Risk analysts often gloss over the differences between probabilistic risk and scientific uncertainty. This paper analyzes some of the important differences using ideas from the philosophy of science and subjective probability. The paper includes a discussion of the ways in which numerical probability judgments become incomplete proxies for the real uncertainties associated with different risks. A foundational discussion of subjective probability is included relating the modern ideas of behavioral researchers such as Amos Tversky to the original conception of subjective probability devised by Frank Ramsey in the 1920s.