Dear John,
On 31 May 2015, at 22:10, John Mikes wrote:
whatever you said (and I condone most of it) is WITHIN the scope of
the
--- H U M A N --- mindwork (logic, math, observation-explanations
etc) -
based on the limited access humanity so far achieved from the
infinite complexity we may call "WORLD" or "NATURE".
or "GOD" or "INFINITY" or "REALITY" or "ONE" etc.
You are interested in the limitation of humans. I am interested in the
limitations of all machines, including machines using big infinities
as Oracle. They remain limited, even just about the 3p Arithmetical
Truth. Yet the 1p of the machine does not feel *that*, it will demand
an act of faith, on the part of the machine's soul, to bet that she is
a machine at some level.
Every new addition to such information (access?) may change the
prior notions, theories, axioms, logic, computations and all our
'science'.
I think it will be time I repeat why Church's thesis change everything
here.
Let me be clear: I agree with you when you say that "every new
addition to such information (access?) may change the prior notions,
theories, axioms, logic, and all our science".
But I have withdrew "computations" from your list.
Church's thesis makes the notion of computability absolute, and it
makes the notion effective, as it provides the universal algorithm,
the code of the universal (Turing or others) machine/number.
I do not want to 'support' JohnKC or even participate in HIS
discussion.
You are very wise.
I just want to feel content in my own (limited?) agnosticism and the
belief
I have IN IT. Maybe you would call it "MY" theology.
When you say that adding information leads to change in science, what
happens is that when you add the information that there are universal
numbers, you can understand why the wise machine is necessarily
agnostic. That is why a (genuine) scientist will never commit itself
in an ontological commitment, even if in private he might assess some
preferences and hopes.
Modern mathematical logic provides the tools to study how science
varies with theories. Theoretical artificial intelligence illustrates
that there is something uncomputably more competent than an inferrer,
an inferer which can change its mind.
Scope of 'physical law'?
Looking back some millennia: it is a constantly changing view.
For a platonist, and exaggerating a little bit to be short: ---the
physical universe is an invention of the devil to distract the
universal numbers from something else.
All the best,
Bruno
On Sun, May 31, 2015 at 10:49 AM, Bruno Marchal <[email protected]>
wrote:
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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