^{1}*Collected Papers*, ed. Charles Hartshorne and Paul Weiss, vol. 5. Cambridge: Harvard UP, 1965 5.392.

^{2}*Realistic Rationalism*. Cambridge: MIT Press, 1998. Page citations will be given in parentheses in the text.

^{3}*Enquiry Concerning Human Understanding*, sec. 4, pt. 1, par. 1.

^{4}*Issues in the Philosophy of Language*, ed. Alfred F. MacKay and Daniel D. Merrill. New Haven: Yale UP, 1976.

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^{7}*The Problem of Universals*. New York: Basic Books, 1971, for excellent reasons for being averse to accepting set theory except as a hypothetical mathematical construction. I believe that this was Wittgenstein's view as well.

^{8}*Essay Concerning Human Understanding*, bk. 2, ch. 8, 9. For a further elaboration, see Penelope Maddy, “Perception and Mathematical Intuition,”*The Philosophy of Mathematics*, ed. W. D. Hart. Oxford: Oxford UP, 1996.

^{9}*Foundations of Arithmetic*, trans. J. L. Austin. Oxford: Basil Blackwell, 1953, sec. 46.

^{10}*a priori* as to whether the number of things in the world is finite or infinite. . . . The axiom of infinity will be true in some possible worlds and false in others; whether it is true or false in this world, we cannot tell.” (*Introduction to Mathematical Philosophy*. London: George Allen and Unwin, 1953; p. 141). In effect, Russell is accepting the Humean view that the system of pure infinite arithmetic is hypothetical.

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^{13}*The Basic Laws of Arithmetic*, trans. Mongomery Furth. Los Angeles: U of CP, 1964, 6n.