Hi Bruno On Fri, Sep 14, 2012 at 1:20 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:
> Hi Brian, > > > > On 13 Sep 2012, at 22:04, Brian Tenneson wrote: > > Bruno, >> >> You use B as a predicate symbol for "belief" I think. >> > > I use for the modal unspecified box, in some context (in place of the more > common ""). > Then I use it mainly for the box corresponding to Gödel's beweisbar > (provability) arithmetical predicate (definable with the symbols E, A, &, > ->, ~, s, 0 and parentheses. > Thanks to the fact that Bp -> p is not a theorem, it can plays the role of > believability for the ideally correct machines. > > > How come Bp->p is not a theorem? > > > > > What are some properties of B and is there a predicate for knowing/being >> aware of that might lead to a definition for self-awareness? >> > > Yes, B and its variants: > B_1 p == Bp & p > B_2 p = Bp & Dt > B_3 p = Bp & Dt & t, > and others. > > D? B_1? B_2? B_3? > > > > >> btw, what is a machine and what types of machines are there? >> > > With comp we bet that we are, at some level, digital machine. The theory > is one studied by logicians (Post, Church, Turing, etc.). > > I am also curious as to the definition of a digital machine. > > > > >> Is there a generic description for a structure (in the math logic sense) >> to have a belief or to be aware; something like >> A |= "I am the structure A" >> ? >> > > Yes, by using the Dx = xx method, you can define a machine having its > integral 3p plan available. But the 1p-self, given by Bp & p, does not > admit any name. It is the difference between "I have two legs" and "I have > a pain in a leg, even if a phantom one". G* proves them equivalent (for > correct machines), but G cannot identify them, and they obeys different > logic (G and S4Grz). > > DX = xx? > > > > >> Finally, on a different note, if there is a structure for which all >> structures can be 1-1 injected into it, does that in itself imply a sort of >> ultimate structure perhaps what Max Tegmark views as the level IV >> multiverse? >> > > A 1-1 map is too cheap for that, and the set structure is a too much > structural flattening. Comp used the simulation, notion, at a non > specifiable level substitution. > > This structure I have in mind having the property that all structures can be injected into it has more structure than a set structure. See, I have revised my thoughts and put them into a fairly short document. You helped me a year or two ago to show me some flaws with my thoughts in a document. I could send it to you. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to firstname.lastname@example.org. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.