tag:blogger.com,1999:blog-3891434218564545511.post2788504479362289014..comments2024-03-28T19:56:42.305-05:00Comments on Alexander Pruss's Blog: Certainty and probabilityAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-3891434218564545511.post-58615504169591731722012-10-24T11:22:09.083-05:002012-10-24T11:22:09.083-05:00Hmm... I found mathematics to be a counter-example...Hmm... I found mathematics to be a counter-example to that!<br /><br />(It was by disagreeing with proofs of theorems of functional analysis that I was led to doubt, not so much the axioms of the real number field, or those of arithmetic, but some formulations of the set-theoretic axiom of infinity, or rather, some of the assumptions underlying those formulations.)Martin Cookehttps://www.blogger.com/profile/11425491938517935179noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-8712868804714541532012-10-24T10:34:22.131-05:002012-10-24T10:34:22.131-05:00Once we have good axioms that we agree on, we will...Once we have good axioms that we agree on, we will have theorems that we agree on.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-16832411145508118072012-10-24T10:31:45.038-05:002012-10-24T10:31:45.038-05:00But, should we axiomatise probability? Where would...But, should we axiomatise probability? Where would we get the axioms from, if not from conceptions that are able to judge axioms? We may need to clarify our conceptions of probability, but do axioms always add clarity? Borel's law of thought was that very unlikely things do not happen, and if so then a probabiilty of 1 is always certainty.<br /><br />That may be counter-intuitive, but there is intuitive support for Borel's law. Suppose I put four red balls and one blue ball into an empty box, and you blindly put your hand into the box and pick out a ball. You would be surprised to find that the ball was green, but then, I did not say that I only put five balls into the box. So that might happen. What will certainly not happen is that you will pick out a tiny ballroom in which there is a ball. And yet that is not logically impossible, only very, very unlikely, given all we have seen.Martin Cookehttps://www.blogger.com/profile/11425491938517935179noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-21898884823407742782012-10-22T09:21:30.540-05:002012-10-22T09:21:30.540-05:00It's worth remembering that certainty here is ...It's worth remembering that certainty here is not psychological certainty but some other notion, maybe certainty by a perfect epistemic agent?Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-50012159189531898902012-10-19T00:19:28.783-05:002012-10-19T00:19:28.783-05:00You could still axiomatize certainty for fun. Math...You could still axiomatize certainty for fun. Math is fun! It is just Pruss's preamble that makes me feel qualmy logically. And, I doubt that there is any other good reason to axiomatize.Martin Cookehttps://www.blogger.com/profile/11425491938517935179noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-27602187285038505732012-10-18T19:36:37.359-05:002012-10-18T19:36:37.359-05:00enigMan:
"You conclude that we could then sa...enigMan:<br /><br />"You conclude that we could then say that the former is certain, and yet you began by saying that very thing. Why not just say that the solution is that probabilities of 1 do not always mean certainty? . . ." When you make it that simple it just isn't any fun. :-) Dagmara Lizlovshttps://www.blogger.com/profile/14744785407281199347noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-9445679684169736832012-10-18T02:51:06.116-05:002012-10-18T02:51:06.116-05:00You conclude that we could then say that the forme...You conclude that we could then say that the former is certain, and yet you began by saying that very thing. Why not just say that the solution is that probabilities of 1 do not always mean certainty? That is, I fail to see what an axiomatization would add.Martin Cookehttps://www.blogger.com/profile/11425491938517935179noreply@blogger.com