On 28 Sep 2015, at 02:48, John Clark wrote:
On Sun, Sep 27, 2015 at 12:04 PM, Bruno Marchal <[email protected]>
wrote:
> The constructible set of Gödel can be use to show that ZF
and ZFC proves the same arithmetical theorems.
That is incorrect, ZF can not prove that the Banach-Tarski
construction works, ZFC can.
The Banach-Tarski theorem is a theorem in set theory, not in arithmetic.
What Godel discovered in 1938 was that the theorems that ZF can
prove will produce no contradictions if you assume that the Axiom
of Choice is TRUE; what Paul Cohen discovered in 1963 was that the
theorems that ZF can prove will produce no contradictions if you
assume that the Axiom of Choice is FALSE, thus in 1963 we knew that
ZF has nothing to with choice and that's why it's called a axiom.
That is not related to what I say.
>> If a axiom has been verified, that is to say if it can be
derived from other axioms,
> I meant verified in a model, not prove in a theory.
In this case ZF is the model.
ZF is a theory (a finite or RE being). It cannot be a model (an
infinite mathematical structure). A theory is just not a model.
> If a proposition is verified in a model, its negation can
still be verified in another model.
Yes, a set of axioms other than ZF could derive the Axiom Of
Choice and yet another set of axioms could derive the
negation of the Axiom Of Choice.
No, the same set of axiom, ZF, can have a model verifying AC and a
model verifying ~AC, like Euclid's axiom of geometry can have a model
in which parallel lines cross, and one in which parallel lines do not
cross.
> But of course richer theory can prove more theorem
ZF is intuitively true and it is powerful, although not powerful
enough to derive the Axiom of Choice; finding another set of axioms
that are equally intuitive but even more powerful is not easy.
>>Yes perfectly true, you need physical hardware. But my
question is WHY? The only answer can be that physical hardware has
something that "arithmetical truth" does not.
> Then you artificial brain is not Turing emulable, and
computationalism is false.
The above statement does not compute. In other word the above
statement is bullshit.
?
>> We may not be certain what that something is but the fact
that computer hardware companies have non zero manufacturing costs
is proof that one has something the other does not.
> No, because that relative cost exost also in arithmetic
reelatively to the people emulated in arithmetic.
That is another statement that does not compute; emulated people
have access to arithmetic just like non emulated people, so
regardless of if they are emulated or not why do the employees at
INTEL bother to use silicon?
To share the computations that they are living. To manifest themselves
relatively to each other. Even the people in arithmetic needs hardware
to do that. But us, from outside the arithmetical reality we can see
that their hardware are given by the internal FPI limits. hardware is
not something which exist, it is only an appearance. Nobody has ever
given an existence for an ontology, which can be explaned by
computationalism and the seocnd incompleteness theorem. nobody can
prove the existence of a model satisfying their own belief, because by
the *completeness* theorem, that is akin to prove their own
consistency, which is impossible by the *incompleteness* theorem.
>>> I need to implement the universal machine in that
hardware.
>> Yes exactly you need to implement it, but
to implement it mathematics needs help, it needs physics!
> We agree on this,
Good.
but that is not a proof that hardware exist,
If " We agree on this" and if computations exist then
physical hardware exists.
yes, but as an apperance only. Physics is branch of machine's
epistemology (assuming classical computationalism).
>>> Numbers ==> computations ==> dreams ===> physical
reality ===> physical computation ===> hardware company
>> OK, but the hardware company certainly has access to
numbers so why doesn't INTEL just make calculations directly and
forget about all that unnecessary and expensive messing around with
silicon?
> Because if we want to share computations, we need to
implement them
And you agreed above that physics is needed to do that, physics
can do something that arithmetic can not.
Yes, right. Arithmetic let physics emerging from the (arithmetical)
computations, and the physics let human to implement computations in
it. And that relation is not transitive, so even in the physics
extracted from arithmetic, physics do things that arithmetic cannot
do. It is like RA which can simulate PA, but RA does not become PA in
that process.
> in the first person plural reality that we share to begin
with. but that reality is itself emerging from infinitely many
computations in arithmetic
Then I was right, matter can do something arithmetic can't, a
finite amount of matter can embody a infinite amount of
mathematics but a finite amount of mathematics can not.
>> arithmetical truth is certainly lacking something that
physics has.
> That is a theorem in machine's theology.
No, that is a machine in theology's theorem. Hey... if words no
longer have any meaning I can arrange them in any sequence I want
just like you do.
>>> like someone can emulate Einstein's brain
>> Then that emulation is Einstein.
> Better: that emulation makes it possible for Einstein to
manifest itself.
You can call it "manifest" if you like or "implement" or "emulate"
or "simulate" but the fact remains that if you want anything to
change anything in any way you're going to need physics, there is no
evidence that mathematics by itself can do a damn thing.
If we are machine, physics is a branch of machine theology, which is a
branch of computer science, which is a branch of number theory. The
term "branch" is used up to some representation, so the technical
wording would be longer, but I don't want introduce too much technical
jargon here. See the representation theorem used in my more technical
text.
>>> making a course in GR without any understanding of
GR.
>> Then Einstein didn't "understand" GR
> No, you confuse the level.
Like hell I do!
> The guy who manipulate the pages of the book can talk with
Einstein, but it does not become Einstein by emulating it!
I really REALLY hope I'm misunderstanding you and you're not
refereeing to Searle and his imbecilic Chinese room.
You were doing an error isiomorphic to Searle's one.
> ZF can prove that PA is consistent.
But can not prove that PA is complete and that's a good thing
because if it could then ZF would be inconsistent because there are
true statements that PA can not prove.
> Theology is a science.
Then either "theology" or "science" has no meaning, and I was
right, at this rate of word destruction grunts will soon be our only
means of communication.
That is the prejudice of the bigot atheists. They are responsible for
letting theology in the hand of the politics and Ayatollah. Yet, it
was born a science, and you would read proclos, or even Spinoza, you
might develop some familiarity with the idea. refusing doing theology
will just make people doing the same mistake again and again, even if
with different labels (atheist, muslims, christians, etc.).
> Then primitive matter is more fundamental than
arithmetic. QED.
> OK, but then we are not Turing emulable, and you need to
explain me what magical thing, or actual infinite, you are using for
that primitive matter to select the computations, or just abandon
comp, and revised the contract asking for them to keep intact the
actual infinities in the primitive matter of your brain (good luck
explaining them what you mean).
I can not parse that sentence, it does not compute.
I said that if primitive matter is assumed in the theory, then you
cannot be a machine, and you should say no to the doctor to remain
consistent.
>> Can RA also give an answer that INTEL stockholders would
accept to explain why shutting down all their silicon chip
fabrication plants and just ordering their employees to meditate
about numbers didn't turn out to be a wise business move?
> RA cannot do that anymore than you can make a pizza by
solving Everett Dewitt Wheeler Universal Wave Equation.
I know that RA can't do that and I know that the Wave
Equation can't do that and I also have a explanation WHY they can't
do that, but you do not.
But you would not criticize a theoy like QM fro not being able to make
a pizza, but you do that critics for RA. That is not valid. You are
confusing the theory and what is supposed to be explained by the
theory. RA explains why we feel like being able to eat a pizza, but QM
fails on this, once we assume computationalism (but of course you need
to be a bit more far in the UD reasoning to grasp this, so I refer to
my previous thread on this).
Bruno
> if comp is true [...]
I don't care if "comp" is true.
John K Clark
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