On 09 Feb 2011, at 16:49, 1Z wrote:

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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 usingonlythe 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 andJeffrey, or Mendelson, or the Dover book by Martin Davis areexcellent.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 GĂ¶del 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/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.