AGAINST THE LEGITIMIZATION ARGUMENT, AND AGAINST BRACKETING
I now want to argue, then, that even if we grant its premises, the legitimization argument fails—neither the autonomy thesis for Xs (step 4) nor the claim that we can engage in the as-if practice forXs and bracket with impunity (step 5) follows. The first of my two main conclusions will thus be that we lack a justification for the unobvious claim that we can bracket questions about the existence and nature of Xs when putting forward core accounts which engage in the as-if practice for Xs. Along the way, an argument will emerge that that claim is, moreover, false, and so my second and stronger conclusion will be that the bracketing strategy is in fact unavailable to us in such situations.
Suppose, then, that we know that premise (1) is true: we know that any adequate account of our ordinary and scientific discourse will legitimize our ordinary and scientific ways of talking about Xs. Suppose we also know that, as premise (2) maintains, the as-if practice for Xs is encompassed by our ordinary and scientific ways of talking about Xs.  It follows that any adequate account of our ordinary and scientific discourse will legitimize the use of the as-if practice for Xs in our work as philosophers of science, constructing accounts of scientific representation, modeling, explanation, confirmation, or the like (step ). And to make things as propitious as possible for the bracketer, suppose we know, too, that there is at least one adequate account of our ordinary and scientific discourse, and that the correct account is an adequate one, so that we have compelling reason to believe that the as-if practice for Xs is in fact legitimate. The idea we are examining is then that if we find ourselves in such an epistemic situation, it follows that (i) we can engage in the as-if practice for Xs in constructing our core accounts, and furthermore, that (ii) in doing so, we need not address questions about the existence and nature ofXs, and (so) need not adopt any particular account of the semantics or ontology of that practice. I will argue, however, that neither thing follows.
My arguments will rest, first, on the observation that there is more than one variety of legitimization, and second, on the assumption that in constructing accounts of scientific representation, modeling, explanation, and so on, we are aiming to know the truth about those things, and to understand them. (This assumption about the aims of our philosophical work may not meet with universal agreement, but I will not attempt to defend it here.) The problem is, first, that if one or more of the adequate accounts of ordinary and scientific discourse which (we are supposing) we know there to be legitimizes the as-if practice in the wrong way, (i) may still be false, for without knowing more we cannot be sure that engaging in the as-if practice will not be at odds with aiming to know the truth; and second, that even if all adequate accounts legitimize the practice in the right way, so that engaging in the as-if practice is perfectly compatible with our interest in knowing the truth, (ii) will be false nonetheless, as engaging in the as-if practice without further insight into the semantics and ontology of that practice will make it impossible to achieve the aim of understanding scientific representation, modeling, explanation, and so on.
The crucial distinction among varieties of legitimization here is between those which rule out the knowable truth of as-if utterances aboutXs and those which do not. So, for example, some adequate account of ordinary and scientific discourse might legitimize the as-if practice by making it clear that, although speaking as if there are models, mathematical structures, or fictional objects is ipso facto a matter of uttering falsehoods, say, or of uttering meaningless sentences, it is useful nonetheless to treat some such utterances as true in the right context. If we normally take some of the as-if utterances in question to be true, an account which legitimizes the as-if practice in one of these ways might even come equipped with a story about why we are so easily gulled into doing so—an error theory. Regardless, legitimization of either of these two sorts is incompatible with the supposition that our as-if utterances are true, and so, a fortiori, precludes the possibility that they are knowably true.
The same goes for an account which legitimizes by insisting that utterances about models, mathematical structures, and fictional objects make claims which, though truth-valued, are unknowable, but then goes on to explain how the claims in question can be “acceptable” in something like the sense in which some scientific claims about the unobservable world are acceptable according to the constructive empiricist—a sense of “acceptable” in which P’s acceptability does not entail its truth, its falsehood, or its believability. An account of our ordinary and scientific discourse which legitimizes the as-if practice in this way, too, precludes the possibility that our as-if utterances are true and known to be.
Now, if an account of ordinary and scientific discourse legitimizes the as-if practice in a way which involves ruling out the knowable truth of the claims we make when we engage in that practice, then given that account, claim (i) will be false: we cannot engage in the as-if practice in constructing accounts of scientific representation, modeling, explanation, and the rest, given that we are aiming to know the truth about the targets of those accounts in constructing them, for the accounts will then necessarily contain either false claims or unknowable ones. If, for example, we offer an account of scientific representation which commits us to uttering sentences like “Scientists use fictional objects to represent real systems in the domain of inquiry,” but utterances which involve speaking as though there are fictional objects are all false, or unknowable, then at least some important part of our account of scientific representation is either false or unknowable.
