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Counting and the Natural Numbers

Published online by Cambridge University Press:  14 March 2022

Jeffrey F. Sicha
Jeffrey F. Sicha*
Affiliation:
Amherst College
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Abstract

Early sections of the paper develop a view of the natural numbers and a view of counting which are suggested by the remarks of several modern philosophers. Further investigation of these views leads to one of the main theses of the paper : a special kind of quantifier, the “numerical quantifier” is essential to counting. The remainder of the paper suggests the rudiments of a new view of the natural numbers, a view which maintains that numerical quantifiers are one kind of natural number.

Type
Research Article
Information
Philosophy of Science , Volume 37 , Issue 3 , September 1970 , pp. 405 - 416
Copyright
Copyright © 1970 by The Philosophy of Science Association

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Footnotes

1

This paper is a revised version of one presented to the Department of Philosophy at the University of Massachusetts. I should like to thank the members of that department and the reviewers of this journal for their helpful criticisms. Special thanks are due Professor B. A. Aune who was kind enough to provide many penetrating and important comments on this and an earlier version of this paper.

References

REFERENCES

[1] Aune, B. A., Knowledge, Mind, and Nature, Random House, New York, 1967.Google Scholar
[2] Benacerraf, P., “What Numbers Could Not Be,” Phil. Rev., vol. LXXIV, 1965, pp. 47–73.10.2307/2183530CrossRefGoogle Scholar
[3] Brouwer, L. E. J., “Consciousness, Philosophy and Mathemetics,” Proc. 10th Int. Congress of Philosophy, Amsterdam, 1948, pp. 1234–1249.Google Scholar
[4] Brouwer, L. E. J., “Historical Background, Principles and Methods of Intuitionism,” S. African J. of Science, vol. 49, 1952, pp. 139–146.Google Scholar
[5] Quine, W. V. O., Methods of Logic, Henry Holt and Co., New York, 1959.Google Scholar
[6] Quine, W. V. O., Word and Object, The Technology Press of MIT and John Wiley and Sons, New York, 1960.Google Scholar
[7] Sellars, W., “Some Reflections on Language Games,” Science, Perception and Reality, Routledge and Kegan Paul, London, 1963, pp. 321–358.Google Scholar
[8] Sellars, W., “Abstract Entities,” Rev. of Metaphysics, vol. 16, 1963, pp. 627–671.Google Scholar
[9] Schwayder, R., Modes of Referring and the Problem of Universals, University of California Publications in Philosophy, University of California Press, Berkeley and Los Angeles, 1961, vol. XXXV.Google Scholar
[10] Waismann, F., Introduction to Mathematical Thinking, Harper Torchbooks, New York, 1959.Google Scholar