On 11/2/2012 12:49 PM, Bruno Marchal wrote:

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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 10/31/2012Dear Roger,I think that this idea is exactly wrong. The idea that "numbersfloat in a sea of universal mind (the One)" makes the explanationan infinite regress.Replace the One by arithmetical truth, and the infinite regressdisappear.Dear Bruno, Only if arithmetic truth is theory independent,Gödel + Tarski => Arithmetical Truth is so independent of anyeffective theory that no such theory can get it. mathematical logic,and math, cannot have any meaning without arithmetical truth beingindependent of theories.

Dear Bruno,

`"Truth is Independence of theories" cannot mean that truth is a`

`meaningful value in the primitive ontological level. The relation 'Gödel`

`+ Tarski => Arithmetical Truth' cannot even exist as a meaningful`

`expression because there is no differentiation of expression at the`

`ontologically primitive level. The same argument that disallows for the`

`existence of a self-aware Universal mind applies. Let me step through a`

`crude sketch of the argument here.`

`A Universal`

`<http://oxforddictionaries.com/definition/english/universal> collection`

`of facts is such that there is no facts that is not included, it must`

`cover all possible worlds (ala Kripke), it must be Complete.`

`The universal set of all facts is not a self-consistent set as`

`there exists facts in one world that are inconsistent with facts in some`

`other possible world.`

`A mind is such that its facts are mutually consistent or else it is`

`insane or non-self-aware.`

`A self-aware mind must have some knowledge of facts concerning its`

`existence or else it is not self-aware.`

`A universal`

`<http://oxforddictionaries.com/definition/english/universal> mind must`

`"know all facts of all possible worlds" or else it would not be universal.`

A Universal mind is thus either insane (inconsistent) or non-self-aware.

but that ruins your result! It truth is theory independent then it isimpossible for us to be able to know of it.That is mathematical solipsism.

`I know! My point is that comp implies the singular existence of a`

`mind (universal number that is the sum of all other universal numbers)`

`that is incapable of knowing what it is as there is nothing within its`

`preview that is it not. It is a Universal Mind`

It is obviously false.

We disagree.

Theories are lantern on little pieces of the truth, which does notdepend on the theory, even if the lantern can bring shadows, and alsohid some other piece of truth.

`You insist on the concept of truth as a Platonic Object with innate`

`properties. I disagree with this concept as I see it as incoherent.`

All this makes sense only because such truth does not depend on us andon our theories.

`No, that is an incoherent statement as it pretends to be meaningful`

`in the absence of any means to evaluate its meaningfulness. In the`

`absence of a means to determine some property, it is incoherent and`

`sometimes inconsistent to claim that the property has some particular`

`value and the absence of all other possible values. This is like`

`claiming to know exactly what is in a black box that cannot ever be`

`opened or even located.`

All knowledge is 'theory laden' - as David Deutsch explains well.They reappear *in* arithmetical truth, but have fixed points (someprovably, some non provably). No problem.Maybe you might write up an explanation of how arithmetic truth isindependent of any ability to prove it.Gödel's proof explains this very well. The idea that truth = proof isintuitionism, and technically, it changes nothing for arithmetic (onlyfor analysis).

`Wrong. Gödel's proof does not prove that truth has a particular`

`value independent of the means to know that value. Gödel's proof tells`

`is that theories what (as individuals) include Arithmetic will contain`

`statements that cannot be evaluated by those theories as individuals. We`

`can build infinite towers of theories that allow evaluation of the truth`

`of statments, but int he absence of those towers, there is no such thing`

`as definiteness for truths.`

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