The position developed in this volume combines features of both the strong and the weak viewpoint.
The tool perspective underlines the inevitably provisional validity of mathematics: any tool can be adjusted, improved, or lose its adequacy upon changing practical conditions. In accordance with the former, mathematics is assigned an active and even shaping role in the sciences, but at the same time, employing mathematics as a tool is taken to be independent from the possible mathematical structure of the objects under consideration. There is a spectrum of means that will normally differ in how well they serve particular purposes. Furthermore, tool-use has to respect conditions like suitability, efficacy, optimality, and others.