1 Carnap, R. ‘Empiricism, Semantics, and Ontology,’ reprinted as a supplement to Meaning and Necessity: A Study in Semantics and Modal Logic (Chicago: University of Chicago Press 1956), 205–21Google Scholar

2 The move from reference-failure to untruth (falsity or lack of truth-value) may be questioned. Perhaps some genuine singular terms have a semantic function other than reference; perhaps sentences can be true or false even if some of their constituents lack semantic value. Since such proposals involve non-standard semantics for the F-discourse and since one of the main motivations for fictional ism is to preserve semantic simplicity, I will regard them as incompatible with fictional ism. Fictionalists about Greek mythology can maintain that a sentence like ‘Pegasus is a winged horse’ is true in some sense, but they must deny that it is literally true.

3 Cf. Quine, W.V.O. ‘Two Dogmas of Empiricism,’ reprinted in From a Logical Point of View (Cambridge, MA: Harvard University Press 1961), 20–46Google Scholar, and Putnam, H. ‘Philosophy of Logic,’ reprinted in Mathematics, Matter, and Method: Philosophical Papers, vol. 1 (Cambridge: Cambridge University Press 1979), 323–57.CrossRefGoogle Scholar

4 Cf. Field, H. Science Without Numbers (Princeton: Princeton University Press 1980)Google Scholar.

5 Cf. van Fraassen, B. The Scientific Image (Oxford: Clarendon 1980)CrossRefGoogle Scholar.

6 For a discussion of the tension between fictionalist nominalism and naturalism, sec Burgess, J.P. and Rosen, G. A Subject with No Object (Oxford: Clarendon 1997), esp. 214–25Google Scholar

7 Cf. Melia, J. ‘On What There Isn't,’ Analysis 55 (1995) 223–9CrossRefGoogle Scholar; Balaguer, M. ‘A Fictionalist Account of the Indispensable Applications of Mathematics,’ Philosophical Studies 83 (1996), 291–314CrossRefGoogle Scholar; Balaguer, M. Platonism and Anti-Platonism in Mathematics (Oxford: Oxford University Press 1998)Google Scholar; Yablo, S. ‘Does Ontology Rest on a Mistake?’ in Proceedings of the Aristotelian Society, supp. vol. 72 (1998) 229–61CrossRefGoogle Scholar; and Yablo, S. ‘A Paradox of Existence,’ in Everett, A.J. and Hofweber, T. eds., Empty Names, Fiction and the Puzzles of Non-Existence (Palo Alto: CSLI 2000)Google Scholar.

8 An illusion of understanding may arise, for we might think that the infinite sentence is logically equivalent to ‘The ratio of the number of planets and the number of stars is 2.4.’ But thinking this would be wrong: the proposed substitute sentence entails the existence of ratios; the infinite sentence does not.

9 Higginbotham suggests that we capture the relevant interpretation of ‘average’ adverbially. Cf. Higginbotham, J. ‘On Semantics,’ Linguistic Inquiry 16 (1983) 547–93Google Scholar. So, Melia's ‘The average star has 2.4 planets’ would be interpreted as ‘Stars on the average have 2.4 planets.’

10 The phrase and the example are from G. Berkeley, A Treatise Concerning the Principles of Human Knowledge, §51 in Luce, A.A. and Jessop, T.E. eds., The Works of George Berkeley, Bishop of Cloyne, 9 vols. (London: Thomas Nelson and Sons 1948-57)Google Scholar. They serve to defend his immaterialism (a kind of fictionalism about material objects) against the charge of verbal impropriety.

11 Cf. Moore, G.E. ‘A Reply to my Critics,’ in Schlipp, P.A. ed., The Philosophy of G.E. Moore (Evanston, IL: Northwestern University Press 1942), 542–3Google Scholar, and Moore, G.E. ‘Moore's Paradox,’ originally untitled manuscript in Baldwin, T. ed., G.E. Moore: Selected Writings (London: Routledge 1993), 207Google Scholar.

