[1] Both authors are philosophers, not mathematicians.
[2] If you are interested in the philosophy of Bayesianism, Probability Theory : The Logic of Science by E. T. Jaynes is definitely better.
[3] The knowledge required for reading this book is almost nothing, so it is useful to complete beginners of probability theory.
[4] Good Bayesian guys are always good philosophers and skilled at traditional theories. So what? Read the books written by good Bayesian mathematicians.
[5] 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.