Proceedings of the Annual Meeting of the Cognitive Science Society

We discuss the process of mathematization in science, focusing on uses that theorists make of physical representations that w e refer to as abstracted models. W e review abstracted models constructed by Faraday and Maxwell in the mathematization of electromagnetic phenomena, including Maxwell's use of an analogy between continuum dynamics and electromagnetism. W e discuss ways in which this example requires major modifications of current cognitive theories of analogical reasoning and scientific induction, especially in the need to understand the use of abstracted models containing theoretically meaningful objects that can be manipulated and modified in the development of new concepts and mathematized representations.