Consequently, if, for all we know, one or more of the adequate accounts of ordinary and scientific discourse which (we are supposing) we know there to be legitimizes the as-if practice in a way which precludes the knowable truth of the as-if utterances, and we know no more, then for all we know the correct account of the as-if practice is one which rules out knowable truth. And this means that, for all we know, engaging in the as-if practice in developing accounts of representation, modeling, explanation, and the rest is entirely at odds with aiming to know the truth about those things. We will thus not be justified in continuing to engage in the practice in such an epistemic situation.
Suppose instead, then, that we do know, somehow, that all adequate accounts of ordinary and scientific discourse legitimize the as-if practice for Xs by reassuring us that a good range of the utterances we produce when engaging in that practice make claims which are both true and knowable. Being in this epistemic situation does not give us reason to eschew the as-if practice in constructing our core accounts; but that is not to say that we will then be justified in employing the bracketing strategy. Establishing that engaging in the as-if practice is not at odds with achieving our philosophical aims does not amount to showing that we can achieve those aims without an articulated understanding of the as-if practice. And I want to argue that if we engage in the as-i f practice when developing our core accounts, then those core accounts will yield an understanding of their targets (scientific representation, modeling, explanation, etc.) only when supplemented by an understanding of the as-if practice. Bracketing is thus at odds with the immediate aim of understanding representation, modeling, explanation, and the rest.
To see this, consider the two metaphysical questions which lie at the center of an inquiry into the semantics and ontology of modeling discourse, mathematical discourse, or fictive and metafictive discourse: Are there objects which are the referents of the noun phrases of that discourse (“the simple pendulum model,” “the Hilbert space which is the state space of the proton,” “Emma Bovary”)? And if so, what sorts of things are they? Call these the existence question and the nature question, respectively. The issue at hand is whether we can arrive at an understanding of scientific representation, explanation, and so on by speaking as though there are such objects and as though they have certain features, knowing (somehow) that we are speaking truly in doing so, but putting off the task of answering those two questions.
Take the existence question first. To show that this question cannot be bracketed consistently with our philosophical aims, I will take as an example an account of modeling which employs talk of fictional objects; the argument carries over, muta- tis mutandis, to any account of modeling which centrally relies on talk about models, mathematical structures, or fictional objects, and to accounts of idealization, theory structure, the nature of models, explanation, confirmation, and so on which do so.
Suppose, then, that we have an account of modeling which centers on claims expressed by sentences such as this:
(S) Scientists often model real pendula by exploring the ways in which they are similar to and differ from fictional objects such as the simple pendulum.
In having us utter sentences such as (S), the account engages in the as-if practice for fictional objects. That fact alone does not preclude our knowing the account to be true, given the assumption we are now making that a good range of the utterances which make up the as-if practice express knowably true claims. The account might be false nonetheless, of course (or, perhaps, true but unknowable), as the assumption in question does not guarantee the knowable truth of the claims expressed by any particular set of utterances; but in that case appealing to it would be at odds with the aim of knowing the truth about modeling. So let us suppose then, that the account is knowably true; suppose, in fact, that we somehow know it to be true. The remaining problem is simply that without an answer to the existence question, we cannot claim to know what this account of modeling says, and so we cannot claim to have arrived an understanding of modeling by considering it.
The argument for this last claim is as follows. Either there are fictional objects such as the simple pendulum, or there are not. If there are, then presumably sentence (S) should be taken literally, along with the rest of the account of which it is a part. If there are not, on the other hand, then scientific modeling does not involve such objects; and as the sentence in question says otherwise on its surface, then (given our assumption that the sentence is making a true claim) the sentence is not to be taken literally, and nor, by extension, is the account of which it is a part. So if we do not know whether there are fictional objects—if we do not know the answer to the existence question—we cannot know whether the account of modeling is to be taken literally. We also do not know how the account should be taken if it is not to be taken literally. If there are no fictional objects, and so no such fictional object as the simple pendulum, but (S) is true nonetheless, then it is not obvious what (S) means; so what does it mean? We surely cannot claim to have arrived at an understanding of modeling by invoking such an account in the midst of such fundamental uncertainty about how the account should be taken. Yet removing that uncertainty will at least involve answering the existence question about fictional objects, and so will require us to reject the bracketing strategy.
