On 31 Aug, 15:14, Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 30 Aug 2009, at 23:21, David Nyman wrote:
> > 2009/8/28 Brent Meeker <meeke...@dslextreme.com>:
> >> 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
if it doesn't, there is no UD, and no existential conclusions follow
from your arguments.
> 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
Bivalence (AR qua truth) is indeed used by a lot of people,
but it doesn't buy you an ontologically exisiting UD.
> 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 = 0 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.
> AR = Arithmetical realism,
> PM = primary substance exists
> CT = Church's Thesis (Post's law, Turing's thesis, Church-Turing's
> thesis, etc.).
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