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 19491939 (1948, 1961), Good's Probability & the Weighing of Evidence of 1950 and Savage's Foundations of Statistics of 1954.