|Appears in Collections:||Law and Philosophy Journal Articles|
|Peer Review Status:||Refereed|
|Title:||Probability as a Measure of Information Added|
|Citation:||Milne P (2012) Probability as a Measure of Information Added. Journal of Logic, Language and Information, 21 (2), pp. 163-188. http://www.scopus.com/inward/record.url?partnerID=yv4JPVwI&eid=2-s2.0-84858745390&md5=4bed76ec97860ab2a63e88d5e07ce9cd; https://doi.org/10.1007/s10849-011-9142-0|
|Abstract:||Some propositions add more information to bodies of propositions than do others. We start with intuitive considerations on qualitative comparisons of information added. Central to these are considerations bearing on conjunctions and on negations. We find that we can discern two distinct, incompatible, notions of information added. From the comparative notions we pass to quantitative measurement of information added. In this we borrow heavily from the literature on quantitative representations of qualitative, comparative conditional probability. We look at two ways to obtain a quantitative conception of information added. One, the most direct, mirrors Bernard Koopman's construction of conditional probability: by making a strong structural assumption, it leads to a measure that is, transparently, some function of a function P which is, formally, an assignment of conditional probability (in fact, a Popper function). P reverses the information added order and mislocates the natural zero of the scale so some transformation of this scale is needed but the derivation of P falls out so readily that no particular transformation suggests itself. The Cox-Good-Aczél method assumes the existence of a quantitative measure matching the qualitative relation, and builds on the structural constraints to obtain ameasure of information that can be rescaled as, formally, an assignment of conditional probability. A classical result of Cantor's, subsequently strengthened by Debreu, goes some way towards justifying the assumption of the existence of a quantitative scale. What the two approaches give us is a pointer towards a novel interpretation of probability as a rescaling of a measure of information added.|
|Rights:||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.|
|Milne-Probability2012.pdf||Fulltext - Published Version||431.99 kB||Adobe PDF||Under Embargo until 2999-12-25 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.