Le 14-août-06, à 17:44, David Nyman wrote :
>
> Bruno Marchal wrote:
>
>> It just means that I (Bruno) believes that Bruno (I) is not so
>> important in the sense that if I die, a perfect number will still
>> either exist or not exist. I do interpret Penrose's mathematical
>> platonism in that way, and I agree with him (on that), like I think
>> david Deutsch and other physicists (but not all!).
>
>> This should suits "centrality of first person notion", but with comp,
>> as I try to explain, even that first person will emerge from more
>> primitive non personal notion (like numbers ...), and this
>> independently of the fact you like to recall and with which I agree
>> which is that I have only access to a personal view on numbers.
>
> I feel I must press you on this.
Please, don't hesitate.
> I think using 'exists' in this sense
> is playing with words. I'm asking that whatever you posit as
> fundamental (even when it's in the spirit of seeing where it leads -
> which of course I respect and support) you are prepared to defend as
> 'real' in as strong a sense as 'indexical 1st person' (i.e. our sole
> experiential/ existential point of departure). This IMO is crucial.
> Without this sense, I genuinely can't see what 'a perfect number will
> either exist or not exist' can possibly *mean* - i.e. do any conceptual
> or other kind of work. What is 'meaning' but a metaphorisation,
> analogising, or mapping of some observation in terms of another? e.g.
> '5' is the 'cardinality' of the fingers of my hand. And the 'arena' in
> which this 'meaning' is instantiated is always the 'indexical 1st
> person'.
>
> So, I can give 'meaning' to an 'indexical 1st-person Bruno'
> instantiating the *idea* of 'a perfect number', because its 'indexical
> existence' is part of this 'Bruno'.
I think the only way you can do that is with "David" instead of "Bruno".
It seems to me that when you accept an 'indexical 1st person Bruno" you
are accepting something far more complex than the notion of six being a
perfect number.
> But the only way I could assign an
> analogous existence to 'a perfect number' by itself, in the absence of
> this instantiation, is to assign 'indexical existence' to the number
> realm itself. This realm is then your posited 'medium of instantiation'
> (or 'fundamental reality') But isn't this '1st-person primacy'? Or
> maybe it's just 'indexical primacy'. Either way it's OK by me, but why
> not you?
Because I need, if only to communicate, a simple "ontological" reality,
and numbers (natural numbers) can be proved to be essential in the
sense that it is impossible to get them without postulating them.
Remember that I do postulate the comp hyp. I am willing to assign
consciousness to some computation (and then I show the inverse map
cannot be one-one: to any consciousness I am forced to assign an
infinity of computations). Although I agree that the first person
notions are central, they are not primary. 1-notions emerge from the
relations between numbers (where numbers are always conceived together
with their additive and multiplicative structures). The computations
are relatively embedded in that arithmetical reality. Of course, we
have access to numbers only via our first person view. But this fact
does not logically entails that numbers themselves are a necessarily
personal or an indexical construction per se.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Tue Aug 15 2006 - 08:29:53 PDT