On 08 Oct 2013, at 11:51, Russell Standish wrote:

On Mon, Oct 07, 2013 at 10:20:14AM +0200, Bruno Marchal wrote:

On 07 Oct 2013, at 07:36, Russell Standish wrote:

Unfortunately, the thread about AUDA and its relation to pronouncs got
mixed up with another thread, and thus got delete on my computer.

Picking up from where we left off, I'm still trying to see the
relationship between Bp, Bp&p, 1-I, 3-I and the plain ordinary I
pronoun in English.

As I said, in natural language we usually mix 1-I (Bp) and 3-I (Bp & p).
The reason is that we think we have only one body, and so, in all
practical situation it does not matter. (That's also why some people
will say I am my body, or I am my brain, like Searles, which used
that against comp, but if that was valid, the math shows that
machines can validly shows that they are not machine, which is

The difference 1-I/3-I is felt sometimes by people looking at a
video of themselves. The objective situation can describe many
people, and you feel bizarre that you are one of them. That video
lacks of course the first person perspective.

The distinction is brought when we study the mind body problem. You
might red the best text ever on this: the Theaetetus of Plato. But
the indians have written many texts on this, and some are
chef-d'oeuvre (rigorous).

OK, although I don't have time to read those ancient texts, alas :(.

OK. I can understand.
The Theaetetus is very short, though.

I understand Bp can be read as "I can prove p", and "Bp&p" as "I know p". But in the case, the difference between Bp and Bp&p is entirely in
the verb, the pronoun "I" stays the same, AFAICT.

Correct. Only the perspective change. "Bp" is "Toto proves p", said
by Toto.
"Bp & p" is "Toto proves p" and p is true, as said by Toto (or not),
and the math shows that this behaves like a knowledge opertaor (but
not arithmetical predicate).

It's the same Toto in both cases... What's the point?

The difference is crucial. Bp obeys to the logic G, which does not define a knower as we don't have Bp -> p.
At best, it defines a rational believer, or science. Not knowledge.
But differentiating W from M, is knowledge, even non communicable knowledge. You can't explain to another, that you are the one in Washington, as for the other, you are also in Moscow. Knowledge logic invite us to define the first person by the knower. He is the only one who can know that his pain is not fake, for example.

So, the ideally correct machine will
never been able to ascribe a name or a description to it.
Intuitively, for the machine, that "I" is not assertable, and indeed
such opertair refer to something without a name.

What does it mean to assert an "I"?

I was meaning to assert "I", with the idea that you refer to something understandable for another.
You can assert the 3-I, in this sense, but not the 1-I.

Now, without duplication, it looks all the time like there is a simple link between 3-I, and 1-I, and that is why we confuse them, but with the experience of duplication, at some point, the distinction is unavoidable, and crucial, and the simple link between is broken, forcing the reversal between math and physics (arithmetic and physics).

Also, switching viewpoints, one could equally say the Bp can be read
as "he can prove p",

but the point is that it is asserted by "he", in the language of "he".

But the statements can also be asserted by some other agent?

Of course. But in that case it is no more a third person *self*- reference (3-I).

"My hat is green" contains a third person self-reference.

My wife's hat is green" contains a third person self-reference.

"The hat of Napoleon is green" does not. Only third person references.

The logic of provable (third person) self-reference is given by the modal logic G (by Gödel, Löb, Solovay).
The logic of true (third person) self-reference is given by G*.

It always concerns, in our setting, what an ideally correct machine can rationally believe on itself.

The interesting thing is that G* proves Bp <-> (Bp & p), but G does not prove it. It shows that both the rational believer and the knower see the same (tiny) part of Arithmetic, yet see it from different points of view, and the logic will mathematically differ. The logic of B is G, and the logic of Bp & p is S4Grz.

and Bp&p as "he knows p", so the person order of
the pronoun is also not relevant.

Yes, you can read that in that way, but you get only the 3-view of
the 1-view.

Let us define [o]p by Bp & p

I am just pointing on the difference between B([o]p) and [o]([o]p).


B([o]p) is the statement made by the ideal rationalist believer (B) on a first person point of view ([o]). Here [o]p can be seen as an abbreviation for Bp & p.

[o]([o]p is the first person statement ([o]) on a first person point of view ([o]).

Just to illustrate John Clark's probable confusion, roughly translated in arithmetical terms, is the confusion of B and [o]. But sometimes he showed that he understood it very well, but then he shows that he was still confusing, or want to confuse,
B([o]p) and
It is what I called the 3-view on the 1-views, and the 1-view on the 1- view. He looked at the entire duplication like if it was filmed on a video, but he forgot, I think, that to survive the duplication, it has to have a memory which is only W, or only M. He managed well the "out-of-body" experience that you need somehow to get a third person view on yourself, but he forgot that to survive, you have to come back and reintegrate the body, and that can only be in *one* body!

Note that [o]p can be translated in arithmetic only for precise arithmetical statements p. There is no arithmetical predicate defining [o] in general, unlike the "B". But this is nice, as it makes the S4Grz logic closer to Brouwer and Dogen's theory of consciousness. It makes [o] closer to Plotinus "universal soul", and it makes it closer to the mystical "inner god". It put light on many Indian texts too, like what Ramani Maharshi extracts from the "koan" "Who am I?".

"Who am I" is a good question. It is a gate to quite a deep rabbit hole, when asked to any platonist universal machine capable of believing in enough induction axioms (the Löbian machines). (a machine is "platonist" when she believes in (p v ~p).



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