On 02 Nov 2012, at 21:19, Stephen P. King wrote:

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

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.

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 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 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.

You are to much precise in a too much fuzzy theory.

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.

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.

Then all your references to Boolean algebra becomes nonsensical. Sometimes I can make sense of what you say, but then you add some assertion which put so much confusion that I think I was projecting sense on a sentence which was comp-meaningfully serendipitously.

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.

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.

I don't consider truth as an object. The numbers can be considered as the (only) object. truth concerns only the propositions about those objects and the derivative notions.

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

No, that is an incoherent statement as it pretends to be meaningful in the absence of any means to evaluate its meaningfulness.

That is arithmetical realism. A statement like Church thesis and comp makes no sense at all without it. I have never heard about someone not believing in arithmetical realism. It is really basic. To pretend that arithmetical realism is false already needs arithmetical realism.

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.

In math this is called (mathematical) solipsism.

This is like claiming to know exactly what is in a black box that cannot ever be opened or even located.

Not at all. (Arithmetical) Truth on the contrary is beyond the knowledge of any machine.

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).

Wrong. Gödel's proof does not prove that truth has a particular value independent of the means to know that value.

Gödel did not prove that, but everyone believe this, and Gödel's proof illustrates this very clearly.

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.

Then why did you mention the non standard model of PA? Such notion assumes you can give sense to the standard model, which makes definite the notion of Arithmetical Truth, and the application of boolean logic on the whole of arithmetical truth.



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