> On 8 May 2019, at 20:41, 'Brent Meeker' via Everything List > <everything-list@googlegroups.com> wrote: > > > > On 5/8/2019 9:20 AM, Bruno Marchal wrote: >> >>> On 3 May 2019, at 20:17, 'Brent Meeker' via Everything List >>> <everything-list@googlegroups.com >>> <mailto:everything-list@googlegroups.com>> wrote: >>> >>> >>> >>> On 5/3/2019 8:47 AM, Bruno Marchal wrote: >>>> >>>>> On 3 May 2019, at 14:06, Quentin Anciaux <allco...@gmail.com >>>>> <mailto:allco...@gmail.com>> wrote: >>>>> >>>>> Pleasure for the all loving god to have creatures to torture ? >>>>> >>>>> But the problem of evil is not that simple. >>>> >>>> Indeed. >>>> >>>> But note that just the second theorem of Gödel provides a clue. >>>> >>>> With provable(p) written []p >>>> consistent(p) = ~provable(~p) = <>p >>>> f = false, t = true >>>> consistent = ~[]f = <>t = consistent(t), >>>> >>>> Gödel’s second I. Theorem, put in equivalent version: >>>> >>>> <>t -> ~[]<>t >>>> >>>> <>t -> <>~<>t >>>> <>t -> <>[]f >>>> >>>> It is that last one where the clue is the more apparent: >>>> >>>> Said by PA, or ZF, or any sound Löbian machine: it says the following: >>>> >>>> If I am consistent, then it is consistent that I am inconsistent >>> >>> Notice however that this assumes you know what t and f are. >> >> No, that is not assumed. t and f are only boolean constant. In the >> arithmetical interpretation, you can take any simple theorems of your >> (Church-Turing universal) theory (that you are supposed to believe in). >> Usually t is interested by “1=1” and f by “~(1=1)”. But in the combinators t >> is interpreted by K and f by KI. >> >> With digital mechanism, just to define what is a digital machine, we need >> some acknowledgement on elementary arithmetic, for which we do have a notion >> of truth, indeed made mathematically precise by Tarski. In the usual >> mathematical sense, and not definable in arithmetic, like all good notion of >> god should be. >> >> >> >>> In the formalism they are just markers that are invariant under the rules >>> of inference. >> >> Yes, except that here they correspond to direct conclusion of the logical >> rule. Now “1” is represented by "s(0)” (or its Gödel number), and what you >> say will apply to all symbols, or symbols of symbols. The interpretation is >> in the truth, that is here is the stantard model of arithmetic (the >> structure (N, 0, s, +, x). >> Your remark applies also to brain and (physical or not) realities. >> >> >> >>> In the semantics they refer to some model. >> >> Exactly. >> >> >>> Beware of the priest who tells you he knows the real model. >> >> Exactly. > > Above you are telling us the standard model of arithmetic is the real model.
Like everyone. In this case, the standard model can be shown to be the least model, and the intersection of all models. Nobody believe in non standard natural number, as they are infinite. Non standard natural number can be used in non standard analysis, but all the understanding on “non standard” makes precise sense in arithmetic, because we do have a good intuition of what the standard numbers are. Keep in mind that a non standard model contains all the standard numbers 0, 1, 2, …, plus infinite objects which have infinitely any predecessor (transitively). Keep in mind that we assume computationalism. In the non standard model of arithmetic, addition and multiplication are already NOT computable. The understanding of the natural numbers corresponds to the standard model. But “finite” is not a first order property, so we can’t define the natural numbers entirely in first order logic, and the non standard model is a mess due to that restriction. The standard model can be defined in analysis, as much well as any limit of a Cauchy sequence. The standard model is the intersection of on what everybody agree on the natural numbers. It is taught in primary school. You need to learn a bit of mathematical logic to even grasp the notion of non standard numbers, and that requires also the understanding of standard numbers. Bruno > > Brent > >> >> The universal machine which knows that she is universal say no better, >> indeed. >> >> Bruno >> >> >> >>> >>> Brent >>> >>>> >>>> Or >>>> >>>> If I am consistent then it is consistent that I will prove a falsity >>>> >>>> Peano arithmetic, or ZF, remains consistent when adding the axiom that >>>> they are (respectively) inconsistent. >>>> >>>> Loosely, this says: >>>> >>>> If shit does not happen, shit might happen. >>>> >>>> This might be part of the shadow explaining the origin of evil ([]f) in >>>> the internal states realised in arithmetic. >>>> >>>> Bruno >>>> >>>> PS Exercise; show that Gödel’s theorem (in its modal form) is just Löb’s >>>> formula with p replaced by false( f). >>>> >>>> Solution: Löb’s formula is []([]p -> p) -> []p, >>>> >>>> with p = f, this becomes >>>> >>>> []f([]f -> f) -> []f >>>> >>>> Which is, as ~p = (p -> f), obvious by truth table of ~ and ->. >>>> >>>> [](~[]f) -> []f >>>> >>>> By transposition (using the fact that p -> q is equivalent with ~q -> ~p), >>>> we get >>>> >>>> ~[]f -> ~[](~[]f), or, >>>> >>>> by using ~[]p = <>~p, and ~f = t, or ~~p -> p. >>>> >>>> <>t -> <>([]f) >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>>> >>>>> Le ven. 3 mai 2019 à 12:46, smitra <smi...