Bruno Marchal wrote:
> > 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.
Of course, you're right. So, to correct myself:
I can give 'meaning' to an 'indexical 1st-person David' instantiating
the *idea* of 'a perfect number', because its 'indexical existence' is
part of this 'David'.
> 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.
Not hesitating, then, to press you again:
But don't we just 'derive' natural numbers by establishing a semantic
equivalence between '6' and the collection of faces on a cube? And
their additive and multiplicative structures likewise by analogy and
generalisation? Must it not be the case that all we can know of the
number realm is in practice wholly instantiated in indexical
1st-persons as information, and that ideas about its further extent,
while possibly justified as theory, are not, empirically, instantiated
*anywhere* to our knowledge? As far as I can see, the only alternative
to this is the belief that we have 'direct contact' with this realm, as
Penrose claims, which is surely equivalent to claiming knowledge of God
by 'direct revelation'. In this case we're merely substituting 'numbers
made us', for 'God made us'. While any such belief may be *true*, it
isn't logical or necessary truth. So what precisely is 'essential'
about the number realm, in the sense of making it the basis of
'indexical David' - whom I claim and assert to be necessarily real?
> 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.
Despite your claim that they are the basis both of the personal and
indexical? I ask you again, for them to play such a profound role, what
status, beyond that of an idealised notion, are you giving them?
Having remonstrated with you thus, might I suggest that I could
understand your meaning better thus:
"Let's proceed *as if* the number realm were the sole 'primitive', and
everything else we observe could be derived from it. If we succeed in
this venture, we will have gained much in the way of insight. No doubt,
there will still remain further questions as to the nature and true
origins of the 'reality' so conjured into existence, possibly
unanswerable. But since the question - why am I in this situation at
all in which I am able to be surprised that I am in this situation at
all? - regresses inevitably to a point beyond reason, perhaps it
doesn't put us in a worse position in this regard than any other
assumption."
Does this work for you?
David
> 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 - 14:34:42 PDT