24 May 2022, The Utrecht Logic in Progress Series (TULIPS), Theodora Achourioti

Abstract: A first-order model is what makes a given theory true. But it may also be a limit of a suitable family of models in some well-regimented construction. Assuming a structuralist perspective, these are situations where ‘cross-structural identification’ makes sense, that is, where objects may be identified as place-holders in different structures. We argue that such cases are interesting for testing some of the stru​cturalist intuitions. We consider particular examples, such as countable structures generated as limits of a suitable set of finite structures, and we revisit some of the standard questions that structuralist theories wrestle with; for example, how to meet the identity challenge, what constitute the structural properties of the positions in the structure, how to gain epistemological access.