Knowledge and Uncertainty
  One purpose -- quite a few thinkers would say the main purpose -- of seeking
knowledge about the world is to enhance our ability to make good decisions. An
item of knowledge that can make no conceivable difference with regard to
anything we might do would strike many as frivolous. Whether or not we want to
be philosophical pragmatists in this strong sense with regard to everything we
might want to enquire about, it seems a perfectly appropriate attitude to adopt
toward artificial knowledge systems. If is granted that we are ultimately
concerned with decisions, then some constraints are imposed on our measures of
uncertainty at the level of decision making. If our measure of uncertainty is
real-valued, then it isn't hard to show that it must satisfy the classical
probability axioms. For example, if an act has a real-valued utility U(E) if
the event E obtains, and the same real-valued utility if the denial of E
obtains, so that U(E) = U(-E), then the expected utility of that act must be
U(E), and that must be the same as the uncertainty-weighted average of the
returns of the act, p-U(E) + q-U('E), where p and q represent the uncertainty
of E and-E respectively. But then we must have p + q = 1.
