On Feb 10, 5:51 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
> Hi Stephen,
> On 10 Feb 2011, at 16:20, Stephen Paul King wrote:
> > Hi Bruno,
> > -----Original Message----- From: Bruno Marchal
> > Sent: Thursday, February 10, 2011 8:24 AM
> > To: everything-list@googlegroups.com
> > Subject: Re: Maudlin & How many times does COMP have to be false  
> > before its
> > false?
> >> 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.
> >   Are you claiming that numbers have an existence that has no  
> > connection
> > what so ever to the possibility of being known or understood or any  
> > other
> > form of prehension or whatever might be considered as being the  
> > subject of
> > awareness in any way?
> I was just saying that number does not need to be real in a sense  
> deeper than the usual mathematical, informal or formal, sense.

There is no usual sense.

> usual sense is enough to understand that the additive and  
> multiplicative structure emulates the UD, and that universal machines  
> project their experience on its border so that they perceive (and at  
> the least pretend and belief so) a physical reality, and this  
> correctly, assuming comp.
> >   What then establishes the mere possibility of this existence?
> The existence of the natural number is forever a mystery, provably so  
> assuming comp. You cannot extract the integers from a hat without  
> integers already in the hat.

However, they don't exist, so there is no mystery. You just
have to pretend they do in order to play certain games.

> >   I have the idea that your reasoning behind your argument is a very  
> > deep
> > and subtle version of Goedel's diagonalization. Is this true?
> Only the translation (AUDA) of the reasoning in arithmetic (with the  
> classical theory of knowledge). The reasoning itself is made possible  
> by the closure of the class of partial computable functions for the  
> diagonalization, and that runs deep, indeed. But that's part of  
> arithmetical truth.
> Bruno
> http://iridia.ulb.ac.be/~marchal/

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