What is a good book about the philosophy behind Bayesian thinking? What is a good book about Bayesian philosophy, contrasting subjectivists against objectivists, explaining the view of probability as state of knowledge in Bayesian statistics, etc.? Maybe Savage's book?
At first I thought Berger (1986) could work, but it is not what I am looking for. Searching for such a book just doesn't quite lead to the results I am looking for.
 A: I'm a particular fan of Understanding Uncertainty by Dennis Lindley.  I actually emailed Jay Kadane a while back to ask the same question you did, and he recommended me this book.
A: Probability, The Logic of Science by E.T. Jaynes, provides excellent discussions around this subject. Jaynes is on the side of Objective Bayesianism.
Related books that influenced Jaynes' book are Jeffreys' Theory of Probability of 1939 (1948, 1961), Good's Probability & the Weighing of Evidence of 1950 and Savage's Foundations of Statistics of 1954.
A: Here is a recent title with a focus on regression: Bayesian and Frequentist Regression Methods
A: Jay Kadane's Principles of uncertainty is a recent and highly coherent introduction to subjective Bayesian thinking. I reviewed it there and definitely recommend it.
A: One of the most lucid expositions of Bayesian Thinking can be found in "Bayes' Rule" by Jim Stone. The same book comes in a several versions, with accompanying R, Python and MATLAB code. 
http://jim-stone.staff.shef.ac.uk/BookBayes2012/BayesRuleBookMain.html 
