On 15 Feb 2011, at 16:09, 1Z wrote:
On Feb 15, 1:16 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 14 Feb 2011, at 19:53, 1Z wrote:
CT needs arithmetical platonism/realism.
No it doesn't. It may need bivalence, which is not the same thing
Reread the definition of AR. I define AR by bivalence.
Fine. Then it isn't an ontological premiss, and the ontological
that I am an Immaterial Dreaming Machine doesn't follow.
But comp is not just CT. Comp is also "yes" doctor, which uses some
ontological commitment, notably is physical reality (albeit not
necessarily a primitive one), and bet on self-consciousness. And the
conclusion is not ontological per se. The reasoning does not show that
primary matter does not exist, only that it cannot be used to select
my consciousness evolution.
If you believe the contrary,
could you give me a form of CT which does not presuppose it?
"Every effectively calculable function is a computable function"
What is an effectively computable function?
Something a human can work out given instruction
No. That is a computable function.
What is a computable
Something a computer can do given a programme
No. You need CT to define a computer as anything computing what a
universal machine (an immaterial mathematical concept) computes.
Function computable form what to what?
I answer for you: from N to N. N is the set of natural numbers.
See my papers.
That is just what I am criticising. You need the ontological
premise that mathematical entities have real existence,
and it is a separate premise from comp. That is my
response to your writings.
The only ontology is my conciousness, and some amount of
reality (doctor, brain, etc.).
If I agree only to the existence of doctors, brains and silicon
the conclusion that I am an immaterial dreaming machine cannot
Then you have to present a refutation of UDA+MGA, without begging
No, I can just present a refutation of Platonism. The conlcusion
Platonism in your sense is not used at all in the reasoning.
The the conclusion doesn't follow.
It does not assume that physical things
"really" or primitively exists, nor does it assume that numbers
exist in any sense. Just that they exist in the mathematical
There is no generally agreed mathematical sense. If mathematical
anti-realists are right, they don't exist at all and I am
Mathematicians don't care about the nature of the existence of
Fine. Such an ontologically non-commital idea of AR cannot support
Because the conclusions of ontolgocial arguments either
follow from ontological premisses, or don't follow at all.
Yes. I have already acquiesce ten times on this. And then?
They all agree with statement like "there exist prime
Yes, they tend to agree on a set of true existence statements, and
what existence means.
Only during the pause café. It does not change their mind on the
issues in their papers.
Why would it, since they are not doing *philosophy* of maths.
So why would I?
Read a book on logic and computability.
Read a book on philosophy, on the limitations of
apriori reasoning, on the contentious nature of mathematical
You are the one opposing a paper in applied logic in the
physical science. I suggest you look at books to better see what
You are the one who is doing ontology without realising it.
On consciousness. Not on numbers,
You're saying *my* consciousness *is* a number!
Where? Consciousness, like truth, is not even definable in
I keep insisting on that all the time.
Fine. Then consc. doesn't emerge from aritmetic, and physics does't
You are quick here. I don't see argument. Just assertions.
which I use in the usual
mathematical or theoretical computer sense. The reasoning is
on God, primary universe, mind, etc. at the start.
The only ontology used in the reasoning is the ontology of my
consciousness, and some amount of consensual reality (existence of
universe, brains, doctors, ...). Of course I do not assume either
such things are primitoively material, except at step 8 for the
reductio ad absurdo. Up to step seven you can still believe in a
primitively material reality.
You cannot eliminate the existence of matter in favour of the
of numbers without assuming the existence of numbers
I assume no more than the axiom of Robinson Arithmetic.
You obviously don't adopt those axioms in the sense that
an anti realist would. Why keep arguing against anti realism?
I don't argue against anti-realism. I argue against the relevance of
anti-realism, and philosophy for showing the validity or non validity
of a reasoning.
assumes them too, albeit not explicitly.
Jeffrey, or Mendelson, or the Dover book by Martin Davis are
It is a traditional exercise to define those machine in
I have no doubt, but you don't get real minds and universes
out of hypothetical machines.
You mean mathematical machine. They are not hypothetical. Unless
believe that the number seven is hypothetical,
I do. Haven't you got that yet?
I did understand that seven is immaterial.
Not just immaterial. Non existent.
Ex(x = s(s(s(s(s(s(s(0)))))) is provable in Robinson Arithmetic.
Yes. But it means nothing ontologically.
