Infinitesimal Idealization, Easy Road Nominalism, and Fractional Quantum Statistics

It has been recently debated whether there exists a so-called “easy road” to nominalism. In this essay, I attempt to fill a lacuna in the debate by making a connection with the literature on infinite and infinitesimal idealization in science through an example from mathematical physics that has been largely ignored by philosophers. Specifically, by appealing to John Norton’s distinction between idealization and approximation, I argue that the phenomena of fractional quantum statistics bears negatively on Mary Leng’s proposed path to easy road nominalism, thereby partially defending Mark Colyvan’s claim that there is no easy road to nominalism

The Exploratory Role of Idealizations and Limiting Cases in Models

In this article we argue that idealizations and limiting cases in models play an exploratory role in science. Four senses of exploration are presented: exploration of the structure and representational capacities of theory; proof-of-principle demonstrations; potential explanations; and exploring the suitability of target systems. We illustrate our claims through three case studies, including the Aharonov-Bohm effect, the emergence of anyons and fractional quantum statistics, and the Hubbard model of the Mott phase transitions. We end by reflecting on how our case studies and claims compare to accounts of idealization in the philosophy of science literature such as Michael Weisberg’s three-fold taxonomy

ASSUME A SPHERICAL COW: STUDIES ON REPRESENTATION AND IDEALIZATION

This dissertation concerns the philosophical underpinnings of representation and idealization in science. I begin by looking at the philosophical debate revolving around phase transitions and use it as a foil to bring out what I take to be most interesting about phase transitions, namely, the manner by which they illustrate the problem of essential idealizations. I continue to solve the problem in several steps. First, I conduct an interdisciplinary comparative study of different types of representations (e.g., mental, linguistic, pictorial) and consequently promote a content-based account of scientific representation intended to accommodate the practice of idealization and misrepresentation. I then critically asses the literature on idealizations in science in order to identify the manner by which to justify appeals to idealizations in science, and implement such techniques in two case studies that merit special attention: the Aharonov-Bohm effect and the quantum Hall effects. I proceed to offer a characterization of essential idealizations meant to alleviate the woes associated with said problem, and argue that particular types of idealizations, dubbed pathological idealizations, ought to be dispensed with. My motto is that idealizations are essential to explanation and representation, as well as to methodology and pedagogy, but they essentially misrepresent. Implications for the debate on platonism about mathematical objects are outlined

The Exploratory Role of Idealizations and Limiting Cases in Models

In this article we argue that idealizations and limiting cases in models play an exploratory role in science. Four senses of exploration are presented: exploration of the structure and representational capacities of theory; proof-of-principle demonstrations; potential explanations; and exploring the suitability of target systems. We illustrate our claims through three case studies, including the Aharonov-Bohm effect, the emergence of anyons and fractional quantum statistics, and the Hubbard model of the Mott phase transition. We end by reflecting on how our case studies and claims compare to accounts of idealization in the philosophy of science literature such as Michael Weisberg’s three-fold taxonomy

The Problem of Perceptual Agreement

We present the problem of perceptual agreement (of determinate color) and submit that it proves to be a serious and long overlooked obstacle for those insisting that colors are not objective features of objects, viz., nonobjectivist theories like C. L. Hardin’s (2003) eliminativism and Jonathan Cohen’s (2009) relationalism

Roles of mitonuclear ecology and sex in conceptualizing evolutionary fitness

We look to mitonuclear ecology and the phenomenon of Mother’s Curse to argue that the sex of parents and offspring among populations of eukaryotic organisms, as well as the mitochondrial genome, ought to be taken into account in the conceptualization of evolutionary fitness. Subsequently, we show how characterizations of fitness considered by philosophers that do not take sex and the mitochondrial genome into account may suffer. Last, we reflect on the debate regarding the fundamentality of trait versus organism fitness and gesture at the idea that the former lies at the conceptual basis of evolutionary theory

Machine Understanding and Deep Learning Representation

Practical ability manifested through robust and reliable task performance, as well as information relevance and well-structured representation, are key factors indicative of understanding in philosophical literature. We explore these factors in the context of deep learning, identifying prominent patterns in how the results of these algorithms represent information. While the estimation applications of modern neural networks do not qualify as the mental activity of minded agents, we argue that coupling analyses from philosophical accounts with the empirical and theoretical basis for identifying these factors in deep learning representations provides a framework for discussing and critically evaluating potential machine understanding given the continually improving task performance enabled by such algorithms

Understanding from Deep Learning Models in Context

This paper places into context how the term model in machine learning (ML) contrasts with traditional usages of scientific models for understanding and we show how direct analysis of an estimator’s learned transformations (specifically, the hidden layers of a deep learning model) can improve understanding of the target phenomenon and reveal how the model organizes relevant information. Specifically, three modes of understanding will be identified, the difference between implementation irrelevance and functionally approximate irrelevance will be disambiguated, and how this distinction impacts potential understanding with these models will be explored. Additionally, by distinguishing between empirical link failures from representational ones, an ambiguity in the concept of link uncertainty will be addressed thus clarifying the role played by scientific background knowledge in enabling understanding with ML

Infinite Idealizations in Science: An Introduction

We offer a framework for organizing the literature regarding the debates revolving around infinite idealizations in science, and a short summary of the contributions to this special issue