On 31 Mar 2015, at 07:42, Bruce Kellett wrote:
Bruno Marchal wrote:
On 29 Mar 2015, at 10:04, Bruce Kellett wrote:
OK. If all the connections and inputs remain intact, and the
digital simulation is accurate, I don't see a problem. But I might
object if the doctor plans to replace my brain with an abstract
computation in Platonia
The doctor propose a real physical computer. Either a cheap PC or a
more expensive MAC, but it is done with matter guarantied of
stellar origin!
But what sort of program will it be running?
Anyone you agree on, discussing with your doctor, and that you can
afford.
A physical simulation, or some abstract computationalist AI model?
See my reply to Brent.
Given today's knowledge, I might say yes to a doctor making a machine
simulating ell the main metabolism of all cells in the brain, neurons,
glial cells and the bacteria.
But the reasoning does not depend on the level, only that one exist.
See my previews post.
-- because I don't know what such a thing might be,
Nor do I.
and don't believe it actually exists absent some physical
instantiation.
Do you thing prime numbers needs physics to exist? If yes, show me
what is wrong in Euclid's proof, which define and prove the
mathematical existence of the prime numbers without assuming
anything physical.
I am assuming that Euclid, himself, is physical,
OK, but that is not part of Euclid's assumption. Euclid has convinced
me that even if its parents never met, primes numbers would exist.
and that he devised the proof -- it did not drop into his lap
unsought.
I agree that he has a physical body (indeed, an infinity), and that
his mind explored a spirtitual or immaterial realm, the realm of
numbers relation. Like I don't believe that telescopes created the
galaxies, I don't believe Euclid's created the prime numbers.
In a phrase I have used before, It did not spring forth fully armed,
like Athena from Zeus's brow. Numbers were a hard-won abstraction
from everyday physical reality. They do not have any independent
existence.
In which theory? What has independent existence?
As someone has said, you do not come across a number "5" running
wild in the undergrowth.
I am not sure, when I run I might not count them, but five incarnate
in my feet and hands all the time, and even if I did not have legs,
like a snake, 5 would still be prime, independently of me thinking
about it or not.
I know that many, if not most, mathematicians report that in their
research it is as though they are exploring a landscape that exists
-- they are discovering things that are already there, they are not
constructing them. Hence most mathematicians are realists about
mathematics, which is Platonism.
I am not such a "platonist" for mathematics, except for arithmetic, or
even just its sigma_1 restricted part.
Then given we got Plato's theology for the self-introspecting machine,
I prefer to reserve Platonism to that (which is much different from
mathematical realism or arithmetical realism.
I am not set theoretical realist. The notion of sets is already
epistemology in disguise. A very useful one, but I prefer to not
assume infinite sets at the basic ontological level.
But I think we need to distinguish two senses in which something can
be said to exist. There is mathematical existence, Exist_{math}, and
physical existence, Exist_{phys}.
I agree. And those are quite different mode of existence.
These are not the same, and are not even approximately equivalent,
although it might seem that way to a mathematician.
Only one who never think outside mathematics.
Exist_{math} is the set of all implications of a set of axioms and
some rules of inference.
Not at all. That would give only a tiny sigma_1 set. Even arithmetic
is larger than that, and non unifiable in any effective theory.
The arithmetical truth or reality is inexhaustible, and beyond all
theories. machines can only scratch at the surface of the arithmetical
reality.
It is not necessary that everything that exists_{math} can be proved
as a theorem withing the system, or that the completeness and/or
consistency of this system can ever be established. But it is an
abstract system, and exist_{math} resides in Platonia, outside of
any physical existence.
OK.
Exist_{phys} is the hardware of the universe.
OK. But then comp is false, there are zombies, etc.
If you get UDA, you will see that basic existence is number existence:
what exists are just 0, s(0), s(s(0)), etc.
Plus the axioms given.
Then we can say that relations among number can 'exist" in the sense
of being true, and sometimes provable, or not, by this or that machines.
The physical existence will be a different mode of existence, the
ostensive confirmation by those multiplied on all computations.
Physical existence will be defined by a more complex self)referential
(indexical, ostensive) mode. It will look like []Ex [] P(x), in some
modal logic (justified in detail), instead of the ontic ExP(x).
It is not defined axiomatically, but ostensively.
See my ironical answer to Brent: I define "physical" by an axiomatic
of the machine's possible ostensive abilities.
You point and say "That is a rock, cat, or whatever." In more
sophisticated laboratory settings, you construct models to explain
atomic spectra, tracks in bubble chambers, and so on. The scientific
realist would claim that the theoretical entities entailed by his
most mature and well-tested scientific theories "exist_{phys}", and
form part of the furniture of the external objective physical world.
No, that's when he get wrong, with respect of the computationalist
hypothesis.
The physical has also an origin, the coherence of some machines dreams
capable of having stable long histories. They need to be multiplied
strongly.
The experienced scientist, though, always recognizes that any such
claims of ontology are, at best, provisional, and are always subject
to revision on the advent of new and better date, more general and
sophistical models, and so on.
Yes.
So there is a very clear difference between the mathematical and
physical worlds.
Yes, but science has not yet decided which is the most fundamental.
With computationalism, there is a complex video game in play, without
assuming more than combinators or elementary arithmetic. So let us
test comp.
One is axiomatic and subject to proof. Valid proofs are not open to
revision -- they may be abandoned as useless, but once proved, they
remain proved and transfer truth values from the premises to the
conclusions.
Hmm... It is more complex, but OK. Anyway, computationalism is an
hypothesis in the science of the mind. It is not pure math.
This is not the case for physics.
Nor is it for cognitive science. But computer science is a branch of
math, and the comp hypothesis, once taken seriously, reminds us that
we don't have a proof of the existence of a primitive physical universe.
That is not axiomatic, it is ultimately based on observation and
experiment. Any theories that might be constructed are always
provisional and subject to revision.
Absolutely.
So prime numbers might exist_{math}, but they do not exist_{phys}.
Sure. I have not verified, but I do think the universal machine would
say the same. Physical is a sophisticated internal view of arithmetic/
There still might be too much much white rabbits, but prime numbers
are not of the type "observable" there.
If we keep this distinction clear we will avoid a lot of unnecessary
confusion.
Not only computationalism does not do that confusion, but it shows
precisely how much different math and physics are. It shows also how
much machine's theology is different from math and physics, yet they
are all unified by representation theorem in the self-referential
processes.
I know some do equate math and physical existence. They are wrong
(assuming comp). Theological, physical, and mathematical existence are
related, but they are quite different.
Of course I have to explain more of the machine theory to make you see
it has to be like that, but even with just UDA steps 1-7, you can see
that physics is a measure on infinities of infinite computations, when
the ontic reality is infinities of finite things (a priori). The
difference is already apparent before the formalization in the
language of a UTM. But she too insists (in some sense) on that
difference.
Bruno
Bruce
Likewize, all computations can be proved to exists, and have some
weight, in a theory as weak as Robinson arithmetic.
The doctor will not propose an abstract immaterial brain to you.
But the problem, shown by the UD-Argument, is that you already have
an infinity of abstract immaterial brain in elementary arithmetic,
and you can detect the difference, and that leads to the necessity
of justifying the stability of the physical laws from a measure on
all computation, extending Everett methodology on Arithmetic.
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