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? .It is enough it has ontological premise. > > > > > .which is that a > >> machine is arithmetical realist if she believes in the axiom of > >> elementary arithmetic *with* (the realist part) the principle of the > >> third excluded middle (allowing non constructive reasoning, as > >> usual). > > > What machine? Show me one! > > 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. >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. > 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. > 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. > I will search it. > And I encourage you to interpret all this, including my thesis in > purely formal term. AUDA shows, notably, that this is possible. > > You might also read the book by Judson Webb, which has been recently > republished and which shows the positive impact of Gödel on both > formalism and mechanism. Actually Webb argues that formalism and > mechanism are basically the same philosophy, or the same type of > philosophy. As ever, it is not the mechanisability aspect of formalism which is at issue; what is at is the side of formalism that says maths is ontologically non-commital game playing. > And I do follow him on that. A machine is before all a > form. A digital machine is a form which can be described locally > (relatively to a universal number) by a number. Webb call the kind of > AR used here: finitism. > > > > >> And with AUDA you get a conversation with a machine, and a quasi > >> correct explanation why she is not a machine? How could a formalist > >> not love that .... > > >> Gödel is not just the discovery of the provability limitations of > >> formalisms and machines, > > > Godel has no impact on "game playing" formalism. > > ? > Because GPF is about ontology, not mechanisability. > (Well the more usual critic in our context is that Gödel has *only* > impact on "game playing" formalism). > > I was just saying that Gödel's second incompleteness theorem is a > theorem in Peano arithmetic, about Peano arithmetic. Or by Peano > Arithmetic, about Peano arithmetic. > > 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.
