“There has been much unnecessary controversy over Cox’s Theorem due
to differing implicit assumptions as to the nature of its plausibility function.
Halpern [11, 12] claims to demonstrate a counterexample to Cox’s Theorem
by examining a finite problem domain, but his argument presumes that there
is a different plausibility function for every problem domain.”
FWIW, Van Horn says:
“There has been much unnecessary controversy over Cox’s Theorem due to differing implicit assumptions as to the nature of its plausibility function. Halpern [11, 12] claims to demonstrate a counterexample to Cox’s Theorem by examining a finite problem domain, but his argument presumes that there is a different plausibility function for every problem domain.”