On Tuesday, December 18, 2018 at 9:24:12 AM UTC-6, Philip Thrift wrote: > > > > 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]> 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 >
I should add: Why is fictionalism compelling? When you get down to the bottom of it, *numbers are spiritual entities*. Many are compelled to want to eliminate spiritual entities. -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.
