On Tue, Oct 08, 2013 at 08:17:17PM +0200, Bruno Marchal wrote: > > On 08 Oct 2013, at 11:51, Russell Standish wrote: >
> >> > >>> > >>>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. > You've hinted at fixed points being relevant here for the concept of I. So to have an 'I', you need the statement []p->p to be a theorem? > > > > > >> > >> > >>>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. In English, the first statement is that I believe I know something, and the second is that I know I know somthing. > > > [o]([o]p is the first person statement ([o]) on a first person point > of view ([o]). > So, according to you, knowledge is a first person point of view. What I still get stuck on is that we may know many things, but the only things we can know we know are essentially private things things, such as the fact that we are conscious, or what the colour red seems like to us. Are these all things you would say satisfy the proposition [o]([o]p) -- ---------------------------------------------------------------------------- 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. 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.
