Metaphysics is sensitive to the conceptual tools we choose to articulate metaphysical problems. Those tools are a lens through which we view metaphysical problems; the same problems look different when we change the lens. There has recently been a shift to "postmodal" conceptual tools: concepts of ground, essence, and fundamentality. This shift transforms the debate over structuralism, in many ways. For instance: structuralist theses say that "patterns" are prior to the "nodes" in the patterns. In modal terms it is clear what this means: the nodes cannot vary independently of the pattern. But it's far less clear what its postmodal meaning is. One expects it to mean that the pattern is fundamental, the entities in the pattern, derivative. But what would a fundamental account of reality that speaks only of patterns and not objects in the patterns look like? I examine three structuralist positions through a postmodal lens. First, nomic essentialism, which says that scientific properties are secondary and lawlike relationships among them are primary. Second, structuralism about individuals, a general position of which mathematical structuralism and structural realism are instances, which says that scientific and mathematical objects are secondary and the pattern of relations among them is primary. Third, comparativism about quantities, which says that particular values of scientific quantities, such as having exactly 1000g mass, are secondary, and quantitative relations, such as being-twice-as-massive-as, are primary. Finally, I take a step back and examine the meta-question of when theories are equivalent, and how that impacts the debate over structuralism.
Methodological Frames: Paul Bernays, Mathematical Structuralism, and Proof Theory
