Graduate studies at Western
Journal of Logic, Language and Information 21 (2):163-188 (2012)
|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)|
|Through your library||Configure|
Similar books and articles
Charles G. Morgan (1999). Conditionals, Comparative Probability, and Triviality: The Conditional of Conditional Probability Cannot Be Represented in the Object Language. Topoi 18 (2):97-116.
Louis Narens (1980). On Qualitative Axiomatizations for Probability Theory. Journal of Philosophical Logic 9 (2):143 - 151.
Kevin Nelson (2009). On Background: Using Two-Argument Chance. Synthese 166 (1):165 - 186.
Luciano Floridi (2004). Outline of a Theory of Strongly Semantic Information. Minds and Machines 14 (2):197-221.
John C. Bigelow (1979). Quantum Probability in Logical Space. Philosophy of Science 46 (2):223-243.
Louis-Marie Vincent (1994). Reflexions Sur l'Usage, En Biologie, de la Theorie de L'Information. Acta Biotheoretica 42 (2-3).
James Woodward (1987). On an Information-Theoretic Model of Explanation. Philosophy of Science 54 (1):21-44.
Michael Huemer (2007). Weak Bayesian Coherentism. Synthese 157 (3):337 - 346.
G. Schurz & H. Leitgeb (2008). Finitistic and Frequentistic Approximation of Probability Measures with or Without Σ -Additivity. Studia Logica 89 (2):257 - 283.
M. von Thun (2001). Probability Theory and Probability Semantics. Australasian Journal of Philosophy 79 (4):570 – 571.
Robert C. Stalnaker (1970). Probability and Conditionals. Philosophy of Science 37 (1):64-80.
Added to index2012-03-23
Total downloads15 ( #86,056 of 739,396 )
Recent downloads (6 months)1 ( #61,680 of 739,396 )
How can I increase my downloads?