On 11 Jan 2014, at 00:54, meekerdb wrote:

On 1/10/2014 1:42 AM, Bruno Marchal wrote:
Second, a reality can exist without being computed. the best and simple example is arithmetic. Only a very tiny part of it is computable (this is provable if you accept the Church Turing thesis).

But it's questionable whether it "exists".

In which sense?

Note that in the arithmetical expression: "ExAyEzAt P(x, y, z, t)", the "E" has the same meaning than in the constructive sigma_1 ExP(x). Existence in math is never necessarily computable in the usual classical math, unless we work in non classical intuitionist logic (but this recovered by the existence in the quantified S4Grz).

Keep in mind that "exists" has 8 different meaning in the eight different hypostases, and you should say precisely if you talk of psychological existence, physical existence, arithmetical existence ...

Bruno




Brent

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http://iridia.ulb.ac.be/~marchal/



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