Nominalistic content, grounding, and covering generalizations: Reply to ‘Grounding and the indispensability argument’

  1. Matteo Plebani
Revista:
Synthese

ISSN: 1573-0964

Ano de publicación: 2016

Volume: 193

Número: 2

Páxinas: 549-558

Tipo: Artigo

Outras publicacións en: Synthese

Resumo

‘Grounding and the indispensability argument’ presents a number of ways in which nominalists can use the notion of grounding to rebut the indispensability argument for the existence of mathematical objects. I will begin by considering the strategy that puts grounding to the service of easy-road nominalists (“Nominalistic content meets grounding” section). I will give some support to this strategy by addressing a worry some may have about it (“A misguided worry about the grounding strategy” section). I will then consider a problem for the fast-lane strategy (“Grounding and generality: a problem for the fast lane” section) and a problem for easy-road nominalists willing to accept Liggins’ grounding strategy (“More on the grounding strategy and easy-road nominalism” section). Both are related to the problem of formulating nominalistic explanations at the right level of generality. I will then consider a problem that Liggins only hints at (“Mathematics and covering generalizations” section). This problem has to do with mathematics’ function of providing the sort of covering generalizations we need in scientific explanations.