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Notes
- 1.
This understanding of a substructure, even though it is related to, does not fully conform to the understanding of a substructure in model theory. There, substructures are commonly understood as structures that are obtained by restricting the domain of interpretation of a given structure. In the present case, by contrast, substructure (intended application) and complete structure (T-extension) must agree on the domain of interpretation.
- 2.
The price one has to pay for expressing extensivity of a quantity by means of a theory-element as opposed to a link concerns merely the aesthetics of theory-nets. With the introduction of extensivity theory-elements for quantities, certain theory-nets, such as that of classical mechanics, will loose their nicely looking tree structure.
- 3.
The former problem is addressed in Carnap [34], where he uses Hilbert’s 𝜖-operator for expressing that the Carnap sentence yields only an indefinite description of theoretical terms. For a translation of the present semantics of theoretical terms into the language of the epsilon operator, see Andreas and Schiemer [12].
- 4.
Here is an example of such a contrived postulate: α → β with α being an L(V o) sentence and being falsified by \(\mathcal {A}_o\) and β being a theoretical sentence.
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Andreas, H. (2020). Postulates for Structuralism. In: Dynamic Tractable Reasoning. Synthese Library, vol 420. Springer, Cham. https://doi.org/10.1007/978-3-030-36233-1_5
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