On Wednesday, December 19, 2018 at 9:19:50 AM UTC-6, Bruno Marchal wrote: > > > On 18 Dec 2018, at 16:40, Philip Thrift <[email protected] <javascript:>> > wrote: > > > > 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? >> > > > Except that with Mechanism, it is has be proven, or explain, that Matter > cannot be a primary notion. With Mechanism, Matter is what emerge from a > statistics on all relative computations. > > > > >> - pt >> > > > I should add: Why is fictionalism compelling? > > When you get down to the bottom of it, *numbers are spiritual entities*. > > > I have no problem with that. I have some evidence for spiritual entities, > indeed all the mathematical notions are spiritual or immaterial, then > consciousness mind, etc. > > > > Many are compelled to want to eliminate spiritual entities. > > > > Like you apparently. If you put the spiritual entities, like numbers and > math in fictionalism, it will look you consider them as fiction, it seems > to me. > > I am problem driven. And my favorite problem is the mind-body problem. I > reduce the mind-body problem into the justification why universal spiritual > entities get the (admittedly persistent) impression of a primitively > material world. I found it. All universal “spiritual” entities go through > this. > > Bruno > > >
A: There is arithmetical reality where there are "simulated" entities that surmise a material reality (but matter itself does not actually exist). M. There is material reality where arithmetic is a language (or language group) created by material entities. But to have A producing matter in reality, or matter "emerging from" A (A→M), is a kind of dualism. And what would be the need for A→M if A is enough? In M, "mind" comes from the psychical states of matter (Strawson, et al., who say of course that the "mechanistic", "physicalistic", whatever materialists are misguided). - 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.
