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

DC FieldValueLanguage
dc.contributor.authorLenzen, Wolfgang
dc.date.accessioned2021-12-23T16:05:00Z-
dc.date.available2021-12-23T16:05:00Z-
dc.date.issued2016
dc.identifier.issn16618297
dc.identifier.urihttps://osnascholar.ub.uni-osnabrueck.de/handle/unios/6727-
dc.description.abstractAfter 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.
dc.language.isoen
dc.publisherSPRINGER BASEL AG
dc.relation.ispartofLOGICA UNIVERSALIS
dc.subjectconcept logic
dc.subjectindividual concepts
dc.subjectLeibniz
dc.subjectLogic
dc.subjectquantification of the predicate
dc.subjectScience & Technology - Other Topics
dc.subjectSquare of opposition
dc.subjecttheory of the syllogism
dc.titleLeibniz's Logic and the ``Cube of Opposition''
dc.typejournal article
dc.identifier.doi10.1007/s11787-016-0143-2
dc.identifier.isiISI:000411396400004
dc.description.volume10
dc.description.issue2-3, SI
dc.description.startpage171
dc.description.endpage189
dc.identifier.eissn16618300
dc.publisher.placePICASSOPLATZ 4, BASEL, 4052, SWITZERLAND
dcterms.isPartOf.abbreviationLog Universalis
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