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 < > [email protected] <javascript:>> wrote: > > > > On 5/3/2019 8:47 AM, Bruno Marchal wrote: > > > On 3 May 2019, at 14:06, Quentin Anciaux <[email protected] <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 [email protected]. To post to this group, send email to [email protected]. 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.
