Analytic philosophers apply the term ‘object’ both to concreta and to abstracta of certain kinds. The theory of objects which this implies is shown to rest on a dichotomy between object-entities on the one hand and meaning-entities on the other, and it is suggested that the most adequate account of the latter is provided by Husserl’s theory of noemata. A two-story ontology of objects and meanings (concepts, classes) is defended, and Löwenheim’s work on class-representatives is cited as an indication of (...) how the need for higher types may be obviated, even in mathematical contexts. The paper concludes with a sketch of the taxonomy of the object realm which results from the above. (shrink)

The paper deals with the semantics of mathematical notation. In arithmetic, for example, the syntactic shape of a formula represents a particular way of specifying, arriving at, or constructing an arithmetical object (that is, a number, a function, or a truth value). A general definition of this sense of "construction" is proposed and compared with related notions, in particular with Frege's concept of "function" and Carnap's concept of "intensional isomorphism." It is argued that constructions constitute the proper subject matter of (...) both logic and mathematics, and that a coherent semantic account of mathematical formulas cannot be given without assuming that they serve as names of constructions. (shrink)