Abstract

I recognize within Hume’s philosophical texts several occurrences of doubly negated propositions whose corresponding affirmative propositions lack of evidence; in these cases the double negation law fails and the propositions belong to intuitionist logic. Their mere sequence preserves the logical thread of the illustration of the subject. Moreover the texts present intuitionist ad absurdum arguments. All that proves that Hume was unaware he made use of intuitionist logic. Since he considered only classical logic his philosophy represents no more than an attempt to obtain a new way of arguing; owing to the same reason the empiricist program remained incomplete.