  Uncertainty may be taken to characterize inferences, their conclusions, their
premises or all three. Under some treatments of uncertainty, the inferences
itself is never characterized by uncertainty. We explore both the significance
of uncertainty in the premises and in the conclusion of an argument that
involves uncertainty. We argue that for uncertainty to characterize the
conclusion of an inference is natural, but that there is an interplay between
uncertainty in the premises and uncertainty in the procedure of argument
itself. We show that it is possible in principle to incorporate all uncertainty
in the premises, rendering uncertainty arguments deductively valid. But we then
argue (1) that this does not reflect human argument, (2) that it is
computationally costly, and (3) that the gain in simplicity obtained by
allowing uncertainty inference can sometimes outweigh the loss of flexibility
it entails.
