On 7/20/2011 6:43 AM, Bruno Marchal wrote:

I'm afraid this is not true. Some people even argue that computation does not exist, the physical world only approximate them, according to them. I have not yet seen a physical definition of computation## Advertising

How about "a series of causally connected states which process information"Can you give me a physical definition of the terms "series", "causal","connected, "states", "process", and "information"?And I am very demanding: I would like an axiomatic definition.In absence of such a definition, you are just describing animplementation of a computation in what you assume, implicitly, to bea natural universal system., except by natural phenomenon emulating a mathematical computation. Computer and computations have been discovered by mathematicians, and there many equivalent definition of the concept, but only if we accept Church thesis. Now if you accept the idea that the propositions like "if x divides 4 then x divides 8", or "there is an infinity of twin primes" are true or false independently of you, then arithmetical truth makes *all* the propositions about all computations true or false independently of you. The root of why it is so is GĂ¶del arithmetization of the syntax of arithmetic (or Principia). To be a piece of a computation is arithmetical, even if intensional (can depend on the *existence* of coding, but the coding is entirely arithmetical itself. In short, I can prove to you that there is computations in elementary arithmetical truth, but you have to speculate on many things to claim that there are physical computations. Locally, typing on this computer, makes me OK with the idea that the physical reality emulates computations, and that makes the white rabbit problems even more complex, but then we have not the choice, given the assumption.So I assumed I didn't understand Bruno's argument correctly.You seem to have a difficulty to see that elementary arithmetic "run" the UD, not in time and space, but in the arithmetical truth.He should. Truth is not existence.What is "existence"? If you refer to physics, then you are begging thequestion, or you are just assuming that we are not machine.Bruno

`But I think you beg the question by demanding an axiomatic definition`

`and rejecting ostensive ones. Axiomatics are already in Platonia so of`

`course that forces computation to be there.`

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