On Thu, May 30, 2013 at 12:04:13PM -0700, meekerdb wrote: > You mean unprovable? I get confused because it seems that you > sometimes use Bp to mean "proves p" and sometimes "believes p" >
To a mathematician, belief and proof are the same thing. I believe in this theorem because I can prove it. If I can't prove it, then I don't believe it - it is merely a conjecture. In modal logic, the operator B captures both proof and supposedly belief. Obviously it captures a mathematician's notion of belief - whether that extends to a scientists notion of belief, or a Christian's notion is another matter entirely. When it comes to Bp & p capturing the notion of knowledge, I can see it captures the notion of mathematical knowledge, ie true theorems, as opposed to true conjectures, say, which aren't knowledge. But I am vaguely sceptical it captures the notion of scientific knowledge, which has more to do with falsifiability, than with proof. And that's about where I left it - years ago. Cheers -- ---------------------------------------------------------------------------- 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 ---------------------------------------------------------------------------- -- 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?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
