Purity of Methods

Detlefsen, Michael; Arana, Andrew

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Purity of Methods

Michael Detlefsen; Andrew Arana

January 2011, Volume 11, No. 2, pp. 1-20

Permalink: http://hdl.handle.net/2027/spo.3521354.0011.002

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Abstract

Throughout history, mathematicians have expressed preference for solutions to problems that avoid introducing concepts that are in one sense or another “foreign” or “alien” to the problem under investigation. This preference for “purity” (which German writers commonly referred to as “methoden Reinheit”) has taken various forms. It has also been persistent. This notwithstanding, it has not been analyzed at even a basic philosophical level. In this paper we give a basic analysis of one conception of purity—what we call topical purity—and discuss its epistemological significance.

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This in itself is reason enough to seek a better understanding of purity and its supposed worth, and these are our chief goals here. We would make it clear at the outset, though, that we do not claim to offer a general account of purity—an account that does justice to the full variety of forms it has assumed and the ends it has been taken to have throughout its history. Our aim is the more modest one of clarifying the character and epistemic significance of what we think is the or at least a central conception of purity—a conception we call the topical conception.