Author's Draft (PDF)
Recognition: Winner of the 2019 Jakob Laub Prize
Published: Macalester College Journal of Philosophy, Vol. 28 (Spring 2019)
Abstract: In this paper, I outline the history of the Continuum Problem and its place in mathematics and philosophy. Then, I provide a simplified summary of the independence proofs, as adapted from the original papers and subsequent published explanations. From this, I offer reflections on the proof techniques used within the proof, and connect the independence proof to a broader conversation of philosophical ideas of truth in mathematics, discussing the semantic implications of the proofs.
Author's
Draft (PDF)
Published: Macalester College Journal of Philosophy, Vol. 29 (Spring 2020)
Abstract: In this paper, I refute the inefficacy objection to consequentialism, which states that consequentialism is untenable because it recommends courses of action contrary to our basic moral principles. For instance, it appears that because the average consumer holds no real effective purchasing power against the factory farming industry, a consequentialist might argue that we ought or can purchase factory farmed meat because it doesn't make a difference whether we purchase it or not, but it would certainly give us pleasure if we did. However, I argue that the inefficacy objection relies on a premise which presents an inaccurate reading of consequentialism. Having presented the case that consequentialists would not argue that we ought to purchase factory-farmed meat, I present a virtue-consequentialist approach which strengths the utilitarian case for vegetarianism. By isolating virtues which have merit on consequentialist grounds, the consequentialist consumer is still able to make the case for vegetarianism even in their uncertain and perhaps insignificant relationship to the factory farming industry.
Author's Draft (PDF)
Abstract: Topological Data Analysis (TDA) is a field of applied mathematics
in which tools
from topology are used to analyze a dataset. The intuition is that by forming a geometric
representation that
models the data space, important structural features are revealed by analyzing its homological
features, which
may then have significance in the context of the collected data. Thus, TDA provides an avenue to
explore large,
potentially high-dimensional data sets in a mathematically rigorous way.
This paper focuses on an application of TDA to Natural Language Processing (NLP), a
multidisciplinary area of
study which broadly aims to develop computational tools and models to analyze language. By
employing NLP techniques
to transform text into vectors, I develop a way of analyzing a data set of books downloaded from
Project Gutenberg
and differentiate them by their listed genre. An algorithm (Zhu 2013) is explored and
implemented to capture the
“shape of text”, and topological tools are applied to extract the homological features of each
book.
I discuss two different perspectives on classification (1) a t-test on homological statistics
(dimensions of H1,
feature birth location, etc.) and (2) a k-medoids approach in which clusters of the vector space
are formed by
associating points close to a medoid. The results of this experiment confirm that TDA provides a
powerful way of
analyzing text, and I conclude by reflecting on future work necessary to improve the usage of
TDA in NLP.