The Routledge Companion to Philosophy of Science

Martin Curd, Stathis Psillos, Martin Curd, Stathis Psillos

• Publisher: Routledge
• Year: 2013
• Print ISBN:
  9780415518741
• eBook ISBN:
  9781135011086
• Topic: Philosophy
• Subtopic: Epistemology in Philosophy

The Routledge Companion to Philosophy of Science is an indispensable reference source and guide to the major themes, debates, problems and topics in philosophy of science. It contains sixty-two specially commissioned entries by a leading team of international contributors. Organized into four parts it covers:

• historical and philosophical context
• debates
• concepts
• the individual sciences.

The Routledge Companion to Philosophy of Science addresses all of the essential topics that students of philosophy of science need to know - from empiricism, explanation and experiment to causation, observation, prediction and more - and contains many helpful features including chapters on individual sciences (such as biology, chemistry, physics and psychology), further reading and cross-referencing at the end of each chapter.

Expanded and revised throughout, this second edition includes new chapters on Conventionalism, Social Epistemology, Computer Simulation, Thought Experiments, Pseudoscience, Species and Taxonomy, and Cosmology.

Part I

Historical and Philosophical Context

1

Conventionalism

Robert DiSalle

Conventionalism, as an epistemological doctrine in the philosophy of science, is the fairly straightforward view that some scientific principles – perhaps the central theoretical principles of a given science – are incapable of being decided by empirical evidence, so that their adoption is necessarily a matter of conventional choice by the relevant group of scientists.

This is a relatively uncontroversial view to take of some kinds of scientific proposition, such as those that establish systems or units of measurement. It would obviously be absurd to suppose that a particular system of units is true, or that its adoption is anything but a free choice among equivalent alternatives, which can differ only in their relative convenience. But one generally thinks of a system of units not as a description of the world, but, rather, as a kind of language form that facilitates descriptions of the world; to compare such language forms by their convenience for facilitating scientific descriptions is obviously not to judge their conformity to the truth or to the empirical evidence, and it would make no sense to regard their adoption as anything but a choice. It is an old, even ancient, philosophical aim to identify conventions of the first sort, and to distinguish them from principles that are genuinely descriptive; in this way philosophical inquiry may be thought to arrive at the underlying nature of things, independent of particular modes of description. Then conventions would concern equivalent representations of an underlying structure that is the true object of scientific inquiry.

The less obvious, more challenging application of this view is to the actual scientific description of the world, as the claim that precisely the theoretical description of the world – not just the linguistic or mathematical forms that it employs – depends on conventional choice. There are various considerations from which such a claim might originate, but one obvious source is the underdetermination of theory by evidence: the same finite body of evidence will be compatible, in principle, with any number of theories if it is compatible with one. In that case, the adoption of a given theory necessarily involves some decision: either the choice of one compatible theory over all the others, or the decision simply to ignore the possibility of alternatives altogether and to accept the theory that one has in hand. It could be argued that this, too, is a harmless form of conventionalism, given the actual history of science, in which empirically equivalent alternative theories are not as common, or as easy to construct, as philosophical discussions of underdetermination might suggest. Even so, this form has implications for larger questions in philosophy of science, perhaps especially for the question of scientific realism; the mere possibility of equivalent alternative theories suggests a degree of contingency in our adoption of any one theory, and challenges the notion that empirically better theories are objectively closer to representing reality.

Neither of these views, each profound in itself, captures the historic importance of conventionalism, not only for the history of the philosophy of science, but also for the history of science itself, and particularly the history of mathematical physics. In fact it would be impossible to understand the contemporary place of conventionalism in the philosophy of science – as opposed to its general role as a broadly skeptical theme, from ancient times – without understanding its connection with very specific problems in the foundations of geometry and physics that arose in the middle of the nineteenth century. On the one hand, conventionalism was a response to new developments in geometry, and the foundational questions that those developments posed regarding the relation between geometry and the world of experience. On the other hand, the light that conventionalism shed on these questions influenced further reflections on the nature of mathematical structures and their empirical interpretations, reflections which, in turn, played a decisive role in the dramatic transformations of mathematical physics that took place in the early twentieth century. A clear grasp of the origins and meaning of conventionalism, as well as its relevance to enduring issues in the philosophy of science, begins with an appreciation of its engagement with the foundations of science.

