 There have been different interpretations of what Hume means by “demonstrative” and “probable” arguments. Sometimes “demonstrative” is equated with “deductive”, and probable with “inductive” (e.g., Salmon 1966). Then the first horn of Hume’s dilemma would eliminate the possibility of a deductive argument, and the second would eliminate the possibility of an inductive argument. However, under this interpretation,  premise P3  would not hold, because it is possible for the conclusion of a deductive argument to be a non-necessary proposition. Premise  P3  could be modified to say that a demonstrative (deductive) argument establishes a conclusion that cannot be false if the premises are true. But then it becomes possible that the supposition that the future resembles the past, which is not a necessary proposition, could be established by a deductive argument from some premises, though not from a priori premises (in contradiction to conclusion  C1).