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! :-)
Regards
Mark Peaty CDES
mpeaty.domain.name.hidden
http://www.arach.net.au/~mpeaty/
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?
>>
>> Regards
>>
>> Mark Peaty CDES
>>
>> mpeaty.domain.name.hidden
>>
>> http://www.arach.net.au/~mpeaty/
>>
>
>
>
> --------BRUNO's "COMP" INCLUDES ARITHMETICAL REALISM-------------
>
> BM:
>
> '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
> integers
> 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
> justify
> 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
> universe
> 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
> Godel,
> Lob, Solovay, build on Kleene, Turing, Post etc...)'
>
>
>
> REALISM AND PLATONONISM
> --------------------------------------------------------------------------------------------------------------
>
>
>
> 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
> Pythagoreanism
> in insisting that everything is derivable from existing numbers of all
> kinds,
> natural or not? Is Platonism not being taken a s alcaim about
> existinence
> here, not just a claim about truth ?
>
> BM: "A machine will be
> said an Arithmetical Platonist if the machine believes enough
> elementary
> 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
> (x,t)]
> 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 -----------------
>
> BM:
>
> 'Numbers are not physically real does not entails
> that numbers don't exist at all, unless you define "real" by "physical
> real"'.
>
> '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
> or
> PA axioms when I interview the machine, or by accepting the independent
> truth of arithmetical statements, like in UDA.'
>
> ------------ BRUNO ADMITS TO (ONTOLOGIAL) PLATONISM (2)
> -----------------
>
> 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)
> Ex(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.'
>
>
> -------------BRUNO AGNOSTIC BUT TENDING TOWARDS PLATONISM
> ----------------------------
>
> BM: Now, many people does take as axiom the unprovable assertion that
> there
> 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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Received on Fri Jan 05 2007 - 23:14:20 PST