Research

Recent Talks:

• “Machines, Trees, Games, and Symmetries: An Introduction to Computability (and Non-Computability) Theory”
  Greg Nuckols, Ph.D., Acting Division Head of Mathematics
  April 13, 2012 – 3 p.m.

  Summary:
  Over the past 50 years, the computer revolution has transformed nearly every aspect of modern society. However, many people might not know that the idea of the stored-program computer was first devised (by Alan Turing) for theoretical purposes—to formalize the notion of computability. In this talk, I will informally present some of the fundamental ideas of computability theory, with a focus on computably enumerable sets. After discussing register machines, non-computable sets, and the use of priority arguments, I will present a bit of my own research on definability in the lattice of computably enumerable sets under inclusion. Along the way, I hope to illustrate the importance of conceptual tools and frameworks in contemporary mathematical research.

• “Queen Emma in History and Legend”
  Meg Lamont, Ph.D., Division Head of English
  January 27, 2012 – 3 p.m.

  Summary:
  This presentation will focus on medieval English Queen Emma in exploring the intersection and competition between fact and fiction and shifting conceptions of each.
  

• “Dispositions: Properties of Powers”
  Jonathan Weil, Ph.D., Core Instructor
  February 10, 2012 – 3 p.m.

  Summary:
  As a first pass, the following concepts are paradigmatically dispositional: fragile, soluble, and explosive. These examples exhibit an intuitive conceptual connection between having certain tendencies on one hand, and the entailment of conditionals on the other: fragile objects tend to break if they are struck properly in normal circumstances.
  
  Against this, properties such as tall, breaking, dead, and spatially located are paradigmatically categorical. Such qualities characterize how things are independent of any behavior or tendencies for action. To be sure there might be behavioral tendencies displayed by any and all things to which, say, dead is accurately ascribed - for instance, perhaps all dead things tend to become stiff and tend not to conduct electricity. Regardless, qualitative properties intuitively are not defined by such tendencies, in the manner dispositions do somehow intuitively seem to be.
  
  Jonathan Weil argues that dispositions, or powers, are among the most fundamental properties of the world. In particular, he maintains that certain kinds of properties are exclusively dispositional. He first details some important conceptual space in the philosophical literature on dispositions by precisely elucidating several major points of contention. Ultimately he appeals to a characterization of the scientific project to support the claim that brute powers do exist, and argues that this in turn counts in favor of a related account of dispositions. Along the way Dr. Weil details more general theories of dispositions reflected by various approaches to answering these contentious questions.

• “Philosophy in Secondary Education: The Case of the Online High School at Stanford University”
  Tomohiro Hoshi, Ph.D., Division Head of Core
  December 2, 2011 – 3 p.m.

  Summary:
  The heart of the Core curriculum at the Online High School may be characterized as "teaching philosophy in high school." Tomohiro Hoshi addressed the practical values of teaching philosophy, and discuss the methodological ideas underlying the OHS Core program about how to make philosophy possible in high school. The short talk was followed by a panel discussion with OHS philosophy instructors, Karen Kenkel, Jeffrey Scarborough, and Jonathan Weil, and students from each of the four Core courses.