I show that the partial truth of a sentence in a partial structure is equivalent to the truth of that sentence in an expansion of a structure that corresponds naturally to the partial structure. Further, a mapping is a partial homomorphism/partial isomorphism between two partial structures if and only if it is a homomorphism/isomorphism between their corresponding structures. It is a corollary that the partial truth of a sentence in a partial structure is equivalent to the truth of a specific Ramsey sentence in a corresponding structure. Hence the partial structures approach can be expressed in standard first or second-order model theory, and it can be captured in the received view on scientific theories as developed by Carnap and Hempel.
CITATION STYLE
Lutz, S. (2015). Partial Model Theory as Model Theory. Ergo, an Open Access Journal of Philosophy, 2(20201214). https://doi.org/10.3998/ergo.12405314.0002.022
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