 Three years later, in his “Description of a Notation for the Logic of Relatives” (1870) Peirce produced a major expansion of Boole’s system. De Morgan had pointed out (De Morgan 1864) that the Aristotelian syllogistic was incapable of handling such inferences as, “If every man is an animal, then every head of a man is a head of an animal”. De Morgan had introduced a logic of relations, defined the converse and the contrary of a relation, and, for relations such as “X is a lover of Y” and “Z is a servant of W”, had explored such compositions of relations as “x is the lover of a servant of y”. This work successfully expanded the Aristotelian syllogistic logic, but was also limited in several ways. First, De Morgan only operated with binary relations. Secondly, his notation was clumsy. (For example: if \(X\pdot\pdot LY\) designates that X is a lover of Y, then \(X\pdot LY\) designates that X is not a lover of Y. De Morgan has no separate sign for negation, nor for the Boolean propositional connectives.)