Leibniz's Logic and the ``Cube of Opposition''

Autor(en): Lenzen, Wolfgang
Stichwörter: concept logic; individual concepts; Leibniz; Logic; quantification of the predicate; Science & Technology - Other Topics; Square of opposition; theory of the syllogism
Erscheinungsdatum: 2016
Herausgeber: SPRINGER BASEL AG
Journal: LOGICA UNIVERSALIS
Volumen: 10
Ausgabe: 2-3, SI
Startseite: 171
Seitenende: 189
Zusammenfassung: 
After giving a short summary of the traditional theory of the syllogism, it is shown how the square of opposition reappears in the much more powerful concept logic of Leibniz (1646-1716). Within Leibniz's algebra of concepts (which may be regarded as an ``intensional'' counterpart of the extensional Boolean algebra of sets), the categorical forms are formalized straightforwardly by means of the relation of concept-containment plus the operator of concept-negation as `S contains P' and `S contains Not-P', `S doesn't contain P' and `S doesn't contain Not-P', respectively. Next we consider Leibniz's version of the so-called Quantification of the Predicate which consists in the introduction of four additional forms `Every S is every P', `Some S is every P', `Every S isn't some P', and `Some S isn't some P'. Given the logical interpretation suggested by Leibniz, these unorthodox propositions also form a Square of Opposition which, when added to the traditional Square, yields a ``Cube of Opposition''. Finally it is shown that besides the categorical forms, also the non-categorical forms can be formalized within an extension of Leibniz's logic where ``indefinite concepts'' X, Y, Z ... function as quantifiers and where individual concepts are introduced as maximally consistent concepts.
ISSN: 16618297
DOI: 10.1007/s11787-016-0143-2

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