On Wednesday, 1 June 2016, 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. >
In prediction markets, people are inclined to stake something of value only to the extent that they actually think the belief is likely to be true; whereas if they are just asked what their belief is they are more likely to say what they think ought to be true. -- Stathis Papaioannou -- 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.
