Bruno Marchal wrote:
> Hi Ronald,
> On 02 Jun 2009, at 16:45, ronaldheld wrote:
>> Since I program in Fortran, I am uncertain how to interpret things.
> I was alluding to old, and less old, disputes again programmers, about
> which programming language to prefer.
> It is a version of Church Thesis that all algorithm can be written in
> FORTRAN. But this does not mean that it is relevant to define an
> algorithm by a fortran program. I thought this was obvious, and I was
> using that "known" confusion to point on a similar confusion in Set
> Theory, like Langan can be said to perform.
> In Set Theorist, we still find often the error consisting in defining
> a mathematical object by a set. I have done that error in my youth.
> What you can do, indeed, is to *represent* (almost all) mathematical
> objects by sets. Langan seems to make that mistake.
> The point is just that we have to distinguish a mathematical object
> and the representation of that object in some mathematical theory.
Just so I'm sure I understand you; do you mean that, for example, the
natural numbers exist in a way that is independent of Peano's axioms and
the theorems that can be proven from them. In other words you could add
to Peano's axioms something like Goldbach's conjecture and you would
still have the same mathematical object?
> I will have the opportunity to give a precise example in the 7th
> thread later.
> In usual mathematical practice, this mistake is really not important,
> yet, in logic it is more important to take into account that
> distinction, and then in cognitive science it is *very* important.
> Crucial, I would say. The error consisting in identifying
> consciousness and brain state belongs to that family, for example. To
> confuse a person and its body belongs to that family of error too.
> All such error are of the form of the confusion between the Moon and
> the finger which point to the moon, or the confusion between a map and
> the territory.
> I have nothing against the use of FORTRAN. On the contrary I have a
> big respect for that old venerable high level programming language :)
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