> On 20 May 2019, at 21:17, 'Brent Meeker' via Everything List > <everything-list@googlegroups.com> wrote: > > > > On 5/20/2019 2:59 AM, Bruno Marchal wrote: >>> On 17 May 2019, at 23:24, 'Brent Meeker' via Everything List >>> <everything-list@googlegroups.com> wrote: >>> >>> >>> >>> On 5/17/2019 5:10 AM, Bruno Marchal wrote: >>>>> On 16 May 2019, at 01:40, 'Brent Meeker' via Everything List >>>>> <everything-list@googlegroups.com> wrote: >>>>> >>>>> >>>>> >>>>> On 5/15/2019 9:01 AM, Bruno Marchal wrote: >>>>>>> On 13 May 2019, at 23:46, 'Brent Meeker' via Everything List >>>>>>> <everything-list@googlegroups.com> wrote: >>>>>>> >>>>>>> >>>>>>> >>>>>>> On 5/13/2019 8:50 AM, Jason Resch wrote: >>>>>>>> But then what is arithmetical truth? We have no label for it. It >>>>>>>> cannot be derived from or defined by labels. >>>>>>> And it depends on the model. Which is why it's undefinable within the >>>>>>> system. And also why it's not the same as the "true" in "It is true >>>>>>> that snow is white.” >>>>>> ? >>>>>> >>>>>> I don’t see the difference. The standard model of arithmetic is given by >>>>>> the intersection between all models. >>>>> Isn't the intersection of all models just the provable part? >>>> By incompleteness that is not the case. The provable part is much smaller >>>> than the true part. >>> Isn't that what I said? >> No, what you can prove is true in all models, but what is true in all models >> can be proved (by completeness), > > So what is true in the all models is what can be proved...which is what I > wrote as a question four lines above. >
Yes, that was the correct part, but then I added: >> but that is not equal to what is true in the standard model. So, the standard model is NOT the provable part. It is huge compared to the provable part. >> >> Consistent(PA) is true in the standard model, but is not provable, for >> example. >> >> All what you can prive is sigma_1 ([] is a sigma_1-complete predicate), but >> it is not pi_1-complete, nor sigma_i or pi_i-complete for any big i). >> >> The standard arithmetical truth is highly not computable. It is bigger than >> any sigma_i or pi_i complete sets. >> >> >> >> >> >>>> The true undecidable sentences are true in the standard sense, just >>>> possibly false in the non start sense. >>> Right. All the models make the provable part "true"; otherwise they >>> wouldn't be models. What you mean by the "true undecidable sentences are >>> true in the standard sense" is that they are true in the standard model, >>> which is the abstraction from empirically counting, adding, subtracting, >>> and multiplying sets of objects. It is that empirical basis which makes >>> the standard model standard and is the reason everyone agree on "it”. >> Maybe. Maybe not. The discovery of the distinction between standard and not >> standard has waited for the discovery of Löwenheim, Skolem, Gödel, etc. >> >> The human conception of numbers is the standard one, almost by definition, >> and there is few doubt that Nature has an important teaching role in this, >> but that does not entail that Nature could not be an hallucination by >> (sheaves of) consciousness flux arising from the universal numbers in >> arithmetic. > > I don't know how to understand things like "hallucination arising from > universal numbers” With YD+CT, the actual state of your brain is “reconstituted” in finitely many universal number in arithmetic, and in some of those stories the “you” associated with them (by YD) might develop some false beliefs, with respect to the the number “you” are confronted with in those stories; that is what I call hallucination. > and "sheaves of consciousness flux”. Take any universal (and Löbian) number u in the arithmetical reality. An let us call u’, u’’, u’’’ … all the variant of that u (i.e. phi_u’ = phi_u, etc.). They support consciousness, by mechanism, that consciousness differentiate on all consistent extensions of the u, u’, u’’, u’’’, etc. The determine a flux of consciousness starting from all universal numbers, in arithmetic. > I don't know whether you're waxing poetic or just talking gibberish. I hope it is clearer now. I could add more details, but some revision of the phi_i would be needed, and if I explains to much, I will be criticised for jargon, etc. I try to find some intermediate between being comprehensible and exact. Normally you have followed the seven steps, so such images should make sense. Bruno > > Brent > >> At this stage, that could be invalid; and we know with mechanism that this >> cannot be the case. >> >> Bruno >> >> >> >> >>> Brent >>>> Typical example: the consistency of PA. Everyone familiar with natural >>>> numbers believe that PA is consistent, but PA cannot prove this, and thus >>>> there is a model of PA where “PA is inconsistent” is true. It means that >>>> some “omega” (see my preceding posts) is a proof of “0=1”; but as omega is >>>> not accessible by the successor relation, that they is still consistent. >>>> PA + (PA is inconsistent) is a consistent theory of natural numbers, but >>>> it is not a sound theory. It is false in the standard model. >>>> >>>> Bruno >>>> >>>> >>>> >>>>> Brent >>>>> >>>>>> See my other recent explanations. >>>>>> >>>>>> Bruno >>>>>> >>>>>> >>>>>> >>>>>>> Brent >>>>>>> >>>>>>> -- >>>>>>> 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 everything-list+unsubscr...@googlegroups.com. >>>>>>> To view this discussion on the web visit >>>>>>> https://groups.google.com/d/msgid/everything-list/816e0c3c-76cc-82c8-a3b3-18f6af30b042%40verizon.net. >>>>> -- >>>>> 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 everything-list+unsubscr...@googlegroups.com. >>>>> To view this discussion on the web visit >>>>> https://groups.google.com/d/msgid/everything-list/ab8bbe0f-a236-9628-c030-4de2928ca181%40verizon.net. >>> >>> -- >>> 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 everything-list+unsubscr...@googlegroups.com. >>> To view this discussion on the web visit >>> https://groups.google.com/d/msgid/everything-list/d0ad3345-c0f4-878f-9271-07db96cb5190%40verizon.net. > > > -- > 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 everything-list+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/f11eff9c-db1a-7c7c-d437-c193517ca26e%40verizon.net. -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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