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Martin Thomson-Jones


There are at least two ways metaphysical questions can arise in philosophical thinking about the sciences. First, we can ask metaphysical questions when we ponder the interpretation of particular scientific theories: Are species individuals in evolutionary theory? Do many-particle systems violate the principle of the identity of indiscernibles in quantum mechanics? Is time an emergent phenomenon according to string theory or loop quantum gravity? Second, we can ask metaphysical questions about notions which show up in connection with many parts of the sciences, whether in scientific talk or in philosophers’ accounts of the sciences at large. Much of the work which has been going on under the heading “metaphysics of science” in recent years deals in questions of the second sort. For example, there has been quite a bit of work on questions centering on such notions as law of nature, causation, and disposition. Among the central questions have been these: Are there such things as laws of nature? Causal relations? Dispositions? If so, what kinds of things are they? And how are they connected, to the extent that they are?[1]

The questions I want to consider here arise in the second way—they concern notions which show up in scientific talk in many parts of the sciences, and in philosophers’ accounts of the sciences at large. Attempting to answer these questions, which focus on such notions as model, mathematical structure, and fictional object, has not generally been seen as part of an investigation of the metaphysics of science, and they have been less widely pursued than the questions about laws, causation, and dispositions. These questions are recognizably metaphysical nonetheless, and they parallel the more familiar questions perfectly: Are there such things as models, mathematical structures, and fictional objects? If so, what sorts of things are they? And how are they connected, to the extent that they are ?[2]

At the same time, there are differences between questions about dispositions, laws, and causation, on the one hand, and the questions about models, mathematical structures, and fictional objects, on the other. Questions in the first cluster are at least sometimes questions about the content of our scientific pictures of the world. Some think that the sciences, or many of them, picture the world as containing or being governed by laws; others disagree. Among those who agree, there is disagreement about what sorts of things laws must be, and how they are related to causation and to dispositions, given the way the sciences picture the world. The same goes for causation and for dispositions, mutatis mutandis. Here, then, the “metaphysics of science” is the metaphysics of the scientific world-picture, or of the various scientific world-pictures.

The questions I want to consider here, however, might be described as questions about the metaphysics of science as an activity. Models, mathematical structures, and fictional objects are not part of the content of our scientific pictures of the world; rather, if they exist, they are among the tools we use to paint the pictures. Scientists, in talking about the things they do, describe themselves as constructing models, and as employing both mathematical structures and fictional, imaginary, or hypothetical objects to model and to represent.[3] And when philosophers of science offer their own, usually more systematic accounts of scientific representation, modeling, explanation, confirmation, and various other scientific activities, some of them say the same sorts of things. It is now a commonplace in the philosophy of science that scientists construct and use models; some philosophers of science present accounts of scientific representation or of modeling which place a central emphasis on the role of mathematical structures; some offer accounts of at least some important varieties of scientific representation on which those kinds of representation involve the use of fictional objects.[4] Presented with scientific talk and philosophical accounts of these sorts, we can ask whether there are such things as models, mathematical structures, and fictional objects; if so, what sorts of things they are; and how they are related. In asking such questions, we can again be said to be investigating the metaphysics of science, but this time we are investigating the metaphysics of scientific practice.[5]

These last questions, then, are the questions which provide my starting point. My concern here, however, is not to try and answer these questions about the metaphysics ofscientific practice; I and others have made attempts in that direction elsewhere.[6] Instead, I want to consider a particular reaction to the raising of these questions. Some philosophers of science are prone to brute expressions of impatience or disgust when they get a whiff of metaphysics, but that is not the reaction I have in mind. Rather, I want to consider the claim that, whatever the merits or demerits of such questions in themselves, there is simply no need, from the point of view of the philosophy of science, to grapple with them. On this view, we can give satisfying answers to the methodological and epistemological questions which concern us in the philosophy of science—questions about scientific representation, modeling, explanation, confirmation, and so on—without answering questions about the existence and nature of models, mathematical structures, or fictional objects, even if our answers to the philosophy-of-science questions appeal to such entities.[7] The proposal, then, is that we employ what I will call the bracketing strategy: the strategy of putting aside such questions as irrelevant to our purposes in the philosophy of science.[8] I want to examine a particular justification for this strategy, one which rests on the claim that any adequate account of ordinary and scientific discourse will legitimize our ordinary and scientific ways of talking about models, mathematical structures, or fictional objects—call this the legitimization argument.9 In consequence, the idea goes, we philosophers of science can simply get on with constructing accounts of scientific representation, modeling, theory structure, idealization, confirmation, explanation, and the rest, and rely on talk about such objects when it is useful to do so, safe in the assumption that when philosophers of language, metaphysicians, philosophers of mathematics, and aestheticians settle on satisfactory accounts of such talk, we will simply be able to add those accounts as appendices to our own work. The questions we are trying to answer in the philosophy of science are thus seen as swinging free of the metaphysical issues in question—call this the autonomy thesis.

