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


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 an implementation of a computation in what you assume, implicitly, to be a 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 Gödel 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 the question, 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.

Brent

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