On 17 Oct 2012, at 20:01, Stephen P. King wrote:
On 10/17/2012 9:33 AM, Bruno Marchal wrote:
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.
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.
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.
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.
Yes! We are able to define a recursively enumerable function to
represent the new "fact" in an a posteriori sense, but never a priori.
That happens often, and is a basis of the learning process.
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
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
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
It might be. That's enough for my point.
If other minds are not necessary then we are back the the consistent
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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