• Gauss' quadratic reciprocity theorem and mathematical fruitfulness
    Studies in History and Philosophy of Science Part A 42 (3): 410-415. 2011.
  • Analogical arguments -- Philosophical theories -- Computational theories -- The articulation model -- Analogies in mathematics -- Similarity and patterns of generalization -- Analogy and epistemic values -- Analogy and symmetry -- A wider role for analogies.
  • Paraphrase Strategies in Metaphysics
    Philosophy Compass 9 (8): 570-582. 2014.
    Philosophers often aim to demonstrate that the things we ordinarily think and say can be reconciled with our considered beliefs about the world. To this end, many philosophers try to paraphrase ordinary language claims by finding equivalent sentences that are less misleading. For instance, though we know that there is no British family that is the average one, we want to say that the average British family has 1.8 children, and we might do that by paraphrasing this claim as: there are nearly twi…Read more
  • Beyond Binary: Genderqueer as Critical Gender Kind
    Philosophers' Imprint 20 (9): 1-23. 2020.
    We want to know what gender is. But metaphysical approaches to this question solely have focused on the binary gender kinds men and women. By overlooking those who identify outside of the binary–the group I call ‘genderqueer’–we are left without tools for understanding these new and quickly growing gender identifications. This metaphysical gap in turn creates a conceptual lacuna that contributes to systematic misunderstanding of genderqueer persons. In this paper, I argue that to better u…Read more
  • Mechanistic Explanation and Explanatory Proofs in Mathematics
    Joachim Frans and Erik Weber
    Philosophia Mathematica 22 (2): 231-248. 2014.
    Although there is a consensus among philosophers of mathematics and mathematicians that mathematical explanations exist, only a few authors have proposed accounts of explanation in mathematics. These accounts fit into the unificationist or top-down approach to explanation. We argue that these models can be complemented by a bottom-up approach to explanation in mathematics. We introduce the mechanistic model of explanation in science and discuss the possibility of using this model in mathematics,…Read more
  • Towards a Taxonomy of the Model-Ladenness of Data
    PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association. forthcoming.
    Model-data symbiosis is the view that there is an interdependent and mutually beneficial relationship between data and models, whereby models are not only data-laden, but data are also model-laden or model filtered. In this paper I elaborate and defend the second, more controversial, component of the symbiosis view. In particular, I construct a preliminary taxonomy of the different ways in which theoretical and simulation models are used in the production of data sets. These include data convers…Read more
  • Ground and Explanation in Mathematics
    Philosophers' Imprint 19. 2019.
    This paper explores whether there is any relation between mathematical proofs that specify the grounds of the theorem being proved and mathematical proofs that explain why the theorem obtains. The paper argues that a mathematical fact’s grounds do not, simply by virtue of grounding it, thereby explain why that fact obtains. It argues that oftentimes, a proof specifying a mathematical fact’s grounds fails to explain why that fact obtains whereas any explanation of the fact does not specify its gr…Read more
  • Functional explanation in mathematics
    Matthew Inglis and Juan Pablo Mejía Ramos
    Synthese 1-24. forthcoming.
    Mathematical explanations are poorly understood. Although mathematicians seem to regularly suggest that some proofs are explanatory whereas others are not, none of the philosophical accounts of what such claims mean has become widely accepted. In this paper we explore Wilkenfeld’s suggestion that explanations are those sorts of things that generate understanding. By considering a basic model of human cognitive architecture, we suggest that existing accounts of mathematical explanation are all de…Read more
  • The ontic conception of explanation, according to which explanations are "full-bodied things in the world," is fundamentally misguided. I argue instead for what I call the eikonic conception, according to which explanations are the product of an epistemic activity involving representations of the phenomena to be explained. What is explained in the first instance is a particular conceptualization of the explanandum phenomenon, contextualized within a given research program or explanatory project.…Read more
  • In this paper, I identify a form of epistemic insensitivity that occurs when someone fails to make proper use of the epistemic tools at their disposal in order to bring their beliefs in line with epistemically relevant evidence that is available to them. I call this kind of insensitivity agential insensitivity because it stems from the epistemic behavior of an individual agent. Agential insensitivity can manifest as a failure to either attend to relevant and available evidence, or appropriately …Read more