A Reinterpretation of Jespersen’s Notion of Negation

Abstract

In his various works (1917, 1924, 1933), Jespersen proposed a tripartite analysis of negation. While the two predicates “is rich” and “is not rich” are contradictory, he argues, for instance, that the two sentences “John is rich” and “John is not rich” are not contradictory, but only contrary because the term “John” may refer to someone who is neither rich nor non-rich. This argument cannot, however, be validated on the bassis of the normal bivalent logic, thus requiring some particular interpretation of his notion of negation. This paper aims at reinterpreting Jespersen’s so-called tripartite analysis of negation without violating the traditional principles of logics. By introducing possible worlds semantics, attempts will be made on reinterpreting some of Jespersen’s analyses of negation and accommodating his tripartite view of negation within the formal elementary logics. Some modal notions of necessity or certainty may be called for to support the present analysis.