On 8/7/2014 12:34 PM, Bruno Marchal wrote:
Comp gives the 3p identity criterium, from the level of susbstitution you bet
on.
What does level of substitution have to do with it. You've defined the correct level
substitution as one below which consciousness is unchanged. So the the definition
already requires that we know what it means for a consciousness to be the same, i.e.
unchanged.
We don't need that definition.
I didn't say we needed a definition. I said we needed to know what it means for one's
consciousness to be the same.
We don't need it no more than we need a definition of "staying alive" when accepting an
heart operation, or accepting taking a plane, or sleeping a night. We need to bet on a
level, but no more than that.
But we need to know whether or not we've won the bet, otherwise it's meaningless - one
level is as good as another.
Then the 1p recognizance criteria is very simple. All the copies are declared the same
person as the one copied, except that now they differentiate.
And that can help to understand that we are all already the same person, having
multiplied and differentiate.
I guess it would if I were a copy of somebody.
You are plausibly already a sort of half copy of your father + half copy of your mother,
with some variance.
But that's just playing with words. I my father's dead, but I'm not half-dead.
Plausibly nature bet on comp too, as with the genetic code, which is a universal number
relatively to the turing universal carbon chemistry (in some condition of pressure,
temperature and humidity).
Then computer science shows that there is indeed a universal notion of first person,
given by the knowability (non arithmetic) operator, provided by the definition of
knowledge by Theaetetus.
Having a notion of person doesn't imply that all persons are the same person.
Correct. And the number of persons, nor the notion of personal identity is relevant to
understand the reversal.
I think it's relevant because it relies on maintaining consciousness and personal
identity, whether that requires memory or not.
But to understand the translation in arithmetic, we need to define the 3p self. This is
done with the usual second theorem of Kleene, which I explained the basic by the formal
diagonal applied to itself (D"X" = "X"X"", and variants). This leads mathematically to
the logic G and G* (by Gödel, Löb, Solovay).
Then incompleteness makes Theaetetus' definition of "knowability" (say) working.
I don't see that incompleteness makes Theaetetus definition work. I would work as well (or
poorly) in a complete theory too. It captures some aspects of "know", but I think it
misses the aspect of causal relation. It models knowledge as only provable theorems (from
some axioms). It implies that knowledge is not particular to a person. Yet it is obvious
that some people know things others don't.
With "'[]p" obeying to G, the new operator "[-]p, defined by []p & p (in the
arithmetical intepretation of "[]", that is Gödel's beweisbar predicate, and p some
arithmetical sentences (for matter, we restrict them on the sigma_1 sentences).
And we get the miracle needed, which saves both the modern (who likes []p & p), and the
ancients mystic/rationalist/platonist who like the idea, or respect the introspective
data, that the knowing is non propositional, and the knower being not a machine, and
being not definable.
Gerson thinks that by defining knowledge by true belief, we make knowledge as a sort of
particular belief, and that it makes knowledge representational. With comp, that is
partially true, in some sense, but only in G*. It makes no sense from its first person
point of view, and correctly so. Gerson confuse the informal "[]p" and p, with the
formal "[]p & p", which for "Tarski-Gödel-Epimenides" reason, get no more definable in
the language of the universal machine concerned.
Like Judson Webb shows that incompleteness protects Church's Thesis, incompleteness
protects the soul from any possible 3p definition. With comp, you can luckily bet on a
correct sublevel (too much grained) but in no way you can prove that you get the precise
correct description of yourself capable of supporting your soul.
What would it mean for a description to support my soul? That sound like mere
poetic metaphor.
If you could, you would be able to prove that []p -> []p & p, and, although G* can do
that, G you can't, and you can't.
Is the S4Grz person a universal person. Assuredly.
Then who are all these people?
Is it *the* universal person?
On your definition of person it would seem that any two universal persons would have to be
the same person.
Brent
That is not needed neither for auda, nor of course for uda, but although I doubt this
could make sense, I am not that sure. Thanks to salvia, I have one more doubt.
Bruno
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