On 31 Aug, 15:14, Bruno Marchal <marc....domain.name.hidden> wrote:
> I would not put AR on the same par as PM(*).
>
> I know that Peter have problem with this, but AR does not commit you
> ontologically. It is just the idea that arithmetical propositions are
> either true or false.
Yes, I think I finally understand your view on this. It relies on the
denial of CTM+PM as a theory of mind, but does not thereby rule out
the conceivability of a level of zero-virtuality supervening on PM.
Rather it shows that, for any putative computational realisation of
mind, any such attribution is both absolutely unknowable and causally
irrelevant. This clearly unmasks any such notion of PM as a
superfluous assumption with respect to CTM, and Occam consequently
dictates that we discard it as any part of the theory. IOW it is the
prior assumption of CTM itself that drives the chain of inference, as
you have always claimed. And I further agree that *on the basis of
CTM* it then follows that no meaning of 'exist' should be taken
literally. It is very much to your credit that you have laid bare
these hidden implications of CTM, as I think they are central to most
of the myriad confusions that surround it. If people have a complaint
about the implications, they cannot now dodge the fact that this
disquiet is unavoidably entailed by CTM itself.
David
> On 30 Aug 2009, at 23:21, David Nyman wrote:
>
>
>
> > 2009/8/28 Brent Meeker <meeke....domain.name.hidden>:
>
> >> Ok, so you want to solve the "hard problem" right at the beginning by
> >> taking conscious thoughts as the basic elements of your ontology.
>
> > No I don't - that's why I said I'd rather not use the word
> > consciousness. What I have in mind at this point in the argument is a
> > primitive, not an elaborated, notion - like PM vis-a-vis materialism,
> > or AR vis-a-vis comp.
>
> I would not put AR on the same par as PM(*).
>
> I know that Peter have problem with this, but AR does not commit you
> ontologically. It is just the idea that arithmetical propositions are
> either true or false. It is an initial segment of all theories capable
> to prove the existence of universal machine (be it quantum mechanics,
> Newtonian Physics, real numbers + trigonometry, etc.). Only
> philosopher of mathematics can doubt it, and even here, few doubt it.
> A slightly variant of AR works for intuitionism. I really think you
> have to be an ultrafinitist to believe that AR is false. AR is used
> implicitly by formalist, and formalist can use formal version of AR,
> except the day they do say "consciopusly" (aware of the risk) "yes" to
> a digitalist doctor
>
> PM is a metaphysical commitment that a primary substance exists. It is
> already part of a theology, in the large sense of the word. AR is used
> by everyone, PM is argued by theologians and philosophers. PM does not
> really appears in the theories by physicists. AR is explicitly used by
> them. AR is used when you say that sin2pix = 00 has an infinity of
> solutions, for example. You can doubt it, of course, but then you
> have to accept ultra-finitism, or something like that.
>
> CT is a principle already far stronger and far more counter-intuitive
> than AR. yet I have never met someone doubting CT, and as I will show
> in detail soon enough, CT just makes no sense at all without AR.
>
> Bruno
>
> (*)
> AR = Arithmetical realism,
> PM = primary substance exists
> CT = Church's Thesis (Post's law, Turing's thesis, Church-Turing's
> thesis, etc.).
>
> http://iridia.ulb.ac.be/~marchal/
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Received on Mon Aug 31 2009 - 17:21:58 PDT