On 30 Sep 2015, at 19:25, John Clark wrote:
On Wed, Sep 30, 2015 Bruno Marchal <marc...@ulb.ac.be> wrote:
>> And that my friends is exactly why examples are so superior
to definitions, it avoids the absurd "define that word" endless loop
that people always use when they're losing a debate.
> So by asking example when I give a definition, and asking a
efinition when I give example is just to win the debate, and not to
progress in understanding.
When I say "physical computation" and you demand a definition
of that and when I respond with "a computation done with physics"
and you demand a definition of that too then I believe it is
perfectly acceptable for me to either get off the silly definition
merry-go-round or to demand a definition of my own, a definition of
definition.
But this distracts us from what we should focus on.
>> as of today there is ZERO evidence that arithmetic can
calculate anything without the help of physics;
> Because
Because? It doesn't matter why there is zero evidence
that arithmetic can calculate anything without the help of
physics because whatever the reason is it doesn't change the
fact that there is ZERO evidence that arithmetic can calculate
anything without the help of physics. Excuses don't cut the
mustard in science only evidence does.
But here I have a problem. A computation can be defined by what
universal machines do. A universal machine is defined by a number u
such that phi_u(x, y) = phi_x(y). The universal dovetailing is a
example of non terminating computations, and it emulates all
computations.
All you need is to believe in some Turing complete reality, and I
hesitate since 40 years between the Diophantine polynomial of degree
4, or just one of them, or the Turing machine, or the von Neuman
Computer, or the combinators, or Robinson arithmetic. The choice of
the theory does not matter, and I illustrated the ideas in many of
them but usually with combinators, or lambda expression, or Lisp
programs.
None of those theories assume anything material.
I can do that explicitly, but it is long, and well known by the
theoreticians.
> you use the term computation in the sense of Church-Turing.
I use the term "computation" in the sense of actually finding a
particular solution to a particular problem in arithmetic; and
neither Church nor Turing were fools so they meant the same thing.
Come on! You are the guy which pretend to accept computationalisme. By
computation we mean the process made by any universal number that your
brain seems to approximate well enough to make you conscious, or
better allow your consciousness to manifest itself here and now. Such
a u exists, by computationalism, and indeed it is the number that we
sent to Moscow and Washington, awaiting using the local physical u' to
be reimplemented locally to the third person observer.
In particular we are interested in non terminating computations, as
much as on the terminating one.
Then by mentioning "solving a problem", you allude to solvation, which
is related to computation, notably through the domain w_i of the
phi_i, but at some point we must be careful in distinguishing those
two, and relating them correctly.
There is a notion of universal problem, it is the creative (in the
sense of post) set or number. u is creative if W_u is creative in the
set of Post. technically I use two different definition of
universality, both given by Martin Davis. The 1956 definition allows a
creative number to be a universal number, and the 1957 definition in
which the creative number are not universal, which can be useful to
get nice recursive equivalence relation of the extensional computable
functions.
>They do not assume anything physical to define computation.
A Turing Machine is physical,
Absolutely not. Turing made it looking like that because he wanted to
capture the essence of what a human does when he compute a function
with pencil and paper. But he gave a purely mathematical definition,
as did Church, Post, etc.
Those system can be specified in formal "set of beliefs", and that
leads to the creative set, and the Gödel-Löbian one are those who
reflects those facts. Gödel could arithmetize meta-arithmetic, because
mathematical reasoning system can reason mathematically on themselves.
not that it matters a hoot in hell what Turing or Church assumed
because the fact remains there is ZERO evidence that arithmetic can
calculate anything without the help of physics.
Zero evidence is enough when we prove a theorem!
I don't pretend it is simple to explain. It is already more or less
explictly explained in Gödel 1931 paper, and the peak of that
endeavour is perhaps in some chapter of Matiyazevic's book where he
shows how diophantine polynomial emulates Turing machine.
> I say only that 0+ x = 0, and things like that. I define
computation and proof without assuming more.
In the entire history of the world nobody has ever seen a proof or a
definition make a calculation;
Of course.
as of September 30 2015 every calculation ever observed has involved
matter that obeys the laws of physics. No exceptions, not a single
one.
But I am not talking about the computations that we (perhaps) observe.
I am talking about the computations which exist in arithmetic.
And you have clairvoyance abilities if you accept computationalism and
claim that you can see the difference between the John Clark in the
physical reality and the John Clark emulated by RA in arithmetic.
Bruno
John K Clark
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