Counting and the natural numbers

Philosophy of Science 37 (3):405-416 (1970)
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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



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Citations of this work

I-counting is counting.Steven Savitt - 1972 - Philosophy of Science 39 (1):72-73.

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References found in this work

Word and Object.Willard Van Orman Quine - 1960 - Les Etudes Philosophiques 17 (2):278-279.
What numbers could not be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Methods of Logic.P. L. Heath & Willard Van Orman Quine - 1955 - Philosophical Quarterly 5 (21):376.
Consciousness, Philosophy, and Mathematics.L. E. J. Brouwer - 1949 - Proceedings of the Tenth International Congress of Philosophy 2:1235-1249.

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