It remains possible to construct a demonstrative argument establishing only that the conclusion of an inductive inference is probable or likely

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