On 06 Oct 2013, at 01:29, Russell Standish wrote:
On Sat, Oct 05, 2013 at 10:34:11AM +0200, Bruno Marchal wrote:
On 05 Oct 2013, at 10:05, Russell Standish wrote:
I get that Bp is the statement that I can prove p, and that Bp & p
is
the statement that I know p (assuming Theatetus, of course), but in
both cases, I would say the pronoun "I" refers to the same
entity.
G* proves that they are the same, but G does not. It is (in God's
eye) the same entity, but the machine is unable to know, or to prove
that, and that explains the difference of the perspective. 3-I has a
name/description, but the 1-I has no name.
What is the modal logic statement corresponding to I? This is most
unclear.
B is the modal operator, which through the arithmetical
interpretation, describes the machine, in the language of the machine,
and uttered by the machine. If you want, the machine is TOTO, and says
something like TOTO has two legs. It is third person reference.
In term of modal statement: Bp means "PA proves p", as is uttered by PA.
This is the standard theory of arithmetical self-reference. See
Smoryinski book "modal logic and self-reference" or Boolos books.
English, and AFAIK French, do not make a distinction between
3-I and 1-I, so this is some new terminology that you have
introduced,
with unclear connection to real pronouns. Why do you say they are
pronouns?
Because 1-I and 3-I are variant of the pronoun "I". Natural language
use the same word, because we tend to confuse them.
Above, you stated that 1-I was Bp & p and 3-I was Bp. How do those
modal concepts relate to the English language pronoun I? Sorry to
press on this - I just want to know if there is something
interesting here.
The english language, like most language, does not distinguish Bp and
Bp & p.
It is normal, as the difference needed duplication (UDA), of Gödel's
theorem (AUDA) to be realized as being quite different. Of course
people working on the mind-body problem knows that it is different, as
Bp will usually refer to a code or body, and the Bp & p will refer to
personal feeling or consciousness.
Bp can work for "I have two legs"
Bp & p can work for "I am hungry"
You can also use "phantom limbs" to sibgle out the difference. the
fact that english language does not mlake the difference, and that the
diffrence is not entirely obvious, if that for a long time, people
having pain in a ohantom limb where considered as crazy, and where not
believed.
The duplication
experiences are the simplest tool for distinguishing them. The
Theatetus' definition, when applied to Gödel's beweisbar also
distinguish them, rather miraculously.
At this point in time, I do not see any connection between the UDA and
the AUDA. They seem to be based on entirely different sets of
propositions:
UDA:
COMP (Yes doctor, etc)
AUDA:
Theatetus and brethren, Sigma_1 restriction
I made the connection precise in "conscience & mécanisme", but I think
that it is not necessary, as UDA shows only that physics has to be
given by a statistic on computation, and AUDA use the classical theory
of knowledge, and actually gives the physics from the math of the
points of view.
If you are alluding to the distinction between communicable and
incommunicable statements, then I do understand the difference between
G and G*\G. But these don't seem to be pronouns...
G is the machine's logic of the machine's 3-I
G* is the true logic of the the machine's 3-I
Both G and G* talk about the same pronoun: the 3-I.
The start "*" does not change the reference of the pronouns, or points
of view, unlike the intensional nuance (adding "Dt" and/or "& p")
Whether the G-G* distinction can be related to the FPI of the UDA, I'm
not sure.
It works, following the axiomatics given. You need to agree only that
G does well describe the logic of 3-I (this is standard), and that the
first person is a knower, and that knowledge obeys S4 (that is
standard too). Then the theaetetus' definition applied on the 3-I
gives a knower (S4Grz), and the other intensional gives the quantum
structure that we need to proceed.
Plausibly so, I would say, but not definitively proved,
AFAICT, as they seem to be quite different theories.
In UDA I interview the reader (you).
In AUDA, I interview the machine, and its guardian angel, so to speak
(the "* logics). You need only to understand Gödel's self-reference,
and accept the traditional analytical definition of belief, knowledge,
observation and in the qualia.
Best,
Bruno
Plotinus and most serious people approaching the mind body problem
saw the difference, but the 1-I is typically eliminated by the
Aristotelian theologian (like the atheists, the fundamentalists,
etc.).
It is almost the difference between the body and the soul. The first
does admit third person descriptions, the second has none (like
Truth).
Bruno
Cheers
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