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 (me,
> > passim)
> 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.
>> 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
> What is a computable
Something a computer can do given a programme
> Function computable form what to what?
> >>>>>> 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 consensual
> >>>> reality (doctor, brain, etc.).
> >>> If I agree only to the existence of doctors, brains and silicon
> >>> computers,
> >>> the conclusion that I am an immaterial dreaming machine cannot
> >>> follow
> >> Then you have to present a refutation of UDA+MGA, without begging the
> >> question.
> > No, I can just present a refutation of Platonism. The conlcusion
> > does't follo
> > without it.
> 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
> >>>> really
> >>>> exist in any sense. Just that they exist in the mathematical sense.
> >>> There is no generally agreed mathematical sense. If mathematical
> >>> anti-realists are right, they don't exist at all and I am therefore
> >>> not one.
> >> Mathematicians don't care about the nature of the existence of
> >> natural
> >> numbers.
> > Fine. Such an ontologically non-commital idea of AR cannot support
> > your conclusion
Because the conclusions of ontolgocial arguments either
follow from ontological premisses, or don't follow at all.
> >> They all agree with statement like "there exist prime
> >> number", etc.
> > Yes, they tend to agree on a set of true existence statements, and to
> > disagree on
> > 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.
> >>>>>> Read a book on logic and computability.
> >>>>> Read a book on philosophy, on the limitations of
> >>>>> apriori reasoning, on the contentious nature of mathematical
> >>>>> ontology.
> >>>> You are the one opposing a paper in applied logic in the cognitive
> >>>> and
> >>>> physical science. I suggest you look at books to better see what
> >>>> i am
> >>>> taking about.
> >>> 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 arithmetic.
> I keep insisting on that all the time.
Fine. Then consc. doesn't emerge from aritmetic, and physics does't
> >> which I use in the usual
> >> mathematical or theoretical computer sense. The reasoning is agonstic
> >> 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
> >> that
> >> 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
> > existence
> > 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?
> assumes them too, albeit not explicitly.
> >>>>>> Boolos and
> >>>>>> Jeffrey, or Mendelson, or the Dover book by Martin Davis are
> >>>>>> excellent.
> >>>>>> It is a traditional exercise to define those machine in
> >>>>>> arithmetic.
> >>>>> 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
> >>>> you
> >>>> 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. 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.
> 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 to be
> >> reduced to number theory, and such a primary matter is an invisible
> >> epiphenomena.
> > Physics cannot be eliminated in favour of non existent numbers.
> > 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.
> 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 that
> 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.
> >> Occam does the rest.
> >>>> This has
> >>>> been refuted.
> >>> By whom?
> >> 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 completely by
> >> *any* theory.
> > 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
> > propositions...
> > he doesn't, since what is unproveable in one system may be proveable
> > in another.
> 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.
> >>>> We know today that we have to posit numbers to reason on
> >>>> them. We don't have to posit their "real" existence (whatever that
> >>>> 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 address
> >> 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.
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