On Wed, Jun 1, 2016 at 8:58 PM, Brent Meeker <[email protected]> wrote:
> > > On 6/1/2016 2:01 AM, Telmo Menezes wrote: > > > > On Wed, Jun 1, 2016 at 9:53 AM, Pierz <[email protected]> wrote: > >> >> >> On Wednesday, June 1, 2016 at 4:44:33 AM UTC+10, Brent wrote: >>> >>> >>> >>> On 5/31/2016 10:08 AM, Bruno Marchal wrote: >>> > >>> > On 31 May 2016, at 00:36, Pierz wrote: >>> > >>> >> Clark v Marchal! I love this match-up. I predict it will go 47000 >>> >> rounds without a knockout! >>> > >>> > >>> > I am interested in the problem why some machine get stuck at step 3 of >>> > the UDA :) >>> > >>> > The translation into arithmetic of the reasoning does provide light on >>> > this, if not an answer to that question. An ideally arithmetically >>> > correct machines cannot believe in computationalism, she will not >>> > identify her soul with her body or relative Gödel number, that is she >>> > will not identify herself with any third person description of what >>> > she really feel to be herself. The soul of the machine is not a >>> > machine from the soul's machine point of view. >>> > >>> > That is well sum up by simple theorem in G and G*. The machine's body >>> > can be identified with its provability predicate []p. When PA talk >>> > about her provability abilities, she derives them from a specific >>> > thrid person description of its beliefs and how to generate them. >>> > Now, accepting the classical analysis of knowledge, and defining it in >>> > the Theaetetus' manner, by []p & p (p sigma_1 arithmetical >>> > propositions) and "[]" representing Gödel's arithmetical beweisbar), >>> > we get that >>> > >>> > 1) G* proves []p <-> ([]p & p) >>> > >>> > 2) G can't prove in general that []p <-> ([]p & p) >>> > >>> > and indeed, the logic of []p & p will be quite different from the >>> > logic of []p, due to incompleteness. >>> > >>> > I define the (proper) theology of the machine by G* minus G. The local >>> > identity of the soul ([]p & p) and the body-brain-program ([]p) is >>> > true, but not provable, not even taken as an axiom. It is necessarily >>> > a non justifiable belief, an hope or a fear. >>> > >>> > The other very nice thing, also, is that "[]p & p" does indeed not >>> > admit any third person description available in its/her/his language. >>> > Then it also defines an arithmetical interpretation of intuitionistic >>> > logic (with the solipsist identity of truth and the personal mental >>> > constructions), and when p is restricted in the sigma_1 (complete) >>> > domain (= UD*), we get a quantum logic, which was expected for the UDA >>> > reson, but still surprising as it marries antisymmetry (related to the >>> > logic of []p & p (S4Grz)) with symmetry (related to []p & p when p is >>> > sigma_1). >>> > >>> > Judson Webb said that Gödel's theorem was a lucky chance for the >>> > Mechanist theory of mind, but here we see that (Everett) QM, even >>> > formally, is even a bigger chance for Mechanism. >>> > >>> > Now this remark, that machines cannot believe in Mechanism (and its >>> > consequences), might apply better to someone like Craig Weinberg, (if >>> > you remember the conversations here) and less to John Clark, who >>> > "accept (and even practice) Mechanism, but still get stuck for unknown >>> > reason (at step 3). We need another theory, which I think might >>> > involve notion of susceptibility and more emotional human stuff. Now, >>> > if you can make (logical) sense of his refutation of step 3, you would >>> > help! >>> > >>> > Note: I have introduced a new term: the surrational. It is, like G* >>> > minus G, the part of the truth *on* a machine that a sound machine >>> > cannot believe/prove/justify. >>> >>> In that formulation you take believe, prove, and justify to have the >>> same extension. But that's not a good model of anyone I know. In >>> general believe many things they cannot prove from some set of axioms - >>> and even if they could, their "proof" is contingent on the axioms. >>> >>> Brent >>> >> I tend to agree. Indeed the notion of "belief" is a very complex one, >> psychologically. For example, a person might believe (or more properly, >> believe they believe) in a doomsday prophecy, and yet as the moment arrives >> uneventfully, find themselves quite unsurprised. In other words, they were >> wrong about what they thought they believed. Or a person might believe >> their husband to be a good person, but upon his being charged with murder, >> discover that they "knew all along, deep down". And so on. Sometimes I >> think what we "believe" is merely what we assert to ourselves to be true, >> and this assertion is in real life often not based upon rational evidence, >> let alone anything as rigorous or abstract as an "axiom". I'm not sure >> where that leaves a theory of humans as arithmetical machines, but the >> level at which human beliefs about the self and the world are formed and >> justified seems a long long way from the level at which the "beliefs" of >> logicians are formed. >> > > It seems to me that "belief" might have at least two distinct meanings. > You are alluding to belief in the sense of ideological belief or political > belief, for example. Bruno appears to be alluding to the sense of belief as > in "I believe there is a computer in front of me right now". The latter is > a perceptual "short-circuit" if you want. I have no doubt or choice over > the matter. To make it more clear: > > > How is the perceptual "short circuit" the same as proof from axioms? > I don't know. My point was that all the psychological complexities associated with some meanings of "belief" are not really necessary here. We are talking about things like "I believe the walls of my office are white". My comment was more about Pierz's remark than yours. Telmo. > > Brent > > > > I might have some doubt that the computer exists under some sophisticated > intellectual construct, but if my life is threatened I am going to trust my > senses 100%. I will not doubt for a second that the guy coming in my > direction with a baseball bat exists. I think this is belief in Bruno's > sense of recovering physics from machine dreams. > > I agree with you that people fool themselves about what they really > believe, but this applies to the first sense of the word I alluded to. > Sometimes you can apply the "skin in the game" test. Someone believes the > world is going to end in 3 months? Why don't they max out their credit card? > > >> >> >>> >>> > It helps to see that between the irrational (false) and the rational >>> > (justifiable), there are lands of true but non provable, and of false >>> > but non refutable, associated to each machie is merely nes (defined by >>> its >>> > believability predicate (its own beweisbar). The proper theology of a >>> > machine is the study of (its) surrational land. I limit myself to >>> > correct or sound machine, so that the surrational just extends the >>> > rational (justifiable), like G is included in G*. >>> > >>> > I recall that "forever undecided" by Raymond Smullyan is an excellent >>> > introduction at the logic G. The relation with mathematical logic and >>> > computability theory comes from the theorems of Gödel, Löb, >>> > Grzegorczyk, Solovay, Boolos, Goldblatt, Visser. I think all the >>> > pieces of the computationalist mind-body puzzle fits, including about >>> > what we can't explain and what we cannot talk about. >>> > >>> > Bruno >>> > >>> > >>> >> >>> >> -- >>> >> 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 <https://groups.google.com/group/everything-list> >>> https://groups.google.com/group/everything-list. >>> >> For more options, visit <https://groups.google.com/d/optout> >>> https://groups.google.com/d/optout. >>> > >>> > >>> > >>> > >>> > >>> >>> -- >> 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]> >> [email protected]. >> To post to this group, send email to <[email protected]> >> [email protected]. >> Visit this group at https://groups.google.com/group/everything-list. >> For more options, visit https://groups.google.com/d/optout. >> > > -- > 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 https://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > > > -- > 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 https://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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