On Sat, Jan 24, 2015 at 09:55:19AM -0800, meekerdb wrote: > On 1/24/2015 12:20 AM, Bruno Marchal wrote: > >Do you see the relationship between Gödel's second incompleteness > >theorem and the modal formula > > > ><>t -> ~[] <>t ? > > I don't see it, because I don't understand what <>t means. t is a > tautology, the negation of a contradiction. Yet you seem to use t > to mean "has a model"? And I'm not clear on how one is supposed to > know the true propositions of a model. > > Brent
<>t can be read as "consistent" The theorem therefore states "consistent theories cannot prove their own consistency". -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics [email protected] University of New South Wales http://www.hpcoders.com.au Latest project: The Amoeba's Secret (http://www.hpcoders.com.au/AmoebasSecret.html) ---------------------------------------------------------------------------- -- 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 http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
