On Feb 14, 10:16 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 11 Feb 2011, at 19:10, 1Z wrote:
> > On Feb 10, 1:24 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
> >> On 09 Feb 2011, at 16:49, 1Z wrote:
> >>> On Feb 8, 6:17 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
> >>>> On 07 Feb 2011, at 23:58, 1Z wrote:
> >>>>> On Feb 7, 6:29 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
> >>>>>> Peter,
> >>>>>> Everything is fine. You should understand the reasoning by using
> >>>>>> only
> >>>>>> the formal definition of "arithmetical realism",
> >>>>> You reasoning *cannot* be both valid and ontologically
> >>>>> neutral because it has ontological conclusions.
> >>>> Wrong.
> >>> Wrong about what?
> >> You were wrong on the idea that an argument cannot be valid and
> >> ontological. It is enough that the premises have ontological clauses.
> > So which is the ontological premise? You don't say
> > that Platonism is an explicit premise. But it isn't
> > a corollary of CT either.
> CT needs arithmetical platonism/realism.

No it doesn't. It may need bivalence, which is not the same thing (me,

> 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"

> >>>> 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.

> >> 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

>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.

> >>>> 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!

>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
of numbers without assuming the existence of numbers

> >>>> 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.

> 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


> >> in which case I get
> >> hypothetical minds and hypothetical universes.
> > I am not generated by a hypothesis: I generate hypotheses.
> Confusion level. If you suppose a TOE you are supposed to be explained  
> by that TOE.

Explained by, not caused by. Things fell before Newton explained

> In that sense you are generated by an hypothesis,

I am not generated by a hypothesis, even a true one, any more
than my house is built on a map, even an accurate one.

>even if  
> your own consciousness here and now is plausibly not an hypothesis.
> >> It is not a big deal to
> >> accomodate the vocabulary.
> >>>> Recently Brent Meeker sent an excellent reference by Calude
> >>>> illustrating how PA can prove the existence of universal machine  
> >>>> (or
> >>>> number).
> >>> Oh good grief....it can only prove the *mathematical* existence. If
> >>> mathematical "existence" is not real existence, I am not an  
> >>> immaterial
> >>> machine.
> >> Comp can explain why mathematical machine believes that they are made
> >> of stuff. If you have an argument that stuff is primary, then you  
> >> have
> >> an argument against comp.
> > That doesn't follow. An immaterial machine might believe it is
> > material,
> > but so might a material machine. So arguing that matter is prmiary
> > has no impact on comp.
> 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.
have to exist for the conclusion to follow

> 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.
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
in another.

> >> 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

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