Taking mathematical fictions seriously

I argue on the basis of an example, Fourier theory applied to the problem of vibration, that Field's program for nominalizing science is unlikely to succeed generally, since no nominalistic variant will provide us with the kind of physical insight into the phenomena that the standard theory supplies. Consideration of the same example also shows, I argue, that some of the motivation for mathematical fictionalism, particularly the alleged problem of cognitive access, is more apparent than real.I would like to thank Mark Wilson, who first suggested that I look at the literature on applied Fourier theory, and whose paper Honorable Intensions (1993) helped me understand it better. I would also like to acknowledge gratefully support from a UWM Graduate School Research Committee Award.