Bruno Marchal wrote:
Hi Bruno
Good to see this. First off some grandmotherly-ish questions:
> 1) The computationalist hypothesis (comp),
>
> This is the hypothesis that "I am a digital machine" in the
> quasi-operational sense that I can survive through an artificial
> digital body/brain. I make it precise by adding Church thesis and some
> amount of Arithmetical Realism (without which those terms are
> ambiguous).
> To be sure this is what Peter D. Jones called "standard
> computationallism".
I need to ask you to make this more precise for me. When I say I *am* a
digital machine, what is my instantiation? IOW, am 'I' just the *idea*
of a dmc for the purposes of a gedanken experiment, or am I to conceive
of myself as equivalent to a collection of bits under certain
operations, instantiated - well, how? You may be going to tell me that
this is irrelevant, or as you say a little further on:
> From a strictly logical point of view this is not a proof that "matter"
> does not exist. Only that "primitive matter" is devoid of any
> explanatory purposes, both for the physical (quanta) and psychological
> (qualia) appearances (once comp is assumed of course).
Ignoring for the moment the risk of circularity in the foregoing logic,
I'm not insisting on 'matter' here. Rather, in the same spirit as my
'pressing' you on the number realm, if I claim 'I am indexical
dmc-David', I thereby assert my *necessary* indexical existence. If my
instantiation is a collection of bits, then equivalently I am asserting
the necessary indexical existence of this collection of bits. Is this
supposed to reside in the 'directly revealed' Pythagorean realm with
number etc and consequently is it a matter of faith? I just want to
know if it is a case of 'yes monseigneur' before we get to 'yes
doctor'.
> B does capture a notion of self-reference, but it is really a third
> person form of self-reference. It is the same as the one given by your
> contemplation of your own body or any correct third person description
> of yourself, like the encoding proposed by the doctor, in case he is
> lucky.
Now we come to the 'encoding proposed by the doctor'. I hope he's
lucky, BTW, it's a good characteristic in a doctor (this is grandma
remember). Do we have a theory of the correct encoding of a third
person description, or is this an idealisation? Penrose would claim, of
course, that it is impossible for any such decription to be
instantiated in a digital computer, and his argument derives largely
from the putative direct contact of the brain with the Platonic/
Pythagorean realm of number, which instantiates his 'non-computable'
procedures. But is your claim that a correct digital 3rd-person
description can indeed be achieved if the level of digital
'substitution' instantiates non-computability, as Penrose claims for
the brain/ Pythagorean dyad? And if so what is that substitution level,
and what is that instantiation (in the sense previously requested)?
What a curious and ignorant grandmother!
> Basically a theology for a machine M is just the whole truth about
> machine M. This is not normative, nobody pretend knowing such truth.
> Plotinus' ONE, or "GOD", or "GOOD" or its "big unnameable" ... is
> (arithmetical, analytical) truth. A theorem by Tarski can justified
> what this notion is already not nameable by any correct (arithmetical
> or analytical) machine. Now such truth does not depend on the machine,
> still less from machine representation, and thus is a zero-person
> notion. From this I will qualify as "divine" anything related to truth,
> and as terrestrial, anything related to "provable by the machine".
So here we arrive at the theology, and I think I finally see what you
intend by a zero-person notion - i.e. one that does not depend on
instantiation in persons, but I'm not yet convinced of the 'reality' of
this. I hope to be able to stop pressing you on this 'indexical
instantiation' mystery, so if the above are simply the articles of
faith for this 'as if' belief system, then I'll stop questioning them
for the duration of the experiment.
> Meanwhile you could try to guess where qualia and quanta appear.
> (I will see too if this table survives the electronic voyage ...)
Hmm... Well, I guess I would expect qualia to be 'sensible', and quanta
to be 'intelligible', but then I wouldn't know that quanta were
intelligible until they were sensible as qualia. So if you mean
'appear' as in 'appears from the pov of indexical dmc-David', I guess
it would have to be 'sensible matter' for both. But grandma grows
weary......
G
> Hi,
>
>
> 1) The computationalist hypothesis (comp),
>
> This is the hypothesis that "I am a digital machine" in the
> quasi-operational sense that I can survive through an artificial
> digital body/brain. I make it precise by adding Church thesis and some
> amount of Arithmetical Realism (without which those terms are
> ambiguous).
> To be sure this is what Peter D. Jones called "standard
> computationallism".
> Let us call momentarily "Pythagorean comp" the thesis that there is
> only numbers and that all the rest emerge through numbers dream
> (including possible sharable dreams); where dreams will be, thanks to
> comp, captured by infinite collection of computations as seen from some
> first person perspective. Then ...
>
>
>
>
> 2) The Universal Dovetailer argumentation (UDA)
>
> ... then the Universal Dovetailer Argumentation (UDA) is literally a
> proof that
>
> Standard computationalism implies Pythagorean computationalism.
>
> From a strictly logical point of view this is not a proof that "matter"
> does not exist. Only that "primitive matter" is devoid of any
> explanatory purposes, both for the physical (quanta) and psychological
> (qualia) appearances (once comp is assumed of course).
> The UDA needs only a passive understanding of Church Thesis (to make
> sense of the *universal* dovetailing).
>
>
>
>
> 3) The lobian interview and the rise of the arithmetical "plotinian"
> hypostases, or n-person perspectives.
>
> The difference between the UDA and the lobian interview is that in the
> UDA, *you* are interviewed. *you* are asked to implicate yourself a
> little bit; but in the lobian interview, instead of interviewing
> humans, I directly interview a "self-referentially correct" and
> sufficiently "rich" universal machine (which I call lobian for short).
