Re: Who is the subject?

From: Marchal <>
Date: Fri Jul 9 06:51:03 1999

Romanos Avaqian wrote:

>Before long talks about consciousness, may be there is a sense to discuss at
>first who/what is the subject of perception ? The world is the object, the
>intellect is the tool, but who/what is the subject? Who perceives ?
>The second important question: can the subject be perceived ? Otherwise
>saying: can the subject become an object for himself ?

In Theoretical Computer Science,
there is a traditional way to handle self-reference.
Basicaly self-reference is builded upon the so called
 second recursion theorem by Kleene 1938 see (1).
This theorem says that for any computable
 transformation, you can build
a program which applies that transformation to itself.
The theorem is constructive. Given the
the code of the transformation T you can build the
program which applies T to itself. For exemple, in case T
computes the identity function, you get a self-reproducing program.

The second recursion theorem is also true about the set of
metaprograms and the metametaprograms ... This has been
shown by John Case, a modern 'specialist' on self-reference: see his
WEB pages for more links to self-reference:
This makes for exemple possible the building of self-referential
of machines, like self-regenerating nets of machines, similar
to hydra or planaria.

In that sense the machine can be an object to itself.
Suppose a machine has some ability to prove, like an automatic
proving machine or an automated deduction system.
What can an automated deduction system proves about itself ?
What can a consistent automated deduction system says about itself ?

An incredible use of, still the second recursion theorem (or his
formalised version known as the diagonalisation lemma) has make
it possible for Solovay to settle that question, in 1985, after
 Godel 1931 and Lob 1955 deep breaktroughs. At least he settles
that question concerning sound machines (or theories) which believe
(or proves theorems) in
 classical logic and elementary arithmetic.
The results are astonishing : not only there is a decidable
axiomatic system (G) which formalises completely what the machines
can prove, but there is also an axiomatic system (G*) which formalizes
completely what is true about the machine (including what the
machine is unable to prove). (all this at the propositional level!).

NOW THE BIG PROBLEM: we have hardly talk on
 any suject here. The classical
theory of self-reference talks only about what a
 machine-object can correctly tell
about itself seen as an object. It is a sort of third-person
Only intellect and object are at work until here.
So, how to define an subject coherently with the classical
self-reference theory ?

Believe it or not, Romanos, but an answer
can be found in Plato's Thaetetus.
Or at least an attempt toward an answer.
The basic idea is to define the subject
as the one who knows (as opposed to the intellect
who proves or communicates convincingly), and then
to define "knowing p" by "justifying (proving) p AND p".

Another basic motivation for this strategy can perhaps be provided by
some interpretation of
Descartes' first meditations or by the traditional idealist use of
the dream (the old natural virtual reality!), in Pythagore's
and Platon (still the Thaetetus) philosophy
or in some Indian idealist philosophical school (think
about the yogavasistha(2).
... or Lewis Carroll.

I am aware that such a definition of knowledge is still very
debated among philosophers.

Nevertheless, in that case, with such definition,
it is an exercice, even an easy
one for those who read at least that wonderfull recreative book
"Forever Undecided" by Raymond Smullyan (another professional of
classical self-reference), to show that
the subject cannot be a object for itself.

This, I hope provide an answer to your question, and a path
(the godelian one) toward some communicable light bearing on
similar question.
More details and references are given in
Note also that it is not necessary to believe in Thaetetus' strategy
to use it to invalide arguments, as I do for Lucas-Penrose
type of argument in
Even for non-computationalist such an approach can provide an
*etalon philosophy* useful for possible comparisons between
various philosophies.

What about "the observer" ? I give reasons to *define* it
by *I observe p* = "I justify p AND p is consistent", for
a class of atomic "verifiable" proposition p (in computer
science those are the sigma-1 propositions).
This is a way to internalise the Many-Consistent-Worlds
idea, including the fact that we are searching a probability
defined on the set of those worlds (or states).

In that case we find indeed a sort of probability
logic rather similar to classical Birckhof-Von Neumann Quantum
This gives tools for extracting a precise measure on the
*set of relative
computational histories* having a welcome Quantum smell.
Thanks to the difference between G and G*, we get two Quantum
Logics, one for the observable and communicable propositions,
i.e. *the physical propositions*, and one for the observable
but non communicable propositions. This last logic is a good
candidate for a Logic of Qualia.


(1) Kleene, S. K., Introduction to metamathematics, 1952, North-Holland,
page 352.
(2) A nice (occidental) relevant book here is Wendy Doniger O'Flaherty's
"Dreams, Illusion and other Realities". The University of Chicago Press
Other reference in
See also my 1992 paper "Amoeba, Planaria, and Dreaming Machines".
Received on Fri Jul 09 1999 - 06:51:03 PDT

This archive was generated by hypermail 2.3.0 : Fri Feb 16 2018 - 13:20:06 PST