Caramuel and the “Quantification of the Predicate”

  • Wolfgang Lenzen
Part of the Studies in Universal Logic book series (SUL)


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.


History of logic 17th century Categorical forms Quantification of the predicate Juan Caramuel y Lobkowitz Gottfried Ploucquet Gottfried Wilhelm Leibniz 

Mathematics Subject Classification

03A05 03B65 03B99 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.University of OsnabrückOsnabrückGermany

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