مقاله انگلیسی حلقه ، ضروریات ، و توضیح ریاضی در علم
Abstract
Keywords
Introduction
Local circularity and the cicada example
Global circularity
Type 1 circularity: justification
Type 2 circularity: explanatory urgency
The roles of mathematics in science
Conclusions
Author statement
Appendix A. Supplementary data
Research Data
References
ABSTRACT
In this paper I consider the objection that the Enhanced Indispensability Argument (EIA) is circular and hence fails to support mathematical platonism. The objection is that the explanandum in any mathematical explanation of a physical phenomenon is itself identified using mathematical concepts. Hence the explanandum is only genuine if the truth of some mathematical theory is already presupposed. I argue that this objection deserves to be taken seriously, that it does sometimes undermine support for EIA, but that there is no reason to think that circularity is an unavoidable feature of mathematical explanation in science.
Introduction
A distinctive feature of indispensability arguments for mathematical platonism is that they are ‘leveraging’ arguments. By this I mean that belief in the truth of core mathematical claims is leveraged on belief in the truth of claims from outside of mathematics itself. In the standard Quine-Putnam indispensability argument, these external claims are ordinary scientific claims, and the leveraging takes place by appeal to confirmational holism. Roughly, on the presumption that one takes the totality of our current scientific theories to be our best source for true claims about the world, one ought to also believe in the mathematical theories that form an indispensable component of this totality of scientific theories.