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
To be sure this is what Peter D. Jones called "standard
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
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
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
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)
(deducible) (deducible or non
(the ONE); (p) 0-person (unnameable)
intellect: (3-person) divine intellect: (3
provability Bp (G) provability Bp (G*, )
the all-soul (the knower, Bp & p)
Intelligible matter (Z) Intelligible matter
(1-person plural) (1-person plural)
Sensible matter (X) Sensible matter (X*)
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
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,
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