Not for someone who *(re)defines* the ontology (the formal ontology if
you prefer) by the existence of things which can be proved in Robinson
Arithmetic. REdefine, at the end of the reasoning, not at the start,
If you accept comp, you can accept that RA proves that there exists
relative numbers emulating the computation supporting your current
experience, including all you assertion that primitive matter exists.
It makes not just arithmetic full of zombies, it contradicts the
consequence of MGA.
I can prove that if
Sherlock Holmes is on the room, and Hercules Poirot is in the
room, two detectives are on the room. But it has
nothing to do with reality.
Science illustrates that not only numbers have a relationship with
reality, but if you look at experimental physics, all you see are
people measuring numbers, and if you look at theoretical physics, all
you see are people linking numbers through number relations, or
function (linking numbers) to other functions. Primary matter is just
used to enjoyed holiday without troubling oneself too much, like "God"
is used for similar purposes.
And you tell me that your are formalist, so be it.
But I am OK with seven
being hypothetical. It changes nothing in the reasoning.
I am not running on some immaterial TM that exists only in your head
How do you know that?
Hypotheses cannot generate realities.
Comp will imply that such a primary matter cannnot interfer at all
with your consciousness, so that IF comp is correct physics has
reduced to number theory, and such a primary matter is an invisible
Physics cannot be eliminated in favour of non existent numbers.
have to exist for the conclusion to follow
Physics is not eliminated, on the contrary, physics is explained from
something non physical.
The anti realist position is not that numbers are some existing non-
thing: it is that they are not existent at all.
I disagree, but if that was true it would make anti-realism plainly
false. Numbers exist at least as human ideas.
Pehaps ideas does not exist at all too. Nor humans, nor consciousness,
nor atoms and molecules, just primary matter.
This provides solid foundations for physics.
Numbers have to exist, indeed. But you are formalist, so please take
existence by RA proves Ex P(x). No need for more than that, given
the goal is to have a formal theory explaining qualia and quanta, or
why numbers believes in qualia and quanta.
SInce numbers don't exist , they don't believe anything. Although you
might be able to prove what they would believe if they existed.
Yes. And that is enough to show that primary matter is devoid of any
explanative purpose, both for mind and matter, as matter appeared to us.
Occam does the rest.
By mathematical logicians since Gödel. Perhaps before by Dedekind.
A weak form of formalism can subsist, but conventionalism does not.
Arithmetical reality kicks back, and cannot be captured
There is not mathematical theory of reality: reality is ontology.
I agree, although I would say that reality is ontology+epistemology
+observability+sensibility (among other thing). Sensation are real.
It is a weakness of Tegmark to assume that there is a mathematical
theory of just mathematics. With comp we know that the internal
epistemology of just arithmetic is bigger than the whole of
mathematics itself. I know this is not an easy point. A good analogy
is provided by the 'Skolem paradox' phenomenon.
If what you mean is that Godel proves there are true unproveable
he doesn't, since what is unproveable in one system may be proveable
I agree. But I don't see the relevance at all.
If there were true unproveable propositions, one would be led
in to think that they are true becuase they are mind-independent
in Plato's heaven. However, Godel is quite compatible with the idea
that truth is proof in all cases; since truth can be explained
it doesn't need to be explained ontologically/metaphysically.
No digital machine, immaterial or material, can define or explain a
notion of truth encompassing the propositions referring to itself.
This can be see as a consequence of Tarski theorem on truth. But all
machines can study the notion of truth on simpler machines than
themselves. They can lift on themselves such notion of truth by
betting on their own soundness.
We know today that we have to posit numbers to reason on
them. We don't have to posit their "real" existence (whatever
means), but we have to posit their existence.
Unreal existence is not enough to support the conclusion
that I am a number
Certainly. That is why I give a detailed argument. You don't
it by criticizing its starting definition, by attributing too much
metaphysical sense to arithmetical realism.
The conclusion is metaphysical, so the premiss must be
Comp is theological, and the conclusion is theological.
Comp is theological, already in the sense that it is a belief in the
surviving of oneself through a special technological form of
The conclusion is theological, in the sense that it provides an
arithmetical interpretation of Neoplatonism. That form of neoplatonism
is testable experimentally given that it contains the unique possible
physical laws for universal machine. The math is very complex, but
thanks to Gödel, Löb and Co., the logic of the "measure one" can
easily be derived. This has been done indeed.
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