On Wed, Feb 12, 2014 at 12:24:18PM +0100, Bruno Marchal wrote: > > On 12 Feb 2014, at 02:02, Russell Standish wrote: > > >On Tue, Feb 11, 2014 at 07:31:24PM +0100, Bruno Marchal wrote: > >> > >>You are right, the qualia are in X1* \ X1, like we get quanta in > >>S4Grz1, Z1*, X1*. > > > >The only thing you can say is that qualia ought to obey the axioms of > >X1*\X1, (and even that supposes that Z captures all observations, > >which I think is debatable), > > By UDA, "p" to refer to a "physical certainty" needs to > > 1) UD generated (= sigma_1 arithmetical and true). > 2) provable (true in all consistent extensions) > 3) and non "trivially" provable (= there must be at least one > consistent extension) > > This give the []p & <>t, with p sigma_1. > > So the logic of observable certainty should be given by the Z1* logic. > >
This is certainly an interesting understanding that I hadn't met in your writings before. In associating provable with "true in all consistent extensions", are you meaning that so long as something (ie proposition) is computed by all programs instantiating your current state, no matter how far in the future that calculation might require, then that something is (sigma_1) provable. Then 1&2 gives your hypostase for knowledge, ie S4Grz1. It is, of course the sigma_1 restriction of Theatetus's definition of knowledge, which both Brent & I share quibbles with, but accept for the "sake of the argument". But assuming 3) above is equivalent to assuming the no cul-de-sac conjecture by fiat. I don't feel comfortable in assuming that axiomatically - I was hoping for a proof, or even just a better justification for that. 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+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.
