The structure of epistemic probabilities
- PDF / 709,992 Bytes
- 30 Pages / 439.37 x 666.142 pts Page_size
- 74 Downloads / 182 Views
The structure of epistemic probabilities Nevin Climenhaga1
Springer Nature B.V. 2019
Abstract The epistemic probability of A given B is the degree to which B evidentially supports A, or makes A plausible. This paper is a first step in answering the question of what determines the values of epistemic probabilities. I break this question into two parts: the structural question and the substantive question. Just as an object’s weight is determined by its mass and gravitational acceleration, some probabilities are determined by other, more basic ones. The structural question asks what probabilities are not determined in this way—these are the basic probabilities which determine values for all other probabilities. The substantive question asks how the values of these basic probabilities are determined. I defend an answer to the structural question on which basic probabilities are the probabilities of atomic propositions conditional on potential direct explanations. I defend this against the view, implicit in orthodox mathematical treatments of probability, that basic probabilities are the unconditional probabilities of complete worlds. I then apply my answer to the structural question to clear up common confusions in expositions of Bayesianism and shed light on the ‘‘problem of the priors.’’ Keywords Bayesian epistemology Bayesian networks Explanation Probability Inference to the best explanation
1 Introduction Were the dinosaurs killed by an asteroid? I don’t know—and neither do you. How confident ought we to be that this proposition is true?
& Nevin Climenhaga [email protected] 1
Australian Catholic University, Fitzroy, VIC, Australia
123
N. Climenhaga
A plausible answer is that our confidence that the dinosaurs were killed by an asteroid ought to be equal to the probability of that proposition given our evidence. This raises two further questions: what is our evidence, and how is the probability of a proposition given some evidence determined? This paper is a first step in the (very large) project of answering the second of these questions. The relevant sense of probability here is epistemic probability. The epistemic probability of A given B—notated PðAjBÞ—is a relation between the propositions B and A. It is the degree to which B supports A, or makes A plausible. Entailment is a limiting case of this relationship; if B entails A, then PðAjBÞ ¼ 1: It constrains rational degrees of belief, in that, if PðAjBÞ ¼ n; then someone with B as their evidence ought to be confident in A to degree n.1 Keynes (1921), Jeffreys (1939), Cox (1946), Carnap (1950), Williamson (2000: ch. 10), Swinburne (2001), Jaynes (2003), Hawthorne (2005), and Maher (2006) offer similar explications of probability.2 There is a great deal more that could be said about the nature of epistemic probability. Most of the above authors claim that epistemic probability relations are necessary and knowable a priori. I am sympathetic to these claims, but the approach to the structure of epistemic probabilities I go on to defend c
Data Loading...
