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Epistemologists have developed a diverse group of theories, known as hinge epistemology, about our epistemic practices that resort to and expand on Wittgenstein's concept of ‘hinges’ in On Certainty. Within hinge epistemology there is a debate over the epistemic status of hinges. Some hold that hinges are non-epistemic (neither known, justified, nor warranted), while others contend that they are epistemic. Philosophers on both sides of the debate have often connected this discussion to Wittgenstein's later views on mathematics. Others have directly (...) |
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On the one hand, I show that the later Wittgenstein's practice-based approach to meaning, including the idea that the meaningfulness of mathematics ultimately is rooted in the everyday ‘applications’ it emerged from, as well as his insistence on the variability in and contingency of mathematical and mathematics-like practices, foreshadows more recent work in Philosophy of Mathematical Practice (PMP), although Wittgenstein's approach was more radically practice-based than what is prevalent in present-day PMP. On the other hand, I also show that Wittgenstein's (...) |
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Additional theorizing about mathematical practice is needed in order to ground appeals to truly useful notions of the virtues in mathematics. This paper aims to contribute to this theorizing, first, by characterizing mathematical practice as being epistemic and “objectual” in the sense of Knorr Cetina The practice turn in contemporary theory, Routledge, London, 2001). Then, it elaborates a MacIntyrean framework for extracting conceptions of the virtues related to mathematical practice so understood. Finally, it makes the case that Wittgenstein’s methodology for (...) |
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We give an overview of Lakatos’ life, his philosophy of mathematics and science, as well as of this issue. Firstly, we briefly delineate Lakatos’ key contributions to philosophy: his anti-formalist philosophy of mathematics, and his methodology of scientific research programmes in the philosophy of science. Secondly, we outline the themes and structure of the masterclass Lakatos’ Undone Work – The Practical Turn and the Division of Philosophy of Mathematics and Philosophy of Science, which gave rise to this special issue. Lastly, (...) |
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We give an overview of Lakatos’ life, his philosophy of mathematics and science, as well as of this issue. Firstly, we briefly delineate Lakatos’ key contributions to philosophy: his anti-formalist philosophy of mathematics, and his methodology of scientific research programmes in the philosophy of science. Secondly, we outline the themes and structure of the masterclass Lakatos’ Undone Work – The Practical Turn and the Division of Philosophy of Mathematics and Philosophy of Science, which gave rise to this special issue. Lastly, (...) |
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