On Feb 10, 1:24 pm, Bruno Marchal <[email protected]> wrote: > On 09 Feb 2011, at 16:49, 1Z wrote: > > > > > > > On Feb 8, 6:17 pm, Bruno Marchal <[email protected]> wrote: > >> On 07 Feb 2011, at 23:58, 1Z wrote: > > >>> On Feb 7, 6:29 pm, Bruno Marchal <[email protected]> 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. > >> 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 > 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. > >> 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. > >> 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? > in which case I get > hypothetical minds and hypothetical universes. I am not generated by a hypothesis: I generate hypotheses. > 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. > Not against the validity of the reasoning. > > what is at is the side of formalism > > that says maths is ontologically non-commital game playing. > > That is not formalism. That is conventionalism (in math). So you say. I have quoted a source saying they are the same >This has > been refuted. By whom? >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 > Without assuming the > natural numbers, we cannot prove they exist, not use any of them. > > Bruno > > http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
