This talk addresses the unity of the structured atomic proposition that a is an F. Jespersen addresses both the metaphysical problem of how multiple, heterogeneous parts are unified into one whole that has features none of its parts have, as well as how to decompose the whole back into its parts, and the semantic problem of how propositions are related to truth-conditions. Both an empirical and a non-empirical (e.g. mathematical) variant of the proposition that a is an F is analyzed; for instance, that Pluto is a planet, and that four is prime. The solutions offered are developed within a realist procedural semantics (Transparent Intensional Logic), which identifies meanings with procedures for obtaining output objects from input objects. The general approach is broadly Fregean, but makes do without the notion of unsaturated objects. Jespersen demonstrates how predication holds the key to the unity of at least atomic propositions. Predication is modeled as an instance of the logical procedure of functional application. 


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