 Another common reading is to equate “demonstrative” with “deductively valid with a priori premises”, and “probable” with “having an empirical premise” (e.g., Okasha 2001). This may be closer to the mark, if one thinks, as Hume seems to have done, that premises which can be known a priori cannot be false, and hence are necessary. If the inference is deductively valid, then the conclusion of the inference from a priori premises must also be necessary. What the first horn of the dilemma then rules out is the possibility of a deductively valid argument with a priori premises, and the second horn rules out any argument (deductive or non-deductive), which relies on an empirical premise.