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. The
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.
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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