On Feb 7, 6:29 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
> Everything is fine. You should understand the reasoning by using only
> the formal definition of "arithmetical realism",
You reasoning *cannot* be both valid and ontologically
neutral because it has ontological conclusions.
.which is that a
> machine is arithmetical realist if she believes in the axiom of
> elementary arithmetic *with* (the realist part) the principle of the
> third excluded middle (allowing non constructive reasoning, as usual).
What machine? Show me one!
> And with AUDA you get a conversation with a machine, and a quasi
> correct explanation why she is not a machine? How could a formalist
> not love that ....
> Gödel is not just the discovery of the provability limitations of
> formalisms and machines,
Godel has no impact on "game playing" formalism.
> it is also the discovery by the formalisms
> and by the machines of their own limitations. And of the rich geometry
> and topology of those limitations.
> On 07 Feb 2011, at 17:06, Bruno Marchal wrote:
> > On 06 Feb 2011, at 22:20, 1Z wrote:
> >>>> On Feb 5, 7:43 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
> >>>>> Computationalism needs Church thesis which needs AR (Arithmetical
> >>>>> Realism).
> >>>> Nope, just AT (arithmetic truth).
> >>> Actually, comp needs only, for the ontology, the quite tiny complete
> >>> Sigma_1 truth.
> >> As I have stated many times, it doesn;t matter in the least
> >> how many or few immaterial objects you attribute existence to.
> >> It's like saying pixies exist, but only a few
> > What?
> > It is always better to make a theory precise.
> >>> Please don't put metaphysics where there is only
> >>> religion
> >> Believing in what is not proven is religion. I can
> >> argue for anti realism.
> > I argue in favor of nothing. That's philosophy. You force me to be
> > explicit on this; I do science. I am a logician, and I show that
> > rational agent believing in comp believe that ... etc. I don't know
> > about the truth.
> >>> (saying yes to the admittedly betting doctor).
> >> Saying yes to the doctor will not guarantee your
> >> immaterial existence if there is no immaterial existence.
> > But there is immaterial existence. I recall you that I say in the
> > ontological context that something exist if Ex (bla-bla-bla x) is
> > true in the standard model of arithmetic. I use the standard meaning
> > of existence of numbers, etc.
> >> AR/Platonism is a separate assumption to yes Dr.
> > I have drop out AR. You need AR (in which everyone believes except
> > the ultrafinitists and the bad faith philosophers) to understand the
> > term "digital" used by the doctor.
> >> <And with comp,
> >>> it is math, indeed, even (full, above Sigma_1 arithmetic.
> >>> Arithmetical realism is what you need to apply the excluded middle
> >>> in
> >>> computer science and in arithmetic.
> >> The excluded middle is a much of a formal rule as
> >> anthing else. Formalists can apply it, so it is compatible
> >> with anti realism.
> > The theory admits a formal study. You don't act like a formalist at
> > all. The term "Formalism" makes not an atom of sense without
> > arithmetical realism. In philosophy arithmetical realism is the
> > weaker of all possible realism, except again for the ultrafinitists.
> > If you are formalist and anti realist on the numbers you are in
> > contradiction, or, once and for all, just replace numbers by the
> > following formal expression 0, s(0), s(s(0)), etc. + the axioms I
> > just sent to Andrew, etc.
> > AUDA provides more than a formalism, it provides an arithmetisation,
> > which is a *weakening* of formalism, made possible by AR. Gödel
> > already exploited this.
> >>> To understand the fundamental
> >>> consequences of Church thesis you need to accept that some program
> >>> computes function despite we have no means to know if it is total or
> >>> partial, or that a program will stop or not.
> >> And I can accept that by positing LEM as a formal rule. I don;t
> >> have to posit an immaterial Plato's heaven
> > I make clear that the immaterial Plato Heaven for the machine is
> > just the truth of arithmletical proposition. It is an non
> > arithmetical notion, union of the entire Kleene-Mostowki
> > arithmetical hierarchy, and well know non controversal mathematical
> > object in the field of logic.
> > I use the "immaterial Plato heaven" terminology, either as poetical
> > shortcut, or as a point in the arithmetical representation of some
> > term in Plotinus theory.
> > I explained this already to you, but you keep adding metaphysical
> > stuff which don't exist.
> >>> Only ultrafinitist denies AR.
> >> Wrong. Anti realists deny it. I have pointed this out many
> >> times. You think the only debate is about the minimal
> >> set of mathematical objects, and that is not the only debate. Anti
> >> realists
> >> can accept a maximal set of objects, with the proviso that their
> >> existence is fictive and not real existence
> > I am agnostic on all notion of existence. All, except my own
> > consciousness here and now. I suggest a theory, and derive
> > consequences in that theory.
> >>> AR+, the idea that we don't need more than AR, in this setting, is a
> >>> consequence of the math. From 'outside' the tiny effective universal
> >>> sigma_1 complete set is enough. from inside, even mathematicalism is
> >>> not enough (it is more 'theologicalism').
> >>>> The ontological status of
> >>>> mathematical
> >>>> objects is a area of contention in metaphysics, and not
> >>>> straightforwardly
> >>>> proven by mathematics itself.
> >>> With comp, you don't need more than the part on which almost
> >>> everybody
> >>> agrees: arithmetical realism.
> >> Anti realists do not agee on the real existence of any
> >> part. There are no pixies at all, not just a few pixies.
> > If you believe in prime numbers, and if you are patient and good
> > willing, I can explain that there are all universal numbers, and why
> > assuming comp that's enough and that's necessary to solve the white
> > rabbit problem. And that postulating physical laws miss the
> > epistemological existence of the qualia.
> > The basic ontology is not important. If you take less than a
> > universal system (like numbers, combinators, ...) you don't have
> > enough for comp, if you take more you miss the qualia.
> > No problem with a formalist interpretation of all this. Actually
> > S4Grz formalize at the meta-level what the machine can uderstand to
> > be non formalisable (like consciousness).
> >>> The engineers, the scientists, most
> >>> philosophers.
> >>> Except for Thorgny Tholerus I never met an ultrafinitist. You don't
> >>> have to decide if numbers are idea of the mind or sort of angel in
> >>> Plato Heaven. With comp the very idea of number will itself be a
> >>> number, a sort of second order number, relative to universes
> >>> (universal numbers).
> >> ULtrafinitism has nothing to do with it. For formalists
> >> no number exists. They have no prejudice about any kind,
> > If comp is false because, according to you 7 does not exist, then it
> > is your problem.
> > I told you that I am working in a theory, which is neutral on those
> > question. Formalist have normally less problem with a tiny sigma_1
> > arithmetic than with the real or complex numbers.
> > I just don't believe you don't believe in seven. You confuse
> > 'immaterial' with 'inexistent'.
> > If you don't believe in seven, do you still believe in the formal
> > expression s(s(s(s(s(s(s(0))))))) ?
> >>>>> And you cannot refute an argument by anticipating a refutation.
> >>>>> So if
> >>>>> you have a refutation of MGA you should present it.
> >>>> See Colin Klein;s refutation of Maudlin's Olympia.
> >>> We have already discussed this and Colin Klein does not touch the
> >>> movie graph argument.
> >> Then you had better stop saying the MGA and Olympia are equivalent
> > The movie graph *argument*, is not attacked by Klein. Klein attacks
> > the Olympia *argument*.
> > When I say that Olympia and MGA are equivalent, I am talking about
> > the conclusion, not about the arguments leading to the conclusion.
> > Bruno
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