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. 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