Constructions

Philosophy of Science 53 (4):514-534 (1986)
Abstract
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
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Ken Daley (2010). The Structure of Lexical Concepts. Philosophical Studies 150 (3):349 - 372.
Pavel Materna (2013). Simple Concepts. Acta Analytica 28 (3):295-319.
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