Philosophy of probability
My latest book on foundations of probability,
"Resonance: From Probability to Epistemology and Back",
is available at
Amazon
and at
publisher's Web site (if you quote the code WSMTH1220 at the publisher Web site, you will receive 20% discount).
The back cover blurb:
"
Resonance examines some building blocks of epistemology as a prelude to the careful analysis of the foundations of probability. The concept of resonance is introduced to shed light on the philosophical problems of induction, consciousness, intelligence and free will. The same concept is later applied to provide support for a new philosophical theory of probability.
Although based on existing ideas and theories, the epistemological concept of resonance is investigated for the first time in this book. The bestknown philosophical theories of probability, frequency and subjective, are shown to be unrealistic and dissociated from the two main branches of statistics: frequency statistics and Bayesian statistics.
Written in an accessible style, this book can be enjoyed by philosophers, statisticians and mathematicians, and also by anyone looking to expand their understanding of the disciplines of epistemology and probability."
My views on the
philosophy of probability were originally presented
in my first book on the subject,
"The Search for Certainty.
On the Clash of Science and Philosophy of Probability".

Free preview:
preface, contents and introduction (PDF, 191kb).
 Visit the
book
Web site at World Scientific and
buy
the book.
 The book is also available at
Amazon.
 See Larry Wasserman's
review
of my book. The review contains a crystal clear
summary of the main ideas in my book.
 The following quotes come from Adrew Gelman's
blog.
 Larry Wasserman: "I think this is an interesting and important book."

Larry Wasserman: "Burdzy makes a convincing case that the philosophy of probability is a
complete failure."

Andrew Gelman: "Chris:
I am in complete agreement with your claim that the theories of von Mises and de Finetti completely fail to describe what statisticians actually do."

Christian Robert quotes my asertion that
"the original theories of von Mises and de Finetti
are completely unrelated to statistics"
in his review of my book.
He calls it "appealing" because he believes that
"[...] their philosophical theories have not had a lasting impact on statistics."

A.I. Dale writes in the Math Review (MR2510150) of the book:
"[...] there is much to absorb, but the careful reader
will find considerable food for thought here."
The slides of the October 23, 2006, talk at the Department
of Statistics, University of Washington, "De Finetti's
ultimate failure":
PowerPoint,
PDF.
The slides of the October 13, 2008, talk at the Department
of Statistics, University of Washington, "Philosophy
of probability and its relationship (?) to statistics":
PowerPoint,
PDF.
The slides of the August 25, 2013, talk at the
59th World Statistics Congress (Hong Kong)
titled `Statistics and philosophy of probability
 six degrees of sepration':
PDF.
I find the following "new prisoner's
paradox"
and its followup dealing with some ethical
questions
entertaining.
An "insider trading
paradox"
is based on a similar probabilistic idea
but does not have much philosophical significance
 I consider it an interesting textbook example.