On 30 Aug 2009, at 23:21, David Nyman wrote:
>
> 2009/8/28 Brent Meeker <meekerdb.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 - 16:14:03 PDT