On 09 Jan 2012, at 14:50, Craig Weinberg wrote:

On Jan 9, 6:06 am, Bruno Marchal <marc...@ulb.ac.be> wrote:

I agree with your general reply to Craig, but I disagree that
computations are physical. That's the revisionist conception of
computation, defended by Deustch, Landauer, etc. Computations have
been discovered by mathematicians when trying to expalin some
foundational difficulties in pure mathematics.

Mathematicians aren't physical? Computations are discovered through a
living nervous system, one that has been highly developed and
conditioned specifically for that purpose.

Computation and mechanism have been discovered by many people since humans are there. It is related to the understanding of the difference between "finite" and "infinite". The modern notion has been discovered independently by many mathematicians, notably Emil Post, Alan Turing, Alonzo Church, Andrzei Markov, etc. With the comp. hyp., this is easily explainable, given that we are somehow "made of" (in some not completely Aristotelian sense to be sure) computations.

We can implement
computation in the physical worlds, but that means only that the
physical reality is (at least) Turing universal. Theoretical computer
science is a branch of pure mathematics, even completely embeddable in
arithmetical truth.

And pure mathematics is a branch of anthropology.

I thought you already agreed that the arithmetical truth are independent of the existence of humans, from old posts you write.

Explain me, please, how the truth or falsity of the Riemann hypothesis, or of Goldbach conjecture depend(s) on anthropology. Please, explain me how the convergence or divergence of phi_(j) depends on the existence of humans (with phi_i = the ith computable function in an enumeration based on some universal system).



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