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THE INADEQUACY OF A PROPOSED PARACONSISTENT SET THEORY

  • FRODE BJØRDAL (a1)
Abstract

We show that a paraconsistent set theory proposed in Weber (2010) is strong enough to provide a quite classical nonprimitive notion of identity, so that the relation is an equivalence relation and also obeys full substitutivity: a = b → (F(a) → F(b)). With this as background it is shown that the proposed theory also proves ∀x(xx). While not by itself showing that the proposed system is trivial in the sense of proving all statements, it is argued that this outcome makes the system inadequate.

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Corresponding author
*DEPARTMENT OF PHILOSOPHY, CLASSICS AND THE HISTORY OF ARTS AND IDEAS, UNIVERSITY OF OSLO, 0315 OSLO, NORWAY. E-mail:frode.bjordal@ifikk.uio.no
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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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