A new look at Counterexamples in topology

The book Counterexamples in Topology is a useful catalogue of topological spaces and properties. This thesis extends that catalogue to the properties of sobriety and packedness, and describes some related theory. A purely topological account of sobriety and sober reflections is given, together with an account of the connection with point-free topology which motivates it. Concrete constructions of the sober, T0 and T1 reflections of a topological space are given, and these are calculated for each space in Counterexamples in Topology. These are used to study the relationship between sobriety and the T1 separation property. The notion of a specialization topology is introduced as a means of constructing topological spaces from quasiordered sets. The Alexandrov, Scott and weak topologies are described and shown to be examples of this notion. The sobriety and sober reflections of specialization topologies are considered, and these motivate a suggestion for a generalization of the notion of a topological space. The calculations in this thesis are summarized in two reference tables

Partial Matrix Techniques.

Partial matrix techniques are those in which gravity models are fitted to a partially observed matrix of trips and journey costs, and used to infer the trips in the unobserved cells. This paper reviews the theoretical basis from which such techniques have been developed, and demonstrates the need to pay careful attention to the - underlying assumptions, which in effect require that the model be a good fit to be observed data (and also a good 'fit' to the unobserved data). Circumstances are described in which the estimates for the unobserved cells may not be uniquely determined, and the effects of data structure on the reliability of the estimates (assuming these to be unique) are discussed. Ways are suggested in which further theoretical and empirical research might demonstrate whether a given pattern of observations would lead to particularly error-prone estimates

The rational field is not universally definable in pseudo-exponentiation

We show that the field of rational numbers is not definable by a universal formula in Zilber's pseudo-exponential field

A note on the axioms for Zilber's pseudo-exponential fields

We show that Zilber's conjecture that complex exponentiation is isomorphic to his pseudo-exponentiation follows from the a priori simpler conjecture that they are elementarily equivalent. An analysis of the first-order types in pseudo-exponentiation leads to a description of the elementary embeddings, and the result that pseudo-exponential fields are precisely the models of their common first-order theory which are atomic over exponential transcendence bases. We also show that the class of all pseudo-exponential fields is an example of a non-finitary abstract elementary class, answering a question of Kes\"al\"a and Baldwin.Comment: 10 pages, v2: substantial alteration

Naturalism and Moral Expertise in the Zhuangzi

This essay will examine scholarly attempts at distilling a proto-ethical philosophy from the Daoist classic known as the Zhuangzi. In opposition to interpretations of the text which characterize it as amoralistic, I will identify elements of a natural normativity in the Zhuangzi. My examination features passages from the Zhuangzi – commonly known as the “knack” passages – which are often interpreted through some sort of linguistic, skeptical, or relativistic lens. Contra such readings, I believe the Zhuangzi prescribes an art of living – or shù [術] – which incorporates a few motifs familiar to certain threads of philosophical naturalism. Building on existing scholarship which treats of the praxeology of the text, I argue that the naturalist themes present in the Zhuangzi support an unusual, but robust, view of moral expertise