On 21 Oct 2013, at 17:59, Platonist Guitar Cowboy wrote:

On Mon, Oct 21, 2013 at 4:26 PM, Bruno Marchal <marc...@ulb.ac.be>wrote:On 21 Oct 2013, at 08:24, Russell Standish wrote:On Mon, Oct 21, 2013 at 04:48:42AM +0200, Platonist Guitar Cowboywrote:Disclaimer: No idea if I am even on the same planet on which this discussion is taking place. So pardon my questions and confusions: You and me both - we're all students here :). I'm just rather doubtful about an axiomatisation of proof that assumes we can prove that we can prove something, as with that we can know that we (Theatetically) know something (since truth is usually inherently unknowable). It reminds me of a 3 year old's question "but why?" Ultimately, you will not be able to answer a question like that. It is quite possible I haven't drunk enough Kool-Aid. Question for Bruno (raised from PGC's earlier comments): Is axiom 4, ie []p -> [][]p, called a fixed point theorem?No. PGC is a bit unclear/mysterious when referring to the fixedpoint theorem here.But I don't refer to fixed point theorem there.Concerning []p -> [][]p, I just stated it is a theory of G, used inall manner of proofs fruitfully.I remember something like "if []p -> [][]p weren't a theory of G asproven by some usual suspect, Kripke I think, then we would extendGL sufficiently until it was!"And that shows how often this is used; almost axiomatically inpractice. Boolos at least seems addicted to it. PGC

`No problem. Minor vocabulary details. I guess you mean theorem of G`

`(or is in the theory G).`

`By Solovay theorem, G is complete and sound for the arithmetical`

`provability, and wht is really oimprtant is that for all arithmetical`

`proposition beweisbar('p') -> beweisbar('beeisbar('p')') is a theorem`

`of (Peano) arithmetic.`

`If G was not proving []p -> [][]p, it would not be arithmetically`

`complete.`

Bruno http://iridia.ulb.ac.be/~marchal/ -- 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 http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.