Kirchhoff’s 1882 theory of optical diffraction forms the centerpiece in the long-term development of wave optics, one that commenced in the 1820s when Fresnel produced an empirically successful theory based on a reinterpretation of Huygens’ principle, but without working from a wave equation. Then, in 1856, Stokes demonstrated that the principle was derivable from such an equation albeit without consideration of boundary conditions. Kirchhoff’s work a quarter century later marked a crucial, and widely influential, point for he produced Fresnel’s results (...) by means of Green’s theorem and function under specific boundary conditions. In the late 1880s, Poincaré uncovered an inconsistency between Kirchhoff’s conditions and his solution, one that seemed to imply that waves should not exist at all. Researchers nevertheless continued to use Kirchhoff’s theory—even though Rayleigh, and much later Sommerfeld, developed a different and mathematically consistent formulation that, however, did not match experimental data better than Kirchhoff’s theory. After all, Kirchhoff’s formula worked quite well in a specific approximation regime. Finally, in 1964, Marchand and Wolf employed the transformation of Kirchhoff’s surface integral that had been developed by Maggi and Rubinowicz for other purposes. The result yielded a consistent boundary condition that, while introducing a species of discontinuity, nevertheless rescued the essential structure of Kirchhoff’s original formulation from Poincaré’s paradox. (shrink)

It has become apparent that the debate between scientific realists and constructive empiricists has come to a stalemate. Neither view can reasonably claim to be the most rational philosophy of science, exclusively capable of making sense of all scientific activities. On one prominent analysis of the situation, whether we accept a realist or an anti-realist account of science actually seems to depend on which values we antecedently accept, rather than our commitment to “rationality” per se. Accordingly, several philosophers have attempted (...) to argue in favour of scientific realism or constructive empiricism by showing that one set of values is exclusively best, for anyone and everyone, and that the downstream choice of the philosophy of science which best serves those values is therefore best, for anyone and everyone. These efforts, however, seem to have failed. In response, I suggest that philosophers of science should suspend the effort to determine which philosophy of science is best for everyone, and instead begin investigating which philosophy of science is best for specific people, with specific values, in specific contexts. I illustrate how this might be done by briefly sketching a single case study from the history of science, which seems to show that different philosophies of science are better at motivating different forms of scientific practice. (shrink)