Euler gets an 'F' in philosophy — but which 'F'?

Brian Hepburn

Center for Science Studies, Dept. of Physics and Astronomy, Aarhus University)

Abstract: 
Euler was one of the most important physicists in that science's history. Yet, at many places in his writings, he seems to make very rudimentary philosophical mistakes. He commits the fallacy of composition, constructs straw-men refutations of Wolffian metaphysics by ignoring key but straightforward distinctions, and gives invalid arguments (not merely unsound) for `necessary' conclusions. It therefore appears he made fundamental contributions to physics while being fundamentally confused about the relevant philosophy of his time. I characterize three ways one might think about this example, three views one might take on the role of philosophy in advances in physics. The `Feynman' view sees no role for philosophy, and reads the case of Euler as proof of its eliminability. On the `Feyerabend' view, the ``badness'' of the philosophy was key. Euler was free to make advances because of the ways he misunderstood metaphysical and philosophical constraints. On the `Friedman' view, philosophical changes are constitutive, and therefore necessary, though they may be implicit. There is no reason to expect Euler to have been able to articulate them clearly. To show that Euler deserves at worst the third 'F', I construct a philosophy of science on his behalf. Three key elements of Eulerian philosophy are: an interpretation of Cartesian clearness and distinctness in terms of problem-solving, a causal interpretation of mathematical descriptions, and a compatibilism between the explanatory domains of mechanics and metaphysics. On this basis I argue that Euler, in fact, had a sophisticated, nuanced, and modern philosophy of science.