Under the deductive/inductive interpretation, premise P3 asserts that a demonstrative argument establishes a necessary conclusion.

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 deductiv