical injunction of the type "dont' ask,
don't
search".
I think it is a just a recognition that Agrippa's trilemma and the
principle of sufficient reason lead to infinite levels of infinite
regress. Which I take as a sign that there's something wrong with
that type of interpretation of our conscious experience.
When put in computer science terms (which computationalism invites
naturally
to do), we inherit of the fixed point solutions of recursive
equation.
I have no problem with people trying different kind of theory, but
to posit
consciousness at the start (or matter, actually) does not satisfy
me. As I
said it prevents further research. I understand that feeling
(consciousness
cannot be explained), but I can at least explain why machine/
numbers develop
discourse invoking similar failure feeling about their own
consciousness/consistency, or true but non provable predicate on
themselves.
Bruno
http://iridia.ulb.ac.be/~marchal/
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