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
http://iridia.ulb.ac.be/~marchal/
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Received on Wed Aug 16 2006 - 09:49:08 PDT