On 31 May 2015, at 04:13, John Clark wrote:
On Sat, May 30, 2015M, Bruno Marchal <[email protected]> wrote:
> See my preceding posts. I have already commented this.
OK, lets think about your previous posts, like the one where you
said "Church's thesis is not related to physics at all" or the one
where you said "Church's thesis say only that intuitively computable
is exhaustively captured by the Lambda Calculus formalism"
Other than randomness nobody has ever seen anything in the physical
world that was not computable.
Physics uses real and complex numbers, and use analysis (which is
second order arithmetic). There are no standard defifinition of
computability for the class of analytical function and sets.
It is not related to the function "intuitively" computable, which is a
priori related to cognitive human ability.
Church thesis only equate a notion of intuitive computability, an
ability to get a result following discrete well determined elementary
digital steps, with computability in some formal system (lambda
calculus, etc.)
CT makes an intuitive epistemic notion into a purely arithmetical
notion.
It does not require the assumption that there is a physical universe.
The thesis equating function computable by physical means and function
computable by Turing machine, is an interesting thesis, but that is a
different thesis.
And Lambda Calculus (in its most powerful form) is equivalent to a
Turing Machine. And you can actually build a Turing Machine in the
real world because it is made of matter.
Not related to physics my ass!
Church thesis is not a thesis related to physics.
This does not mean that we cannot related them, but then you introduce
a different thesis.
A priori quantum computation could have been more powerful (in term of
the size of computable functions) than the function computable with
lambda calculus, and this would not have violated Church thesis,
because making parallel universe interfering on real/complex values,
is not what Turing had on mind when elaborating on the notion of
intuitively computable function.
Bruno
John K Clark
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