Barker is the author of: •
Induction and hypothesis: a study of the logic of confirmation (Cornell University Press, 1957). This study of theories of informal reasoning is structured in four parts: an investigation of the
problem of induction, a rejection of explanations based on overriding premises (such as the uniformity of nature) as a form of
begging the question, an overview of
positivist approaches to the problem, and finally a resolution to the problem based on theories of
John George Kemeny involving the selection of the most likely hypothesis to fit a set of observations. •
Philosophy of mathematics (Prentice-Hall, 1964). Part of a series of books (edited by Elizabeth and
Monroe Beardsley) overviewing the main areas of philosophy, this book describes the main problems in the
philosophy of mathematics and evaluates their proposed solutions. Its five chapters concern
Euclidean and
non-Euclidean geometry, and literalist and non-literalist views on the meaning of numbers. •
The elements of logic (McGraw Hill, 1965) •
Thomas Reid critical interpretations (with Tom L. Beauchamp, Philosophical monographs, 1976) In addition, he edited
John Wisdom's
Proof and explanation: the Virginia lectures (University Press of America, 1991), co-edited
The Legacy of logical positivism; studies in the philosophy of science with
Peter Achinstein (Johns Hopkins Press, 1969), ==References==