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] <javascript:>>
> 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*
then *Matter is All There Is* is the best conclusion from that assumption
(I would argue).
- pt
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