@zonnet.nl >>>>> <mailto:smi...@zonnet.nl>> a écrit : >>>>> What's the point of creating criminals and then to torture those >>>>> criminals for eternity in hell? >>>>> >>>>> On 03-05-2019 04:41, Samiya Illias wrote: >>>>> > Considering how vast we have come to realise the Universe to be, do >>>>> > you honestly think our praise or our insults affect God in any way? Do >>>>> > you even realise how great the Creator of all this must be? Do you >>>>> > think God would need any appreciation from us? Rather, it is we who >>>>> > need to appreciate God! >>>>> > >>>>> > God created the entire creation and He governs it flawlessly according >>>>> > to His Laws. The entire creation submits to His Laws, except some >>>>> > criminals... >>>>> > >>>>> > The way I understand it, we, humans and snakes, are criminals who have >>>>> > been contained on a planet. Our collective crime is that we abused our >>>>> > free will to go against the Universal Laws. We have an appointment, in >>>>> > the Divine Court, that will be kept as scheduled. We have been given a >>>>> > temporal life so that each one of us can generate evidence (data: >>>>> > speech and deeds) for or against ourselves. >>>>> > >>>>> > Remembering God through prayer, and Praising God by repeatedly >>>>> > declaring that God is free from all imperfection, helps us to >>>>> > understand and consequently be pleased with God, contented to submit >>>>> > to His Laws and Decrees, and grateful for the guidance, looking >>>>> > forward to an immortal life of luxury and perhaps the most prestigious >>>>> > jobs anyone can ever aspire for: in service of Allah, The One and Only >>>>> > God, The KIng of the Mighty Throne of The Entire Creation! >>>>> > >>>>> > There is no compulsion to follow God's Laws, but the criminals will >>>>> > not be allowed to leave this planet. They will go from living upon it >>>>> > to living within it, in The Fire! >>>>> > >>>>> > Related Posts [4] >>>>> > >>>>> > Samiya Illias >>>>> > Signs & Science [5] >>>>> > >>>>> > On Thu, May 2, 2019 at 5:00 PM John Clark <johnkcl...@gmail.com >>>>> > <mailto:johnkcl...@gmail.com>> >>>>> > wrote: >>>>> > >>>>> >> On Thu, May 2, 2019 at 1:54 AM 'Brent Meeker' >>>>> >> <everything-list@googlegroups.com >>>>> >> <mailto:everything-list@googlegroups.com>> wrote: >>>>> >> >>>>> >>>> _ _Islam is a religion based almost entirely on threats. >>>>> >> >>>>> >> True, but in all fairness Christianity is also based on threats. It >>>>> >> preaches that faith (believing in something when there is no good >>>>> >> reason for doing so) is not stupidity but is instead the ultimate >>>>> >> virtue, and if you don't believe in all the crap that Christianity >>>>> >> (or Islam) says then a good and loving God will torture you most >>>>> >> fiendishly not for 10^100 years but for an infinite number of years. >>>>> >> I'm no saint but I wouldn't do that to a unrepentant Hitler, and yet >>>>> >> another thing we're suposed to do is constantly flatter God by >>>>> >> telling Him how good He is. >>>>> >> >>>>> >> The Meaning of Life: Praise the Lord [1] >>>>> >> >>>>> >> John K Clark >>>>> >> >>>>> >> -- >>>>> >> 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 >>>>> >> 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https://groups.google.com/group/everything-list >>>>> > <https://groups.google.com/group/everything-list> >>>>> > [2]. >>>>> > For more options, visit https://groups.google.com/d/optout >>>>> > <https://groups.google.com/d/optout> [3]. >>>>> > >>>>> > >>>>> > Links: >>>>> > ------ >>>>> > [1] https://www.youtube.com/watch?v=k7sF4JzjwTg >>>>> > <https://www.youtube.com/watch?v=k7sF4JzjwTg> >>>>> > [2] https://groups.google.com/group/everything-list >>>>> > <https://groups.google.com/group/everything-list> >>>>> > [3] https://groups.google.com/d/optout >>>>> > <https://groups.google.com/d/optout> >>>>> > [4] https://signsandscience.blogspot.com/p/blog-page.html >>>>> > <https://signsandscience.blogspot.com/p/blog-page.html> >>>>> > [5] https://signsandscience.blogspot.com/ >>>>> > <https://signsandscience.blogspot.com/> >>>>> >>>>> -- >>>>> You received this message because you are subscribed to the Google Groups >>>>> "Everything List" group. >>>>> To unsubscribe from this group and 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