Background: Kant and the synthetic a priori

To explain the context in which non-Euclidean geometry came under philosophical scrutiny, and conventionalism eventually developed, it is helpful to recall some aspects of Kant’s theory of the synthetic a priori. First, the theory highlighted the non-logical content of geometry, suggesting that neither our understanding of the basic principles, nor our ability to derive their consequences, could be separated – at least, with the logical resources of Kant’s time – from the representation of geometrical objects in space. So geometry appears to be an a priori science that nevertheless derives its content from sensibility. The objects of our geometrical knowledge are not only recognized, but also exhaustively defined, by the constructive procedures outlined in Euclid’s postulates. It is in virtue of a constructive definition that we know properties of a triangle, for example, beyond those expressed in the verbal definition of a three-sided figure. It is for the same reason, more generally, that the self-evidence of geometry is irreducibly intuitive, and that the rules to which our geometrical constructions conform – approximately in empirical geometry, and precisely in pure geometry – may be said to constitute the “form” of spatial intuition. From this point of view, it could be argued that the mere existence of non-Euclidean geometries, as formal mathematical possibilities, does not touch the certainty of Euclid’s geometry: if our intuitive constructions must conform to, and exhibit, the Euclidean principles, then the latter is justified a priori as the geometry of our space. But from Kant’s point of view this argument is not even necessary: if geometrical proof is inseparable from intuitive construction, then purely formal alternatives to Euclid’s geometry are not even possible. We could neither grasp their first principles nor derive their consequences (cf. Friedman 1992).

These aspects of Kant’s view are, perhaps ironically, precisely those that made it possible to unseat Euclidean geometry as the necessary structure of space. Having undermined any purely rational argument for the uniqueness of Euclidean geometry, Kant’s account makes its necessity and universality entirely dependent on the evidence of its constructive methods, and indeed denies it any content above or beyond its representation in sensible intuition. So, to justify the viability of a non-Euclidean geometry as an account of “our space,” it would be not only necessary, but also sufficient, to show that such a geometry has a constructive representation – an intuitive representation in precisely Kant’s sense – and its theorems admit of constructive proof. Given its complete identification of the foundations of geometry with the space of intuitive constructions, the Kantian view would have no room to retreat from such a challenge.

From empiricism to conventionalism: Helmholtz and Poincaré

It is a misconception, therefore, that Kant’s account of geometry as synthetic a priori knowledge was entirely overthrown by the development of non-Euclidean geometry. The decisive fact was, rather, that the special epistemic ground of Euclidean geometry, as Kant understood it, could provide an equivalent ground for non-Euclidean alternatives. The mere formal consistency of an alternative geometry would challenge Kant’s views of mathematical proof. But it would not necessarily establish the possibility of such a geometry as a synthetic account of space. Kant’s followers could still argue that Euclidean geometry is uniquely tied to our spatial intuition; alternative geometries could be formally developed, but not “visualized” as a possible space of experience (cf. Torretti 1978). It was Helmholtz who raised the decisive challenge to this view, by a conceptual analysis of what is meant by “visualizing” a geometrical structure:

By the much abused expression “to represent to oneself [sich vorstellen]”, or “to be able to imagine [sich denken] how something takes place,” I understand – and I don’t see how one could understand anything else thereby, without giving up all the sense of the expression – that one could depict the series of sense-impressions that one would have if such a thing took place in a particular case.

(Helmholtz 1870: 8)

Helmholtz showed that, in any sense in which we can visualize Euclidean space, we can visualize a homogeneous non-Euclidean space. Kant had already recognized that the Euclidean structure of space is not something that we immediately “intuit”; what we intuit is, rather, the construction of actual or imagined figures, and the systematic changes in the appearances of things that accompany our changes of perspective. To intuit a non-Euclidean space would be, simply, to find that such constructive processes, and such changes of perspective, exhibit the laws of a non-Euclidean geometry.

This conceptual analysis is a revolutionary step, but also somewhat Kantian in spirit, insofar as it admits no other content to the claim that space is Euclidean, or non-Euclidean, beyond the succession of intuitions that conform to one or another structure. But the analysis leads directly to a further analysis, showing that the intuitive practice of geometrical construction depends on empirical features of the world. The basic notions of this practice are the congruence of figures and the straightness of lines, and we come to know each of these through its practical physical correlate: congruence through the displacement of rigid bodies, and straight lines through the optical line of sight, or the path of light-propagation. That is, the comparison of lengths derives its meaning from our ability to bring bodies into coincidence, and our assumption that in the process their size and shape remain constant; analogously, we determine the straightness of any body or path by comparing it to the line of sight. Helmholtz’s analysis thus leads from a broadly Kantian perspective to empiricism: what we bring to spatial experience and geometrical reasoning is not the a priori form of spatial intuition, but the expectations we have developed, and completely internalized, in the course of our experience with nearly-rigid bodies and light rays, and the habits and expectations that we have formed regarding the relations between our own motions and our lines of sight. The “conditions of the possibility” of geometry are therefore facts about the world in which our geometrical conceptions have developed, namely that there really are approximately rigid bodies and that light travels in sufficiently straight lines.

