Uncertain inferences and uncertain conclusions

Uncertainty may be taken to characterize inferences, their conclusions, their premises or all three. Under some treatments of uncertainty, the inference 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 in inference can sometimes outweigh the loss of flexibility it entails.