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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

Carnap, Rudolf (1956), Meaning and Necessity. Chicago: University of Chicago Press.Google Scholar
Church, Alonzo (1956), Introduction to Mathematical Logic. Princeton: Princeton University Press.Google Scholar
Frege, Gottlob (1893), Grundgesetze der Arithmetik. Vol. 1. Jena.Google Scholar
Frege, Gottlob (1967), “On Sense and Nominatum”, in Contemporary Readings in Logical Theory, Copi, Irving M. and Gould, James A., (eds.). New York: Macmillan.Google Scholar
Frege, Gottlob (1979), Posthumous Writings, Oxford: Basil Blackwell.Google Scholar
Kleene, S. C. (1952), Introduction to Metamathematics. New York: van Nostrand.Google Scholar
Kluge, E.-H. W. (1980), The Metaphysics of Gottlob Frege. The Hague: Martinus Nijhoff.CrossRefGoogle Scholar
Marshall, William (1953), “Frege's Theory of Functions and Objects”, The Philosophical Review 62: 374–90.CrossRefGoogle Scholar
Wells, Rulon S. (1951), “Frege's Ontology”, The Review of Metaphysics 4: 537–73.Google Scholar