Yoichi Ishida (Ohio University)
Weisberg and others argue that equations are not mathematical models; equations are statements describing a model. I argue that equations function as iconic representations of physical systems. In the qualitative analysis of ordinary differential equations (ODEs), scientists rely on graphical/visual techniques to analyze ODEs. Using this example and Peirce's and Haugeland's theories of representation, I explain the iconicity of ODEs and show that my account makes better sense of the role of ODEs in mathematical modeling. Equations are like diagrams rather than sentences, and it is not a mistake to regard equations as models.
