  A number of well-known theorems, such as Cox's theorem and de Finetti's
theorem. prove that any model of reasoning with uncertain information that
satisfies specified conditions of "rationality" must satisfy the axioms of
probability theory. I argue here that these theorems do not in themselves
demonstrate that probabilistic models are in fact suitable for any specific
task in automated reasoning or plausible for cognitive models. First, the
theorems only establish that there exists some probabilistic model; they do not
establish that there exists a useful probabilistic model, i.e. one with a
tractably small number of numerical parameters and a large number of
independence assumptions. Second, there are in general many different
probabilistic models for a given situation, many of which may be far more
irrational, in the usual sense of the term, than a model that violates the
axioms of probability theory. I illustrate this second point with an extended
examples of two tasks of induction, of a similar structure, where the
reasonable probabilistic models are very different.

Artificial Intelligence