2009: Volume 7

Linear Algebra Representation of Necker Cubes I: The Crazy Crate
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Chris Mortensen and Steve Leishman
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
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Chris Mortensen
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 higherorder 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
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Patrick Girard
6 pages. May 29, 2009

The Law of NonContradiction as a Metaphysical Principle
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Tuomas E. Tahko
16 pages. Published June 11, 2009
The goals of this paper are twofold: I wish to clarify the Aristotelian conception of the law of noncontradiction 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 noncontradiction is a metaphysical principle. The core idea is that the law of noncontradiction 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 noncontradiction 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 noncontradiction understood as a metaphysical principle.

A Note on Identity and Higher Order Quantification
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Rafal Urbaniak
8 pages. Published July 6, 2009
It is a commonplace remark that the identity relation, even though not expressible in a firstorder language without identity with classical settheoretic semantics, can be defined in a language without identity, as soon as we admit secondorder, settheoretically interpreted quantifiers binding predicate variables that range over all subsets of the domain. However, there are fairly simple and intuitive higherorder languages with settheoretic 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 higherorder languages not only depends on what variables range over, but also is sensitive to how predication is construed. This paper is a followup 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
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Rohan French and Lloyd Humberstone
6 pages. Published July 29, 2009
The purpose of the present note is to advertise an interesting conjecture concerning a wellknown 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.
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