Abstract Summary
Otávio Bueno (University of Miami) - Structural realism, as a realist form of scientific structuralism, crucially relies on there being suitable interpretations of mathematical structures (particularly those used in successful applications in the sciences) in order to derive ontological conclusions about the structure of the world. I argue that mathematical structures are importantly underdetermined for this task: not only are the same mathematical structures compatible with radically different physical interpretations, but also significantly different mathematical structures can be used to account for the same physical phenomena. The result is that, strictly speaking, no significant ontological conclusions from mathematical structures alone can be drawn. These considerations challenge the ontological interpretation of mathematical structures that is at the heart of structural realism. I then provide an alternative form of scientific structuralism, of an empiricist rather than a realist sort, that resists any such reification of mathematical structures and thereby is able to accommodate this ubiquitous structural indeterminacy in a principled way.
