Abstract
This paper distinguishes revolutionary fictionalism from other forms of fictionalism and also from other philosophical views. The paper takes fictionalism about mathematical objects and fictionalism about scientific unobservables as illustrations. The paper evaluates arguments that purport to show that this form of fictionalism is incoherent on the grounds that there is no tenable distinction between believing a sentence and taking the fictionalist's distinctive attitude to that sentence. The argument that fictionalism about mathematics is ‘comically immodest’ is also evaluated. In place of those arguments, an argument against fictionalism about abstract objects of any kind is presented in the last section. This argument takes the form of a trilemma against the fictionalist.
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Notes
There is an important complication and problem here. Consider such sentences as ‘it is a fiction that there are numbers’ or ‘there are no numbers’. The fictionalist does not want to be a fictionalist about those sentences! Intuitively, we want to say that those are sentences about the subject matter of mathematics, rather than sentences which are part of that subject matter. There is, then, a problem about precisely characterising what the scope of a subject matter consists in. Note that this is not a problem peculiar to the fictionalist. A realist about mathematics, for example, also faces this problem of characterising the collection of sentences which he is a mathematical realist about. This complication leads into the deep problem about how in general we should classify sentences according to given subject matter. It was a problem unearthed by Prior (1976), and has since been notably discussed by Humberstone (1996). Again, it is a problem for all.
That of Lewis (1978).
Rosen (1990).
More generally, a possible world is a system of objects which stand in external relations to each other. (There may (at least epistemically) be external relations other than spatiotemporal relations).
This is not the only way to characterize fictionalism. Another approach is to characterise someone’s being a fictionalist about a sentence of S as that person’s pretending that the sentence is true. This approach is modeled on accounts of fictional discourse which treat talk about fictions as a kind of pretend assertion. See Rosen (1994) pp. 150–151.
Cf. Rosen (1994) pp. 149–150.
This is one of the places where interpreting van Fraassen as a fictionalist is uncertain. He says that to quasi-assert a theory is to display that theory and claim certain virtues for it (van Fraassen (1980) p. 10). But if ‘p’ is a sentence of that theory, what is it, on his view, to quasi-assert ‘p’? One can consistently claim that a theory has certain virtues without claiming, of each sentence ‘p’ that is involved in expressing the theory, that ‘p’ has those virtues.
In note 6 I mentioned that fictionalism might be presented not in terms of acceptance (as characterized above), but in terms of pretended belief and pretended assertion. This alternative account will face a parallel to the present challenge: is the belief/pretend belief distinction a distinction without a substantial difference?
O’Leary-Hawthorne (1994) loc. cit.
I assume here for the purposes of argument that conditionals can be objects of de dicto belief. Those who disagree with that assumption are free to substitute an example that is more suitable by their lights.
Rosen and Burgess (2004) p. 526 (their italics).
These are beliefs concerning contingent unrestricted existentially quantified propositions, such as that there are angels, or that there are epiphenomenalons (where an epiphenomenalon is an entity generated by the interaction of subatomic particles, but which can have effects neither on particles nor on minds). See Armstrong (1973) pp. 32 and 100.
Rosen and Burgess (2004) p.516.
Horwich (2004) p. 90. He writes (his italics):
[Fictionalism] presuppose[s] a distinction between, on the one hand, believing a theory and, on the other hand, being disposed to use it, or, in van Fraassen’s terminology, merely accepting it. But there is no such distinction, or so I will argue.
Horwich (2004) p. 89 (his italics).
Horwich (1998) p. 9.
I am grateful to an anonymous referee for this analogy, and also for advice on how to make this part of my discussion better focused.
Horwich (2004) p. 90.
Horwich (2004) pp. 90–91 (his italics).
Horwich (2004) p. 89.
Teller (2001) pp. 139–142.
Van Fraassen (1980) pp. 72–73, and (2002) ch. 4.
Teller (2001) p. 142.
Teller (2001) p. 143.
Van Fraassen (2001) §III.
Blackburn (2003) §IV.
A motivation for arithmetical fictionalism which does not depend on nominalism is given by Wagner. (Wagner is a fictionalist about arithmetic, but not mathematics more generally). The motivation stems from considerations about undecidable mathematical sentences. There seems to be no answer to the question ‘Is the number 2 identical with {{Ø}} or with {Ø, {Ø}}?’ This is analogous to the incompleteness of fictional tales. For instance, there seems to be no answer to the question ‘How many children did Lady Macbeth have?’ (Wagner (1982) p. 256, and Field (1989) p. 22).
