Please use this identifier to cite or link to this item: http://hdl.handle.net/1893/6545
Appears in Collections:Law and Philosophy Journal Articles
Peer Review Status: Refereed
Title: Probability as a Measure of Information Added
Authors: Milne, Peter
Contact Email: peter.milne@stir.ac.uk
Keywords: Information
Probability
Comparative probability
Koopman
Cox
Issue Date: 2012
Publisher: Springer Verlag
Citation: Milne P (2012) Probability as a Measure of Information Added, Journal of Logic, Language and Information, 21 (2), pp. 163-188.
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
Type: Journal Article
URI: http://hdl.handle.net/1893/6545
URL: http://www.scopus.com/inward/record.url?partnerID=yv4JPVwI&eid=2-s2.0-84858745390&md5=4bed76ec97860ab2a63e88d5e07ce9cd
DOI Link: http://dx.doi.org/10.1007/s10849-011-9142-0
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.
Affiliation: Philosophy

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