tag:blogger.com,1999:blog-4987609114415205593.post6994164695848519545..comments2020-07-13T20:26:53.037+01:00Comments on M-Phi: How inaccurate is your total doxastic state?Jeffrey Ketlandhttp://www.blogger.com/profile/01753975411670884721noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-4987609114415205593.post-52115142973019250452014-06-07T23:36:50.315+01:002014-06-07T23:36:50.315+01:00Doesn't setting the level at 0.6 imply the ass...Doesn't setting the level at 0.6 imply the assumption that there are not degrees of validity to the positive end of credences or beliefs?<br /><br />Am I confused on this one?Nathan Coppedgehttps://www.blogger.com/profile/13272730626911068222noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-78076416720325514942014-05-28T12:25:18.679+01:002014-05-28T12:25:18.679+01:00[Part 2:]
The framework is open to different inte...[Part 2:]<br /><br />The framework is open to different interpretations, but my intended interpretation is that neither P nor < (that is, belief) ought to be eliminated, and neither ought to be reduced to the other either, rather each of the two of them has a life on its own; however, in order for the agent who has such a degree of belief function P and a belief ordering < simultaneously to be rational overall, P and < must satisfy a certain bridge principle, and that is just the stability account that I am advocating. (i) above aims to justify that account by considerations on accuracy with respect to truth on both sides, that is, for both P and <; (ii) above aims to justify that account by considerations on accuracy with respect to truth for P (that's just the standard arguments again), and accuracy with respect to P for belief. In that second approach, belief might still be said to aim at truth, but only indirectly: belief aims at P, and P aims at truth.<br /><br />In my intended interpretation, I don't regard either of P or belief to be prior to the other conceptually, or epistemologically, or ontologically, though I would want to say, of course, that P occupies a more complex and fine-grained scale of measurement than belief does, which is also why there will always be some kind of asymmetry between the two of them in terms of "information content" (and this shows up in the theory at various places).<br /><br />Finally, about the Lockean thesis: if degrees of belief and belief satisfy either of the norms formulated above, then one can prove there is always a threshold, such that the corresponding instance of the Lockean thesis for that very threshold must hold as well. So the stability account entails an instance of the Lockean thesis (but only with a special threshold). The difference to your way of proceeding is then that the Lockean thesis is but a corollary to accuracy considerations in my approach, while in your approach the Lockean thesis is presupposed already in the accuracy considerations themselves.Hannes Leitgebhttps://www.blogger.com/profile/03298746732204170101noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-36858425133123479582014-05-28T12:24:53.326+01:002014-05-28T12:24:53.326+01:00Great post, Richard!
For my stability account of ...Great post, Richard!<br /><br />For my stability account of belief, I have two accuracy arguments which work like this (and which I both discuss in the monograph that I am writing):<br /><br />(i) In the first one, inaccuracy is--as usual--distance from the truth. But I use different inaccuracy measures for degrees of belief and for all-or-nothing belief (where belief is analyzed, say, on an ordinal scale, such as in belief revision theory or nonmonotonic reasoning, though the approach also works for belief on a strictly categorical scale); for degrees of belief one may use the Brier score, while for belief I use a class of inaccuracy measures that are generalizations of Hempel's or of your i-functions from above and which also include, e.g., Branden's (from his recent work on inaccuracy for orders of propositions) as a special case. Then I make an additional assumption, and that is: all-or-nothing belief on an ordinal scale is given by a total pre-order < on worlds (rather than propositions); a total pre-order on propositions can be determined from that order on worlds, as this is done in belief revision theory or nonmonotonic reasoning, but the primary object is the order on worlds. (I leave out any defense of that additional assumption here.) Finally, I formulate an accuracy norm simultaneously for the degree of belief function P and for belief as given by the ordering <: the pair (P, <) ought to be such that P minimizes expected inaccuracy relative to P, and < minimizes expected inaccuracy relative to P, where the respective inaccuracy measures in the two cases are as sketched above. One can then prove a theorem to the effect that if (P, <) satisfies the norm, then P is a probability measure (that's just the standard arguments from the literature repeated), and < has the kind of stability property (relative to P) that I want to argue for in my theory.<br /><br />(ii) In the second approach, which I won't explain here in any detail, I also do something like the above, however, this time I determine the inaccuracy of < not with respect to truth but instead with respect to P: taking a subjective probability measure P (and the order on propositions that it induces) as given, I formulate a norm to the effect that < ought to approximate P to best possible extent (the justification being that (P, <) should be, as it were, in "maximal harmony" or coherence with each other). I make precise that this means, and then I prove again that the < that minimize inaccuracy relative to P are precisely those that have the stability property (relative to P) that I aim to defend.<br /><br />[Continued in part 2.]Hannes Leitgebhttps://www.blogger.com/profile/03298746732204170101noreply@blogger.com