What about the nature question? Suppose we somehow managed to convince ourselves that there are fictional objects, thus settling the existence question; could we at least then bracket the question of what sorts of things fictional objects are? Again, the answer is no—not if we hope to come to understand modeling by relying on an account which engages in the as-if practice for fictional objects by centering on claims expressed by sentences such as (S). Inserting different stories about the nature of fictional objects into such an account will yield different final pictures—not only of the sort of thing to which scientists compare real systems when modeling, but of what the comparing involves, and of the kinds of similarity and difference relations that can obtain between fictional objects and real systems. And different pictures of these things make for different ways of understanding of how modeling works.
Three cases will suffice to make the point. (a) Extrapolating from Lewis (1978) and Lewis (1986), we might take the view that fictional objects are concrete inhabitants of other concrete possible worlds. In that case, the simple pendulum can stand in straightforward relations of similarity to actual pendula by sharing certain properties with them, or by having “nearby” determinate values of such shared determin- ables as period of oscillation. (b) According to Thomasson (1999), fictional objects are abstract artifacts. On that approach, the simple pendulum, though it exists, does not have a mass or a period of oscillation, and so cannot stand in straightforward relations of similarity to concrete pendula. Instead, modeling concrete pendula will involve comparing the properties of those concrete pendula with the properties the simple pendulum has according to the relevant fiction (properties it does not in fact have). (c) Given the emphasis on talk of “imagined” objects in Godfrey-Smith (2006) and Frigg (2010), we might consider the view that fictional objects are mental objects of some sort. In that case, too, the simple pendulum will have neither a mass nor a period of oscillation, and so the full story about how it can stand (or be said to stand) in similarity relations to concrete pendula will again have to be more complex than the surface simplicity of an utterance like (S) suggests.
Different answers to the nature question about fictional objects will thus lead to different pictures of modeling, even given that the starting point is the same in each case—namely, a set of utterances like (S). And this example makes it doubtful, I think, that we could claim to have achieved the aim of understanding modeling by appealing to any account which relies on speaking as though there are fictional objects until we have provided an answer to the question of what sort of things fictional objects are (unless, of course, we have already answered the existence question negatively). The same goes, I take it, for other as-if practices, and for accounts of scientific representation, idealization, explanation, confirmation, and other targets of our interest in the philosophy of science. Once again, then, we see that bracketing is at odds with our immediate philosophical aims in constructing core accounts.
One objection to this line of argument focuses on the nature question, and runs as follows: “Certainly there are differences between the pictures of modeling which result from (S) by supplying different accounts of the nature of fictional objects; but it is not clear that those differences will make a difference to anything we care about as philosophers of science. In each of the three cases, (a)-(c), we get a picture on which fictional objects can stand in similarity relations of some sort to real objects, and on which scientists can in some way or other compare fictional objects with real; and perhaps that is all we need to know about this aspect of modeling in order to understand the things we are interested in as philosophers of science. So it is not clear that we cannot bracket the nature question in such a case.”
I am tempted to reply simply by saying that one of the things we are interested in as philosophers of science is how modeling works, and as we get different pictures of that by supplying an (S)-type account with different accounts of the nature of fictional objects, the differences among the pictures do make a difference to at least one of the things we are interested in as philosophers of science. I suspect, however, that this response would do little to address the concerns of someone who takes the objection to have some force in the first place. This might be because such a philosopher finds little interest in the project of understanding how modeling works per se, and is interested in understanding modeling only insofar as doing so will help us to answer various other methodological and epistemological questions. For the sake of argument, then, suppose one sides with the philosopher presenting the objection on the matter of what questions or topics are of ultimate interest in the philosophy of science; still, there is more to be said.
It is first worth pointing out exactly what the objection establishes if it succeeds. At most, it shows that it may be that we can bracket the nature question in the situation at hand; for all this objection says, it may instead turn out that we cannot. That will hinge on whether the differences between the pictures of modeling we get by supplying (S)-type accounts with the various accounts of the nature of fictional objects make a difference to the answers we end up giving to the questions we are ultimately interested in—questions about the nature of explanation, say, or about how models are evaluated in light of the data we have collected. If we grant that understanding how modeling works is of only derivative interest, then because I have not shown that different answers to the nature question will make a difference of that sort, my arguments to this point do perhaps fail to establish that bracketing the nature question is not an option. To put it another way, the objection we are considering does pose a threat to my attempt to argue that the autonomy thesis (step  in the legitimization argument) and claim that we can bracket (step ) are false. But the objection does nothing to undercut my attempt to show that the autonomy thesis and the claim that we can bracket do not follow from the premises of the legitimization argument. Indeed, as the objection allows for the possibility that in the situation at hand the answer to the nature question will make a difference to the answers we give to the questions we are centrally concerned with as philosophers of science, it allows that the conclusions of the legitimization argument do not follow from its premises. Granting even this much, I would maintain, puts the bracketer in an uncomfortable position. When evaluating a core account which engages in the as-if practice forX’s, it is prima facie entirely reasonable to ask, as part of the evaluation, whether there are indeed X’s, and if so, whether they are the right sort of thing to play the roles the core account would seem to require of them. If the legitimization argument fails, the bracketer has more work to do to support her claim that such questions can be brushed aside.
