 As we have seen in  section 1,  Hume takes demonstrative arguments to have conclusions which are “relations of ideas”, whereas “probable” or “moral” arguments have conclusions which are “matters of fact”. Hume’s distinction between “relations of ideas” and “matters of fact” anticipates the distinction drawn by Kant between “analytic” and “synthetic” propositions (Kant 1781). A classic example of an analytic proposition is “Bachelors are unmarried men”, and a synthetic proposition is “My bike tyre is flat”. For Hume, demonstrative arguments, which are based on a priori reasoning, can establish only relations of ideas, or analytic propositions. The association between a prioricity and analyticity underpins  premise P3,  which states that a demonstrative argument establishes a conclusion whose negation is a contradiction.