On 11/1/2012 11:36 AM, Bruno Marchal wrote:
On 01 Nov 2012, at 00:35, Stephen P. King wrote:
On 10/31/2012 9:39 AM, Roger Clough wrote:
1) Yes, numbers float in a sea of universal mind (the One).
2) Here's a thought. If the universe acts like a gigantic
homunculus, with the supreme monad or One as its mind,
then could there be a solipsism to our universe such that
other multiverse versions of oiur universe could not access
(the mind of) ours ? Would this be a problem for multiverse
theories ?
Roger Clough,[email protected] 10/31/2012
Dear Roger,
I think that this idea is exactly wrong. The idea that "numbers
float in a sea of universal mind (the One)" makes the explanation an
infinite regress.
Replace the One by arithmetical truth, and the infinite regress
disappear.
Dear Bruno,
Only if arithmetic truth is theory independent, but that ruins your
result! It truth is theory independent then it is impossible for us to
be able to know of it. All knowledge is 'theory laden' - as David
Deutsch explains well.
They reappear *in* arithmetical truth, but have fixed points (some
provably, some non provably). No problem.
Maybe you might write up an explanation of how arithmetic truth is
independent of any ability to prove it. That might support your idea of
"arithmetic realism" against my claim against it.
That is OK if and only if you allow for the concept of the One to be
Kaufman and Zuckerman's Quine Atom aka Russell operator, but if not
it does not work. Why? Because numbers have to be distinguishable
from to have individual values. The totality of numbers is an
infinity and thus have the property that their proper parts cannot be
distinguished from their totality. How does the One accomplish this?
It seems to me that we have to assume that the One is conscious of
the numbers and that makes the numbers something "different" from the
One for 1) to work and this is no different from what a finite mind
does. My point here is that a mind cannot be infinite because it
would be incapable of distinguishing it's self from any of its proper
parts - making it the ultimate solipsist. Do there exist maps between
the totality of an infinite set to an improper part? If yes, what are
their necessary properties?
The One is solipsist, as the one is unique and alone. But I don't see
why it should be conscious. It might be, but I see no evidence for this.
I agree 100% with you on this.
Bruno
--
Onward!
Stephen
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