On Tuesday, December 18, 2018 at 5:04:32 AM UTC-6, Bruno Marchal wrote: > > > On 17 Dec 2018, at 14:32, Philip Thrift <[email protected] <javascript:>> > wrote: > > > > On Monday, December 17, 2018 at 6:51:19 AM UTC-6, Bruno Marchal wrote: >> >> >> On 16 Dec 2018, at 19:24, Philip Thrift <[email protected]> wrote: >> >> >> >> On Sunday, December 16, 2018 at 11:27:50 AM UTC-6, Bruno Marchal wrote: >>> >>> >>> > On 15 Dec 2018, at 00:00, Brent Meeker <[email protected]> wrote: >>> > >>> > >>> > >>> > On 12/14/2018 2:59 AM, Bruno Marchal wrote: >>> >>> On 13 Dec 2018, at 21:24, Brent Meeker <[email protected]> wrote: >>> >>> >>> >>> >>> >>> >>> >>> On 12/13/2018 3:25 AM, Bruno Marchal wrote: >>> >>>>> 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. >>> >>> So []([]p -> p) -> p or in other words Proof([]p -> p) => (p is >>> true) So in this case proof entails truth?? >>> >> But “[]([]p -> p) -> p” is not a theorem of G, meaning that "[]([]p >>> -> p) -> p” is not true in general for any arithmetic p, with [] = Gödel’s >>> beweisbar. >>> >> >>> >> The Löb’s formula is []([]p -> p) -> []p, not []([]p -> p) -> p. >>> >> >>> >> >>> >> >>> >>> >>> >>>> 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. >>> >>> I'm not sure how to interpret these formulae. Are you asserting >>> them for every substitution of t by a true proposition (even though "true" >>> is undefinable)? >>> >> No, only by either the constant propositional “true”, or any obvious >>> truth you want, like “1 = 1”. >>> >> >>> >> >>> >> >>> >> >>> >>> Or are you asserting that there is at least one true proposition for >>> which []<>t -> <>t is false? >>> >> You can read it beweisbar (consistent(“1 = 1”)) -> (consistent >>> (“1=1”), and indeed that is true, but not provable by the machine too which >>> this provability and consistency referred to. >>> >> >>> >> >>> >> >>> >> >>> >>>> >>> >>>>> Nothing which is proven can be false, >>> >>>> Assuming consistency, which is not provable. >>> >>> So consistency is hard to determine. You just assume it for >>> arithmetic. But finding that an axiom is false is common in argument. >>> >> Explain this to your tax inspector! >>> > >>> > I have. Just because I spent $125,000 on my apartment building >>> doesn't mean it's appraised value must be $125,000 greater. >>> >>> ? >>> >>> >>> >>> > >>> >> >>> >> If elementary arithmetic is inconsistent, all scientific theories are >>> false. >>> > >>> > Not inconsistent, derived from false or inapplicable premises. >>> >>> In classical logic false entails inconsistent. Inapplicable does not >>> mean anything, as the theory’s application are *in* and *about* arithmetic. >>> >>> If we are universal machine emulable at some level of description, then >>> it is absolutely undecidable if there is something more than arithmetic, >>> but the observable must obey some laws, so we can test Mechanism. >>> >>> >>> >>> >>> >>> >>> > >>> >> >>> >> Gödel’s theorem illustrate indirectly the consistency of arithmetic, >>> as no one has ever been able to prove arithmetic’s consistency in >>> arithmetic, which confirms its consistency, given that if arithmetic is >>> consistent, it cannot prove its consistency. >>> > >>> > But it can be proven in bigger systems. >>> >>> Yes, and Ronsion arithmetic emulates all the bigger systems. No need to >>> assume more than Robinson arithmetic to get the emulation of more rich >>> system of belief, which actually can help the finite things to figure more >>> on themselves. Numbers which introspect themselves, and self-transforms, >>> get soon or later the tentation to believe in the induction axioms, and >>> even in the infinity axioms. >>> >>> Before Gödel 1931, the mathematicians thought they could secure the use >>> of the infinities by proving consistent the talk about their descriptions >>> and names, but after Gödel, we understood that we cannot even secure the >>> finite and the numbers with them. The real culprit is that one the system >>> is rich enough to implement a universal machine, like Robinson Arithmetic >>> is, you get an explosion in complexity and uncontrollability. We know now >>> that we understand about nothing on numbers and machine. >>> >>> >>> >>> > >>> >> Gödel’s result does not throw any doubt about arithmetic’s >>> consistency, quite the contrary. >>> >> >>> >> Of course, if arithmetic was inconsistent, it would be able to prove >>> (easily) its consistency. >>> > >>> > Only if you first found the inconsistency, i.e. proved a >>> contradiction. >>> >>> >>> That is []f, that does not necessarily means arithmetic is inconsistent. >>> The proof could be given by a non standard natural numbers. >>> >>> So, at the meta-level, to say that PA is inconsistent means that there >>> is standard number describing a finite proof of f. And in that case, PA >>> would prove any proposition. In classical logic, proving A and proving ~A >>> is equivalent with proving (A & ~A), which []f, interpreted at the >>> meta-level. Now, for the machine, []f is consistent, as the machine cannot >>> prove that []f -> f, which would be her consistency. G* proves <>[]f. >>> >>> It is because the domain here is full of ambiguities, that the logic of >>> G and G*, which capture the consequence of incompleteness are so useful. >>> >>> Bruno >>> >>> >> >> >> In writing [ https://codicalist.wordpress.com/contents/ ], the idea at >> the beginning and now is that math and matter (code and substrate, myth and >> hyle, ...) are married like yang and yin. >> >> After reading Galen Strawson, and a few more recent "panpsychists" coming >> along - that there are psychical (experiential) states of matter (in >> addition to physical states) is the best understanding of consciousness we >> have so far - tips the balance towards matter's role as "head of the >> household" (so to speak). >> >> >> I will take this seriously the day someone provide just one evidence for >> Matter (not matter). Until this is provided, I feel that it is an empty >> speculation which has been used as a simplifying hypothesis in the Natural >> Science, useful as such in physics, but should not be taken as granted when >> we do metaphysics, unless experimental evidence. >> >> It is important to understand that there are no evidences for primary >> matter (Matter), only for matter. >> >> Once you grasp that all computations are realised in arithmetic, that is >> enough for not taking Matter from granted in mechanist philosophy/science. >> Unless a proof is given that Nature does not conform toi the reducible >> notion of Nature entailed by Mechanism, Matter (with the big M) will remain >> an unclear philosophical speculation, and it should not be used as a dogma, >> as this is no more science. >> >> >> Bruno >> >> >> > If one *begins* with the assumption > > *Fictionalism* > > > > But why start from a so much nonsensical assumption? Why not assume that > pigs have wings. > > How to distinguish 2+2=4 and 2+2=5 with fictionalism? > > I certainly doubt less 2+2=4 than the existence of the moon, as I > explained before. > > > > then *Matter is All There Is* is the best conclusion from that > assumption (I would argue). > > > But why assume (primary) Matter? I will wait for at least one evidence. > “Seeing” is not an evidence (that is Aristotle’s criteria for reality). > > To explain the apparent matter from an ontological commitment is not > better than saying “because god decided”. It eliminate problems, without > providing any testable consequence. > > >
But I wasn't assuming Materialism. I was assuming Fictionalism. Fictionalism says *Numbers don't exist.* If something exists (and it can't be numbers) then what is the alternative? Matter seems like the best bet, right? - 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]. 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.
