--- Bruno Marchal <marchal.domain.name.hidden> wrote:
> But "2" is just another notation for "xx".
Why is "x" 'just another notation for "2"? or
why is "xx" not (just) a notation of 3?
(because Peano said so?)
John M
>
>
> Le 16-août-06, à 02:25, Brent Meeker a écrit :
>
> >
> > Bruno Marchal wrote:
> >>
> >> Le 14-août-06, à 19:21, Brent Meeker a écrit :
> >>
> >>
> >>> But how must the perfect number exist or not
> exist? You say you only
> >>> mean
> >>> it must be true that there is a number equal to
> the sum of its
> >>> divsors
> >>> independent of you. Do you mean independent
> only in the sense that
> >>> others
> >>> will know 6 is perfect after you're gone, or do
> you mean 6 is perfect
> >>> independent of all humans, all intelligent
> beings, the whole world?
> >>
> >>
> >>
> >> In the second sense.
> >> The perfectness of 6 is what would make any
> sufficiently clever entity
> >> from any possible (consistent) worlds, existing
> or not, to know that.
> >> In that sense it has to be a primitive truth.
> >>
> >> You can see this through a sequence of stronger
> and stronger modesty
> >> principles:
> >> 1) Bruno is not so important that 6 would loose
> its "perfection" after
> >> Bruno is gone;
> >> 2) The Belgian are not so important that 6 would
> loose its perfectness
> >> after the Belgian are gone;
> >> 3) The European are not so important that 6 would
> loose ...
> >> 4) The Humans are not so ...
> >> 5) The Mammals are not so ...
> >> 6) The creature of Earth are not so ...
> >> 7) the creature of the Solar system are not so
> ...
> >> 8) the creature of the Milky way are not so ...
> >> 9) the creature of the local universe are not so
> ...
> >> 10) the creature of the multiverse are not so ...
> >> 11) the creature of the multi multi verse are not
> so
> >> 11) the possible creatures are not so ...
> >>
> >> Yes, I think (and assume in the Arithmetical
> realist part of comp)
> >> that
> >> the fact that 6 is equal to its proper divisors
> sum, is a truth beyond
> >> time, space, whatever ...
> >> I have the feeling I would lie to myself to think
> the contrary. I am
> >> frankly more sure about that than about the
> presence of coffee in my
> >> cup right now. I cannot imagine that the numbers
> themselves could go
> >> away. They are not eternal, because they are not
> even in the category
> >> of things capable of lasting or not with respect
> to any form of
> >> observable or not reality.
> >
> > There I think I disagree. If there were no
> intelligent creatures like
> > ourselves, the infinite set of integers would not
> "exist" (I don't
> > think
> > they exist like my coffee does anyway). There
> would be "xx" but no
> > number 2
> > that was generated by a sucessor operation under
> Peano's axioms.
>
>
>
> But "2" is just another notation for "xx".
> Note that I agree that the existence of the coffee
> cup has not the same
> status than the existence of the numbers. Numbers
> exist independently
> of me. Stable "cups of coffee" appears only through
> highly involved
> histories/computations views from inside, and makes
> sense only for
> coffee amateurs or perhaps also tea amateurs having
> an open mind.
>
> Bruno
>
>
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Received on Wed Aug 16 2006 - 16:56:24 PDT