In this paper, I consider an argument for the claim that any satisfactory epistemology of mathematics will violate core tenets of naturalism, i.e. that mathematics cannot be naturalized. I find little reason for optimism that the argument can be effectively answered.

Quine is routinely perceived as having changed his mind about the scope of the Duhem-Quine thesis, shifting from what has been called an 'extreme holism' to a more moderate view. Where the Quine of 'Two Dogmas of Empiricism' argues that “the unit of empirical significance is the whole of science” (1951, 42), the later Quine seems to back away from this “needlessly strong statement of holism” (1991, 393). In this paper, I show that the received view is incorrect. I distinguish (...) three ways in which Quine's early holism can be said to be wide-scoped and show that he has never changed his mind about any one of these aspects of his early view. Instead, I argue that Quine's apparent change of mind can be explained away as a mere shift of emphasis. (shrink)

What should a Quinean naturalist say about moral and mathematical truth? If Quine’s naturalism is understood as the view that we should look to natural science as the ultimate ‘arbiter of truth’, this leads rather quickly to what Huw Price has called ‘placement problems’ of placing moral and mathematical truth in an empirical scientific world-view. Against this understanding of the demands of naturalism, I argue that a proper understanding of the reasons Quine gives for privileging ‘natural science’ as authoritative when (...) it comes to questions of truth and existence also apply to other stable and considered elements of our inherited world-view, including, arguably, our firmly held mathematical and moral beliefs. If so, then the ‘thin’ mathematical and moral realisms of Penelope Maddy and T. M. Scanlon, respectively, are vindicated. We do not need to shoehorn mathematical and moral truths into the pushings and pullings of our empirical scientific world-view; for the busy sailor adrift on Neurath’s boat, mathematical and moral truths already have their place. (shrink)

According to the standard story W. V. Quine ’s criticisms of the idea that logic is true by convention are directed against, and completely undermine, Rudolf Carnap’s idea that the logical truths of a language L are the sentences of L that are true-in- L solely in virtue of the linguistic conventions for L, and Quine himself had no interest in or use for any notion of truth by convention. This paper argues that and are both false. Carnap did not (...) endorse any truth -by- convention theses that are undermined by Quine ’s technical observations. Quine knew this. Quine ’s criticisms of the thesis that logic is true by convention are not directed against a truth -by- convention thesis that Carnap actually held, but are part of Quine ’s own project of articulating the consequences of his scientific naturalism. Quine found that logic is not true by convention in any naturalistically acceptable sense. But he also observed that in set theory and other highly abstract parts of science we sometimes deliberately adopt postulates with no justification other than that they are elegant and convenient. For Quine such postulations constitute a naturalistically acceptable and fallible sort of truth by convention. It is only when an act of adopting a postulate is not indispensible to natural science that Quine sees it as affording truth by convention ‘unalloyed’. A naturalist who accepts Quine ’s notion of truth by convention is therefore not limited to accepting only those postulates that she regards as indispensible to natural science. (shrink)

There is a recent and growing trend in philosophy that involves deferring to the claims of certain disciplines outside of philosophy, such as mathematics, the natural sciences, and linguistics. According to this trend— deferentialism , as we will call it—certain disciplines outside of philosophy make claims that have a decisive bearing on philosophical disputes, where those claims are more epistemically justified than any philosophical considerations just because those claims are made by those disciplines. Deferentialists believe that certain longstanding philosophical problems (...) can be swiftly and decisively dispatched by appeal to disciplines other than philosophy. In this paper we will argue that such an attitude of uncritical deference to any non-philosophical discipline is badly misguided. With reference to the work of John Burgess and David Lewis, we consider deference to mathematics. We show that deference to mathematics is implausible and that main arguments for it fail. With reference to the work of Michael Blome-Tillmann, we consider deference to linguistics. We show that his arguments appealing to deference to linguistics are unsuccessful. We then show that naturalism does not entail deferentialism and that naturalistic considerations even motivate some anti-deferentialist views. Finally, we set out deferentialism’s failings and present our own anti-deferentialist approach to philosophical inquiry. (shrink)