> On 13 Dec 2018, at 04:30, Brent Meeker <meeke...@verizon.net> wrote:
> 
> 
> 
> On 12/12/2018 9:18 AM, Bruno Marchal wrote:
>> 
>>> On 12 Dec 2018, at 12:54, Philip Thrift <cloudver...@gmail.com 
>>> <mailto:cloudver...@gmail.com>> 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 <cloud...@gmail.com <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 <cloud...@gmail.com <>> 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
>>> 
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