 In Hume’s argument, the UP plays a central role. As we will see in  section 4.2,  various authors have been doubtful about this principle. Versions of Hume’s argument have also been formulated which do not make reference to the UP. Rather they directly address the question of what arguments can be given in support of the transition from the premises to the conclusion of the specific inductive inference I. What arguments could lead us, for example, to infer that the next piece of bread will nourish from the observations of nourishing bread made so far? For the first horn of the argument, Hume’s argument can be directly applied. A demonstrative argument establishes a conclusion whose negation is a contradiction. The negation of the conclusion of the inductive inference is not a contradiction. It is not a contradiction that the next piece of bread is not nourishing. Therefore, there is no demonstrative argument for the conclusion of the inductive inference. In the second horn of the argument, the problem Hume raises is a circularity. Even if Hume is wrong that all inductive inferences depend on the UP, there may still be a circularity problem, but as we shall see in  section 4.1,  the exact nature of the circularity needs to be carefully considered. But the main point at present is that the Humean argument is often formulated without invoking the UP.