Is Semantic Structuralism Necessarily "Set-Theoretical" Structuralism?

(Philosophy of Science, English)

tandard semantic approaches to scientific structuralism are based on the concept of shared structure between models, most often by adopting a formal frame of set theory. Such framework is then generally used to provide a formal interpretation and analysis of the structure of scientific theories, the problem of applicability of mathematics to a physical theory, and the philosophical account of structural realist_s commitment to the structure shared by successive physical theories. Within such frame, as presented by Suppes, "(...) a model of a theory may be defined as a possible realization in which all valid sentences of the theory are satisfied, and a possible realization of the theory is an entity of the appropriate set-theoretical structure" (Suppes 1962).

Generally, arguments for the necessity of using such formal frame are motivated by the assumption that adopting this approach makes the question about models of an empirical theory, axiomatized within the unified framework, similar to the one about the "shared structure" in terms of isomorphisms between mathematical models (Suppes 1960, French 2000). Following this intuition, the formal framework of set theory allows us to discuss the structure of scientific theories, the applicability of mathematics etc. by making use of precise concepts of a model (as a set-theoretical entity) and of shared structure (as an isomorphism between models).

In my presentation I will try to analyze origins of this assumption and, moreover, its validity. Then, following Landry (2005, 2007), I will make an additional attempt to challenge the idea that both the concept of a model and of shared structure, in order to be accurate and precise, need to be framed within a single unified framework of set theory.

-- Landry E., & Marquis, J-P. (2005). Categories in context: Historical, foundational and philosophical. Philosophia Mathematica, 13(1), 1-43.

-- Landry, E. (2007). Shared structure need not to be shared set-structure. Synthese, 158, 1-17.

-- French, S. (2000). The reasonable effectiveness of mathematics: Partial structures and the application of group theory to physics. Synthese, 125, 103-120.

-- Suppes, P. (1960). A comparison of the meaning and uses of models in mathematics and the empirical sciences. Synthese, 12, 287-301.

-- Suppes, P. (1962). Models of data. In Logic methodology and philosophy of science (pp. 252-261). Stanford: Stanford University Press.

Chair: Laurenz Hudetz

Time: 14:00-14:30, 15 September 2017 (Friday)

Location: SR 1.006

Agnieszka Proszewska

(Jagiellonian University, Poland)

Agnieszka M. Proszewska is a Ph.D. student and teaching assistant in the Department of Philosophy at the Jagiellonian University in Cracow, where she teaches logic and set theory, epistemology and theory of computation. She graduated from Philosophy and Swedish Philology at the Jagiellonian University and currently, she is also working on her Master's thesis in theoretical computer science at the Department of Physics, Astronomy and Applied Computer Science. Her research interests focus on the philosophy of natural sciences, structural frameworks and mathematical logic. Since 2014 she serves as a regular member of Polish Artificial Intelligence Society.

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