THE INADEQUACY OF A PROPOSED PARACONSISTENT SET THEORY REPLY
Source TitleReview of Symbolic Logic
PublisherCAMBRIDGE UNIV PRESS
University of Melbourne Author/sWeber, Zach
AffiliationSchool of Historical and Philosophical Studies, Faculty of Arts
Document TypeJournal Article
CitationsWeber, Z. (2011). THE INADEQUACY OF A PROPOSED PARACONSISTENT SET THEORY REPLY. REVIEW OF SYMBOLIC LOGIC, 4 (1), pp.109-113. https://doi.org/10.1017/S1755020310000304.
Access StatusOpen Access
© 2011 Association for Symbolic Logic. Online edition of the journal is available at http://journals.cambridge.org/RSL
In Bjørdal (2010), Bjørdal presents a paraconsistent set theory in which ∀x(x _= x) is a theorem. The author rightly claims that, while not trivializing (in the sense of proving everything), results like this are to be avoided. The set theory presented in Bjørdal (2010) is based on that of Weber (2010b), but with an introduced definition of identity—which is used, in effect, as a new axiom. With this added notion of identity, the non-self-identity of every object does in fact obtain; and so the set theory presented by Bjørdal is inadequate.......
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