Platonism And Mathematical Explanations: Some Critical Remarks On Explanatory Proofs And Debunking Arguments (I)
Platonism And Mathematical Explanations: Some Critical Remarks On Explanatory Proofs And Debunking Arguments (I)
Author(s): Fabrice PatautSubject(s): Philosophy, Logic, Ethics / Practical Philosophy, Special Branches of Philosophy, Philosophy of Science
Published by: Институт по философия и социология при БАН
Keywords: Abstract Objects; Baker (Alan); Clarke-Doane (Justin); Colyvan (Mark); Debunking Arguments; Explanatory Proof; Field (Hartry); Indispensability Argument; Inference to the Best Explanation;
Summary/Abstract: Ontological parsimony requires that if we can dispense with A when best explaining B, or when deducing a nominalistically statable conclusion B from nominalistically statable premises, we must indeed dispense with A. When A is a mathematical theory and it has been established that its conservativeness undermines the platonistic force of mathematical derivations (Field), or that a nonnumerical formulation of some explanans may be obtained so that the platonistic force of the best numericalbased account of the explanandum is also undermined (Rizza), the parsimony principle has been respected.
Journal: Balkan Journal of Philosophy
- Issue Year: XII/2020
- Issue No: 2
- Page Range: 63-74
- Page Count: 12
- Language: English
- Content File-PDF