> Computer science + mathematical logic makes such an enterprise
> possible. We can indeed study what a correct (by definition) machine is
> able to prove and guess about itself, in some third person way, and
> that's how the other notion of person will appear (cannot not appear).
>
> Let us abbreviate "the machine asserts "2+3=5"" by B(2+3=5). B is for
> Godel's Beweisbar notion of "formally provable". If "p" denotes any
> proposition which we can translate in the machine's language, we write
> Bp for "the machine asserts p".
> For a classical mathematician, or an arithmetical platonist, there is
> no problem with *deciding* to limit the interview to correct machine
> (independently that we will see that no correct machine can know it is
> a correct machine). To say that the machine is correct amounts to say
> that whatever the machine asserts, it is true. So Bp -> p, when
> instantiated, is always true.
> But now, by the incompleteness phenomena, although Bp -> p is always
> true, it happens that no correct machine can prove for any p that Bp ->
> p. For some p, Bp -> p is true, but not provable by the machine. The
> simplest case is when p is some constant falsity, noted f, like "0 = 1"
> for example, or like "p & ~p". In that case Bp -> p is Bf -> f, and
> this is equivalent (cf propositional truth table) to ~Bf, which is a
> self-consistency assertion not provable by the correct machine (by
> Godel's second incompleteness theorem). Due to this, "Bp" does not
> capture a notion of knoowledge, for which "Bp->p" should be not only
> true but known.
> B does capture a notion of self-reference, but it is really a third
> person form of self-reference. It is the same as the one given by your
> contemplation of your own body or any correct third person description
> of yourself, like the encoding proposed by the doctor, in case he is
> lucky.
> This means that "Bp & p", although equivalent with "Bp", cannot be
> proved equivalent by the machine. This means that the logic of "Bp & p"
> will be a different logic than the one of "Bp & p". Now Theaetetus has
> proposed to define "knowledge" by such a "true justified opinion", and
> I propose to define the logic of machine (perfect) knowledge by Bp & p.
> This remains even more true for other "epistemological nuances" arising
> from incompleteness, like the future probabilty or credibility (not
> provability!) notions, which I will capture by Bp & Dp and Bp & Dp & p,
> where Dp abbreviates, as usual (cf my older post) ~B~p (the non
> provability of the negation of p).
>
> Now, note this: I said "Bp & p" is equivalent to "Bp", but the machine
> cannot prove that equivalence. So the proposition "(Bp & p) <-> Bp" is
> an example of true (on the machine) but unprovable (by the machine)
> proposition. So, concerning the correct machine we talk about, we must
> distinguish the provable propositions and the true but unprovable
> propositions. Thanks to Solovay, the logic of the provable proposition
> is captured by a modal logic often named G, and the logic of the true
> proposition is captured by a vaster logic named G*. The corona G* minus
> G gives a logic of the true but non provable statements.
>
> I think I have enough to give you a sketch of the hypostases. I will
> use Plotinian greek neoplatonist vocabulary, because it fits
> completely.
>
> I will associate to any machine, a complete "theology" in the sense of
> the greek (you can take it as a theory of everything). Going from one
> machine to another one does not change the logics related to the
> theology, although the precise sense of the "B" will vary. So you can
> think of "B" as an indexical notion. Please note that it is absolutely
> not obvious that such a B notion exist. That is the main lesson of
> Godel's 1931 work.
> Basically a theology for a machine M is just the whole truth about
> machine M. This is not normative, nobody pretend knowing such truth.
>
> Plotinus' ONE, or "GOD", or "GOOD" or its "big unnameable" ... is
> (arithmetical, analytical) truth. A theorem by Tarski can justified
> what this notion is already not nameable by any correct (arithmetical
> or analytical) machine. Now such truth does not depend on the machine,
> still less from machine representation, and thus is a zero-person
> notion. From this I will qualify as "divine" anything related to truth,
> and as terrestrial, anything related to "provable by the machine".
>
> The hypostases can then be divided into the divine one, and the
> terrestrial one. And like Plotinus, it suits well to divide them also
> into "primary" and "secondary" one.
> The three primary hypostases, in Plotinus, are the ONE (zero-person),
> the DIVINE INTELLECT (third person), and the ALL-SOUL (the "pure" first
> person). Here, the difference between truth and provability divides all
> the hypostases into their communicable or deducible parts and their non
> communicable parts), except for the soul (that is not obvious at all)
> which is invariant for the
> proof->truth path, and "truth", which although "purely divine" will
> have through comp some terrestrial "consequences".
>
>
> (And remember this is just a roadmap)
>
>
> TERRESTRIAL DIVINE
> (deducible) (deducible or non
> deducible)
>
> 1)Primary
> truth
> (the ONE); (p) 0-person (unnameable)
>
> intellect: (3-person) divine intellect: (3
> person)
> provability Bp (G) provability Bp (G*, )
> (nameable) (nameable)
>
> the all-soul (the knower, Bp & p)
> (1-person unnameable)
>
> 2) secondary
> Intelligible matter (Z) Intelligible matter
> (Z*)
> (1-person plural) (1-person plural)
> (nameable) (nameable)
>
>
> Sensible matter (X) Sensible matter (X*)
> (1-person) (1-person)
> (unnameable) (unnameable)
>
>
> All this even without assuming comp!!! It works for a very much larger
> set of self-referentially correct entities (larger than the set of
> those which are turing emulable).
> I must go now, and tomorrow I explain what happens exactly when comp is
> assumed.
> Meanwhile you could try to guess where qualia and quanta appear.
> (I will see too if this table survives the electronic voyage ...)
>
> Hope this will help,
>
> Bruno
>
>
>
> http://iridia.ulb.ac.be/~marchal/
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Received on Tue Aug 15 2006 - 20:53:35 PDT