1 Cartwright uses ‘tendencies’ and ‘natures’ interchangeably. See Cartwright, Nancy ‘Aristotelian Natures and the Modem Experimental Method,’ in Earman, John ed., Inference, Explanation, and Other Frustrations (Berkeley: University of California Press 1992) 44–71Google Scholar; and ‘Fundamentalism vs. The Patchwork of Laws,’ Proceedings of the Aristotelian Society 94 (1994) 279-92. ‘Capacities,’ as she uses the term in Nature's Capacities and Their Measurement (Oxford: Oxford University Press 1989), are special kinds of tendencies which tend to cause, rather than do or be something (226ff.).

2 We shall follow her spelling of the word.

3 For such an account cf., e.g., Laymon, Ronald ‘Cartwright and the Lying Laws of Physics,’ Journal of Philosophy 86 (1989) 353-72CrossRefGoogle Scholar.

4 Cf. how Cartwright characterizes the scientific methods she considers: ‘Parameters are estimated in one context, and those values are assumed to obtain in entirely different contexts …. The methods presuppose that causes have stable tendencies of fixed strengths that they carry about with them from situation to situation’ (Nature's Capacities, 153; italics added). This is supposed to be true of the methods of econometrics as well as of those of physics (ibid., 158).

5 For such a view see, e.g., Rueger, Alexander ‘Complementarity Meets General Relativity,’ Synthese 79 (1989) 559-80CrossRefGoogle Scholar. The issue is somewhat more complicated than the soliton case because of the intrusion of the measurement problem of quantum theories.

6 That the atomist metaphysics may not be correct is suggested, for instance, by the success of scientific methods which are not committed to the existence of stable natures. For discussion of an example of such methods from experimental research in Nonlinear Dynamics, cf. Rueger, Alexander and Sharp, W. David ‘Simple Theories of a Messy World: Truth and Explanatory Power in Nonlinear Dynamics,’ British Journal for the Philosophy of Science 47 (1996) 93–112CrossRefGoogle Scholar.

7 Strictly speaking, structural stability requires that a function not change its form under ‘almost all’ changes in the values of u and v. Thus even though setting v = 0 transforms j(x) into g(x), j(x) can be structurally stable while g(x) is not because f(x) is unstable only under a very special perturbation, namely, the one with v = 0, while g(x) suffers from instability under all values of v.

8 James Woodward has argued, against Cartwright, that tendencies don't have to be stable in the sense of parameter stability. Woodward uses a criterion of invariance to characterize both capacity ascriptions which issue in regular behavior and thus are covered by laws, as well as capacity ascriptions which are not associated with regular behavior. The invariance criterion for the case of laws sounds very much like the requirement of structural stability: such law-covered relations hold ‘at least roughly … in the actual circumstances and … would continue to hold in a similar way under some specified class of interventions or for specified changes in background conditions’ (‘Capacities and In variance,’ in Earman, John et al., eds., Philosophical Problems of the Internal and External Worlds [Konstanz/Pittsburgh: Universitaetsverlag Konstanz 1993] 283–328, at 311)Google Scholar. ‘In a similar way’ means that the equations describing the relation will not change their form under the specified perturbations; parameter values, however, do not have to be preserved (325). Our view is that adopting such a requirement effectively makes capacities dispensable.

9 One could worry that under the constraint of structural stability, we forgo any way to describe systems that actually show some kind of instability, systems that switch in certain parameter regimes from one kind of behavior to a qualitatively different kind, e.g., from regular to chaotic behavior. An extended notion of structural stability, however, can at least partially deal with this worry. Cf. Saunders, 21, and Alexander Rueger and W. David Sharp, ‘Idealization and Stability: A Perspective from Nonlinear Dynamics,’ Poznan Studies in the Philosophy of Science and the Humanities, forthcoming. It is important not to confuse structural stability with the more commonly known stability against variations of initial conditions. Structural stability is stability against variations of the parameters that control the system's dynamics; a structurally unstable system changes its dynamics under parameter perturbations. Systems that are unstable with respect to perturbations of the initial conditions, e.g., chaotic systems, have fixed dynamics; in this respect one is only interested in how the same dynamics behaves under different sets of initial conditions.

10 For structural stability as a requirement for good models, see, for instance, Shirer, Hampton N. Nonlinear Hydrodynamic Modelling (New York: Springer 1987), 19–21; 164fCrossRefGoogle Scholar.

11 Cf. the discussion in Guckenheirner, John and Holmes, Philip Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fluids (New York: Springer 1983), 258f.CrossRefGoogle Scholar, where the authors suggest that structurally unstable features of our theories should not be regarded as referring to any observable aspects of real systems.

12 In Cartwright's example of the (planned) Stanford Gravity Probe experiment, the law takes this form: ‘Whenever the net nonrelativistic torque on the probe is zero, the probe's precession will be the value predicted from the general theory of relativity’ (‘Aristotelian Natures,’ 58).

13 We have dealt with the case of idealization in more detail in Rueger and Sharp, ‘Idealization and Stability.’

14 On the structural stability of solitons cf., for instance, Makhankov, Vladimir G. Soliton Phenomenology (Dordrecht: Kluwer 1989), chs 10 and 12.Google Scholar

15 It doesn't matter for the purposes of our discussion whether or not this tendency ascription is specialized into a capacity ascription.

16 For the following cf., e.g., Haken, Hermann ‘Cooperative Phenomena in Systems far from Thermal Equilibrium and in Non-Physical Systems,’ Reviews of Modern Physics 47 (1975) 67–121, at 69-78CrossRefGoogle Scholar.

17 For different worries about whether Cartwright's analysis of the laser case in terms of tendencies is compatible with scientific practice, see Morrison, Margaret ‘Causes and Contexts: The Foundations of Laser Theory,’ British journal for the Philosophy of Science 45 (1994) 127-51CrossRefGoogle Scholar.

18 More on this topic in Rueger and Sharp, ‘Idealization and Stability.’

19 See Rueger and Sharp, ‘Simple Theories,’ for further discussion of this distinction.

20 For a stimulating discussion of the consequences of this fact see Tavakol, R.K. ’Fragility and Deterministic Modelling in the Exact Sciences,’ British Journal for the Philosophy of Science 42 (1991) 147-56CrossRefGoogle Scholar.

21 Mormann, Thomas in ‘Accessibility, Kinds, and Laws: A Structural Explication,‘ Philosophy of Science 61 (1994) 389–406CrossRefGoogle Scholar, suggests a similar characterization.

22 Thanks to two referees for CJP for helpful comments on an earlier version of this paper.