The metaphysics of realism and structural realism

Abstract

Scientific realism is the default position of many philosophers of science and most working scientists, Alan Musgrave having done much to keep the nature of this default position before us and to provide arguments for it.1 For this, as well as much else, we are all in his debt. But the term realism needs careful handling since not only do the friends of realism offer us definitions that can be misleading, but those who are not its friends offer us tendentious definitions that can also lead us astray. To set matters straight, section 1 offers a definition of (but no argument for) a strong version of ontological (or metaphysical) scientific realism for a number of categories of observable and unobservable items found in science including such particulars as objects, events, processes and tropes, as well as non-particulars such as properties and universals. Given this background it is then possible to characterise structural realism, viz., the view that realists should also admit structures into their ontology, especially mathematical structures expressed by mathematical equations. One task is to give an unproblematic characterisation of such structures. Contrary to positivists and empiricists, metaphysics plays an important role in our account of science. In this paper a liberal stance will be adopted towards all of the metaphysical categories mentioned above (from particulars to universals) in that all will be admitted without discrimination into the ontology of science. This will be contrasted with a more systematic metaphysics for science in which the liberal stance is eschewed and a more parsimonious approach to ontology is adopted in which some of the categories permitted by the liberal metaphysician are admitted, or not, by the systematic metaphysician (from nominalist to Platonist). What ontology we ought to adopt involves complex arguments found in metaphysics that have little to do with science; these will be mentioned only in passing. The liberal approach adopted here is provisional; it is adopted in order to make clear exactly what the metaphysical commitments of structural realism might be in a non-question-begging manner. Often nominalistically inclined realists pursue their metaphysical agenda alongside their realism, and this can obscure issues. In section 2 some aspects of structuralism in the ontology of science are discussed.2 These vary from tropes of structure to laws of nature as relations between universals. Some non-liberal metaphysicians might find this last commitment too high a price to pay; but it is one that some are willing to pay, for example those who follow, say, Armstrong (1983, Part B) in arguing that laws of nature, understood ontologically as part of the furniture of the world, are really higher-order relations of necessitation holding between universals. As will be seen, structural realists do not form a united band. Some would claim: (a) there are structures that can be characterised mathematically; (b) there are particulars, such as objects, which are placeholders in the structures. Given the liberal stance adopted here, both (a) and (b) will be accepted. In addition it will be claimed that we can have knowledge of both (a) and (b). However some structural realists adopt what might be called epistemic structural realism in which it is claimed that while we can have knowledge of (a) we cannot have (much or any) knowledge of (b). That is, we can have knowledge of structures but cannot know the items that are placeholders in such structures (such as objects); they are a something-we-know-not-what. Yet others adopt what might be called Platonistic ontological structural realism in which (a) holds but not (b). That is, all that exists are mathematical structures, and we can have knowledge of these. But there do not exist placeholders, such as objects, within the structures: so we cannot have knowledge of these at all. On the stance adopted in this paper, one need be neither an epistemic nor a Platonistic structural realist. There are a number of different arguments for these positions, only a few central ones being addressed in this paper. Structural realists are realists who accept certain arguments, such as inference to the best explanation, to support their realism. But they also take seriously the pessimistic meta-inductive argument that shows that there are significant ontological discontinuities between successive theories. The ontologies of our evolving theories are alleged to change, so that the (kinds of) objects postulated by earlier theories are denied by later theories, which in turn postulate new (kinds of) objects. This tends to undermine any realism about the (kinds of) objects postulated in theories with theory change. So, are there any significant continuities between theories? If not, realism would be undermined. For structural realists scientific realism is saved by an alleged continuity of laws, mathematical equations or structures between successive theories. It is important for realists to recognise that there might well be such structures (however they are to be understood) and that not all continuity need be sought at the level of objects. In fact, if the pessimistic meta-induction is accepted, it had better not be sought only at that level. However for some there is a downside to structural realism in its strong forms. For both the epistemic and Platonistic structuralist we can only have knowledge of the allegedly invariant structures; we cannot have knowledge of the objects standing in these structures. More extremely, for the Platonistic structuralist discontinuities at the level of objects ceases to be a real issue since there are no such objects to countenance in the first place. Are structural realists right in claiming that there are continuities in mathematical structure with theory change? There is a confusion that needs to be avoided in posing this question that is addressed in section 3. A distinction should be drawn between formulations of laws in some language, and the objective worldly structures they attempt to represent. What is argued is that, at best, structural realists can only appeal to law formulations and not the objective structures that they purportedly represent. Also, even though there are some cases in which law formulations have been invariant with theory change, there are other cases in which there is change in law formulation with theory change; we do renovate our knowledge of the mathematical laws that apply in science. So the structural realists worry about lack of continuity of objects with theory change can also come to infect the very mathematical structures, or more correctly law formulations, to which they appeal in order to overcome the realists problem about lack of continuity with theory change. Structural realists were led to their position through accepting the pessimistic meta-inductive argument. It is argued in section 4 that this involves an unsound inference. This is not to deny that ontological change, either at the level of postulated objects of law formulations, has not occurred in the history of science. Rather it does not have the dire consequences for scientific realism that structural realists have feared. Section 5 examines a further argument that structural realists adopt for their flight from objects. Some structural realists have seen, in the use of the Ramsey sentence to formulate a theory, a way of advocating a version of structuralism in science (see Maxwell, 1970); this reason for structuralism will not be discussed in this paper. But in this section David Lewis version of the Ramsey sentence will be used to show that we can have continuity in objects with theory change in some historical cases where this has been denied to occur. Structural realists claim that there has been a change in ontology, as suggested by Poincar and others following him such as Worrall, in the theory of light from Fresnel to Maxwell, and that this in turn supports an epistemic version of structural realism. But the Ramsey-Lewis theory of reference fixing can be used to show, appearances to the contrary, that there is continuity in our reference to objects between these two theories; and the strategy can be generalised to other cases (not discussed). That there appears to be incommensurability is at best illusory. Further, even if our knowledge of the intrinsic properties of light might still be slim, there are no grounds for drawing the strong conclusion that knowledge of the intrinsic (not the same as essential) properties of such objects is impossible and that all we can ever know are their extrinsic relational properties. The position advocated here is that of a liberal epistemology in which there can be knowledge of objects, events, processes and properties as well as structures; what is resisted is the idea that we can only have knowledge of structures and not the placeholders within the structures. In sum, structural realists have pointed to a feature of the ontology of science that nominalistically inclined realists often obscure. But if one does not adopt the systematic metaphysical stance of the nominalist and is more liberal, then there is room to consider structures as well. But there is no need to go overboard in the opposite direction and adopt the systematic metaphysics of a Platonist and deny the existence of particulars such as objects and admit only Platonistic structures. Nor are there good grounds to support only an epistemic version of structuralism. Of course, a systematic metaphysics will be eliminative with respect to some of the ontological categories admitted by the liberal metaphysician. But it is hard to see how matters only relating to science could resolve these issues. Rather they are the province of a systematic metaphysics not addressed here. © 2006 Springer.