In reply, Burgess (2004) p. 29 points out that a similar phenomenon holds in the case of scientific and commonsense thought and talk. (The phenomenon is what Peter Unger has called ‘the problem of the many’.) Because of vagueness there seems to be no answer to the question ‘Is this table identical to the collection of these million particles, or is it identical to the collection of these million-and-one particles?’ If identifying the number 2 with a particular set is analogous to the continuation of a story, and so is appreciably like a piece of fiction, so too is the identification of a physical object with one particular collection of particles. Given the pervasiveness of vagueness, almost all talk about empirical subject matters should then be construed as fictional talk.
Wagner might reply that the relation between a physical object and a collection of particles is not identity but another relation—composition—and so the above question does not arise. If he should say this, however, Wagner would be open to the parallel reply that the relation between a natural number and a set is not identity but another relation—structural representation—and so Wagner’s question does not arise (For this alternative view of the relation between natural numbers and sets, see Swoyer (1991) pp. 477–478).
Cf. Rosen (1994) pp. 165ff.
Balaguer (1998) p. 13.
Balaguer says that the problem is ‘a special case of a much more general problem with fictionalism, namely, the problem of applicability and indispensability’ (p.14), and that he will solve the problem in chapter 7 of his book. Central to that chapter is that claim that empirical science has a nominalistic content distinct from the Platonistic content of mathematics. His argument for this claim (pp. 133–134) appears to run as follows. (1) Consider sentence (A):
(A) The physical system S is forty degrees Celsius.
(2) The number 40 is causally independent from S’s temperature. So (3) if (A) is true, it is true in virtue of the combination of a fact about S and a fact about 40, where these facts are independent of each other. (4) ‘But this suggests that (A) has a nominalistic content that captures its complete picture of S: that content is just that S holds up its end of the “(A) bargain”, that is, S does its part in making (A) true’ (p.133).
Balaguer subsequently makes repeated use of the metaphors used in (4)—of a complete picture of S, of the (A) bargain, and of S’s doing its part in making (A) true (see pp. 134–136). But he does not explain what non-metaphorical claim (4) is supposed to be making. That aside, it is not clear that (4) follows from (1) to (3). (3) claims that a fact about S and a distinct fact about 40 jointly make (A) true. (4) claims that (S) has a nominalistic content and a Platonistic content. I do not see why (A)’s content should be bifurcated in this fashion solely because certain distinct facts make (A) true. (Balaguer not only assumes that where causally independent facts jointly make a sentence true, that sentence has bifurcated contents, but also that where the facts which jointly make a sentence true are not causally independent, that that sentence does not have a bifurcated content: see pp. 134–135). Balaguer’s treatment is all the more puzzling because it is a commonplace among truthmaker theorists that what makes a given sentence true need not be reflected in its semantic structure.
Furthermore, Balaguer’s case would be helped if he specified what the purely nominalistic content of (A) is. But instead he reports that ‘all we can say here is that the nominalistic content of (A) is that some purely physical fact that involves S holding up its end of the “(A) bargain” obtains’ (pp. 133–134). The use of the bargain metaphor leaves it unclear whether the content ascribed is genuinely nominalistic. So it remains unclear whether Balaguer has accomplished the task which he set himself earlier in his book, namely, answering the fictionalist’s ‘need to find a nominalistic way of describing the fact in question here’ (p. 14).
Lastly, Balaguer does not discuss how his approach is to account for apparent commitment to abstract objects other than to numbers. Yet when he considered such sentences as ‘concrete ‘3–is-prime’ tokens are tokens of a types that is true-in-the-story-of-mathematics’ in the early part of his book (p.14), he promises to show how they pose only a special case of the problem of indispensability and applicability, and which he would solve in chapter 7.
Rosen (1990) p. 338.
Rosen (1990) p. 337.
Linsky and Zalta (1995) §§II and III, and see the references therein.
I’m indebted to an anonymous referee for this journal for the points made in this paragraph.
I take this to be the force of the first paragraph of Nathan Salmon’s review of On The Plurality of Worlds: see Salmon (1988) p. 237.
Rosen (1990) p. 339.
An earlier version of this paper was presented at a seminar at the Centre for Philosophy at Manchester University in 2006. I am grateful to the participants. I am also very grateful to Sven Bernecker, David Liggins, Daniel Nolan, and an anonymous referee for this journal for valuable comments on an earlier draft of this paper.
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Daly, C.J. Fictionalism and the attitudes. Philos Stud 139, 423–440 (2008). https://doi.org/10.1007/s11098-007-9132-x
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DOI: https://doi.org/10.1007/s11098-007-9132-x