Introduction: Mathematics As A Tool

The role mathematics plays in the sciences has been assessed differently and in conflicting ways. Put very roughly, a strong view holds that mathematically formulated laws of nature refer to or reveal the rational structure of the world. By contrast, a weak view denies that these fundamental laws are of an essentially mathematical character, and rather suggests that mathematics is merely a tool for systematizing observational knowledge. We put forward a position that combines features of both viewpoints. The tool perspective is provisional and contextual, rather than ontological.