Stewart Shapiro: "Open Texture and Mathematics"
"Open Texture and Mathematics", by Stewart Shapiro and Craige Roberts.
The purpose of this paper is to explore the extent to which the notion of open texture, as characterized by Friedrich Waismann, applies to the languages of mathematics. Open texture, we argue, is a design feature of natural languages, allowing the flexibility needed to adapt to new situations and new cases and new discoveries. We show that the informal or pre-formal languages of mathematics are indeed subject to open texture, but the ideal of rigor demands that it be eliminated.