This talk has been cancelled

Representation Theorems and Non-eliminative Structuralism

Philosophy of Science Colloquium
The Institute Vienna Circle holds a Philosophy of Science Colloquium with talks by our present fellows.

Date: 22/01/2026

Time: 16h45

Venue: New Institute Building (NIG), Universitätsstraße 7, 1010 Wien, HS 2i

Abstract:

Non-eliminative structuralism holds that mathematics is the study of structures that exist ante rem, and that two systems share the same structure exactly when they are isomorphic (Shapiro 1991, 1997). Yet while the notion of structural properties—properties invariant under isomorphism—has received substantial attention (e.g. Schiemer Korbmacher 2018), the role of representation theorems within this framework has remained almost entirely unexamined.
Representation theorems typically establish an isomorphism between an abstract structure and a more concrete or set-theoretic construction – e.g. Stone’s representation theorem for Boolean algebras (Stone, 1936).
Notably, these theorems concern additional information about the representing domain – information that is not preserved under isomorphism and therefore would count as non-structural from the standpoint of non-eliminative structuralism.
In this talk, I examine this tension by discussing: (1) How representation theorems expose non-structural features of mathematical structures (2) Whether this poses a genuine challenge for non-eliminative structuralism and its theories of structures (Shapiro, 1991,1997, Leitgeb, 2020), and (3) How a more precise account of representation might be developed, drawing on categorical tools such as dualities and equivalences of categories.