Thanks for this response. It'll take me a while to digest, but I'll get back with the inevitable questions :).
On Tue, Oct 08, 2013 at 08:17:17PM +0200, Bruno Marchal wrote: > > 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 > >>absurd). > >> > >>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 > [o]([o]p. > 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). > > Bruno > > > http://iridia.ulb.ac.be/~marchal/ > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to everything-list+unsubscr...@googlegroups.com. > To post to this group, send email to everything-list@googlegroups.com. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/groups/opt_out. -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics hpco...@hpcoders.com.au University of New South Wales http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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