This sort of maneuver is familiar throughout philosophy, of course, and the questions which get bracketed can be of any kind—that is, they need not be metaphysical. Perhaps because the move is so standard, invocations of it with respect to talk of models, mathematical structures, and fictional objects in the philosophy of science typically only arise in conversation, when the metaphysical questions are pressed; or at least, that has been my experience. But one can also find explicit recommendations along the lines just presented. So, for example, Bas van Fraassen advocates the adoption of such a strategy by philosophers of science with regard to worries about the existence and nature of mathematical objects, and he offers exactly the sort of justification I have described, insisting that “for any philosophy of mathematics to be acceptable it must imply that the ordinary use of mathematics is fine” (2005, 97). Thus we can talk about functions and vector spaces and set-theoretical n-tuples in offering accounts of theory structure, representation, and the like, and leave it to philosophers of mathematics to decide the answers to a range of further questions about the interpretation of such talk.10 Similarly, Peter Godfrey-Smith, in pursuing the idea that we might think of model systems as “imaginary objects” on par with fictional characters, seems happy to engage in our ordinary ways of talking about

representation, modeling, confirmation, explanation, and the like, but allows that we might need to answer such questions for certain other purposes we have, or might have, in the philosophy of science. (And there are certainly disagreements about the proper purposes of philosophy of science out there.) My arguments will be arguments against either version.

  • 9 Note the (inclusive) disjunction, “models, mathematical structures, or fictional objects.” Someone who offers an account of scientific representation which involves talk of mathematical structures but not of fictional objects, for example, will be able to justify her bracketing of metaphysical questions about the latter quite straightforwardly. See section 3 for a more careful laying-out of the legitimization argument; and thanks to Kyle Stanford for catching a slip on this point.
  • 10 Anjan Chakravartty has also suggested to me that we should take this sort of approach to mathematical discourse in philosophical accounts of scientific representation (pers. comm.).

fictional characters while developing an account of scientific modeling, and to defer the task of settling on an acceptable interpretation of that talk until later, when we may wish to take it on for “general philosophical reasons” (2006, 734-36; quoted phrases from 735).[9]

There may well be situations in which employing this sort of strategy is unproblematic, but I want to argue that this is not one of them.

  • [1] Of course, the questions themselves have a much longer history.
  • [2] Here and throughout, and purely for the sake of concision, I will use the term “model” in an artificially restrictedsense, to narrow attention to nonconcrete models. That is, I am not addressing metaphysical questions about theexistence or nature of those physical objects which we class as models, such as orreries, or Crick and Watson’stinplate model of DNA.
  • [3] Hereafter, and again for the sake of concision, I will use the term “fictional object” to cover talk of fictional,imaginary, and hypothetical objects.
  • [4] See, for example, van Fraassen (2008) and Weisberg (2013) on mathematical structures, and Godfrey-Smith(2006), Thomson-Jones (2007) and (forthcoming), Contessa (2010), and Frigg (2010) on fictional objects.(There is a question about the precise sense in which Frigg’s and Godfrey-Smith’s accounts picture some varieties of scientific representation as involving fictional objects, but that is a question for another time; all thatmatters here is that both authors talk at central points as though some varieties of scientific representationinvolve the use of fictional objects.)
  • [5] Note, however, that the questions about laws, causation, and dispositions can also be motivated by methodological interests. Consider, for example, the idea that making sense of confirmation or of explanation involvesreliance on a substantive distinction between laws and accidental generalizations, or accounts of experimentaltesting which draw on particular views about causation (such as the account in Cartwright 1989). This is whyI wrote, in the preceding paragraph, that such questions are “at least sometimes” questions about the contentof our scientific pictures of the world.
  • [6] See Thomson-Jones (1997), (2007), (2010), and (2012) on what sorts of things models can be, and their relations to mathematical structures, and Thomson-Jones (2007) and (forthcoming) on models and fictionalobjects. Contessa (2010), Frigg (2010), and Toon (2012) also address questions about the existence and naturefictional objects, and their relationship to models, and Weisberg (2013) discusses the relationship betweenmodels, mathematical structures, and fictional objects.
  • [7] Putting things this way implies that the metaphysical questions about the existence and nature of models,mathematical structures, and fictional objects are not questions for the philosophy of science. My aim here isto challenge that claim, in one sense at least (see section 2). But it is part of the view I am characterizing here.
  • [8] A weaker version of this proposal insists that we need not answer questions about the existence and natureof models, mathematical structures, or fictional objects in order to provide satisfactory accounts of, say,
  • [9] Godfrey-Smith is not explicit about taking bracketing to be justified by the assumption that any acceptableaccount of our talk about fictional entities will legitimize the sorts of things we ordinarily say, but it is hard tosee how the approach he recommends could be a reasonable one without that assumption. No such legitimization assumption would be required, of course, if Godfrey-Smith were aiming only to characterize a particularway of thinking and talking that scientists engage in; but he is also aiming at an understanding of what is happening when scientists think and talk in those ways, and he is recommending an account which itself engagesin talk of “imagined concrete things” (2006, 734-35). Incidentally, Godfrey-Smith does say that “[a]t the end of the day ... some general account must be givenof the imagined objects of both ordinary fiction and scientific modeling” (2006, 735), but given that he mentions ordinary fiction and scientific modeling in the same breath here, and given that he is only requiring thata “general” account be given “[a]t the end of the day,” I still read him as endorsing the idea that we can addressour central concerns as philosophers of science without such an account, even if (to put the point in my terms)we engage in talk of fictional objects in the process. Note also that Godfrey-Smith’s comments appear in just the sort of context I have in mind: one of hisimmediate philosophical concerns is to offer an account of a certain representational strategy we find employedin the sciences—that is, to offer at least a partial account of how representation works in science. Another,closely related to the first, is to say something about the nature of models. Similarly, van Fraassen is defendinghis use of mathematical ways of talking in the philosophy of science (and other parts of his philosophical work)in the passage from which the remark I have just quoted is drawn.
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