Just this principle of geometric empiricism, however, was the first step to conventionalism. For Helmholtz’s analysis introduced a radical insight into the subject matter of geometry: insofar as geometry is the science of the structure of space, its subject matter is the possible displacements of rigid bodies. Helmholtz pointed out that this principle of rigid displacement – thereafter known as the principle of free mobility – is not only the foundation of our notion of congruence; it is also the principle that characterizes our experience of space as such. Spatial relations are first characterized for us, and distinguished from other relations, by the fact that we can freely alter them by our own motion. Changes of relative spatial position are distinguished from other kinds of change in our environment by the fact that they can be produced, combined, and reversed by shifts in the perspective of the observer. We believe that we live in an approximately Euclidean world, Helmholtz concluded, because of the entirely contingent fact that the displacements of approximately rigid bodies exhibit an approximately Euclidean structure, observed in measurements of angles and lengths using rigid instruments. For example, the internal angles of triangles approximately sum to two right angles; if such measurements turned out otherwise, we would know, as a matter of fact, that our space is non-Euclidean.

It is not immediately obvious why this empiricist understanding of the foundations of geometry, with its emphasis on physical measurement and approximation, should turn out to be a step toward conventionalism. Poincaré took this step because he saw more clearly than Helmholtz that the empirical principles on which Helmholtz relied are, in fact, principles of interpretation. That light travels in a straight line is not a law of nature, but a physical interpretation of the geometrical concept of straight line; that rigid bodies move freely without change of dimension is a physical interpretation of the concept of congruence. If such principles were laws of nature, we should be able to state, independently of light propagation, what in nature is a straight line, and “light travels in a straight line” would become an empirical claim. In that case the burden of interpreting the concept of straight line, as a geometrical feature of the world, would fall on some other physical principle. This would begin an infinite regress, unless we recognize that some physical principle – on account of its simplicity, convenience, or other practical virtue – has simply been adopted as the physical definition of straight line. Kant had upheld the synthetic a priori because he had recognized that certain principles, though they apply to the sensible world, nonetheless partake of a kind of necessity because they “constitute” their objects in a strong sense: these principles are the conditions of the possibility of our experience of those objects as objects of knowledge, rather than as mere appearances. Poincaré saw that such principles constitute, rather, the empirical meanings of geometrical concepts. For this reason they are not analytic in Kant’s sense, for they do not merely affirm what is “contained in” those concepts, but provide them with an empirical interpretation; for the same reason, they are revisable, if an alternative interpretation better serves our purposes. They were taken as synthetic a priori principles, in short, because they appeared to be necessary principles in the form of laws of nature. But this appearance is deceptive; in fact they are “definitions in disguise” (Poincaré 1902: 56).

The insight behind conventionalism, then, was that certain principles play a peculiar role in our fundamental theories because they determine the meanings, and the criteria for the application, of fundamental concepts around which these theories are constructed. Conventionalism would be an absurd doctrine if it asserted, in light of this insight, that (for example) straight lines are defined by light rays in accord with some explicit decision by a social group. For Poincaré, at least, the connection between the geometrical straight line and the physical propagation of light arises from a long, successful, and largely unexamined history of empirical practice. The implication of its definitional character is not that it was deliberately legislated but, rather, that, because it is not quite an empirical proposition, it can be rewritten without necessarily defying the empirical evidence; equivalently, it can be maintained in the face of empirical evidence that might otherwise have seemed to contradict it. If the optical measurement of large triangles (for example, surveying large triangles near the surface of the earth, or taking the parallax of celestial bodies) showed that their angles don’t sum to two right angles, we would not have (as Helmholtz had argued) experimental proof that space is non-Euclidean. Such an experiment can only demonstrate a conflict between the definition of space as Euclidean and the definition of straight line that is presupposed in the measurement. The experiment therefore has two epistemically equivalent interpretations: if straight lines are defined by light propagation, then space is non-Euclidean; if straight lines are defined by their conformity to Euclidean geometry, then the light rays forming the sides of the triangle are, by definition, not straight. In that case the principle that light travels in straight lines becomes a mere hypothesis that has turned out to be false, or perhaps there is a force that is systematically disturbing the motion of light. Poincaré illustrated this point by a physical model of a non-Euclidean world. As Helmholtz had argued, from our theoretical account of the behavior of bodies and light in a non-Euclidean space, and our practical knowledge of visual perception and its adaptation to the motions of bodies and light, we can imagine the course of experience in a non-Euclidean world. Poincaré pointed out, however, that we could equally imagine a world whose atmosphere had a peculiar distribution of heat, so that the refractive index of light and the thermal expansion of bodies varied syste...

Table of contents

• Cover Page
• Half Title Page
• Other Page
• Series Page
• Fulltitle Page
• Copyright Page
• Table of Contents
• List of illustrations
• Notes on contributors
• Introduction
• Part I Historical and Philosophical Context
• Part II Debates
• Part III Concepts
• Part IV Individual sciences
• Index