Probabilistic
Confirmation Theory and Bayesian Reasoning

An Annotated Bibliography Compiled by Timothy McGrew

This brief annotated bibliography is intended to help
students get started with their research. It is not a substitute for personal
investigation of the literature, and it is not a comprehensive bibliography on
the subject. For those just beginning to study probabilistic confirmation
theory and Bayesian reasoning, I suggest the starred items as good places to
start your reading.

R. Carnap, *Logical
Foundations of Probability*, 2nd ed. (Chicago: University of Chicago Press,
1962).

Massive and detailed. Carnap's treatment
of confirmation from a probabilistic point of view contrasts sharply with the
approach taken by Hempel in “Studies in the Logic of
Confirmation” (*Mind* 1945). In a later note (Postscript (1964) on
Confirmation) Hempel concedes that Carnap's approach may be necessary after all.

L. Jonathan Cohen, *An**
Introduction to the Philosophy of Induction and Probability* (Oxford: Oxford
University Press, 1989).

Full of interesting
historical information and challenging suggestions. Cohen contrasts two major concepts of
confirmation, which he terms “Baconian” and “Pascalian.” The latter is the common probabilistic concept,
but Cohen argues vigorously that Pascalian probability
cannot be the whole story about the logic of confirmation.

J. Earman, ed., *Testing
Scientific Theories*, vol. 10, *Minnesota**
Studies in the Philosophy of Science* (Minneapolis: University of Minnesota
Press, 1983).

An excellent collection of
essays, many pertaining to Glymour's work.

__________, *Bayes**
or Bust?* (Cambridge,
MA: MIT Press, 1992).

A sympathetic but critical
survey of the state of the art by a self-professed “lapsed Bayesian.” Parts of this are fairly technical.

Clark Glymour,
*Theory and Evidence* (Princeton: Princeton University Press, 1980).

Glymour's book caused quite a stir, largely because of
two features: his novel “bootstrapping” approach (which can look circular at
first glance) and his trenchant essay “Why I am not a Bayesian.”

Mary Hesse, *The** Structure of Scientific Inference*
(Berkeley: University of California Press, 1974).

C. Howson and P. Urbach, *Scientific Reasoning: the Bayesian Approach*
(La Salle, IL: Open Court, 1989).

The standard reference work
for Subjective Bayesians.
Howson and Urbach go well beyond
presenting their position, giving detailed criticisms of alternatives. They are
particularly critical of the classical tradition in statistical inference.

*P. Horwich,
*Probability and Evidence* (Cambridge: Cambridge University Press, 1982).

An elegant and highly
readable elementary treatment of the Bayesian approach to scientific reasoning. Horwich advocates
a “degree of belief” approach to probability, but he rejects Subjective Bayesianism in favor of a “rationalist” construal in which
an individual's probability assignments are subject to stronger constraints
than mere coherence. He then applies the Bayesian methodology to many puzzles
and problems and demonstrates its power. This one is well worth reading even if
you don't accept all of his solutions.

R. Jeffrey, *The**
Logic of Decision*, 2nd ed. (Chicago: University of Chicago Press, 1983).

A standard textbook on
Bayesian inference and decision theory from a Subjectivist or “Personalist” point of view. This book contains Jeffrey's own explication
of “Jeffrey conditioning,” a general probabilistic updating rule of which the
standard Bayesian conditioning is merely a special case.

__________, *Probability and the
Art of Judgment* (Cambridge: Cambridge University Press, 1992).

A collection of Jeffrey's essays applying and
extending Subjective Bayesian methods. Some of the essays are technical: others
are readable without a strong mathematical background so long as one has
mastered the basic probability calculus.

H. Jeffreys, *Scientific
Inference* (Cambridge: Cambridge University Press, 1937).

An early and forceful
presentation of the Objective Bayesian point of view. Though Jeffreys is
a high-powered writer and does not hesitate to invoke mathematics when it is
required, there is much here that can be understood even by readers who lack
strong mathematical preparation. The discussion of simplicity is particularly
important.

__________, *Theory of Probability*,
2nd ed. (Oxford: Oxford University Press, 1948).

A historically important
formulation of Objective Bayesianism. Jeffreys insists
that in situations of complete ignorance, we must select a prior probability in
such a way as to give experience the maximum impact on our posterior
probabilities. In some cases this leads him to endorse “improper” priors that
cannot be normalized. Often challenging reading, but
rewarding.

H. Kyburg, *Epistemology
and Inference* (Minneapolis: University of Minnesota Press, 1983).

Kyburg has long been one of the most vocal critics
of Subjectivism in probability. This collection of his essays is indispensible for anyone who wants to see what can be said
against Subjectivism. The essay on “Subjective Probability” is a classic. (Scan
the subtitle for acronyms.)

