 The first horn of Hume’s argument, as formulated above, is aimed at establishing that there is no demonstrative argument for the UP. There are several ways people have attempted to show that the first horn does not definitively preclude a demonstrative or a priori argument for inductive inferences. One possible escape route from the first horn is to deny  premise P3,  which amounts to admitting the possibility of synthetic a priori propositions  (section 3.1).  Another possibility is to attempt to provide an a priori argument that the conclusion of the inference is probable, though not certain. The first horn of Hume’s dilemma implies that there cannot be a demonstrative argument to the conclusion of an inductive inference because it is possible to conceive of the negation of the conclusion. For instance, it is quite possible to imagine that the next piece of bread I eat will poison me rather than nourish me. However, this does not rule out the possibility of a demonstrative argument that establishes only that the bread is highly likely to nourish, not that it definitely will. One might then also challenge  premise P8,  by saying that it is not necessary for justification of an inductive inference to have a chain of reasoning from its premises to its conclusion. Rather it would suffice if we had an argument from the premises to the claim that the conclusion is probable or likely. Then an a priori justification of the inductive inference would have been provided. There have been attempts to provide a priori justifications for inductive inference based on Inference to the Best Explanation  (section 3.2).  There are also attempts to find an a priori solution based on probabilistic formulations of inductive inference, though many now think that a purely a priori argument cannot be found because there are empirical assumptions involved (sections  3.3  -3.5).