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THE INADEQUACY OF A PROPOSED PARACONSISTENT SET THEORY

Published online by Cambridge University Press:  13 September 2010

FRODE BJØRDAL
FRODE BJØRDAL*
Affiliation:
Department of Philosophy, Classics and the History of Arts and Ideas, University of Oslo
*
*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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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(x ≠ x). 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.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 4 , Issue 1 , March 2011 , pp. 106 - 108
Copyright
Copyright © Association for Symbolic Logic 2010

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References

BIBLIOGRAPHY

Weber, Z. (2010). Transfinite numbers in paraconsistent set theory. Review of Symbolic Logic, 3(1), 71–92.CrossRefGoogle Scholar