Le 09-juil.-06, à 10:07, Jesse Mazer a écrit :

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>
> Lennart Nilsson wrote:
>
>>
>> No, you have the burden of showing what possible worlds could
>> possibly mean
>> outside a real biological setting.
>>
>> Cooper shows that logical laws are dependent on which population
>> model they
>> refer to. Of course that goes for the notion of possibility also...
>
> That sounds incoherent to me...how can you even define "population
> models"
> without assuming various things about math and logic? Do you think the
> (mathematical) laws of population genetics have some sort of objective
> existence outside the human mind, but laws of math and logic
> themselves do
> not?
I agree with you.
> Lennart Nilsson wrote:
> We use mathematics as a meta-language, just like you kan describe what
> is
> said in latin by using italian. That does not make italian
> logically/evolutionary prior to latin of course.
I think you are confusing language and theory. I agree that the
language belongs to human inventions, but even and especially in math
(and numbers) we use those languages to build theories *about* truth
which should be, and mostly are, independent of the choice of the
languages.
You are defending a "conventionalist" philosophy of math. I don't think
that "conventionalism" is coherent either with (simple) mathematics or
with metamathematics.
There is nothing conventional in the distribution of the primes. There
is nothing conventional in the fact that the set of total computable
function is not recursively enumerable. Etc.
It seems to me.
Bruno
http://iridia.ulb.ac.be/~marchal/
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