A Budget of Cross-Type Inferences, or Invention Is the Mother of Necessity

Abstract

From what is contingent nothing necessary follows. And from what is necessary nothing contingent follows. Let us call this ‘the Hume-Leibniz dictum’. These theses never occur full-blown in Hume or Leibniz, but the dictum is implicit within the philosophies history has come to associate with these thinkers. Thus Hume writes:And Leibniz says:Stressing these differences in type between necessary and contingent propositions is proceeding toward a rejection, by Hume and by Leibniz, of the possibility of any genuine, nondegenerate, cross-type inference. For, if P states a possible matter of fact, so does ~P. But then neither P nor ~P implies what is logically false. This much cross-typicality is clearly barred by Hume.