|Appears in Collections:
|Law and Philosophy Journal Articles
|Peer Review Status:
|Information, Confirmation, and Conditionals
Lewis triviality results
|Milne P (2014) Information, Confirmation, and Conditionals. Journal of Applied Logic, 12 (3), pp. 252-262. https://doi.org/10.1016/j.jal.2014.05.003
|Loosely speaking, a proposition adds the more information to corpus b, the greater the proportion of possibilities left open by b that it rules out. Plausible qualitative constraints lead to the result that any measure of information-added is a strictly decreasing rescaling of a conditional probability function sending 1 to 0. The two commonest rescalings are -log P and 1−P. In a similar vein, e is favourable evidence for hypothesis h relative to background b if h rules out a smaller proportion of the possibilities left open by b and e jointly, than left open by b alone. In terms of the underlying probability measure, this secures the familiar positive relevance conception of confirmation and that f is more favourable evidence for h than e iff h rules out a smaller proportion of the possibilities left open by b and f jointly than left open by b and e jointly. In these terms, a measure of confirmation should be a function of the information added by h to b∧e and to b, decreasing with the first and increasing with the second. When e = h, the possibilities that drop out as we narrow the focus with e are exactly the possibilities left open by b but excluded by h. Thus the extent to which hconfirms h relative to b is a measure of the information h adds to b. Given a measure I of information added, we can think of I(ac,b) − I(a,b) as a measure of the “deductive gap”, relative to b, between a and a∧c. When, I(a,b) = P(a|b), I(ac,b) − I(a,b) = -logP(c|ab), the amount of information the indicative conditional ‘if a then c’ adds to b on Ernest Adams' account of that conditional. When I(a,b) = 1−P(a|b), I(ac,b) − I(a,b) = I(a⊃c,b) where a⊃c is a material conditional. What, if anything, can be said in general about “information theoretic” conditionals obtained from measures of information-added in this way? We find that, granted a couple of provisos, all satisfy modus ponens and that the conditionals fall victim to Lewis-style triviality results if, and only if, I(a∧¬a,b) = ∞ (as happens with -logP(.|b)).
|The publisher does not allow this work to be made publicly available in this Repository. Please use the Request a Copy feature at the foot of the Repository record to request a copy directly from the author. You can only request a copy if you wish to use this work for your own research or private study.
|The article appears in a Special Issue on Combining Probability and Logic to Solve Philosophical Problems
|MILNE Information confirmation and conditionals PUBLISHED.pdf
|Fulltext - Published Version
|Under Embargo until 2999-12-27 Request a copy
Note: If any of the files in this item are currently embargoed, you can request a copy directly from the author by clicking the padlock icon above. However, this facility is dependent on the depositor still being contactable at their original email address.
This item is protected by original copyright
Items in the Repository are protected by copyright, with all rights reserved, unless otherwise indicated.
The metadata of the records in the Repository are available under the CC0 public domain dedication: No Rights Reserved https://creativecommons.org/publicdomain/zero/1.0/
If you believe that any material held in STORRE infringes copyright, please contact email@example.com providing details and we will remove the Work from public display in STORRE and investigate your claim.