Caramuel and the “Quantification of the Predicate”

Abstract

The theory of the “Quantification of the Predicate” attempts to transform the traditional logic of the four categorical forms (Every S is P; No S is P; Some S is P; Some S isn't P) into a system of eight or even twelve propositions in which the simple predicate P is replaced by a quantified predicate like ‘some P', ‘every P' and perhaps even ‘no P'. According to the standard historiography of logic, such a theory was invented in the 19th century by W. Hamilton and Augustus De Morgan. However, already in the 17th century, the Spanish logician Juan Caramuel y Lobkowitz published a book “Theologia rationalis” in which propositions with quantified predicates are systematically investigated. By way of a remarkable extension of the traditional theory of conversion, Caramuel arrives at a system of logical inferences which might be considered as a forerunner of Hamilton's theory. However, Caramuel's “method” basically consists only in listing various examples of true and false propositions. Therefore, his theory fails to provide a general semantics for propositions with a quantified predicate. One variant of such a semantics was developed in the 18th century by Gottfried Ploucquet. Another completely different one had been sketched already in the 17th century by Gottfried Wilhelm Leibniz. © Springer International Publishing Switzerland 2015.