Should scientific realists be platonists?

Abstract

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 Explanation (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 inferential route which eschews causes ( §3), and nor is there any direct pressure for Scientific Realists 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).

Mathematical Explanation

“…Until the defenders of the argument clarify what distinctively mathematical explanations are and how they involve mathematical objects, it seems that premise 2' is in trouble. Other versions of this objection may be found in Daly & Langford 2009, Rizza 2011, Tallant 2013, Liggins 2016, Busch & Morrison 2016, Barrantes 2019 and Boyce 2021 (see also Panza & Sereni 2016 for a helpful overview of these debates).…”

Indispensability, causation and explanation

“…The harmony of the marital relation between scientific realism and mathematical nominalism has preoccupied others before, and the papers by Saatsi (2007), Busch (2011) and Busch and Morrison (2015) also deserve special mention. Yet these works don't tackle the issue in the way I intent to do it below.…”