On 01 Nov 2012, at 21:33, Stephen P. King wrote:
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,
Gödel + Tarski => Arithmetical Truth is so independent of any
effective theory that no such theory can get it. mathematical logic,
and math, cannot have any meaning without arithmetical truth being
independent of theories.
but that ruins your result! It truth is theory independent then it
is impossible for us to be able to know of it.
That is mathematical solipsism. It is obviously false. Theories are
lantern on little pieces of the truth, which does not depend on the
theory, even if the lantern can bring shadows, and also hid some other
piece of truth. All this makes sense only because such truth does not
depend on us and on our theories.
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.
Gödel's proof explains this very well. The idea that truth = proof is
intuitionism, and technically, it changes nothing for arithmetic (only
for analysis).
Bruno
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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