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,rclo...@verizon.net  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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