On 17 Oct 2012, at 20:01, Stephen P. King wrote:

On 10/17/2012 9:33 AM, Bruno Marchal wrote:
Dear Stephen,

On 16 Oct 2012, at 16:03, Stephen P. King wrote:

On 10/16/2012 9:57 AM, Bruno Marchal wrote:

Even ideal machines driven by reason have to face their irrationality when looking inward.

Dear Bruno,

I think this sentence of yours is in a deep sense wrong. We or ideal machines can never see or discover with only self-inspection or self-interviewing their own inconsistency!

That is weird.

Dear Bruno,

Yes, it is weird! But novelty, or anything that cannot be defined by an automatic process is, almost by definition weird!

If we are inconsistent, we can discover it.

    Yes, exactly

But this contradicts what you said above.

but it is such that we cannot "know it ahead of time" for to do so would be a contradiction.

This is different. You can't jump from "provability" to "proof" without warning. Those notion obeys different logic at the meta level.

An example in a sentence would be: "I am capable of knowing exactly what it will be like to be me as I will be tomorrow." The various papers that have been written on this. The one that I recommend the most is this one: http://www.metasciences.ac/set8.pdf Zuckerman and Miranker's and Lou Kaufmann's Russell operator is a nice example of the same idea. A self-referential object.

Yes. But you lost me about the point. I will make a post on this on FOAR as it is an obligatiry passage in theoretical computer science. The Dx = "xx" tool, which is an intensional diagonalization (the Dx = xx being the extensional one) is used at each line of whatever I say about machine. It is a both pity, and a chance, that eventually Solovay hides them all in the use of G and G*, and their variants.

All what is needed is a proof of "0=1" from our beliefs.

Not quite. You are thinking of the idea that I am presenting here in the old "universal truth" Platonic model of math.

? I didn't.

It does not make sense that way, thus its weirdness. Think of the idea of "plausible deniability", the ability to "proof" that something is not known by some entity or the idea of an "alibi"; a proof of being somewhere other than "at the scene of the crime". Knowledge is "local" and finite thus there will always be "truths" that can be known by some 1p but not by others.

And that proof will exist, if we are truly inconsistent, and can be found as it is a *finite* object.

Not a *finite* object per se, but an inability to reconcile the "local truths" of multiple 1p into a single Satisfiable Boolean algebra. This is the main reason I claim that QM is not reducible to a classical theory.

I defend something similar, but in a clearer context. It looks 1004 here, to me.

That happens often, and is a basis of the learning process.

Yes! We are able to define a recursively enumerable function to represent the new "fact" in an a posteriori sense, but never a priori.

It would be an automatic solution of the solipsism problem (and your arithmetic body problem!) if true!


We can only see our inconsistencies from reports of "other minds".

If we are consistent, we cannot prove that we are consistent.

Yes, not from within our own individual truths, we can falsify propositions by asking if others have their own internal proofs of their veracity. If we are consistently solipsist and finite, this is not possible.

But if we are inconsistent, we can prove that we are inconsistent (we can even prove that we are also consistent, as we can prove A and ~A for all statements A).

No! This is the domain of semiotic theory. Umberto Echo in his academic textbook A Theory of Semiotics (not his novel) pointed this out nicely by noting that if we are unable to "lie" (state something not true in a universal sense) then it is not possible to communicate. http://books.google.com/books? id=BoXO4ItsuaMC&q=lie#v=snippet&q=lie&f=false page 7.

"...semiotics is in principle the discipline studying everythign which can be used in order to lie. If something cannot be used to tell a lie, conversely it cannot be used "to tell" at all."

That confirms my feeling that G and G* gives an arithmetical semiotic. Semiotic, becomes, with comp, the semantic of Löbian programs. They can lie, can be wrong, can die, can dream, can sleep, etc. All those ability are of the type Bf, the provability of the false.

Other minds can help but are not necessary. A pilot can crash his plane even if alone in the plane.

But that pilot is not just a single mind in an otherwise empty universe!

It might be. That's enough for my point.

If other minds are not necessary then we are back the the consistent solipsist!

Yes, that is why solipsism is not refutable. Solipsism is consistent, but that does not make it true, nor interesting. The same with Bf. The 'provability of the false' (Bf) is consistent with PA, and it does also speed up the provability of PA, yet this does not mean it is true, of course.

The relation between G and G* in comp seems to indicate this idea... (unless I completely misunderstand it.)

You confuse apparently p -> q, with ~p -> ~q. Or you believe that consistent and inconsistent have symmetrical roles, which they don't.

    No, I am not considering those relations.


You need to go through Zuckerman and Miranker's paper or Lou Kaufman's paper (attached) and understand the Russell operator (aka the Quine Atom)!

*They* are considering *those* relations.



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