James Logue, *Projective Probability* (Oxford:
Oxford University Press, 1995).

Logue’s
book develops a version of personalism and claims
that it captures the univocal meaning of “probability.” He is skeptical,
however, about the attempt to resolve all questions about scientific inference
by appealing to Bayesian conditionalization. The book
contains a very interesting discussion of the problem of probabilistic “weight.”

R. Miller, *Fact and Method* (Princeton:
Princeton University Press, 1987).

Miller is deeply critical of Bayesian
approaches to scientific reasoning. His exposition of Subjective Bayesianism is a model of clarity, and his criticisms,
though uneven in quality, are sometimes exceedingly shrewd.

R. Rosenkrantz, *Inference,
Method and Decision: Towards a Bayesian Philosophy of Science* (Dordrecht: D. Reidel, 1977).

Prior to Jaynes’s
work, this was the definitive treatise on Objective Bayesianism.
Rosenkrantz advocates the use of “maximum entropy”
(or “maxent”) priors. His discussion of the
similarities and differences between various Objective Bayesian approaches is
illuminating, and his treatment of simplicity and “sample coverage” merits
close study. Of particular interest is Rosenkrantz's
careful treatment of Popper's philosophy of science; he maintains that many of
Popper's methodological insights can be recaptured within a Bayesian framework.

__________, *Foundations
and Applications of Inductive Probability* (Ridgeview, 1981)

This is a somewhat technical work that offers
the serious student a thorough introduction to probability from an objective
Bayesian standpoint. The book is not attractively printed, one of the sections
of chapter 4 promised in the index does not appear in the book, and my
paperback edition has fallen apart rather quickly under moderate use. But the
material is hard to find elsewhere in one place. Not a work for beginners, but
definitely an interesting book for those who are prepared to put some time into
the mathematics.

__________, “Why Glymour *Is*
a Bayesian,” in Earman (1983), pp. 69-98.

Just what it sounds like. Rosenkrantz argues
that notwithstanding his criticisms of Bayesians, Glymour
is actually more Bayesian than many who march under that banner.

*W. Salmon, *The**
Foundations of Scientific Inference* (Pittsburgh: University of Pittsburgh
Press, 1966).

An early and trenchant
argument for the applicability of Bayesian probability to problems of
scientific inference. The
initial survey of approaches to the problem of induction is very useful, and
the Bayesian sections of the book are worth reading even though they are not
the latest or deepest work on the subject.

__________, “Bayes's Theorem
and the History of Science,” in R. Stuewer, ed.,*
Historical and Philosophical Perspectives of Science*, vol. 5, *Minnesota
Studies in the Philosophy of Science* (Minneapolis: University of Minesota Press, 1970), pp. 68-86.

A classic essay in which
Salmon treats with good sense and sophistication the traditional problem of
separating the context of discovery from the context of justification. In the end he argues for the applicability
of Bayesian analyses to episodes in the history of science and suggests that
the difficult problem of prior probabilities is best approached through “plausibility
constraints.”

__________, “Rationality and Objectivity in Science, *or*
Tom Kuhn Meets Tom Bayes,” in C. W. Savage, ed., *Scientific
Theories*, vol. 14, *Minnesota Studies in the Philosophy of Science* (Minneapolis: University of Minnesota Press,
1990), pp. 175-204.

An attempt to clean up the
subjectivity rampant in Kuhn's philosophy of science by imposing some Bayesian
constraints on scientific inference. Kuhn, in his reply, disavowed even the constraints Salmon wanted to
place on such reasoning, though it's not entirely clear whether he was
caricaturing Salmon's position in so doing.

G. Schlesinger, *The**
Sweep of Probability* (Notre Dame: Notre Dame University Press, 1991).

A wide-ranging survey of
the applications of probability theory in general and Bayesian methods in
particular to various conundrums in epistemology and the philosophy of science.

A. Shimony, *Search for a
Naturalistic World View*, vol. 1, *Scientific Method and Epistemology*
(Cambridge: Cambridge University Press, 1993).

For the past several decades Shimony has made important contributions to Bayesian
epistemology and philosophy of science. This collection of his papers contains
much important material, including the initial essay endorsing “tempered” Bayesianism, the “Adamic
derivation” of the probability calculus, and too many other goodies to list.
Required reading for Bayesians (and non-Bayesians!) of any flavor.

R. Swinburne, *An** Introduction to Confirmation Theory*
(London: Methuen & Co. Ltd., 1973).

A small but rich book,
suitable for diligent readers who do not have much background in the subject. Swinburne surveys
the axioms of probability and discusses various ways in which they have been
criticized and alternative (often weaker) axioms that can be substituted in
their place. He also covers such classic topics as the Nicod
criterion and rightly points out that it cannot be sustained, even in its weak
form, as it stands. (