On 07 Jan 2017, at 02:42, John Clark wrote:
On Thu, Jan 5, 2017 at 3:18 AM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
>>It is insufficient to explain what a computation is, what
is needed is an explanation of how to perform a calculation. In
textbooks on arithmetic it will say something like "take this number
and place it in that set" but how do I "take" a number and how do I
"place" it in a set without matter that obeys the laws of physics?
By using the representation of finite sequence of number by a
number, for example by using Gödel's numbering
What!? that's just passing the buck! How can anything be "used" by
anything if matter that obeys the laws of physics is not
involved somewhere along the line ?
because with the standard definition of computation, they exist and
are realized in all models of Robinson Arithmetic. The definition of
computation does not involve matter, and indeed we can eventually
understand that matter is an appearance from the points of view of
immaterial machine implemented in an non material reality.
You do the same mistake than the people who say that a (physical)
simulation of a typhoon cannot make us wet. The usual answer to this
is that a simulation of "you + the typhoon" will make a "you" feeling
being wet in a relative way. It is the same in arithmetic, where a
simulation (actually infinitely many) of "you", below your
substitution level, will make you feel the appearance of matter
relatively to you.
No universal Turing machine can distinguish the following situations:
A physical device simulating Robinson arithmetic simulating a Lisp
universal program simulating that universal Turing machine,
and
Robinson arithmetic simulating a physical device simulating Robinson
arithmetic simulating a Lisp universal program simulating that
universal Turing machine.
Is this OK for everybody?
If someone believes that some primary matter is needed to get
consciousness of that matter appearance, it is up to them to explain
how that primary matter can have a role in the computation. But if you
succeed, then some primary matter has a rôle in consciousness which is
no more Turing emulable, and computationalism is false.
>> And I still don't see how you can be blithely talking about
the set that contains all true mathematical statements and no false
ones when you must know there is no way to construct such a set even
in theory.
> That set cannot be defined in arithmetic, but admit a simple
definition in set theory or in analysis.
A definition is NOT a construction!
Yes, that is exactly the point. We can define the set of arithmetical
true statements, and so we can *talk* about it, without being able to
construct it, or to generate it mechanically.
The collection of definable set of numbers is larger than the
collection of semi-computable, or recursively enumerable sets. The set
of computable or recursive sets of numbers is not computable.
The set of solutions of a universal diophantine polynomial equation is
semi-computable, but the set of numbers which are not solutions of a
that universal diophantine equation, although easily definable, so
that we can talk about, is not semi-computable (it is pi_1 instead of
sigma_1).
It's extraordinarily easy to define a Faster Than Light
Spaceship, it's right there in the very name of the thing, it's a
spaceship that can move faster than light, but that doesn't mean
anybody can construct such a thing. The very laws of
mathematics you keep talking about tell us there is NO
WAY even in theory to construct a set that has all true mathematical
statements and no false ones; forget practicalities you can't
do it even in theory, not even if you had a infinite
amount of time to work on it. So using such a set to tell
us something about reality is not permissible under the rules
of logic.
> The whole chapter of mathematical logic known as recursion
theory studies and classifies the degree of unsolvability of such set.
A classification is NOT a construction anymore than a definition
is!
Of course. Again that is what I was saying. Nobody said that all sets
of numbers are constructible, indeed the set of definable sets is
larger than the set of recursively enumerable set, itself larger than
the set of totally computable, recursive, sets. You make my point.
The Faster Than Light Spaceship is in the "vehicle" class
and in the "spaceship" class but unfortunately it is also in the
"fictional" class because nobody can construct one.
By mocking the possibility of doing theology in the scientific way,
the gnostic-atheists (believers in a Primary Physical Reality
Does "Primary Physical Reality" mean a belief that matter
is all there is?
No. It means that a Physical Reality which has to be assumed. It means
a Physical reality which would not been able to be explained without
assuming that matter.
As I said often I used "primary" in the sense: "has to be assumed", or
"the appearance of which cannot be derived from something else".
Most people agree that biological facts do not need to be assumed.
They can be derived from the laws of chemistry. That is the reason why
few scientist would assumed a primary vital principle (vitalism).
Similarly, with computationalism, the physical facts do not needed to
be assumed (and worst cannot be assumed in fact). They have to be
derived from the statistics on all computations which exist provably
when we assume Robinson Arithmetic, (or the laws of combinators, ...).
If we can explain the mind from the sigma_1 arithmetical relations,
then we have to expain the appearance of matter by the statistics on
all computations. The Universal Dovetailer Argument explains why we
have to do that, and the interview of (any) Löbian machine shows that
it works: indeed the set of computable states corresponding to
machine's yes-no type of observation inherit a precise quantum logic
derived from the logic of self-reference. It is the logic of []p &
<>t , with p sigma_1 (that is equivalent with an arithmetic formula
having the shape ExP(x, y) with P recursive.
If so then I don't believe in it. Yes nouns exist but so do
adjectives, aka information.
> and believer in the zero personal gods theory) maintain
the field in the hands of the clericals
How long do you suppose the Catholic Church would last if the
Pope said "There is no personal God. God exists but He's an
invisible fuzzy amoral mindless blob." ? I
would estimate about .9 seconds.
That is optimist.
But who care about the opinion of someone still using argument per-
authority in the field?
A personal God who might grant us immortality if we flatter
Him enough is the only type of God that 99.9% of the 1.2 Billion
Catholics are interested in. That's why they go to Mass on Sunday,
to butter Him up. If He's not personal then God is about as
useful to them as a screen door on a submarine.
Who care? We know that they are wrong (methodologically wrong at the
least) since they forbid the greek way to reason on such matter (thus:
since 523, when they banished Platonism and all "pagan non
confessional religions").
You illustrate again that you want to keep the pope and the pseudo-
religious believers happy.
You illustrate again that Gnostic Atheism is a form of catholicism.
Bruno
John K Clark
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it,
send an email to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.