Safety and Pluralism in Mathematics. Erkenntnis. Forthcoming. [Open access]
A belief one has is safe if either (i) it could not easily be false or (ii) in any nearby world in which it is false, it is not formed using the method one uses to form one’s actual belief. It seems our mathematical beliefs are safe if mathematical pluralism is true: if, loosely put, almost any consistent mathematical theory is true. It seems, after all, that in any nearby world where one’s mathematical beliefs differ from one’s actual beliefs, one would believe some other true, consistent theory. Focusing on Justin Clarke-Doane’s recent discussion, I argue the thesis that mathematical beliefs are safe given pluralism faces some obstacles. I argue (i) is true of mathematical belief given pluralism only if we deny plausible claims about the interpretation of non-pluralists who many of us could easily be. Unless strong metasemantic theses are true, it is plausible many of us could easily deny or refuse to believe a consistent and true mathematical theory we actually believe. Since philosophical arguments and controversies permeate the methodology of foundational mathematics, I argue we cannot confidently distinguish the methods we use in mathematics between worlds, thus raising doubts about (ii).
Methodology Maximized: Quine on Empiricism, Naturalism, and Empirical Content. Journal of the History of Philosophy. 60(4): 661–86. 2022. [View or download file]
W.V. Quine calls some general methods of science maxims: general defeasible principles which call on us to approximate, maximize, or minimize a state and which are interpreted and weighed in context-sensitive ways. On my reading, his empiricism asks us to maximize accepting overall theories empirically equivalent to ours but to minimize accepting sentences which both do not affect the empirical content of our overall theory and do not simplify our overall theory. His naturalism asks us to maximize accepting sentences that are solely supported by standards that support our best current scientific theory. Drawing on the Quine archive at Houghton Library at Harvard, I support and apply these interpretations by investigating his rapidly evolving later work on empirical content and empirical equivalence, including some of his views on translation in this later work and his vacillation between what he calls the ecumenical and sectarian attitudes.
Carnap and Quine on Sense and Nonsense. Journal for the History of Analytical Philosophy. 9(10): 1–28. 2021. [Open access]
I offer an interpretation of Carnap and Quine’s views on cognitive significance and insignificance. The basic idea behind their views is as follows: to judge an expression is insignificant is to recommend it not be used in or explicated into languages used to express truth-valued judgments in inquiry; to judge an expression is significant is to recommend it be used in or explicated into such languages. These judgments are pragmatic judgments, made in light of purposes for language use in inquiry. For Carnap at least, these pragmatic judgments are non-cognitive. This basic idea is only a roughly correct statement of their views. This is because the details of the scientific languages they recommend for inquiry are necessary to understand their views and the way they understand their own views. Even so, I offer two reasons to suggest that this basic idea is worthy of our consideration today. First, it provides a conception of significance that captures the natural thought that epistemological concerns can lead us to consider expressions to be insignificant without requiring an objectionable form of verificationism. Second, if we appeal also to Carnap and Quine’s pluralistic attitude toward explication, we can make a pragmatic judgment that an expression is insignificant while judging it to be significant on a distinct explication of significance fit for describing and explaining natural language.
Quine on Naturalism, Nominalism, and Philosophy's Place within Science. Synthese. 198(2): 1549–1567. 2021. [Read-only open access]
W.V. Quine is a well-known proponent of naturalism, the view on which reality is described only in science. He is also well-known for arguing that our current scientific theories commit us to the existence of abstract objects. It is tempting to believe that the naturalistic philosopher should think scientists outside of philosophy are in the best position to assess the merits of revising our current commitment to abstract objects. But Quine rejects this deferential view. On the reading of Quine’s philosophical methodology that I defend in this paper, the naturalistic philosopher not only may assess the merits of revising the commitments of our scientific theories, but also will recommend we make such revisions if doing so simplifies and clarifies our science. To develop my reading, I will examine John Burgess and Gideon Rosen’s naturalism in ontology that includes the deferential view Quine rejects. By explaining how Quine’s naturalism differs from the anti-revisionist, deferential naturalism in philosophy of mathematics that Burgess and Rosen advance, I seek to clarify and advance contemporary debates on naturalism.
Quine's Intuition: Why Quine's Early Nominalism is Naturalistic. Erkenntnis. 85(5): 1199-1218. 2020. [Read-only open access]
According to a growing consensus in the secondary literature on Quine, the judgment Quine makes in favor of the nominalism outlined in “Steps Toward a Constructive Nominalism” is in tension with the naturalism he later adopts. In this paper, I show the consensus view is mistaken by showing that Quine’s judgment is rooted in a naturalistic standard of clarity. Moreover, I argue that Quine late in his career is committed to accepting one plausible reading of his judgment in 1947. In making these arguments, I draw attention to a version of naturalism that misreadings of Quine have prevented philosophers from appreciating, and thereby articulate and clarify a version of naturalism I recommend philosophers investigate today.