Probability as a Measure of Information Added

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 a measure 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
Keywords Information  Probability  Comparative probability  Koopman  Cox
Categories (categorize this paper)
DOI 10.1007/s10849-011-9142-0
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 25,727
Through your library
References found in this work BETA
Truth and Other Enigmas.Michael A. E. Dummett - 1978 - Harvard University Press.
Conjectures and Refutations.K. R. Popper - 1966 - Les Etudes Philosophiques 21 (3):431-434.
Accuracy and Coherence: Prospects for an Alethic Epistemology of Partial Belief.James Joyce - 2009 - In Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of Belief. Synthese. pp. 263-297.
What is a Theory of Meaning? (II).Michael Dummett - 1976 - In Gareth Evans & John McDowell (eds.), Truth and Meaning: Essays in Semantics. Oxford: Clarendon Press.

View all 12 references / Add more references

Citations of this work BETA
Belief, Degrees of Belief, and Assertion.Peter Milne - 2012 - Dialectica 66 (3):331-349.

Add more citations

Similar books and articles

Monthly downloads

Added to index

2012-03-23

Total downloads

41 ( #120,916 of 2,146,486 )

Recent downloads (6 months)

3 ( #226,458 of 2,146,486 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums