Fictionalism and Reasons

Chris Daly

1Introduction

Some philosophers know better than the rest of us. While many (other) philosophers and the folk believe there are Ks – colours, moral facts, sets, properties, composite objects, as the case may be – the former group of philosophers think otherwise. They do not believe that there are Ks but simulate the belief that they do. (Note that not believing that there are Ks does not entail believing that there are no Ks. A fictionalist about Ks might be an agnostic about the existence of Ks). These philosophers are revolutionary fictionalists (hereafter ‘fictionalists’ for short): revolutionary because they enjoin us to cease believing that there are Ks; fictionalist because they seek otherwise to preserve our patterns of talking and reasoning about Ks. Berkeley memorably captured this strategy of philosophical retrenchment:

. . . in such things we ought to think with the learned and speak with the vulgar. They who to demonstration are convinced of the truth of the Copernican system do nevertheless say ‘the sun rises’, ‘the sun sets’, or ‘comes to the meridian’; and if they affected a contrary style in common talk it would without doubt appear very ridiculous (Berkeley 1711 §51).

Some writers dispute a fictionalist reading of Berkeley’s philosophy (Sainsbury 2009: 154-57 and Kroon 2011: 789). I suggest an irenic treatment: that he allowed two ways of thinking with the learned and speaking with the vulgar. One is fictionalist, which is a natural way of reading what he has to say about quotidian ways of talking about the sun’s movement; the other is to reinterpret vulgar talk – folk talk – in the light of what the learned have come to know about the facts. His own philosophy follows the second route: though the folk talk of sticks and stones, the learned know (or so he claimed) that this talk is to be interpreted as talk of certain congeries of ideas. He did not offer a similar reinterpretation of folk talk of the sun rising and setting; hence a fictionalist reading recommends itself for this case.

Berkeley’s particular example may be ill-chosen since, relative to the Earth, the sun moves (O’Leary-Hawthorne and Michaelis 2006: 124 and Jackson 2007). Better examples are forthcoming, however, particularly ones involving popular but mistaken views about how things work. For example, there is the widespread belief that coldness flows from cold objects to hotter objects. You might know better but quite reasonably trade on your waiter having this belief in order to get ice for your drink.

We now have on the table the kind of fictionalism that will concern us. This paper will present a two-part defence of fictionalism. One part consists in a defence of the notions needed to articulate the fictionalist’s position. The other part, which will occupy the bulk of the paper, will be to defend the viability of fictionalism: to show that it is a candidate position worthy of serious consideration and how there might also be reasons to take that position.

2The Balance of Evidence

We have tried to improve on Berkeley. Perhaps, however, better examples lead only to fresh worries:

When it comes to a genuine conflict, Berkeley’s advice to the advocate of revisionary ontologies is harsh. If she has decent arguments against holes, values and propositions, she should stick with them and she should say that although we think there are holes in our cheese, values in our lives, and propositions in our theories, in fact that there are none. (Of course, we are permitted to speak as if we don’t mean what we say). But what is the basis for paying less respect to received views about ontology than to received views about other matters? And, since ontological claims are inferentially connected to countless others, how are we to stop the spillover of immodesty to other areas? Philosophers who deny the authority of received ontology [i.e. the ontology the folk believe] must arbitrarily restrict the scope of their denial or end up rejecting deference to received ontology altogether (Szabó 2010: 23).

The epistemic basis of fictionalists’ claims is found where the balance of evidence lies. If the folk’s acceptance of certain claims is evidence of any kind for them, fictionalists have their reasons for rejecting those claims. But the fact that the fictionalists think the balance of evidence lies there does not commit them to ‘rejecting deference to received ontology altogether’. Consider a humdrum case: you seem to remember leaving the oven on. You go back to the kitchen and feel that the oven is cold and see that the oven light is off. On the balance of evidence you conclude that the oven is off. Your accepting this conclusion does not require rejecting deference to your memory altogether. More generally, in a case where you think the reasons con are stronger than the reasons pro, you need not think that the source of the reasons pro is everywhere and always unreliable.

The fictionalist can then reach her immodest conclusions by familiar and relatively modest means: the weighing of one set of reasons against another. Where though will it all end? How are we to stop immodesty spilling over to other areas? Note, first, that any claims are inferentially connected to countless others, so the issue here is not specifically about ontological claims. And, by the same token, modesty about ontological claims – i.e. upholding the claims of folk ontology – will ‘spill over’ into other areas. That was something that G.E. Moore cultivated in his homely defence of common sense. Will we have to restrict arbitrarily the scope of the acceptance of these claims as well? Second, the above passage seems simply to be an alarming way of putting the point that revising beliefs has ramifications: that if some of your credences change, so too should others. There is nothing untoward in this and so nothing untoward in fictionalism’s bid for a hostile takeover of ordinary thought.

3In Defence of Exploitation

There is a revealing pattern in fictionalist projects. In each case we can distinguish apparatus, selected role, resulting attitude of exploitation, and shifted norm. Consider Field on mathematics (Field 1980). The natural sciences incorporate the apparatus of mathematics. Mathematics has the role of describing the mathematical universe: a paradise of numbers, functions, sets, groups and the like. But ignore that role. Select this other role instead: mathematics facilitates deductions within nominalistic theories. By ignoring the first role and concentrating on the second, you can exploit mathematics without believing it. The norm for mathematics has shifted: the original norm of appraising mathematics in terms of the truth of its contents has been de-selected and replaced by a norm of nominalistic conservativeness (that is, combining science with mathematics does not yield claims about the concrete world not yielded by science alone). Consider van Fraassen on science (van Fraassen 1980) – or, perhaps, a contentious but widespread reading of him. (For reservations about this reading, see Kroon 2011: 792-3. Van Fraassen 1975: 736-40, however, apparently self-identifies as a fictionalist). The sciences incorporate apparatus about unobservables. Sciences have the role of describing an unobservable domain: a wonderland of mesons, quarks, electromagnetic waves and the like. But ignore that role. Select this other role instead: science’s claims about unobservables facilitate claims about observables. By ignoring the first role and concentrating on the second, you can exploit science without believing its claims about unobservables. The norm for science has shifted: the original norm of appraising science in terms of the truth of its contents about both the observable and the unobservable world has been de-selected and replaced by a norm of empirical adequacy (that is, of correctly describing the observable world). Lastly, consider Joyce on morality (Joyce 2006). Ethics incorporates an apparatus about objective moral values. Ethics has the role of describing the ethical universe: a cornucopia of objectively prescriptive values, principles and directives. But ignore that role. Select this other role instead: ethics facilitates self-control against practical irrationality (and secondarily on making yourself the sort of agent that has self-control and so is more reliable). By ignoring the first role and concentrating on the second, you can exploit ethics without heeding its claims about objective prescriptivity and demandingness. The norm for ethics has shifted: the original norm of appraising ethics in terms of the truth of its contents has been de-selected and replaced by a norm of bolstering self-control against practical irrationality.

Just what is it to exploit a theory? This would-be attitude goes under various names including ‘acceptance’, ‘belief as if’ and ‘quasi-belief’. ‘Acceptance’ seems to have the most currency. This may be unfortunate since it is also commonly used as broadly synonymous with ‘belief’ or is used in a way that belief counts as a species of acceptance (Kroon 2011: 799, note 4). I will use the term ‘exploit’ since it is familiar – rather than a made-up term like ‘quasi-belief’ – and there is little chance of eliding it with ‘belief’. But is there a genuine attitude that is being named? And, besides that, is it an attitude that we can really have? I address the first question in this section and the second in the next.

Some philosophers are sceptical about whether there is such an attitude as exploitation (e.g. Stein 1989: 61 and Horwich 1991 §2), so it is worth saying something about the topic here. There are two options for defining exploitation. One option is to take the notion to be specified by its functional role involving other psychological notions. A familiar strategy concerning functionalist theories of mind is to characterize psychological notions via their typical causes and effects. Accordingly, we might specify what it is to exploit a theory T by means of such principles as: believing that T is useful typically causes one to exploit T; that exploiting T typically does not cause one to believe T; that desiring that p and believing that exploiting T would bring it about that p typically causes one to exploit T; and so forth. Another option would be to give an analytically reductive definition of ‘exploitation’. Consider what van Fraassen says about what it is to for you to exploit (‘accept’ in his terminology) a scientific theory T. You believe T’s claims about the observable world; you do not believe T’s claims about the unobservable world. By exploiting T you also ‘immerse’ yourself in T: this is a matter of being committed to using T’s resources in investigating and describing the world (van Fraassen 1980: 81-82). Immersion is then a matter of upholding a decision about how to use T. The exploitation of a scientific theory is then reductively defined in terms of familiar psychological notions: specifically, belief and decision. Similarly, consider what Field says about what it is to be a fictionalist about some body of mathematics M. You do not believe M. You believe that conjoining M with a nominalistically acceptable scientific theory T has no nominalistically acceptable consequences that T does not alone have. You believe that conjoining M with T expedites deducing T’s nominalistic consequences. And since you wish to expedite deducing these consequences, you wish to combine M with T when using T. As before, exploitation is defined in familiar psychological notions.

The fictionalist can supplement these definitions with illustrations. The fictionalist’s go-to examples of theories that are exploited but not believed, and which are governed by a norm other than the truth norm, are various defunct scientific theories. Newton’s theory of mechanics facilitated moon shots, Dalton’s law of partial pressures facilitates filling scuba tanks, and so on. Some critics, however, are unpersuaded:

But [these examples] give us a false analogy: the virtues of these theories are not independent of their truth. They are false but approximately true, and the fact that they come near enough to truth seems to be the reason why they work in certain settings. . . . By contrast, the fictionalist thinks the truth or falsity of his target theory should be of no concern to us (Szabó 2010: 33).

In response, the fictionalist will distinguish between the truth (or otherwise) of a theory and the truth of some of its consequences. The truth of those consequences is not hostage to the truth (or otherwise) of the theory. A defunct theory T is false, so whatever virtues it has are independent of its erstwhile truth. The virtues of T are not independent of the truth of some of its consequences – otherwise T would be of no use. Appealing to approximate truth will not settle matters either. Setting aside the intractable obscurity of that notion, there are defunct theories that are not approximately true but which remain ripe for exploitation. I take it that a theory is approximately true only if its central terms refer. If there are no germs and nothing like them, then a germ theory of disease could not be even approximately true. (By contrast, Newton wasn’t wrong in thinking that there is gravity and Dalton wasn’t wrong in thinking that there are gas mixtures. Their theories were about real things). Consider then a theory whose central terms are known not to refer. Such a theory might still provide true consequences about the observable world. Despite its known falsity, the theory could have some empirical support and be ripe for exploitation. There is a raft of theories with this character, including the phlogiston theory of heat, the theory of the electromagnetic aether and the astronomical theory of crystalline spheres (Laudan 1981: 33). The fictionalist’s contention was correct: defunct scientific theories remain a reliable mainstay.

But a mainstay of what exactly? Perhaps the attitude that the fictionalist prizes isn’t in fact the attitude that we take to defunct theories:

[For] despite the similarities, this is not the attitude the fictionalist advocates. We regard the falsehood of Newtonian mechanics as a defect, something we can ignore in some settings but not in others. Our Newtonian calculations are accompanied by the silent disclaimer that we engage in them only to make things simpler and because we have good reason to believe that the results will be only negligibly incorrect. Fictionalists advocate acceptance without reservations of this sort (Szabó 2011: 377).

Does our attitude differ from the fictionalist’s? Here is what both parties agree on. Whether falsity is a defect in a theory depends on what you want from the theory. If we want the theory to contain no false representations of reality, Newtonian theory’s falsity is a defect: it doesn’t serve that role. If we want Newtonian theory to simplify our calculations and to make some claims that are only negligibly incorrect, its falsity is not a defect: it can serve that role. There doesn’t seem to be anything else at issue between the fictionalist and us. Neither party believes the theory; both parties exploit it nonetheless. Fictionalism does not then require ‘an extraordinary form of acceptance’ (Szabó 2011: 378).

Our attitude to defunct scientific theories also has a bearing on the other query facing the fictionalist: explaining how it is possible for us to have the attitude of exploitation. I turn to this next.

4How To Exploit

According to the fictionalist, the conditions under which it is correct to make a claim shift with context. When seeking to exploit a theory, it is correct to make claims using the theory. By contrast, when what is at issue is what one believes, it is not correct to make claims using the theory. This strategy is open to the following query:

. . . [Exploitation] is supposed to be compatible with philosophical reflection. Someone who bears this attitude towards a theory should be able to endorse it in ordinary contexts and reject it in philosophical ones. In other words, the attitude should be sensitive to the difference between these contexts (Szabó 2010: 33).

The problem is then alleged to be that there is no such difference because there is no such thing as a philosophical context. And since there is no difference between ordinary and philosophical contexts, it is not possible for us to have this attitude of exploitation, an attitude that is supposed to be present only if we are in a philosophical context.

Some comments. First, given the results of the previous section, it’s not just philosophers who exploit theories. A physicist might exploit Newtonian mechanics in the context of NASA’s mission control room but reject it out of hand in a physics research seminar. Correctness conditions for a claim shift here as well: what’s correct to say in mission control isn’t correct to say in the research seminar. So it is not special pleading to suppose that there is an important difference between philosophical and ordinary contexts whereby the correctness conditions for a given claim may shift between these contexts.

Second, Szabó seeks to explain differences in the correctness conditions of claims along other lines: specifically, that unless a challenge is explicitly signaled, it is always inappropriate to challenge the prevailing assumptions. ‘To object that this presupposition is unwarranted would derail the conversation from its current direction – hence it is inappropriate’ (Szabó 2010: 34). But this seems beside the point. The challenge was whether the fictionalist was able to explain the differences in correctness conditions in her own terms. That an alternative explanation is available does not undermine the fact that she has provided an answer to that challenge: namely, that the difference in correctness conditions reflects a difference between philosophical and ordinary contexts.

Szabó thinks there is ‘ample reason to doubt whether we have the ability to reliably identify philosophical contexts’ (Szabó 2011: 382). I think that we are able to identify such contexts just as well as we are able to tell when we are doing philosophy and when we are not. What is Szabó’s reason for scepticism about our ability to identify the different contexts? Simply this: that there is no difference between philosophical and ordinary contexts (Szabó 2011: 383). It follows that we have no ability to detect a difference between these contexts. But what is the ample reason for thinking there is no difference between philosophical and ordinary contexts? Szabó is less forthcoming about this but he insists that the onus lies with the fictionalist: ‘Fictionalists believe that there is such a distinction: they owe us an argument that we are, or at least could be, sensitive to it’ (Szabó 2011: 383).

What the fictionalist needs to do is what other people, including non-philosophers, do when they exploit a theory. Recall our physicist. Her day job is to compute satellite paths. For this purpose she exploits Newtonian mechanics. Whether Newtonian mechanics is true is not something up for debate, so far as her team’s achieving this purpose is concerned. When she goes to research seminars and conferences, however, she makes claims that she knows entail the falsehood of Newtonian theory. Perhaps she publishes in physics journals, teasing out the consequences of general relativity. But again she is exploiting rather than believing general relativity since she entertains serious doubts about it, due to its incompatibility with quantum theory.

Our physicist is an invented character who is sensitive as to whether questions about the truth of given theories are called for. Various eminent historical figures, however, actually fit this pattern. Abraham Robinson combined pioneering work in non-standard analysis with the view that his theory’s description of infinitesimals was a well-founded fiction (Dauben 1995: 471-2). Similarly, Tarski, who was loath to publish his philosophical opinions, used a valedictory symposium to describe his work in set theory and logic with the admission that ‘I believe that there is value even in fairy tales and the study of fairy tales’ (Feferman and Feferman 2004: 52. The Fefermans report Tarski’s attitude, though, as expressing ‘a strange ambivalence’).

In some contexts a given theory is not up for debate but in others it is either up for debate or is already rejected. Though Szabó expresses scepticism about the notion of a philosophical context, presumably this scepticism does not extend to philosophical reasons. He remarks that ‘After all, we don’t think we transport ourselves into a special context when we start discussing astronomy, philology, or stamp-collecting. Why would philosophy be different?’ (Szabó 2010: 34). We do, however, think that there are astronomical or philological reasons for making certain claims. This gives us enough material to address his challenge. In a case in which a philosophical reason is given for putting a given theory T up for debate – for believing or rejecting it, as the case may be – we are considering T in a philosophical context. Otherwise T is not being considered in a philosophical context. Robinson and Tarski were sensitive to whether it is appropriate to deploy philosophical reasons. On my account, this translates into their being sensitive to whether they were in a philosophical context. Unless they took themselves to be in a philosophical context, a context where philosophical reasons pro or con the existence of certain mathematical entities would come into play, they would continue without demur to exploit theories that posit these entities.

The important point here concerns our sensitivity about when a question concerning the truth of a theory T is called for. In some contexts it is not. In those contexts we’re in exploitation mode. In other contexts it is. This is when the truth of T is precisely what’s at issue.

5Is Fictionalism A Fraud?

The fictionalist also faces a challenge concerning switches between worlds – between worlds where fictionalism about Ks is true and worlds where it isn’t. Simon Blackburn raises the challenge in the case of fictionalism about colour, but a quite general form of challenge underlies his comments:

So consider ‘canaries are yellow’ which, on the [fictionalist] account, in our world is told as if true, or should be told as if true, although it is actually just a fiction. Now we ask: is it true in the color fiction that canaries are yellow? To answer we need to understand what it is for ‘canaries are yellow’ to be fact, and to be known as such, although in our world it is not. This is a tall order. If it is neither a fact nor known to be such in our world, what is different in those worlds in which it is? (Blackburn 2005: 325).

I take Blackburn’s argument to be that fictionalism about colour seeks to draw a distinction between worlds that is not marked by a genuine difference between them. Fictionalism is perpetuating a fraud.

To begin with, here are two minor observations about the argument. First, it is curiously reminiscent of verificationism, although verificationists took failure to comply with their semantic requirements to discredit the sentences in question, not to vindicate them. (Compare Blackburn’s argument with the very similar argument against fictionalism that Putnam 1971: 63-64 criticizes both as verificationist and as a bad argument). Second, Blackburn also writes as though fictionalism about Ks has to involve an error theory about Ks – the theory that there are no Ks. Yet the fictionalist might simply be agnostic about whether there are Ks. No matter: the fictionalist thinks there are worlds with coloured things and other worlds without, even though our experiences at the worlds match. That is enough for Blackburn to run his argument.

More importantly, notice how Blackburn’s line of argument would prove too much: if it is good argument for the existence of yellow canaries at this world, it would immediately establish the existence of universals, sets and tropes via such sentences as ‘canaries have the universal yellow’, ‘canaries are members of the set of yellow things’ and ‘canaries have yellow tropes’. If each of these sentences fails to express a fact or something known to be such in our world, what is different in those worlds in which it does? If you cannot say, shouldn’t you admit do they express facts or something known to be such in our world? Take other philosophical exotica such as libertarian free will, haecceities and monads. Error theorists about these entities take ‘Libertarian free will/haecceities/monads exist’ to express neither a fact nor something known to be such in our world. But they may be hard pushed to say what is different in those worlds in which those things exist – other than the trivial point that things like them exist in those worlds. The moral to draw is that there need be nothing more to say about what it takes for (say) monads to exist other than that there are things very similar to the things that Leibniz’s theory of monads describes. Not everything has existence conditions that can be specified in some interesting way. The cases in which they do are just the cases where the claim that there are Ks is coupled with a reductive theory of what Ks are.

In fact, Blackburn’s challenge to fictionalists about colour is on still weaker ground. There are suggestions in the philosophical literature about the conditions under which colour talk would fail to be true. Colours are supposed to be, for the most part, the causes of our colour experiences. But suppose it were the case that it is the properties of the microstructure of objects that in fact cause our colour experiences and that we wrongly ascribe the qualitative content of those experiences to the surfaces of external objects (Mackie 1976: 11). Again, suppose that there were no interesting distal similarities underlying similarities of apparent colour – that, for instance, there isn’t something distinctive and interesting in common to all yellow things (Jackson 1995: 112). Under either of these conditions, it has been contended that there would be no coloured objects. We need not take a stand here on whether these particular suggestions are correct; it is enough for our purposes that they are serious candidates that directly address Blackburn’s challenge.

As to the grounds for knowing that there are yellow canaries in a given world, Mackie’s comments suggest a causal story. (Again, I mention this as a serious candidate for consideration rather than as established fact). You know that there are yellow canaries if yellow canaries (non-deviantly) cause you to believe that there are yellow canaries. There is a good question as to what this non-deviant form of causation involves. Whatever the details of the causal story, though, the same sort of causal story will need to be told for what it is to know other empirical facts besides facts about the colours of things. In the case of universals, sets, monads and the like any epistemic grounds will have to be supplied by philosophical argument. The quality of such an argument may vary across worlds because the truth-values of its premises or the quality of its explanatory inferences may vary across worlds.

Two subsidiary points in closing. First, it is open to the fictionalist to exploit talk of Ks, where Ks are, and are even known to be, impossible entities. For instance, perhaps talk of impossible objects (including impossible worlds) is worth exploiting (Beall 2008). In cases of this sort, the fictionalist is under no obligation to explain the difference between worlds in which there are Ks and worlds in which there are not, for there is no such difference. (One answer to this would be to allow for hyperintensional differences between worlds, but again there may be no especially informative way of specifying these differences). Second, the fictionalist is under no obligation to say how we could know that there are Ks, even if she thinks there are worlds at which there are Ks. For one of her reasons for being a fictionalist about Ks might be that she thinks that we could not know that Ks exist even if they were to exist. I take this, or something close to this, to be Field’s view of mathematical knowledge. Field thinks that we could not have knowledge of mathematical objects because there is no explanation of how there could be reliable informational links between mathematical objects and our beliefs about such objects and also because the Quine-Putnam indispensability argument fails (Field 1989 introduction). In addition, he thinks that it is a contingent fact that there are no mathematical objects (Field 1993). It follows that, even at worlds in which mathematical objects exist, we would lack knowledge of such objects. And it is for this reason, the lack of a suitable account of the epistemology of mathematical objects (at least if such objects are understood as Platonic objects), that Field pursues fictionalism about mathematics.

6The Fictionalist’s Reasons

Szabó reports what he sees as a ‘fairly general problem with fictionalist reasons’ (Szabó 2011: 380). First, we introduce the notion of ideal acceptance:

Everyone agrees that a false claim can be acceptable for certain purposes. The fictionalist’s distinctive claim is that a false claim can be ideally acceptable. For the fictionalist, literal falsity is simply not a defect and literal truth as such is not a virtue (Rosen 2005: 16).

A false claim, then, is ideally acceptable if it is acceptable for all purposes. Szabó draws on this notion in stating the following objection:

The fictionalist says that the aim of a certain theory is something other than truth. Suppose she is right. Then it seems that we have good reasons for accepting the theory for the limited purposes identified by the fictionalist. This leaves the question open whether we have good reason for ideal acceptance. Moreover, it seems that ideal acceptance is ill-advised because it encourages us to turn a blind eye to a mystery: Why is it that this theory – which for all we know is blatantly false – is so successful? If it were true that we are in fact constantly taking special care to employ the theory in question for just the limited purposes the fictionalist has identified, there would not be a mystery. But in the cases fictionalists have focused on there seems to be no sign of such special care. For example, mathematicians do not restrict themselves to formulating theories in order to provide inferential aids for scientists, and ordinary employment of moral discourse is by no means constrained by the purposes of providing effective means of strengthening resolve (Szabó 2011: 380).

There seems to be more than one problem at issue here. There is a problem about the shortfall of the reasons that the fictionalist offers. There is also a problem about a missing explanation of the success of the practices that the fictionalist is concerned with. Take these in turn.

The first problem, as I see it, runs as follows. Fictionalism about theory T provides reasons for exploiting T for limited purposes. But fictionalism aspires to ideal acceptance of T – exploiting T for all ordinary purposes. So the reasons fictionalism provides for exploiting T fall short of providing reasons for ideal acceptance.

Some comments on this. First, the example of mathematical practice prompts the point that the problem Szabó raises is not peculiar to fictionalism about mathematics. Views that take mathematical claims to be justified only by their role in confirmed empirical science – views such as Quine and Putnam’s – face a well documented challenge about how to account for the justification of the swathe of mathematics that does not have applications in empirical science (e.g. Maddy 1992: 279). This puts Field in a strong dialectical position: he regards Quine and Putnam’s view as the chief rival to his own fictionalism. If their view faces Szabó’s objection just as much as his, then fictionalism is no worse off. Furthermore, the responses that have been given to this objection by Quineans are markedly fictionalist in character. Quine himself says that some unapplied mathematics is needed to round out and simplify the mathematics that is applied, and that the excess is to be treated as ‘mathematical recreation and without ontological rights’ (Quine 1986: 400). Mark Colyvan, a supporter of Quine’s view, advocates a form of if-thenism for such cases:

I suggest that when mathematicians believe a particular theorem to be true, independent of whether it has applications, . . . [they] believe that the theorem follows from the relevant axioms but remain agnostic about the ontological commitments of the theorem (or the axioms) (Colyvan 2001: 106).

I take Colyvan’s suggestion to be that when mathematicians apparently believe a theorem, in fact, first, they believe only that the theorem follows from certain axioms and, second, they exploit the theorem. Field can adopt this suggestion – with one amendment. Colyvan’s claim that mathematicians take an if-thenist attitude to theorems that lack application is a tendentious claim about the sociology of mathematics. Given his fictionalism, it would be more in keeping for Field to claim that this is the attitude mathematicians may or should take.

The mathematical sentences that Szabó singles out are ones that have no practical application and are used only in pure mathematics. So I take it that we are concerned with sentences such that fictionalism can give no reason for exploiting them in their ordinary uses. Now, if we had a justified conviction that there has to be some reason to exploit those sentences in their ordinary uses, it would be a mark against fictionalism if it alone was unable to say what that reason was. Yet do we have such a justified conviction? That free of any role in testing and confirming scientific theories, there is a reason to exploit the sentences of pure mathematics? Morality has a role in helping us to rub along together. That’s a reason the fictionalist can offer for exploiting morality. Besides that, though, why be moral? That’s a good question. Yet why suppose that there is a good answer to it that goes beyond one to do with mutual self-interest? Unless there is, it seems no mark against the fictionalist that she is unable to provide the answer. If the fictionalist is understood as advocating a rational reconstruction of some selected practice, and she thinks that the folk’s attitudes may have to be reformed, it should come as no surprise that she may also have to break it to the folk that they do not have good reason to exploit some of these sentences if they are used to promote certain non-instrumental purposes. Fictionalism was never supposed to be a blank cheque, licensing all that specialists or the folk wanted to say about some chosen topic. In my opinion, what is distinctive about fictionalism about Ks is not a commitment to ideal acceptance, but that it takes some norm other than the truth norm to govern talk of Ks.

