On Wednesday, May 8, 2019 at 1:41:30 PM UTC-5, Brent wrote: > > > > On 5/8/2019 9:20 AM, Bruno Marchal wrote: > > > On 3 May 2019, at 20:17, 'Brent Meeker' via Everything List < > everyth...@googlegroups.com <javascript:>> wrote: > > > > On 5/3/2019 8:47 AM, Bruno Marchal wrote: > > > On 3 May 2019, at 14:06, Quentin Anciaux <allc...@gmail.com <javascript:>> > 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. > > Brent > > > The universal machine which knows that she is universal say no better, > indeed. > > Bruno > > > > > Brent > >
Derrida would deconstruct arithmetic and bring nonstandard numbers out from the margins. (WWDD) @philipthrift -- 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 post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/002659ee-765b-4692-b254-b63bf6fe5853%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
