On 23 Mar 2015, at 20:02, meekerdb wrote:
On 3/23/2015 9:59 AM, Bruno Marchal wrote:
On 22 Mar 2015, at 22:57, meekerdb wrote:
On 3/22/2015 11:25 AM, Bruno Marchal wrote:
Who? (Jean-Paul Delahaye? Bill Taylor? Invite them to present
themselves an argument, because if it is a valid argument, you
have not yet succeeded to present it here).
Peter Jones.
I am not sure. In my conversation with him, he admitted somehow is
magical use of matter, to avoid step 8.
I don't know that Bruno is wrong, but would say, in the legal
phrase, he assumes things not in evidence.
Which one?
That every number has a unique successor for one.
I don't assume that. I assume only predicate logic +
0 ≠ s(x)
s(x) = s(y) -> x = y
x = 0 v Ey(x = s(y))
x+0 = x
x+s(y) = s(x+y)
x*0=0
x*s(y)=(x*y)+x
Exercise: prove that x≠ s(x) is not a theorem of that theory. (or ask
me if you don't find it).
I don't assume either that 0 + x = x, nor that x + y = y + x.
RA is a very humble theory. It is sigma_1 complete, but not Löbian.
Once you add the induction axioms, well, you get x ≠ s(x), 0 + x = x
and x+y = y+x as theorems.
Now in RA, you have the computations, or their finite pieces, and I
have decided to interview the Löbian machines, because I want to
consider arbitrary computations, for the FPI. So, I talk with machine
believing in more than what we can prove in the realm accepted. But
that is normal, and is a form of Skolem phenomenon.The other God is
very simple and only potentially infinite, but from from inside
realities and gods are explained to appear much bigger.
Keep also in mind, that I don't propose a new theory, I just reason in
a very old one, and find it linked to a very old conception of reality
(Plato, East, etc.).
I could also use the following theory:
x = x
(x = z) -> ((x = y) -> (z = y)) (Leibniz)
K ≠ S
((K x) y)) = x
(((S x) y) z) = ((x z)(y z))
and the rules: x = y => (x z) = (y z)
and x = y => (z x) = (z y)
That's all. In this case, I don't need to use the predicate logic.
The comp TOE can be finitist. But for the observer, which exists in
that realm, I interview the PA-like Löbian numbers, because it eases
something which is not that easy. It makes also sense when discussing
the theological realm, which, obviously, is beyond our constructive
power.
That 2+2=4 even without me or you to verify it?
Church's thesis?
"yes doctor" (that an artificial brain can work in principle at
some substitution level)?
I am OK with saying that the last one is a strong assumption, in
metaphysics or theology, but it is implicit and usually accepted in
the natural science (even sometimes for reason incompatible with
comp).
Church thesis is also a quite string hypothesis, equivalent with
the existence of universal machine, but there are strong evidence
that numbers, combinators, Fortran, Lisp, etc. are universal
systems. And the closure of the set of partial computable functions
computed for the diagonalization procedure, makes it explanatively
close in some deep sense, and that provides also a strong evidence
for it.
Again, I am not entirely sure what you mean by assuming things not
in evidence.
Well, may be you allude to your temptation of ultrafinitism in
math. You allude that the first three axiom of PA or RA are wrong?
That would be the extraordinary claim, and you give some evidence
of why there is a bigger number, without invoking a God or a
Material Universe, as that would beg the question. Most people
believe that all natural numbers x have a unique successor s(x).
Most people believe God is a big guy in the sky too.
yes, but it is not in the course of math. Did you come back from
school saying that the teachertold you something unbelievable? I don't
think so, like old schoolboy, you did grasp the idea that once we have
a raw of imaginary pebbles we can, in principle, add an imaginary
pebble near it.
you can't be serious. Despite nominalist à-la Field, you can't
formalize many physical theory without assuming x ≠ s(x).
Anyway, I don't assume it. It enter only in the mind or epistemology
of the numbers, whose existence is proved in RA.
Most believe a world must be accessible from itself.
yes. This means only most modal logic use []p -> p as axiom. Now, the
mathematics of machines kicks back. []p -> p is not a theorem of G, it
does not belong to the justifiable statement of the ideally correct
machine, (which we need to get the "correct" computationalist physics.
Most people haven't thought about the infinity of the integers.
Usually young children, get the sense, with the anniversaries,
notably, and the death question.
I am not sure what it your point. Most people are not really
interested in theology, nor in physics, and would prefer to NOT search
truth.
For this (searching truth) we need to make our theory and methodology
precise, and then you can always say: why two wings, why not three
wings, etc.
Keep in mind that my main goal is to show that we can handle the mind
body problem seriously, with the scientific method, where we never
pretend that our theory are true, only testable.
I talk to this list, because it is supposed to be open to Everett
multiplication of observers, which is a prediction of computationalism
(and testable in some precise large sense: no need to believe in any
token worlds)
I give a tool to derive all comp observable tautologies, and it is a
bit sad that up to now, we get the quantum tautologies. We need better
algorithms for X1* & Co. It amazed me it is still not yet refuted.
Bruno
Brent
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