If the objection succeeds, then, it stands in the way of only the second of my two main claims: that the bracketing strategy is unavailable to us when we offer core accounts which engage in the as-if practice for X’s (or, to put it in other words, that the existence and nature questions about X’s cannot be brushed aside in such a situation). But I do not think the objection succeeds even in this direction. To see this, go back to the argument against the possibility of bracketing the existence question. If we take no stand on whether there are fictional objects, then even if we know somehow that (S) says something true, it is hard to see what we could come to understand about how modeling works by invoking (S). Compare this with the situation of someone who speaks not a word of some language, but who knows, somehow, that a certain sentence of it makes a true claim; clearly such a person could not gain any understanding whatever of the topic of the sentence by considering that sentence. I would not claim that the two situations are the same, of course; but it does seem to me that they are far too close for the comfort of the would-be bracketer. Now, the objection we are considering does nothing to cast doubt on this part of my argument. But then there are two points to be made. First, even if my argument succeeds only in showing that the existence question about X’s cannot be bracketed when we are developing and evaluating core accounts which engage in the as-if practice for X’s, that is enough to bring back into the fold just the sort of metaphysical issue the bracketer was hoping to put aside. Second, once we grant that we cannot put aside the existence question about X’s, it will become very difficult to keep the nature question at bay, for the simple reason that deciding whether there are metaphysically controversial X’s typically involves thinking about what sorts of things X’s might be if there are any. Thus it seems that both the spirit and the letter of my second main claim survive the objection in question.
-  “coherence” constraints on adequacy (because we then have good reason to doubt that our ontological beliefs,or our accounts of other kinds of discourse, are correct).
-  Strictly speaking, the assumption we need here is just that the as-if practice for Xs as it is employed by the particular core account at hand is encompassed by our ordinary and scientific ways of talking about Xs; differentaccounts might engage in different versions of an as-if practice about Xs. I will leave this qualification aside tosimplify the discussion.
-  For a reason that these additional assumptions are not entirely trivial, see n. 24.
-  I am taking it here that adopting an account of the semantics and ontology of the as-if practice for Xs would inpart involve addressing questions about the existence and nature ofXs.
-  The conjunction of claims (i) and (ii) here may not be exactly equivalent to the conjunction of claims (4) and(5) in the formulation of the legitimization argument presented in the preceding section, but both (i) and (ii)follow from the conjunction of (4) and (5) (at least when taken in context), and so we can show that (4) and(5) do not follow from the premises of the argument by showing that (i) and (ii) do not.
-  See the second and fourth entries on the list of varieties of legitimization given in the preceding section.
-  See, for example, van Fraassen 1980, 12-13. Note that van Fraassen speaks there only of acceptance, ratherthan of acceptability; by calling the claim P “acceptable,” I mean just that acceptance in van Fraassen’s sense isa reasonable attitude toward P. And I say “something like” the constructive empiricist’s sense of “acceptable”in order to leave open the question of whether the notion of empirical adequacy is directly applicable in thepresent context, or whether some other kind of adequacy might here play the role that empirical adequacy playswhen it is claims about the unobservable that are up for assessment.
-  This notion of legitimization is suggested not only by van Fraassen’s constructive empiricist account of scientificdiscourse about unobservable objects and events, but also by the view that the best way to make sense of mathematical discourse might be to see it as aimed at something other than “true story-telling,” a view van Fraassendescribes himself as “sympathetic to” in “On Taking Stances: An Interview with Bas van Fraassen,” the HarvardReview of Philosophy piece cited above (2005, 96-97). The notion of legitimization just set out clearly goesbeyond the latter sort of view, however: saying that the aim of a kind of discourse is something other than truestory-telling is compatible with saying that the utterances which make it up uniformly express false or truth-valueless claims, or fail to express claims at all (and indeed, it is even compatible with saying that they expressknowable truths).
