2011: Volume 10

Proving Induction
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Alexander Paseau
17 pages. Published February 15, 2011
The hard problem of induction is to argue without begging the question that inductive inference, applied properly in the proper circumstances, is conducive to truth. A recent theorem seems to show that the hard problem has a deductive solution. The theorem, provable in zfc, states that a predictive function M exists with the following property: whatever world we live in, M correctly predicts the world’s present state given its previous states at all times apart from a wellordered subset. On the usual model of time a wellordered subset is small relative to the set of all times. M’s existence therefore seems to provide a solution to the hard problem. My paper argues for two conclusions. First, the theorem does not solve the hard problem of induction. More positively though, it solves a version of the problem in which the structure of time is given modulo our choice of set theory.

The Boxdot Conjecture and the Language of Essence and Accident
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Christopher Steinsvold
18 pages. Published February 15, 2011
We show the Boxdot Conjecture holds for a limited but familiar range of LemmonScott axioms. We reintroduce the language of essence and accident, first introduced by J. Marcos, and show how it aids our strategy.

Adding to Relevant Restricted Quantification
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Jc Beall
9 pages. Published April 14, 2011
This paper presents, in a more general setting, a simple approach to ‘relevant restricted generalizations’ advanced in previous work. After reviewing some desiderata for restricted generalizations, I present the target route towards achieving the desiderata. An objection to the approach, due to David Ripley, is presented, followed by three brief replies, one from a dialetheic perspective and the others more general.

Translatable SelfReference
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Hartley Slater
7 pages. Published May 19, 2011
Stephen Read has advanced a solution of certain semantic paradoxes recently, based on the work of Thomas Bradwardine. One consequence of this approach, however, is that if Socrates utters only ‘Socrates utters a falsehood’ (a), while Plato says ‘Socrates utters a falsehood’ (b), then, for Bradwardine two different propositions are involved on account of (a) being selfreferential, while (b) is not. Problems with this consequence are first discussed before a closely related analysis is provided that escapes it. Moreover, this alternative analysis merely relies on quantification theory at the propositional level, so there is very little to question about it. The paper is the third in a series explaining the superior virtues of a referential form of propositional quantification.

FraenkelCarnap Questions for Equivalence Relations
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George Weaver and Irena Penev
15 pages. Published May 27, 2011
An equivalence is a binary relational system A = (A,ϱ_{A}) where ϱ_{A} is an equivalence relation on A. A simple expansion of an equivalence is a system of the form (Aa_{1}…a_{n}) were A is an equivalence and a_{1},…,a_{n} are members of A. It is shown that the FraenkelCarnap question when restricted to the class of equivalences or to the class of simple expansions of equivalences has a positive answer: that the complete secondorder theory of such a system is categorical, if it is finitely axiomatizable.

Flexibility in Ceteris Paribus Reasoning
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Jeremy Seligman and Patrick Girard
33 pages. Published December 21, 2011
Ceteris Paribus clauses in reasoning are used to allow for defeaters of norms, rules or laws, such as in von Wright’s example “I prefer my raincoat over my umbrella, everything else being equal”. In earlier work, a logical analysis is offered in which sets of formulas Γ, embedded in modal operators, provide necessary and sufficient conditions for things to be equal in ceteris paribus clauses. For most laws, the set of things allowed to vary is small, often finite, and so Γ is typically infinite. Yet the axiomatisation they provide is restricted to the special and atypical case in which Γ is finite. We address this problem by being more flexible about ceteris paribus conditions, in two ways. The first is to offer an alternative, slightly more general semantics, in which the set of formulas only give necessary but not (necessarily) sufficient conditions. This permits a simple axiomatisation.
2011: Volume 8
in memory of Robert K. Meyer
(continued from 2010)

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7 pages. Published April 29, 2011
Methods for unifying inconsistent pairs of theories, which we call collectively MERGE, are defined and their properties outlined.
Copyright © 2011, Philosophy Department, University of Melbourne.
Individual papers are copyright their authors.