Evidential Holism and Indispensability Arguments

The indispensability argument is a method for showing that abstract mathematical objects exist (call this mathematical Platonism). Various versions of this argument have been proposed (§1). Lately, commentators seem to have agreed that a holistic indispensability argument (§2) will not work, and that an explanatory indispensability argument is the best candidate. In this paper I argue that the dominant reasons for rejecting the holistic indispensability argument are mistaken. This is largely due to an overestimation of the consequences that follow from evidential holism. Nevertheless, the holistic indispensability argument should be rejected, but for a different reason (§3)—in order that an indispensability argument relying on holism can work, it must invoke an unmotivated version of evidential holism. Such an argument will be unsound. Correcting the argument with a proper construal of evidential holism means that it can no longer deliver mathematical Platonism as a conclusion: such an argument for Platonism will be invalid. I then show how the reasons for rejecting the holistic indispensability argument importantly constrain what kind of account of explanation will be permissible in explanatory versions (§4).

Should scientific realists be platonists?

Enhanced Indispensability Arguments (EIA) claim that Scientific Realists are committed to the existence of mathematical entities due to their reliance on Inference to the Best Explana- tion (IBE). Our central question concerns this purported parity of reasoning: do people who defend the EIA make an appropriate use of the resources of Scientific Realism (in particular, IBE) to achieve platonism? (§2) We argue that just because a variety of different inferential strategies can be employed by Scientific Realists does not mean that ontological conclusions concerning which things we should be Scientific Realists about are arrived at by any inferen- tial route which eschews causes (§3), and nor is there any direct pressure for Scientific Real- ists to change their inferential methods (§4). We suggest that in order to maintain inferential parity with Scientific Realism, proponents of EIA need to give details about how and in what way the presence of mathematical entities directly contribute to explanations (§5).