On 10/5/2013 1:05 AM, Russell Standish wrote:
On Sat, Oct 05, 2013 at 09:40:18AM +0200, Bruno Marchal wrote:
On 05 Oct 2013, at 01:16, Russell Standish wrote:
On Fri, Oct 04, 2013 at 04:51:02PM +0200, Bruno Marchal wrote:
Read AUDA, where you can find the mathematical definition for each
pronouns, based on Kleene's recursion theorem (using the Dx = "xx"
trick, which I promised to do in term of numbers, phi_i, W_i, etc.
but 99,999% will find the use of them in UDA enough clear for the
reasoning. Yet, I have made AUDA as I was told some scientists were
allergic to thought experiments, and indeed studied only AUDA (and
got no problem with it).
You meade this comment before, and I just passed over it, because it
didn't seem that relevant to the thread. I am familiar with your AUDA
>from your Lille thesis, of course, but don't recall anywhere where you
discuss formalisation of pronouns.
Perhaps you do this in another treatment of the AUDA I haven't
read? Or perhaps
you have some slightly different idea in you mind that I'm missing?
I thought I have explained this very often, but perhaps I have been
unclear, or took some understanding of Gödel 1931 for granted?
Bp (intended for its arithmetical interpretation, thus Gödel's
beweisbar) is the third person "I"; like in I have two legs, or like
in front of my code or body (scanned by the doctor). I refer often
to it by "3-I". This is standard self-reference.
Bp & p, is the knower, which plays the role of the first person in
AUDA. It is a solipsistic person unable to provide any definition or
name for who he is. It is the Plotinus universal soul, or the "inner
God" of the East. It is the non duplicable being which is unable to
"feel the split" in duplication experience. From his own perspective
he is not duplicable, not nameable, and not a machine (!).
The other hypostases are variant of those above. Normally Bp & Dt
should give a first person plural, and is as much nameable, and
definable in arithmetic than the 3-I. It is really the 3-I + a
The sensible person, in a reality is the knower + reality (Bp & p & Dt).
To sum up:
Bp = 3-I,
Bp & p = 1-I.
The Dt can be added, and just transform the provability into
probability (which needs (p -> <>p), in formal treatment).
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),
I'm suspicious of this definition of "know" anyway. There are many things (infinitely
many) that I can prove, but it would take me time and effort to do so; so I don't *know*
them. And in fact I can, in my life, only prove finitely many of them and I as I get
older I suspect I'm forgetting old ones faster than I'm proving new ones. :-)
both cases, I would say the pronoun "I" refers to the same
entity. 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?
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