-  Note that in this case it would be misleading to say that simply that we do not have a justification for the bracketing strategy, as though an appropriate response would be to continue to look for a justification, or to drop thebracketing strategy in favor of investigating the semantics and ontology of the as-if practice right away. Rather,in this case we ought simply to drop the as-if practice itself, for the purposes of the philosophical tasks at hand.(This is not to say that we would have reason to eschew the as-if practice in every context—perhaps it would befine to go on engaging in it at the right moments in our scientific work, for example.) As I noted earlier, some may reject the metaphilosophical assumption that we are aiming to know the truthin constructing philosophical accounts of the nature of models, or theory structure, or idealization. (Rosen[1994, esp. 151-52] lays out a reading of van Fraassen on which he is not aiming at the truth in presentingconstructive empiricism; see van Fraassen  for his reaction.) I am not sure I know how to defend thatassumption. One might appeal to the distinct idea that we are aiming to understand, say, scientific representation by constructing an account of it, and then try to argue that an account cannot yield understanding if itrests on claims which are false, or unknowable, so that aiming to know the truth is part of aiming at understanding. But this is to take on contentious issues, too. van Fraassen, for example, clearly thinks that unknowable claims can explain, as he thinks that claims about the unobservable can explain, but are unknowable (1980,chap. 5); it would not be surprising, then, if he were to insist that unknowable claims can produce understanding. And Frisch (1998) argues that the best explanations are sometimes false. (Of course, Cartwright has arguedthat explanation often involves false law statements, too [e.g., 1983, essay 2], but as I read her, she has gone on toreframe her view. As she conceives it in her later work, the point is just that if the law statements we appeal toin many of our explanations are read in the traditional way, as purportedly exceptionless generalizations aboutwhat happens, then they are false. We should, however, read them differently, as telling us about the capacitiesthat various properties carry with them, and so read, law statements face no special obstacle to truth.)
-  The clause “and we know no more” rules out cases in which we somehow know that the correct account of ourordinary and scientific discourse allows for (or even guarantees) the knowable truth of the as-if utterances. It ishard to see how we would know this without having done enough thinking about the semantics and ontologyof the as-if practice to have already abandoned the bracketing strategy.
-  Here I have moved from considering cases in which an account of ordinary and scientific discourse precludesthe knowable truth of the as-if utterances to considering cases in which knowable truth is entailed. There is athird possibility, of course, at least logically speaking: an account might legitimize the relevant discourse, insome recognizable sense of “legitimize,” while leaving it open whether the as-if utterances are knowably true.At this point, however, it is easy to see that it would be impossible to justify the bracketing strategy if one ormore adequate accounts of our ordinary and scientific discourse were, for all we knew, of this third sort. If oneor more of the legitimizing accounts leaves open the knowable truth of the claims we make when engaging inthe as-if practice, and we bracket further investigation, then for all we know, everything we say when we engagein the as-if practice is false, or unknowable. And as long as we are ignorant on that score, we cannot cometo understand or know the truth about modeling, scientific representation, explanation, or anything else byengaging in the as-if practice.
-  That is, although given this sort of legitimization there is no special problem with part (i) of the idea we areexamining (that we can engage in the as-if practice in constructing our core accounts), I want to argue thatthere is still a problem with part (ii) (that in doing so, we need not adopt any particular account of the semantics or ontology of that practice).
-  Cf. Godfrey-Smith (2006) and Frigg (2010). Both authors tend to prefer the terms “imaginary object” and“imagined object,” but my talk of fictional objects is meant to include imaginary objects, and in any case, bothauthors introduce the talk of imagined objects as part of a project of drawing an analogy between scientificmodeling and ordinary fiction.
-  The point can be put a little more rigorously if we are willing to grant a certain assumption about meaning andlinguistic understanding, as follows: If there are fictional objects such as the simple pendulum, then the simplependulum presumably features in the truth conditions of (S), which will have to do with that fictional objectsstanding in certain relations to scientists and real pendula. If there are no such things as fictional objects, onthe other hand, then clearly no fictional simple pendulum features in the truth conditions of the sentence.Thus if we do not know whether there are such things as fictional objects, we cannot know whether the truthconditions of sentence (S) involve a thing of that sort; and so we cannot know the truth conditions of the sentence. Given the right assumptions about meaning and linguistic understanding, it follows from this that wedo not really know what (S) means, and that we do not understand it. Consequently we do not understand theaccount of modeling we have been offered, and so cannot come to understand modeling itself by consideringthat account. Thus bracketing of the existence question is not an option if we are to pursue such an account.
-  I should stress the word “extrapolating” here, as this is not something Lewis himself claims. On the other hand,he does propose that the idealized systems spoken of in scientific theorizing be taken to be such concrete pos-sibilia (1986, 26-27). See Thomson-Jones (2007, §3.6) for a fuller discussion.
-  Thomasson (2003) offers a variant of her (1999) view on which the story would be different again. See alsoThomson-Jones, forthcoming.