What Scientific Theories Could Not Be

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. According to the semantic view of scientific theories, theories are classes of models. I show that this view-if taken literally-leads to absurdities. In particular, this view equates theories that are distinct, and it distinguishes theories that are equivalent. Furthermore, the semantic view lacks the resources to explicate interesting theoretical relations, such as embeddability of one theory into another. The untenability of the semantic view-as currently formulated-threatens to undermine scientific structuralism.

On Einstein algebras and relativistic spacetimes

“…This criterion is almost exactly the same as the one proposed by Halvorson (2012Halvorson ( , 2015 and Weatherall (2015a). The only difference is that they require the categories of models in question be equivalent, rather than dual.…”

“…We show that according to a formal criterion for theoretical equivalence recently proposed by Halvorson (2012Halvorson ( , 2015 and Weatherall (2015a), the two are equivalent theories. …”

“…But there is more to say about the relationship between Einstein algebras and relativistic spacetimes. 5 There is a sense in which these are equivalent theories, according to a standard of equivalence recently discussed by Halvorson (2012Halvorson ( , 2015 and Weatherall (2015a). 6 More precisely we will show that, on natural definitions of the appropriate categories, the category of Einstein algebras is dual to the category of relativistic spacetimes, where the functors realizing the equivalence preserve the empirical structure of the theories.…”

Deduction and definability in infinite statistical systems

“…12 Category theory has recently made its way into the philosophy of science and philosophy of physics literatures as a tool for answering questions about equivalence and the structure of scientific theories. Halvorson (2012Halvorson ( , 2016 and Halvorson and Tsementzis (2017) argue that scientific theories can be represented using the tools of category theory rather than mathematical logic or model theory. Barrett (2017a) and Weatherall (2016aWeatherall ( ,b,c, 2017 argue that the tools of category theory can help us determine when two scientific theories are theoretically equivalent.…”

Similarity, Topology, and Physical Significance in Relativity Theory

“…They underlie Lewis's famous system for counterfactual semantics, modal logic, laws of nature and causation [Lewis, 1973[Lewis, , 1986. More recently, Halvorson [2012] has suggested that similarity is salient for characterizing scientific theories formally: one cannot recover a theory from its models unless one encodes the similarity amongst the models' truth-valuations topologically. And in philosophy of physics, Manchak [2012] has remarked that placing a topology on models of general relativity can describe how different possible relativistic worlds (i.e., relativistic spacetimes) are "nearby" one another.…”