2009: Volume 7

• Linear Algebra Representation of Necker Cubes I: The Crazy Crate
  Chris Mortensen and Steve Leishman

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  9 pages. Published March 27, 2009

  We apply linear algebra to the study of the inconsistent figure known as the Crazy Crate. Disambiguation by means of occlusions leads to a class of sixteen such figures: consistent, complete, both and neither. Necessary and sufficient conditions for inconsistency are obtained.

• Linear Algebra Representation of Necker Cubes II: The Routley Functor and Necker Chains
  Chris Mortensen

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  16 pages. Published March 27, 2009

  In this sequel, linear algebra methods are used to study the Routley Functor, both in single Neckers and in Necker chains. The latter display a certain irreducible higher-order inconsistency. A definition of degree of inconsistency is given, which classifies such inconsistency correctly with other examples of local and global inconsistency.

• Review: H. van Ditmarsch, W. van der Hoek and B. Kooi’s Dynamic Epistemic Logic
  Patrick Girard

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  6 pages. May 29, 2009

• The Law of Non-Contradiction as a Metaphysical Principle
  Tuomas E.  Tahko

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  16 pages. Published June 11, 2009

  The goals of this paper are two-fold: I wish to clarify the Aristotelian conception of the law of non-contradiction as a metaphysical rather than a semantic or logical principle, and to defend the truth of the principle in this sense. First I will explain what it in fact means that the law of non-contradiction is a metaphysical principle. The core idea is that the law of non-contradiction is a general principle derived from how things are in the world. For example, there are certain constraints as to what kind of properties an object can have, and especially: some of these properties are mutually exclusive. Given this characterisation, I will advance to examine what kind of challenges the law of non-contradiction faces—the main opponent here is Graham Priest. I will consider these challenges and conclude that they do not threaten the truth of the law of non-contradiction understood as a metaphysical principle.

• A Note on Identity and Higher Order Quantification
  Rafal Urbaniak

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  8 pages. Published July 6, 2009

  It is a commonplace remark that the identity relation, even though not expressible in a first-order language without identity with classical set-theoretic semantics, can be defined in a language without identity, as soon as we admit second-order, set-theoretically interpreted quantifiers binding predicate variables that range over all subsets of the domain. However, there are fairly simple and intuitive higher-order languages with set-theoretic semantics (where the variables range over all subsets of the domain) in which the identity relation is not definable. The point is that the definability of identity in higher-order languages not only depends on what variables range over, but also is sensitive to how predication is construed. This paper is a follow-up to (Urbaniak 2006), where it has been proven that no actual axiomatization of Leśniewski’s Ontology determines the standard semantics for the epsilon connective.

• Partial Confirmation of a Conjecture on the Boxdot Translation in Modal Logic
  Rohan French and Lloyd Humberstone

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  6 pages. Published July 29, 2009

  The purpose of the present note is to advertise an interesting conjecture concerning a well-known translation in modal logic, by confirming a (highly restricted) special case of the conjecture.

Copyright © 2009, School of Philosophy, Anthropology and Social Inquiry, University of Melbourne.
Individual papers are copyright their authors.