"I shall adopt the convention by which particular propositions are taken as implying the existence of their subjects, and universal propositions as not implying the existence of their subjects. would infer that the two propositions The sea-serpent is not found in the water, The sea-serpent is not found out of the water, are contradictory; bur , , and would infer that the sea-serpent does not exist. With this convention, contradiction can never exist between universal propositions nor between particular propositions taken by themselves. A universal proportion can be contradicted only by a particular proposition, and a particular only by a universal. The above premises are inconsistent with The sea-serpent has (at least once) has been found. With this convention, hypothetical and categorical propositions receive the same formal treatment. If a, then b = all a is b = a implies b. (Peirce.)"