On Feb 7, 6:29 pm, Bruno Marchal <marc...@ulb.ac.be> wrote: > Peter, > > Everything is fine. You should understand the reasoning by using only > the formal definition of "arithmetical realism",

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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. > > Bruno > > 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))))))) ? > > >>>>http://en.wikipedia.org/wiki/Philosophy_of_mathematics > > >>>>> 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 > > >http://iridia.ulb.ac.be/~marchal/ > > > -- > > You received this message because you are subscribed to the Google > > Groups "Everything List" group. > > To post to this group, send email to everything-list@googlegroups.com. > > To unsubscribe from this group, send email to > > everything-list+unsubscr...@googlegroups.com > > . > > For more options, visit this group > > athttp://groups.google.com/group/everything-list?hl=en > > . > > http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. 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