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.



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

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