Seminar on History and Philosophy of Science

Abstract: It is widely accepted that symmetry-related models (SRMs) in physics should represent the same physical situation. However, there is disagreement on whether further work is needed to demonstrate that they indeed do (let's call this claim "SE"). Do we need to find a reduced model that captures the common ontology of SRMs? Reductionists say yes, while interpretationists say no, arguing that SRMs invariably represent the same physical situation. Specifically, strong interpretationism (also known as "external sophistication" in Dewar's terminology) proposes that we can treat SRMs "as if" they are isomorphic. According to this view, SE is automatically justified by the principle (from sophisticated substantivalism) that isomorphic models represent the same physical situation. Strong interpretationism has been heavily critiqued for its opaqueness. In this talk, I aim to develop interpretationism in the following ways. First, I will present a rigorous category-theoretic strategy for strong interpretationism, mathematically reconceptualizing SRMs as isomorphic, and contrast the resulting models with both reduced models and "sophisticated" models. Second, I will introduce an alternative algebraic framework in which SRMs are not only isomorphic but also no longer "opaque". I will conclude by discussing the advantages of interpretationism over reductionism. (Most of the discussions will be centered on the case of gauge symmetries in classical electromagnetism, as is standard in the literature.)