Thanks for this Peter: I am still chewing on this, with a view to ultimate digestion.

I do get a certain kind of Angels and pinheads impression about some of it though. Hopefully that is just an illusion! :-)


Mark Peaty  CDES


1Z wrote:

1Z wrote:
> Mark Peaty wrote:
>> SP: 'using the term "comp" as short for "computationalism" as something
>> picked up from Bruno. On the face of it, computationalism seems quite
>> sensible: the best theory of consciousness and the most promising
>> candidate for producing artificial intelligence/consciousness'
> What Bruno calls comp isn't standard computationalism, it has
> an element of Platonism.

Mark Peaty wrote:
For my benefit, could you flesh that out in plain English please?


Mark Peaty  CDES




'The precise comp version is given by

a) the "yes doctor" act of faith  YD
b) Church (Hypo) Thesis   CT
c) Arithmetical Realism hypothesis   AR '

BM:'Now, it is a fact, the failure of logicism, that you cannot define
without implicitely postulating them. So Arithmetical existence is a
quasi necessary departure reality. It is big and not unifiable by any
axiomatisable theory (by Godel).
(axiomatizable theory = theory such that you can verify algorithmically
the proofs of the theorems)
I refer often to Arithmetical Realism AR; and it constitutes 1/3 of
the computationalist hypothesis, alias the comp. hyp., alias COMP:

COMP = AR + CT + YD (Yes, more acronyms, sorry!)

AR = Arithmetical Realism (cf also the "Hardy post")
CT = Church Thesis
YD = (I propose) the "Yes Doctor", It is the belief that you can be
decomposed into part such that you don't experience anything when
those parts are substituted by functionnaly equivalent digital parts.
It makes possible to give sense saying yes to a surgeon who propose
you some artificial substitution of your body. With COMP you can
why this needs an irreductible act of faith (the consistency of
COMP entails the consistency of the negation of COMP, this is akin
to Godel's second incompleteness theorem.
It has nothing to do with the hypothesis that there is a physical
which would be either the running or the output of a computer program.
Hal, with COMP the "identity problem" is tackled by the venerable old
computer science/logic approach to self-reference (with the result by
Lob, Solovay, build on Kleene, Turing, Post etc...)'


BM: 'Arithmetical Realism (AR). This is the assumption that
arithmetical proposition, like
''1+1=2,'' or Goldbach conjecture, or the inexistence of a
bigger prime, or the statement
that some digital machine will stop, or any Boolean formula bearing on
numbers, are
true independently of me, you, humanity, the physical universe (if that
exists), etc. '

PJ: That's an epistemological claim then....

BM: 'It is
a version of Platonism limited at least to arithmetical truth'.

PJ: Is it ? But Platonism is an ontoligcal thesis. As a standard
reference work has it: "The philosophy of Plato, or an
approach to philosophy resembling his. For  example, someone who
asserts that numbers exist  independently of the
things they number could be called a Platonist."

BM: 'It should not be confused
with the much stronger Pythagorean form of AR, AR+, which asserts that
only natural
numbers exist together with their nameable relations: all the rest
being derivative from
those relations.

If Pythagoreanism is stronger than Platonism in insisting that
everything is
derivable from (existing) natural numbers, is Platonism weaker than
in insisting that everything is derivable from existing numbers of all
natural or not? Is Platonism not being taken a s alcaim about
here, not just a claim about truth ?

BM: "A machine will be
said an Arithmetical Platonist if the machine believes enough
arithmetical truth (including some scheme of induction axiom)."

PJ: Switching back to an epistemological definition of "platonism"

BM:'Instead of linking [the pain I feel] at space-time (x,t) to
[a machine state] at space-time
(x,t), we are obliged to associate [the pain I feel at space-time
to a type or a sheaf of
computations (existing forever in the arithmetical Platonia which is
accepted as existing
independently of our selves with arithmetical realism).'

PJ: Another use of Realism as a thesis about existence.

PJ: And if the pain-feeling "you" exists eternally, how do
ever *not* feel pain ? There is an ontological gulf
between tokens and types, between the temporal
and the eternal, which has been leaped over  at a bound here.

------------ BRUNO ADMITS TO (ONTOLOGIAL) PLATONISM -----------------


'Numbers are not physically real does not entails
that numbers don't exist at all, unless you define "real" by "physical

'I reduce the stable appearance of a "physical universe" to "stable
belief" by numbers, which are existing mathematically'

'That is why I explicitly assume the existence of numbers, through RA
PA axioms when I interview the machine, or by accepting the independent
truth of arithmetical statements, like in UDA.'


PJ: But you *also* think that numbers do have some sort
of existence (even if you want to call that "realism" or
Plotinism, or something other than Platonism).

BM: Yes. Mathematical existence.

PJ: Where are these machines?

BM: Where you could be, assuming comp, and no fatal
error in the UDA argumentation. I was used to call it arithmetical
platonia. Logician call it the standard model (logician sense) of PA. I
use a generalisation of that for lobian machine. Incompleteness prevent
any complete theory describing that.
BM: Where the numbers are.

------------ BRUNO DENYING PLATONISM ----------------------
BM: 'I don't need to have that  "2" exists.

In that sense I am an anti-platonist, if you want.

I only need "2 exists", and then it is a simple exercise to derive it

from "2+2 = 4":

2+2 = 4
Ex(x+2 = 4 & x = 2)

Or perhaps you are telling me that an anti-platonist does not accept
the quantifier introduction inference rule (from A(t) infer Ex(Ax))???

 After all this would be coherent given that I have defined an
(arithmetical)  platonist to be just someone accepting classical logic
(in arithmetic). Lobian machine, like PA or ZF, are platonist, for
example. You can see this, in the AUDA part, as a kind of "formalism"
if you want. Judson Web, see the ref in my thesis" makes such a case.'


BM: Now, many people does take as axiom the unprovable assertion that
is a physical universe. I don't. I am not "atheist" about the universe,
but I am agnostic. I believe less in a primitive physical universe
(especially as an explanation of physics) than in more general
"god-like" or "mathematical-like" reality.


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