I am working on the following projects.
Statistical Learning Theory and the Problem of Induction
One “easier” form of the problem of induction questions our ability to pick out true regularities in nature, using limited data, with the assumption that such regularities do exist. Harman and Kulkarni (2012) take this problem to be a challenge on our ability to identify precise conditions under which the method of picking hypotheses based on limited datasets is or is not reliable. They identify an influential result from statistical learning theory, hereafter referred to as the VC theorem (Vapnik and Chervonenkis, 2015), which states that, under the condition that the starting hypotheses set has finite VC dimension, the hypothesis chosen from it converges to the true regularity as the size of the dataset goes to infinity.
This result seems to provide us with a condition (i.e., having finite VC dimension) under which a method (i.e., choosing a hypothesis based on its performance over data), is reliable. Indeed, Harman and Kulkarni take this result to be an answer to the form of the problem of induction they have identified. This paper examines this claim. By discussing the details of how VC theorem may be construed as an answer and the connection between VC theorem in statistical learning theory and the NIP property in model theory, I conclude that the VC theorem cannot give us the kind of general answers needed for Harman and Kulkarni’s response to the problem of induction.
A shorter version of the draft that was presented in the 2018 PSA meeting can be found here.
Sample Representation in the Social Sciences
This project examines the practice of sample-based inference, discusses the challenges associated with sample gathering in the social sciences, and proposes practical mitigations for those challenges. I begin by tracing the history of survey sampling and the establishment of the design-based based framework where random sampling is the golden standard. I identify two major arguments for this framework: the statistical support of random sampling and the claim that randomness eliminates systematic bias. I then explain how these arguments are largely irrelevant in the reality of social science research, because ideally random sampling is impossible to achieve with human subjects, and that any deviation from this ideal prevents the guaranteed link to sample representation. I then review the model-based framework to sampling and argue for its applicability in the social sciences. In particular, I argue that the model-based framework allows for improvements in resource-limited settings. I end with practical proposals for such improvements.
Click here to read a draft.
Realism about Psychological Traits
Intuitionistic Probabilism in Epistemology
This paper examines the plausibility of a thesis of probabilism that is based on intuitionistic logic and exposits the difficulties faced by such a program. The paper starts by motivating intuitionistic logic as the logic of investigation along a similar reasoning as Bayesian epistemology. It then considers two existing axiom systems for intuitionistic probability functions — that of Weatherson (2003) and of Roeper and Leblanc (1999) — and discusses the relationship between the two. It will be shown that a natural adaptation of an accuracy argument in the style of Joyce (1998) and de Finetti (1974) to these systems fails. The paper concludes with some philosophical reflections on the results.
The paper has not been published. You can read a draft of it here. It was presented at the 2018 Philosophy of Logic, Mathematics, and Physics Graduate Conference (LMP) at the University of Western Ontario.