The conflict of narrowness and precision in direct inference occurs if a body of evidence contains estimates for frequencies in a certain reference class and less precise estimates for frequencies in a narrower reference class. To develop a solution to this conflict, I draw on ideas developed by Paul Thorn and John Pollock. First, I argue that Kyburg and Teng’s solution to the conflict of narrowness and precision leads to unreasonable direct inference probabilities. I then show that Thorn’s recent solution (...) to the conflict leads to unreasonable direct inference probabilities. Based on my analysis of Thorn’s approach, I propose a natural distribution for a Bayesian analysis of the data directly obtained from studying members of the narrowest reference class. (shrink)

Direct inferences identify certain probabilistic credences or confirmation-function-likelihoods with values of objective chances or relative frequencies. The best known version of a direct inference principle is David Lewis’s Principal Principle. Certain kinds of statements undermine direct inferences. Lewis calls such statements inadmissible. We show that on any Bayesian account of direct inference several kinds of intuitively innocent statements turn out to be inadmissible. This may pose a significant challenge to Bayesian accounts of direct inference. We suggest some ways in which (...) these challenges may be addressed. (shrink)