Both authors are philosophers, not mathematicians.
 If you are interested in the philosophy of Bayesianism, Probability Theory : The Logic of Science by E. T. Jaynes is definitely better.
 The knowledge required for reading this book is almost nothing, so it is useful to complete beginners of probability theory.
 Good Bayesian guys are always good philosophers and skilled at traditional theories. So what? Read the books written by good Bayesian mathematicians.
 The title is awesome, but the content is not commensurate.
This book contains lots of useful information for the budding Baysian. Excellent discussions on many topics. However, I have to give this only 3 stars, because on a cardinal point, the authors give very bad advice: they give the impression that Komogorov complexity-based methods are ill motivated. In fact, Kolmogorov complexity is one of the most fruitful new developments in Baysianism, and I have personally used it many times in industrial settings to solve otherwise intractible problems.
However, on most points the book is very useful. I recommend buying the first edition over the second, because the second edition doesn't really add that much useful info over the first. I also recommend buying in addition to this book Ming Li and Paul Vianyi's book on Kolmogorov complexity, for a comprehensive intro to a whole wonderland of Baysianism which Howson & Urbach have overlooked.