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1012Poincaré on the Foundation of Geometry in the UnderstandingIn Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics: The CSHPM 2016 Annual Meeting in Calgary, Alberta, Springer. pp. 19-37. 2017.This paper is about Poincaré’s view of the foundations of geometry. According to the established view, which has been inherited from the logical positivists, Poincaré, like Hilbert, held that axioms in geometry are schemata that provide implicit definitions of geometric terms, a view he expresses by stating that the axioms of geometry are “definitions in disguise.” I argue that this view does not accord well with Poincaré’s core commitment in the philosophy of geometry: the view that geometry is…Read more
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161Frege on the Foundation of Geometry in IntuitionJournal for the History of Analytical Philosophy 3 (6). 2015.I investigate the role of geometric intuition in Frege’s early mathematical works and the significance of his view of the role of intuition in geometry to properly understanding the aims of his logicist project. I critically evaluate the interpretations of Mark Wilson, Jamie Tappenden, and Michael Dummett. The final analysis that I provide clarifies the relationship of Frege’s restricted logicist project to dominant trends in German mathematical research, in particular to Weierstrassian arithmet…Read more
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62Thick credence and pragmatic encroachmentPhilosophical Studies 178 (2): 339-361. 2020.Pragmatic factors encroach on epistemic predicates not solely because the threshold for actionable belief may shift with an epistemic agent’s context, as an evidential Bayesian might insist, but also because what our inductive policy should be may shift with that context. I argue for this thesis in the context of imprecise probabilities, maintaining that the choice of the defining hyperparameter for an Imprecise Dirichlet Model for nonparametric predictive inference may correspond to the choice …Read more
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40Why Russell Was Not an Epistemic Structural RealistRussell: The Journal of Bertrand Russell Studies 40 5-26. 2020.Bertrand Russell’s work in philosophy of science has been identified as a progenitor of structuralism in contemporary philosophy. It is often unclear, however, how the philosophical problems facing contemporary structuralist programmes relate to the problems of philosophy as Russell saw them. We contend that Russell has been mistakenly identified as an epistemic structural realist. The goal of this essay is to clarify the relationship between Russell’s programme and contemporary structuralist pr…Read more
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13In this thesis I argue forin re structuralism in the philosophy of mathematics. In the first chapters of the thesis I argue that there is a genuine epistemic access problem for Platonism, that the semantic challenge to nominalism may be met by paraphrase strategies, and that nominalizations of scientific theories have had adequate success to blunt the force of the indispensability argument for Platonism. In the second part of the thesis I discuss the development of logicism and structuralism as …Read more
Jeremy Shipley
Volunteer State Community College
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Volunteer State Community CollegeAssistant Professor
Areas of Interest
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