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.
> >> 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
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
> >> 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
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
> been refuted.
>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.
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