:-) Those realms can be avoided, especially if one is flexible with where one... but off-topic. PGC
On Mon, Dec 30, 2013 at 10:21 PM, Alberto G. Corona <[email protected]>wrote: > > > > 2013/12/30 Platonist Guitar Cowboy <[email protected]> > >> >> >> >> On Mon, Dec 30, 2013 at 8:02 PM, Alberto G. Corona >> <[email protected]>wrote: >> >>> To summarize, there is no possible pure knowledge, only rules to extract >>> knowledge from assumed beliefs. Thanks. But I already knew so. >>> >>> But i the realm of reality, >>> >> >> And where may one find this realm of realms? >> > > Is the realm where you pay taxes. > >> >> >>> i.e. sensible experience, Edgar is right here. >>> >> >> The only truth Edgar is unearthing for me is: >> >> You can enlist entire mailing lists as free reviewers for any book >> project you may have, without paying them one cent for doing so. Vanity and >> altruism make good bedfellows. PGC >> >> >>> >>> >>> >>> >>> 2013/12/30 Bruno Marchal <[email protected]> >>> >>>> >>>> On 30 Dec 2013, at 15:25, Alberto G. Corona wrote: >>>> >>>> >>>> >>>> >>>> 2013/12/30 Bruno Marchal <[email protected]> >>>> >>>>> >>>>> On 30 Dec 2013, at 12:39, Edgar L. Owen wrote: >>>>> >>>>> All, >>>>>> >>>>>> In response to the discussion of the possibility of a "Final Theory" >>>>>> I'm starting a new topic on the Nature of Truth since this is an >>>>>> important >>>>>> and separate issue from previous discussions. >>>>>> >>>>>> >>>>>> 1, it is impossible to directly know the external fundamental >>>>>> reality, we know external reality only filtered through the structures of >>>>>> our own minds. What we really know is only our own mental model of >>>>>> external >>>>>> reality which is provably very very different than actual external >>>>>> reality. >>>>>> >>>>>> 2, However we can easily prove that we do know external fundamental >>>>>> reality to an extent sufficient for us to function reasonably effectively >>>>>> within it. If we didn't have some actual true knowledge of external >>>>>> reality >>>>>> we could not even function within it and thus could not exist. So our >>>>>> very >>>>>> existence in actual reality demonstrates we do have some true knowledge >>>>>> of >>>>>> it. (This true knowledge consists of snippets of logical structure rather >>>>>> than the physical world we believe it to be.) >>>>>> >>>>> >>>>> That are belief, not knowledge. >>>>> >>>>> Then, what is knowledge? the one derived from mathematical deductions >>>> based on the belief on + and succ ? >>>> >>>> >>>> >>>> That one is still on the type belief (a consequence of Gödel's >>>> incompleteness). >>>> >>>> To know that 1+ 1 = 2, you need to >>>> >>>> 1) believe that 1 + 1 = 2, but you need also that >>>> >>>> 2) it is the case that 1 + 1 = 2 (in your "reality") >>>> >>>> If you put arithmetical realism on the table, anyone believing that 1 + >>>> 1 = 2, knows that 1 + 1 = 2. This needs some "reality" satisfying the fact >>>> that 1+1=2, and we do suspect its existence indeed, as the structure (N, 0, >>>> s, +, *) taught in high school. >>>> >>>> Usually "rational belief" in a large sense is axiomatized by the modal >>>> axiom K >>>> >>>> B(x -> y) ->(Bx -> By), >>>> >>>> with or without the necessitation rule (inferring Bx from x), but >>>> (almost) always with the modus ponens (inferring B from A -> B and A). >>>> >>>> Then a form of self-awareness is captured by the possible axioms Bx -> >>>> BBx. >>>> >>>> Gödel provability obeys that. That are the K4 reasoners. 4 is the name >>>> (sic) of the formula Bx -> BBx, as it was the main axiom of the fourth >>>> system by Lewis (S4). >>>> >>>> S4 is the knowledge theory. It is K4 together with the axiom Bx -> x. >>>> By definition of knowledge, if you know x, x is true. If p were not true, >>>> i.e; if it was not the case that p, you would just be believing wrongly. >>>> >>>> Gödel's provability obeys K4 (indeed K4 + B(Bx->x)->Bx), but does not >>>> obeys Bx -> x, at least from the machine 3p points' of view on itself. >>>> >>>> But the conjunction of Bx & x does obeys S4 (indeed S4 + >>>> B(B(x->Bx)->x)->x, the Grzegorczyk formula). >>>> >>>> Set theoretically, knowledge is the intersection of your beliefs and >>>> truth. >>>> >>>> It can be explained that some machine, like PA and ZF, already >>>> understand (prove, or prove from some Dt conditional, or more) that their >>>> *personal* knowledge escape all possible 3p definitions. They can't >>>> believe they are any machine. They still can bet on it, like "nature" >>>> apparently already did. >>>> >>>> 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 [email protected]. >>>> To post to this group, send email to [email protected]. >>>> Visit this group at http://groups.google.com/group/everything-list. >>>> For more options, visit https://groups.google.com/groups/opt_out. >>>> >>> >>> >>> >>> -- >>> Alberto. >>> >>> -- >>> 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 [email protected]. >>> To post to this group, send email to [email protected]. >>> Visit this group at http://groups.google.com/group/everything-list. >>> For more options, visit https://groups.google.com/groups/opt_out. >>> >> >> -- >> 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 [email protected]. >> To post to this group, send email to [email protected]. >> Visit this group at http://groups.google.com/group/everything-list. >> For more options, visit https://groups.google.com/groups/opt_out. >> > > > > -- > Alberto. > > -- > 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 [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/groups/opt_out. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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