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.
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.). 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.
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.
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, in which case I get
hypothetical minds and hypothetical universes. 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. Not against the validity of the reasoning.
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;
I did not say that.
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). This has
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. Without assuming the
natural numbers, we cannot prove they exist, not use any of them.
Bruno
http://iridia.ulb.ac.be/~marchal/
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