Two Problems of Direct Inference
The article begins by describing two longstanding problems associated with direct inference. One problem concerns the role of uninformative frequency statements in inferring probabilities by direct inference. A second problem concerns the role of frequency statements with gerrymandered reference classes. I show that past approaches to the problem associated with uninformative frequency statements yield the wrong conclusions in some cases. I propose a modification of Kyburg’s approach to the problem that yields the right conclusions. Past theories of direct inference have postponed treatment of the problem associated with gerrymandered reference classes by appealing to an unexplicated notion of projectability. I address the lacuna in past theories by introducing criteria for being a relevant statistic. The prescription that only relevant statistics play a role in direct inference corresponds to the sort of projectability constraints envisioned by past theories.
- Bacchus, F. (1990). Representing and reasoning with probabilistic knowledge. Cambridge, Massachusetts: MIT Press.Google Scholar
- Fitelson, B., Hájek, A., & Hall, N. (2005). Probability. In S. Sarkar & J. Pfeifer (Eds.), Philosophy of science: An encyclopedia. Oxford: Routledge.Google Scholar
- Goodman, N. (1955). Fact, fiction, and forecast. Cambridge: Harvard University Press.Google Scholar
- Halpern, J. (2003). Reasoning about uncertainty. Cambridge: Harvard University Press.Google Scholar
- Kyburg, H. (1961). Probability and the logic of rational belief. Middleton, Connecticut: Wesleyan University Press.Google Scholar
- Pollock, J. (1990). Nomic probability and the foundations of induction. Oxford: Oxford University Press.Google Scholar
- Pollock, J. (2007). The Y-function. In G. Wheeler & B. Harper (Eds.), Probability and evidence: Essays in honour of Henry E. Kyburg Jr. London: College Publications.Google Scholar
- Pollock, J. (unpublished). Probable probabilities. PhilSci Archive, at: http://philsci-archive.pitt.edu/3340/.
- Pust, J. (2011). Sleeping beauty and direct inference. Analysis.Google Scholar
- Reichenbach, H. (1949). A theory of probability. Berkeley: Berkeley University Press.Google Scholar
- Salmon, W. (1971). Statistical explanation. In W. Salmon (Ed.), Statistical explanation and statistical relevance. Pittsburgh: University of Pittsburgh Press.Google Scholar
- Salmon, W. (1984). Scientific explanation and the causal structure of the world. Princeton: Princeton University Press.Google Scholar
- Thorn, P. (2007). Three problems of direct inference. Dissertation, University of Arizona.Google Scholar
- Thorn, P. (forthcoming). Undercutting defeat via reference properties of differing arity: a reply to Pust. Analysis. http://analysis.oxfordjournals.org/content/early/2011/09/02/analys.anr099.abstract.
- Venn, J. (1866). The logic of chance. New York: Chelsea Publishing Company.Google Scholar