Steve Gardner

In this second volume of The Antipodean Philosopher, Graham Oppy and N.N. Trakakis have brought together fourteen leading Australasian philosophers, inviting them to speak in a frank and accessible way about their philosophical lives: for example, what drew them to a career in philosophy, what philosophy means to them, and their perceptions and criticisms of the ways in which philosophy is studied and taught in Australia and New Zealand. The philosophers interviewed include Brian Ellis, Frank Jackson, Jeff Malpas, Alan Musgrave, Philip Pettit, Graham Priest, Peter Singer and Michael Smith – philosophers who have distinguished themselves in the discipline, both nationally and internationally, over many years and in various branches of philosophy. What emerges from the discussion with these philosophers is a distinctive and engaging narrative of the history of philosophy in Australasia, its recent successes and flourishing, and the problems and prospects facing it in the twenty-first century. These interviews will challenge and entertain anyone with an interest in contemporary philosophy and the challenges of living out the examined life today.

Philosophy in both Australia and New Zealand has been has been experiencing, for some time now, something of a 'golden age', exercising an influence in the global arena that is disproportionate to the population of the two countries. To capture the distinctive and internationally recognised contributions Australasian philosophers have made to their discipline, a series of public talks by leading Australasian philosophers was convened at various literary events and festivals across Australia and New Zealand from 2006 to 2009. These engaging and often entertaining talks attracted large audiences, and covered diverse themes ranging from local histories of philosophy (in particular, the fortunes of philosophy in Melbourne, Sydney, Brisbane, Adelaide, and New Zealand); to discussions of specific topics (including love, free will, religion, ecology, feminism, and civilisation), especially as these have featured in the Australasian philosophy; and to examinations of the intellectual state of universities in Australasia at the beginning of the twenty-first century. These talks are now collected here for the first time, to provide not only students and scholars, but also the wider community with a deeper appreciation of the philosophical heritage of Australia and New Zealand.

The advent of formal definitions of the simplicity of a theory has important implications for model selection. But what is the best way to define simplicity? Forster and Sober ([1994]) advocate the use of Akaike's Information Criterion (AIC), a non-Bayesian formalisation of the notion of simplicity. This forms an important part of their wider attack on Bayesianism in the philosophy of science. We defend a Bayesian alternative: the simplicity of a theory is to be characterised in terms of Wallace's Minimum Message Length (MML). We show that AIC is inadequate for many statistical problems where MML performs well. Whereas MML is always defined, AIC can be undefined. Whereas MML is not known ever to be statistically inconsistent, AIC can be. Even when defined and consistent, AIC performs worse than MML on small sample sizes. MML is statistically invariant under 1-to-1 re-parametrisation, thus avoiding a common criticism of Bayesian approaches. We also show that MML provides answers to many of Forster's objections to Bayesianism. Hence an important part of the attack on Bayesianism fails. 1. Introduction2. The Curve Fitting Problem2.1 Curves and families of curves2.2 Noise2.3 The method of Maximum Likelihood2.4 ML and over-fitting3. Akaike's Information Criterion (AIC)4. The Predictive Accuracy Framework5. The Minimum Message Length (MML) Principle5.1 The Strict MML estimator5.2 An example: The binomial distribution5.3 Properties of the SMML estimator5.3.1 Bayesianism5.3.2 Language invariance5.3.3Generality5.3.4 Consistency and efficiency5.4 Similarity to false oracles5.5 Approximations to SMML6. Criticisms of AIC6.1 Problems with ML6.1.1 Small sample bias in a Gaussian distribution6.1.2 The von Mises circular and von Mises—Fisher spherical distributions6.1.3 The Neyman–Scott problem6.1.4 Neyman–Scott, predictive accuracy and minimum expected KL distance6.2 Other problems with AIC6.2.1 Univariate polynomial regression6.2.2 Autoregressive econometric time series6.2.3 Multivariate second-order polynomial model selection6.2.4 Gap or no gap: a clustering-like problem for AIC6.3 Conclusions from the comparison of MML and AIC7. Meeting Forster's objections to Bayesianism7.1 The sub-family problem7.2 The problem of approximation, or, which framework for statistics?8. ConclusionA. Details of the derivation of the Strict MML estimatorB. MML, AIC and the Gap vs. No Gap ProblemB.1 Expected size of the largest gapB.2 Performance of AIC on the gap vs. no gap problemB.3 Performance of MML in the gap vs. no gap problem.

James McAllister’s 2003 article, “Algorithmic randomness in empirical data” claims that empirical data sets are algorithmically random, and hence incompressible. We show that this claim is mistaken. We present theoretical arguments and empirical evidence for compressibility, and discuss the matter in the framework of Minimum Message Length (MML) inference, which shows that the theory which best compresses the data is the one with highest posterior probability, and the best explanation of the data.