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, passim) > 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 existence 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 gravity > 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. 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 propositions... 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 -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to email@example.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. 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