An Analysis of Inconsistent and Incomplete Necker Cubes

  • Chris Mortensen Departments of Philosophy, Universities of Adelaide and Melbourne

Abstract

This paper aims to distinguish and classify sixteen versions of the Necker cube. In particular, it is shown how to describe inconsistent and incomplete theories which correspond in a systematic way to these sixteen diagrams. Concerning two of these sixteen cubes, there is a natural intuition that there is a sense in which they inconsistent. It is seen that this intuition is vindicated by an analysis in which their corresponding theories turn out to be globally inconsistent but not locally inconsistent, while various other cubes of the sixteen are merely locally inconsistent. The Routley functor is seen to be useful in classifying the relations between these diagrams.

Author Biography

Chris Mortensen, Departments of Philosophy, Universities of Adelaide and Melbourne
Published
2006-03-30
How to Cite
MORTENSEN, Chris. An Analysis of Inconsistent and Incomplete Necker Cubes. The Australasian Journal of Logic, [S.l.], v. 4, mar. 2006. ISSN 1448-5052. Available at: <https://ojs.victoria.ac.nz/ajl/article/view/1781>. Date accessed: 18 july 2019. doi: https://doi.org/10.26686/ajl.v4i0.1781.