Let’s turn to the second problem: that the fictionalist owes us an explanation of the success of the practices she is concerned with. Science harnesses mathematics to predict and explain events. Why is this possible? Society harnesses ethics to shape people’s behaviour. Why is this possible? These are good questions but again they seem to be compulsory questions for everyone and not questions that are particularly acute for the fictionalist. (See also Leng 2010 chapter 9 for a fictionalist response to the challenge). Even if Platonism about mathematics were true, there would still be a question about the unreasonable effectiveness of mathematics in the natural sciences.

Two subsidiary points. First, Penelope Maddy thinks the unreasonable effectiveness of mathematics is more apparent than real and she offers a debunking explanation (Maddy 2007 part IV chapter 2). She thinks that much of mathematics was developed with an eye on related applications. Moreover, there’s a tendency to forget both the failures and the trial-and-error process that lead to the relatively few successes. We also underestimate the likelihood that the vast storehouse of mathematics contains a solution to a given problem. Second, Jody Azzouni promotes a maverick view according to which there is no problem about the application of mathematics to the concrete world (Azzouni 2000). Each of these approaches blunts Szabó’s challenge.

Again, even if moral realism were true, there would still be a question about why morality has a hold on us. Even if, necessarily, believing that doing A would be of moral value gives you a reason to do A, people often do not do what they have reason to do – even what they have overall reason to do. The original question recurs: why is that morality shapes people’s behaviour as much as it does? And perhaps that question is not in philosophers’ remit to answer but is something to be addressed by social psychologists.

In short, the mystery Szabó identifies, ‘Why is it that this theory – which for all we know is blatantly false – is so successful?’, is a mystery for everyone (subsidiary points aside). There is as much a mystery if the theory is true as if it is false. A shared problem is not a special problem for the fictionalist; why think that the fictionalist is worse placed to solve it?

7Conclusion

Although the terminology of ‘revolutionary’ and ‘hermeneutic fictionalism’ has a good deal of currency, perhaps a better way of describing the present approach would be as a rational reconstruction which seeks to answer certain metascientific or metamathematical questions that science and mathematics do not normally consider (Hellman 1998: 342). The inquiries and answers fictionalism pursues then complement those of mathematics and the sciences. Accordingly, it is not the case that data unearthed by mathematics and science and the success of those disciplines undermines fictionalism. Some critics, however, do not see things this way:

The fictionalist concedes that predictive power and ‘simplicity’ (i.e., overall plausibility in comparison with rival hypotheses, as scientists and rational men actually judge these matters) are the hallmarks of a good theory, and that they make it rational to accept a theory, at least ‘for scientific purposes’. But then . . . what further reasons could one want before one regarded it as rational to believe a theory? (Putnam 1971: 69-70. See also Burgess 2004).

This is doubly odd. The fictionalist is not obliged to say how her opponent’s deficit of reasons can be overcome. Nor, in any case, does she think that it can be overcome. After all, she has reasons for her fictionalism – reasons concerning, for example, the difficulty of epistemic access to mathematical objects or objective values, or reasons for economizing ontological commitment – that are not defeated by marshaling data from mathematics or ethics. And, according to her, the hallmarks of a good theory in these fields are just the hallmarks of a good theory ripe for exploitation.

Acknowledgements: Many thanks to Helen Beebee and Daniel Nolan for very helpful comments on an earlier draft.

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