What's a Bayesian? Well, I'm one, for example. But not according to Clark Glymour (1980, pp. 68-69) and some other definers of Bayesianism and personalism, such as Ian Hacking (1967, p. 314) and Isaac Levi (1980, p. xiv). Thus it behooves me to give an explicit account of the species of Bayesianism I espouse (sections 1 and 2) before adding my bit (section 3, with lots ofhelp from my friends) to Daniel Garber's treatment in this volume ofthe problem of new explanation of common knowledge: the so-called problem ofold evidence. With Clark Glymour, I take there to be identifiable canons of good thinking that get used on a large scale in scientific inquiry at its best; but unlike him, I take Bayesianism (what I call "Bayesianism") to do a splendid job of validating the valid ones and appropriately restricting the invalid ones among the commonly cited methodological rules. With Daniel Garber, I think that bootstrapping does well, too-when applied with a tact of which Bayesianism can give an account. But my aim here is to elaborate and defend Bayesianism (of a certain sort), not to attack bootstrapping. Perhaps the main novelty is the further rounding-out in section 3 (by John Etchemendy, David Lewis, Calvin Nonnore, and me) of Daniel Garber's treatment of what I have always seen as the really troubling one of Clark Glymour's strictures against Bayesianism. After that there is a coda (section 4) in which I try to display and explain how probability logic does so much more than truth-value logic. 1. Response to New Evidence In Clark Glymour's book, you aren't a Bayesian unless you update your personal probabilities by conditioning (a.k.a. "conditionalization"), i.e., like this: As new evidence accumulates, the probability of a proposition changes according to Bayes' rule: the posterior probability of a hypothesis on the new evidence is equal to the prior conditional probability of the hypothesis on the evidence. (p. 69) 133
[1]
P. Diaconis,et al.
Updating Subjective Probability
,
1982
.
[2]
Marc Snir,et al.
Probabilities over rich languages, testing and randomness
,
1982,
Journal of Symbolic Logic.
[3]
William Harper,et al.
Toward an Optimization Procedure for Applying Minimum Change Principles in Probability Kinematic
,
1976
.
[4]
R. Jeffrey.
Carnap's Empiricism
,
1975
.
[5]
I. Levi.
On Indeterminate Probabilities
,
1974
.
[6]
Henry E. Kyburg,et al.
Probability, Induction and Statistics. Bruno de Finetti
,
1973
.
[7]
Bruno de Finetti,et al.
Probability, induction and statistics
,
1972
.
[8]
R. Jeffrey.
Dracula Meets Wolfman: Acceptance vs. Partial Belief
,
1970
.
[9]
Ian Hacking,et al.
Slightly More Realistic Personal Probability
,
1967,
Philosophy of Science.
[10]
D. F. Kerridge,et al.
The Logic of Decision
,
1967
.
[11]
Ethan D. Bolker,et al.
Functions resembling quotients of measures
,
1966
.
[12]
T. Hailperin,et al.
Best Possible Inequalities for the Probability of a Logical Function of Events
,
1965
.
[13]
H. Gaifman.
Concerning measures in first order calculi
,
1964
.
[14]
L. J. Savage,et al.
The Foundations of Statistics
,
1955
.
[15]
Abraham Wald,et al.
Statistical Decision Functions
,
1951
.
[16]
R. Carnap,et al.
On Inductive Logic
,
1945,
Philosophy of Science.
[17]
B. O. Koopman.
The Axioms and Algebra of Intuitive Probability
,
1940
.
[18]
J. Keynes.
A Treatise on Probability.
,
1923
.