"A Silly Answer to a Psillos Question: Objects in Mathematics and Physics"
In this talk I offer an answer to
Psillos’ (2006) question: How can one speak of structures without objects?
Specifically, I use category theory to show that, mathematically speaking,
structures do not need objects. Next, I argue that, scientifically speaking,
this category-theoretic answer is silly because it does not speak to the
scientific structuralist’s appeal to the appropriate kind of morphism to make
precise the concept of shared structure. Against French et al’s
approach, I note that to account for the scientific structuralist’s uses of
shared structure we do not need to formally frame either the structure of a
scientific theory or the concept of shared structure. Here I restate my (2006)
claim that the concept of shared structure can be made precise by appealing to
a kind of morphism, but, in science, it is methodological contexts (and
not any category or set-theoretic frameworks) that determine the appropriate
kind. Returning to my aim, I reconsider French’s example of the role of group
theory in quantum mechanics to show that French already has an answer to
Psillos’ question but this answer is not found in either his set-theoretic
formal framework or his ontic structural realism. Thus, the answer to Psillos
is found both by recognizing that it is the context that determines what the
appropriate kind of morphism is and, as Psillos himself suggests, by adopting a
methodological approach to scientific structuralism.