Partial Model Theory as Model Theory

Ergo: An Open Access Journal of Philosophy 2 (2015)
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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.



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Sebastian Lutz
Uppsala University

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What Was the Syntax‐Semantics Debate in the Philosophy of Science About?Sebastian Lutz - 2017 - Philosophy and Phenomenological Research 95 (2):319-352.

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