12 Cf. Moore, G.E. ‘Moore's Paradox,’ 207.Google Scholar

13 The nature of this commitment is subject to debate. But according to any plausible account, those who assert something they do not believe will thereby violate at least one of the central norms of assertion.

14 The notion of pretending to assert something is similar to Grice's notion of making it as if one said something. Cf. Grice, P. ‘Logic and Conversation,’ in Studies in the Ways of Words (Cambridge, MA: Harvard 1989), 30Google Scholar; and Grice, P. ‘Further Notes on Logic and Conversation,’ 41CrossRefGoogle Scholar.

15 Embedded uses of a sentence would not typically qualify as assertive; if a sentence occurs within the scope of a modal operator or in the antecedent of a conditional, any competent speaker would know that it is not asserted. The same holds for ordinary quotation: the fact that one speaks in someone else's voice must be made clear either by explicitly saying this or at least by using special intonation. By contrast, the actor on stage reciting the words of the playwright will refrain from these devices and hence, although she does not assert she speaks assertively.

16 Couldn't the fictionalist insist that we should refrain from using ‘S but I don't believe that S’ simply because this would not be in conformity with the ordinary use of ‘S’? He could, but this extra prohibition would remain unexplained. True enough, the use of a Moorean sentence would tip off anyone that the speaker has some highly non-standard attitude towards ‘S.’ But surely, the fictionalist cannot recommend that in engaging in the F-discourse we must hide the fact that we lack belief in the F-theory. This would not go very far in calming our worries about the hypocrisy of the suggestion.

17 We know independently that if shifts of context are allowed utterances of Moorean sentences may be unproblematic. For example, if one utters assertively, ‘It is raining’ in a loud voice and then one continues by whispering to a nearby friend, still assertively, ‘…but I don't believe it is raining’ the utterance is mischievous, but by no means absurd. Cf. Moore, G.E. ‘Moore's Paradox,’ 207-8Google Scholar.

18 It is unclear whether they could do so; whether we could overcome our cognitive limitations with their help depends on what sort of cognitive limitations are at issue. If all we lack is sufficient evidence, perhaps we can come to believe the F-free theory on the basis of testimony from the sophisticates. But if the theory is only presentable in a language we in principle cannot understand, we will never come to believe it even with their help.

19 Of course, if we mention, rather than use such a sentence the quasi-translation would be homophonic. So, for example, if ‘S’ is a sentence of the F-theory and ‘S” is its quasi-translation, then, the quasi-translation of ‘We are trying to prove the hypothe-sis that S’ is ‘We are trying to prove the hypothesis that S',’ whereas the quasi-trans¬lation of ‘You just uttered the sentence ‘S” is ‘You just uttered the sentence ‘S’.’

20 This assumes that the F-discourse is not psvchnlogy, and hence the quasi-translation of expressions like ‘I’ and ‘believe’ are homophonic. The present argument does not work without such an assumption.

21 Cf. Yablo, ‘A Paradox of Existence.’

22 Consider the case of dead metaphors. A sentence like ‘Mary lived at the foot of the hill’ is literally true. ‘Foot of the hill’ is an idiom whose meaning must be learned independently of the meanings of its constituent expressions.

23 There are two important differences between this case and the one discussed in the previous section. The first is that we can all become sophisticates regarding our ordinary talk about the sun; there is no deep epistemic barrier between those who know how the paraphrases would go and those who don't. The second is that the false theory that underwrites utterances of ‘The sun is rising’ is by no means indispensable. Neither of these differences would justify the claim that in this case, as opposed to the one discussed in the previous section, the Moorean sentence is not quasi-assertable.

24 I thank Richard Boyd, Tamar Szabó Gendler, John Hawthorne, Harold Hodes, Sydney Shoemaker, Ted Sider, Jason Stanley, and two anonymous referees for discussion and comments.