Book reviewed:

Jerrold J. Katz, *Realistic Rationalism*

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^{2}*Language and Other Abstract Objects* (Totowa, NJ: Rowman and Littlefield, 1981) ch. 6; D. Lewis, *On the Plurality of Worlds* (Oxford: Basil Blackwell, 1986) sec. 2.4.

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^{4}*thin* way here. On this usage, five-year-olds have beliefs about Santa Claus. There are, of course, thicker senses of ‘about’ on which no one could have a belief about Santa Claus, because there is no such person. When I say that it is obvious that humans can have beliefs about abstracta, I mean this in the thin sense. And the reason I think this is the relevant sense of aboutness here is that I think that this sort of belief is sufficient to ground knowledge of abstract objects (if indeed there are any). I cannot argue for this claim here, but I justify it in my *Platonism and Anti-Platonism in Mathematics* (New York: Oxford University Press, 1998).

^{5}*Realistic Rationalism* unless otherwise noted.

^{6}*Platonism and Anti-Platonism in Mathematics.*

^{7}*Platonism and Anti-Platonism in Mathematics*, Chapter 3.

^{8}*which* mathematical objects exist, given that some do exist.

^{9}*Realism, Mathematics, and Modality* (New York: Basil Blackwell, 1989) 235–37.

^{10}*Der Grundlagen die Arithmetic* [*The Foundations of Arithmetic*], trans. J. L. Austin (Oxford: Basil Blackwell, 1953); P. Maddy, *Realism in Mathematics* (Oxford: Oxford University Press, 1990).

^{11}*Platonism and Anti-Platonism in Mathematics*, and in private correspondence, Maddy approved of this sort of interpretation. It should be noted, though, that the ‘taken together’ clause is not to be read psychologistically, that is, as requiring a person who takes them together. As we will see, it has to be read as involving something nonphysical.

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^{13}*Platonism and Anti-Platonism in Mathematics*, I explain how Platonists can avoid claims of uniqueness in connection with purely abstract mathematical objects, for example, pure sets and numbers. I think that a similar story can be told about impure sets, but I will not go into this here.

^{14}*Science without Numbers* (Princeton, NJ: Princeton University Press, 1980) and *Realism, Mathematics and Modality*, and also my *Platonism and Anti-Platonism in Mathematics*.

^{15}*Science without Numbers*) tries to block the argument by arguing that, in fact, mathematics is not indispensable to empirical science. I (*Platonism and Anti-Platonism in Mathematics* [ch. 7]) have argued that even if mathematics is indispensable to empirical science we can account for this from a fictionalistic point of view.

^{16}*Platonism and Anti-Platonism in Mathematics* (ch. 7).

^{17}*Platonism and Anti-Platonism in Mathematics*, I respond to several objections to fictionalism, including the one mentioned in the text about the nature of stories.

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