Disagreements that resist rational resolution, often termed “deep disagreements”, have been the focus of much work in epistemology and informal logic. In this paper, I argue that they also deserve the attention of philosophers of mathematics. I link the question of whether there can be deep disagreements in mathematics to a more familiar debate over whether there can be revolutions in mathematics. I propose an affirmative answer to both questions, using the controversy over Shinichi Mochizuki’s work on the abc conjecture (...) as a potential example of both phenomena. I conclude by investigating the prospects for the resolution of mathematical deep disagreements in virtue-theoretic approaches to informal logic and mathematical practice. (shrink)

I argue that forays into history of science in Kuhn’s The Structure of Scientific Revolutions (1962/1996) are by and large instances of “Great Man” history of science. “Great Man” history is the idea that history is the biography of great men. The “Great Man” of science model not only excludes women and people of color from science but also suggests that only special, exceptional people can succeed in science. If this is correct, then Kuhn (1962/1996) fails to usher in a (...) “historiographic revolution in the study of science” or a “new historiography” (Kuhn 1962/1996, 3), as the book purports to do. Instead, it merely perpetuates the defunct historiography of the “Great Man” of science. (shrink)

In this paper, we analyze the debate between the Modern Synthesis and the Extended Evolutionary Synthesis in light of the concept of incommensurability developed by Thomas Kuhn. In order to do so, first we briefly present both the Modern Synthesis and the Extended Evolutionary Synthesis. Then, we clarify the meaning and interpretations of incommensurability throughout Kuhn’s works, concluding that the version of this concept deployed in The Structure of Scientific Revolutions is the best suited to the analysis of scientific disputes. (...) After discussing incommensurability in Kuhn’s works, we address the question of whether the Modern Synthesis and the Extended Evolutionary Synthesis can be considered semantically, methodologically, and ontologically incommensurable, concluding that they can. Finally, we discuss three problems that arise from such a conclusion: firstly, what are the consequences of incommensurability; secondly, which mode of scientific change better explains this current dispute in evolutionary biology; and thirdly, whether rational theory comparison is possible given incommensurability. We suggest that the main consequence of incommensurability is profound disagreement, that the kind of scientific change that better explains the current dispute between the MS and the EES may be scientific specialization, and that incommensurability does not preclude rational theory comparison. (shrink)

I reply to Patton's "Incommensurability and the Bonfire of the Meta-Theories".

In a famous debate between Thomas Kuhn and Karl Popper, Popper accused Kuhn and Quine of propagating the “Myth of the Framework”: that some broad set of specific background commitments are required for interlocutors to be able to have a fruitful conversation. The Myth of the Framework could be used to argue for a beneficial version of the canon: that training in these shared background commitments allows for the growth of a robust community of inquiry. Popper argues, however, that the (...) position that truth or inquiry can be framework-dependent is a pernicious form of relativism, and undermines the possibility of rational inquiry. I subject Popper’s view to criticism, showing that it can be used to undermine “orthodoxy” and the canon in some ways, but that it props up the canon in others. In closing, the paper examines the connections between Popper’s position on the community of inquiry and standpoint epistemology, and argues for the claim that Popper’s view, to be persuasive, requires a more robust account of how critical inquiry relies on the evaluative capacities of rational agents within a community. (shrink)

I reply to James Marcum’s “What’s the Support for Kuhn’s Incommensurability Thesis? A Response to Mizrahi and Patton”.