> On 13 Dec 2018, at 04:30, Brent Meeker <[email protected]> wrote: > > > > On 12/12/2018 9:18 AM, Bruno Marchal wrote: >> >>> On 12 Dec 2018, at 12:54, Philip Thrift <[email protected] >>> <mailto:[email protected]>> wrote: >>> >>> >>> >>> On Wednesday, December 12, 2018 at 5:09:00 AM UTC-6, Bruno Marchal wrote: >>> >>>> On 11 Dec 2018, at 12:58, Philip Thrift <[email protected] <javascript:>> >>>> wrote: >>>> >>>> >>>> >>>> On Tuesday, December 11, 2018 at 5:41:49 AM UTC-6, Bruno Marchal wrote: >>>> >>>>> On 11 Dec 2018, at 12:11, Philip Thrift <[email protected] <>> wrote: >>>>> >>>>> >>>>> Nothing is "confirmed" and "made precise". >>>>> >>>>> (Derrida, Rorty, …) >>>> >>>> That would make Derrida and Rorty into obscurantism. Confirmation does not >>>> make an idea true, but it is better than nothing, once we postulate some >>>> reality. >>>> >>>> Some “philosophies” prevents the scientific attitude, like some >>>> “religions” do, although only when they are used for that purpose. Some >>>> philosophies vindicate their lack of rigour into a principle. That leads >>>> to relativisme, and obscurantism. It looks nice as anyone can defend any >>>> idea, but eventually it hurts in front of the truth. >>>> >>>> Bruno >>>> >>>> >>>> >>>> Have you read some of the Opinions* or watched some of the (youtube) >>>> lectures of Rutgers math professor Doron Zeilberger? >>>> >>>> I've been following him like forever. >>>> >>>> * e.g. >>>> Mathematics is so useful because physical scientists and engineers have >>>> the good sense to largely ignore the "religious" fanaticism of >>>> professional mathematicians, and their insistence on so-called rigor, that >>>> in many cases is misplaced and hypocritical, since it is based on "axioms" >>>> that are completely fictional, i.e. those that involve the so-called >>>> infinity. >>> Mechanism proves this. Arithmetic, without infinity axiom, even without the >>> induction axiom, is the “ontological things”. Induction axioms, infinity, >>> physics, humans, etc. belongs to the phenomenology. The phenomenology is >>> not less real, but its is not primary, it is second order, and that fiction >>> is needed to survive, even if fictionally. >>> >>> Bruno >>> >>> >>> >>> To experiential realists, phenomenal consciousness is a real thing. >> >> That is what the soul of the machine ([]p & p) says to itself (1p) >> correctly. It is real indeed. But it is non definable, and non provable. The >> machine’s soul knows that her soul is not a machine, nor even anything >> describable in any 3p terms. >> >> >> >> >> >>> >>> To real (experiential) materialists (panpsychism), consciousness is >>> intrinsic to matter (like electric charge, etc.). So that would make >>> consciousness primary. >> >> Then you better need to say “no” to the doctor who propose you a digital >> body. >> >> But are you OK that your daughter marry a man who got one such digital body >> in his childhood, to survive some disease? >> >> You might say yes, and invoke the fact that he is material. The point will >> be that if he survives through a *digital* substitution, it can be shown >> that no universal machine at all is unable to distinguish, without >> observable clue, a physical reality from any of infinitely many emulation of >> approximations of that physical reality at some level of substitution (fine >> grained, with 10^100 decimals correct, for example). Then, infinitely many >> such approximation exists in arithmetic, even in diophantine polynomial >> equation, and the invariance of the first person for “delays of >> reconstitution” (definable by the number of steps done by the universal >> dovetailer to get the relevant states) entails that the 1p is confronted >> with a continuum. The math shows that it has to be a special (models of []p >> & p, and []p & <>t & p. [] is the arithmetical “beweisbar” predicate of >> provability of Gödel 1931. It is my generic Gödel-Löbian machine, shortly: >> Löbian. They obeys to the formula of modesty of Löb: []([]p -> p) -> []p. It >> represents a scheme of theorems of PA saying that PA is close for the Löb >> rule: if you convince PA that the provability of the existence of Santa >> Klauss entails the existence of Santa Klauss, then PA will soon or later >> prove the existence of Santa Klauss. > > But that is the same as saying proof=>truth.
I don’t think so. It says that []p -> p is not provable, unless p is proved. For example []f -> f (consistency) is not provable. It will belong to G* \ G. Another example is that []<>t -> <>t is false, despite <>t being true. In fact <>t -> ~[]<>t. Or <>t -> <>[]f. Consistency implies the consistency of inconsistency. > Nothing which is proven can be false, Assuming consistency, which is not provable. > which in tern implies that no axiom can ever be false. Which is of course easily refuted. > Which makes my point that the mathematical idea of "true" is very different > from the common one. “BBBBBBB” is true just in case it is the case that BBBBBBB. I am not sure, but the point is that no machine can prove []p -> p in general. And the machine can know that, making her “modest” (Löbian). Bruno > > Brent > >> Put in another way, unless PA proves something, she will never prove that >> the provability of something entails that something. PA is maximally modest >> on her own provability ability. >> >> In particular, with f the constant proposition false, consistency, the ~[]f, >> equivalent with []f -> f, is not provable, so []p -> p is in general not >> provable and is not a theorem of PA. >> >> Incompleteness enforces the nuances between >> >> Truth p >> Provable []p >> Knowable []p & p >> Observable []p & <>t. (t = propositional constant true, <> = ~[]~ >> = consistent) >> Sensible []p & <>t >> >> And incompleteness also doubles, or split, the provable, the observable and >> the sensible along the provable/true parts, G and G*. >> That gives 8 personal points of view on the (sigma_1) Arithmetic. 5 >> “terrestrial” (provable) and 5 “divine” (true but non provable) modes on the >> Self, with two of them (Truth and Knowable) at the intersection of Earth >> (effective, provable) and Heaven (truth). >> >> The beauty is that G* proves p <-> []p <-> []p&p <-> []p&<>t <-> []p&<>t&p, >> but G proves virtually none. (p sigma_1). In this setting p -> []p is >> equivalent with sigma_1 completeness, or Turing universality, and the Löbian >> entities typically can prove all p -> []p formula. But the consistent >> machine cannot prove []p -> p in general. That is why the logic and the >> mathematics of all the nuances differ a lot from the machine's local point >> of view, despite they true equivalence. >> >> Bruno >> >> >>> >>> >>> https://www.nybooks.com/daily/2018/03/13/the-consciousness-deniers/ >>> <https://www.nybooks.com/daily/2018/03/13/the-consciousness-deniers/> >>> >>> - pt >>> >>> -- >>> 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] >>> <mailto:[email protected]>. >>> To post to this group, send email to [email protected] >>> <mailto:[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] >> <mailto:[email protected]>. >> To post to this group, send email to [email protected] >> <mailto:[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] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[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]. 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.
