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 Cowboy wrote: >> >>> 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 fixed point > 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 in all manner of proofs fruitfully. I remember something like "if []p -> [][]p weren't a theory of G as proven by some usual suspect, Kripke I think, then we would extend GL sufficiently until it was!" And that shows how often this is used; almost axiomatically in practice. Boolos at least seems addicted to it. PGC > Bruno > > > > >> Cheers >> >> -- >> >> ------------------------------**------------------------------** >> ---------------- >> Prof Russell Standish Phone 0425 253119 (mobile) >> Principal, High Performance Coders >> Visiting Professor of Mathematics hpco...@hpcoders.com.au >> University of New South Wales http://www.hpcoders.com.au >> ------------------------------**------------------------------** >> ---------------- >> >> -- >> 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+unsubscribe@**googlegroups.com<everything-list%2bunsubscr...@googlegroups.com> >> . >> To post to this group, send email to >> everything-list@googlegroups.**com<everything-list@googlegroups.com> >> . >> Visit this group at >> http://groups.google.com/**group/everything-list<http://groups.google.com/group/everything-list> >> . >> For more options, visit >> https://groups.google.com/**groups/opt_out<https://groups.google.com/groups/opt_out> >> . >> > > http://iridia.ulb.ac.be/~**marchal/ <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+unsubscribe@**googlegroups.com<everything-list%2bunsubscr...@googlegroups.com> > . > To post to this group, send email to > everything-list@googlegroups.**com<everything-list@googlegroups.com> > . > Visit this group at > http://groups.google.com/**group/everything-list<http://groups.google.com/group/everything-list> > . > For more options, visit > https://groups.google.com/**groups/opt_out<https://groups.google.com/groups/opt_out> > . > -- 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.
