I don't know if these are what you're looking for but:

Probability Theory: The Logic of Science by Jaynes, spends its first chapter explaining why we need a 'calculus of plausibility' and what such a calculus should hope to achieve. The rest of the book is mostly about setting it up and showing what it can do. (The link does not contain the whole book, only the first few chapters, you may need to buy or borrow it to get the rest).

Yudkowsky's Technical explanation, which assumes the reader is already familiar with the theorem, explains some of its implications for scientific thinking in general.