  Some criticisms that have been raised against the Cox approach to probability
theory are addressed. Should we use a single real number to measure a degree of
rational belief? Can beliefs be compared? Are the Cox axioms obvious? Are there
counterexamples to Cox? Rather than justifying Cox's choice of axioms we follow
a different path and derive the sum and product rules of probability theory as
the unique (up to regraduations) consistent representations of the Boolean AND
and OR operations.
