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Constructions

Published online by Cambridge University Press:  01 April 2022

Pavel Tichy
Pavel Tichy*
Affiliation:
Department of Philosophy, University of Otago
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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.

Type
Research Article
Information
Philosophy of Science , Volume 53 , Issue 4 , December 1986 , pp. 514 - 534
Copyright
Copyright © The Philosophy of Science Association 1986

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Footnotes

†

The author is indebted to Jane Hogg for a number of helpful suggestions.

References

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