In this work Henry Kyburg presents his views on a wide range of philosophical problems associated with the study and practice of science and mathematics. The main structure of the book consists of a presentation of Kyburg's notions of epistemic probability and its use in the scientific enterprise i.e., the effort to modify previously adopted beliefs in the light of experience. Intended for cognitive scientists and people in artificial intelligence as well as for technically oriented philosophers, the book also provides a general overview of the philosophy of science for the non-philosopher by one of the leading authorities in the field.