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Reduction, Unity and the Nature of Science: Kant's Legacy?

Published online by Cambridge University Press:  16 October 2008

Margaret Morrison
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One of the hallmarks of Kantian philosophy, especially in connection with its characterization of scientific knowledge, is the importance of unity, a theme that is also the driving force behind a good deal of contemporary high energy physics. There are a variety of ways that unity figures in modern science—there is unity of method where the same kinds of mathematical techniques are used in different sciences, like physics and biology; the search for unified theories like the unification of electromagnetism and optics by Maxwell; and, more recently, the project of grand unification or the quest for a theory of everything which involves a reduction of the four fundamental forces (gravity, electromagnetism, weak and strong) under the umbrella of a single theory. In this latter case it is thought that when energies are high enough, the forces (interactions), while very different in strength, range and the types of particles on which they act, become one and the same force. The fact that these interactions are known to have many underlying mathematical features in common suggests that they can all be described by a unified field theory. Such a theory describes elementary particles in terms of force fields which further unifies all the interactions by treating particles and interactions in a technically and conceptually similar way. It is this theoretical framework that allows for the prediction that measurements made at a certain energy level will supposedly indicate that there is only one type of force. In other words, not only is there an ontological reduction of the forces themselves but the mathematical framework used to describe the fields associated with these forces facilitates their description in a unified theory. Specific types of symmetries serve an important function in establishing these kinds of unity, not only in the construction of quantum field theories but also in the classification of particles; classifications that can lead to new predictions and new ways of understanding properties like quantum numbers. Hence, in order to address issues about unification and reduction in contemporary physics we must also address the way that symmetries facilitate these processes.

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Papers
Information
Royal Institute of Philosophy Supplements , Volume 63 , October 2008 , pp. 37 - 62
Copyright
Copyright © The Royal Institute of Philosophy and the contributors 2008

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References

1 Kitcher (1983), (1986); Buchdahl (1992); Guyer (1990); Morrison (1989).

2 I shall henceforth use Smith's, Norman Kemp (1929) translation of the Critique of Pure Reason (New York: St. Martin's)Google Scholar.

3 I do not intend this claim as a resolution of the tension; in fact, as we shall see below the relation between the subjective and objective features of unity is a fundamental feature of Kant's transcendental program. The importance of this ‘tension’ and the role it plays will be discussed in section two.

4 Henceforth, I shall be using Ellington's, James (1985) translation of the Metaphysische Anfangsgründe der Naturwissenschaft (Indianapolis: Hackett)Google Scholar; and Förster, and Rosen's, (1993) translation of the Opus postumum (Cambridge: Cambridge University Press)Google Scholar.

5 These are not just questions that preoccupy philosophers of science, they are very much a part of the scientific discussions that address the nature of fundamental physics. Many contemporary physicists are concerned with issues surrounding reduction and emergence and whether the search for a theory of everything is simply a metaphysical hope. See, for example, recent articles by Laughlin and Pines (2000) as well as Weinberg (1993) and Anderson (1972).

6 Because scientific knowledge constitutes a logical system the practice of constructing such a system involves logical principles. But, as Kant insists, these logical principles only have methodological force because they are grounded in transcendental principles.

7 Similarly, in the case of specification, empirical inquiry soon comes to a stop in the distinction of the manifold, if it is not guided by the antecedent transcendental law of specification, which not only leads us to always seek further differentiation but suspects these differences even where the senses are unable to disclose them (A657/B685). Such discoveries are possible, Kant claims, only under the guidance of an antecedent rule of reason. We assume the presence of differences before we prescribe the understanding the task of searching for them.

8 The important point is that the methodology is grounded, ultimately, in transcendental principles.

9 My remark about the impossibility of theory construction on the basis of phenomenology is simply meant to indicate that there were no reasons to assume that electromagnetism bore any relation to the weak force. In the former case the particle carrying the force is the massless photon, while in the latter much heavier massive bosons were required. No indication that two such theories could be unified emerged from the physical phenomenology.

10 There have been some suggestions in the literature about interpreting symmetry principles (and their role in physics) as Kantian transcendental principles, see Falkenburg (1988) and Mainzer (1996). While this initially appears as an attractive approach, my claim is that it is ultimately unsuccessful, for the reasons I discuss below.

11 For an interesting account of the omega minus case, see Bangu (2008).

12 The very notion of symmetry itself is related to unity in the sense that the symmetry transformations of a group relate the elements to each other and to the whole. See Morrison (2000).

13 Two further arguments for the ontological status of symmetries are given on the basis of the geometrical symmetries of spacetime and the relation between symmetries and conservation laws as shown by Noether's theorem. For details of these arguments, see Brading and Brown (2003).

14 Falkenburg (1988), p. 134.

15 Mainzer (1996), p. 287.

16 Weinberg (1993).

17 An irreducible representation is one that cannot be split up into smaller pieces, each of which would transform under a smaller representation of the same group. All the basic fields of physics transform as irreducible representations of the Lorentz and Poincaré groups. The complete set of finite dimensional representations of the rotation group O(2) or the orthogonal group comes in two classes, the tensors and spinors.

18 Kant identifies this mode of explication with the atomistic or corpuscular philosophy (MAN 533).

19 The specific details of that story have been systematically spelled out by Friedman (1992a), Plaass (1965) and others.

20 I realize, of course, that one cannot in principle separate the transcendental and empirical levels, but what I have in mind here is a claim about how Kant saw reduction and forces as essential features of the practice of physics.

21 Kant claims that the concept of force supplies us with a ‘datum’ for a ‘mechanical construction’ (MAN 498), a requirement for proving the ‘real possibility’ of matter. Here again the details surrounding Kant's theory of matter rise important philosophical points of interpretation, see especially Friedman (2001b) and Carrier (2001).

22 There is a good deal of philosophical debate about the nature of the field and the role of particles in QFT. While these debates are extremely interesting, the details are not really relevant for the issue I am addressing in the paper.

23 For a detailed discussion of these issues, see Guyer (1990).

24 Kant (1766), English translation (1992), p. 354.