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Nature's Capacities and Their Measurements
Ever since David Hume, empiricists have barred powers and capacities from nature. In this book Cartwright argues that capacities are essential in our scientific world, and, contrary to empiricist orthodoxy, that they can meet sufficiently strict demands for testability. Econometrics is one discipline where probabilities are used to measure causal capacities, and the technology of modern physics provides several examples of testing capacities (such as lasers). Cartwright concludes by applying the lessons of the book about capacities and probabilities to the explanation of the role of causality in quantum mechanics.
- GenresPhilosophy
278 pages, Paperback
First published August 10, 1989
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April 25, 2026
After an impressive debut with How the Laws of Physics Lie (Oxford University Press, 1983), the idiosyncratic philosopher of science Nancy Cartwright has followed up with Nature’s Capacities and their Measurement (Oxford University Press, 1989). Here, she unveils what will turn out to be her signature contribution, for her critique of foundationalism in her early work is largely negative in tone. With the idea of capacities she alights upon a positive side to her position, but what can she mean by them? As, for instance, Ernst Cassirer has stressed (see our review of his essay on Goethe and mathematical physics in Idee und Gestalt, here), ever since Galileo the characteristic move of modern physics has been to reduce the system under study to its representation in terms of a collection of numbers with which one can perform calculations in order to predict its behavior. Any inherent virtue or occult power that once may have been ascribed to a body by Aristotle or his medieval continuators has no longer any relevance to our conceptual understanding of the physics (and therefore may be dismissed as metaphysical). Seduced by the monumental triumph of modern empirical science, Bertrand Russell, for one, argues in an influential article [On the notion of cause, Proceedings of the Aristotelian Society 13, 1-26 (1913)] that we may henceforth dispense with the notion of cause altogether. All we need to underpin our knowledge of the natural world are the functional relationships expressed by the overarching laws of nature, which, in every case, lend themselves to a purely mathematical formulation of the problem at hand.
Russell’s radicalization of David Hume’s celebrated skeptical position on causation in A Treatise of Human Nature (1739) appeals to many observers in our day, no doubt. Yet Cartwright will not have any of it. Why? Cartwright’s strategy is to play off J.S. Mill’s logic against Humean empiricism. J.S. Mill, in his trend-setting System of Logic (first published in 1843) anticipates her capacities, calling them ‘tendencies’. Mill was motivated by the intractability of calculations in the usual hypothetico-deductive method so another method is required in the social sciences. As Cartwright puts it:
Mill proposes, then, that political economy should be modeled on mechanics and not on geometry [seeing that the former allows for interference of effects as in Newton’s parallelogram of forces]….But his view of mechanics is peculiar from the standpoint of a modern empiricist, who will construct mechanics itself on the model of geometry. [p. 173]
Thus, Mill. As an original philosopher of science, however, Cartwright takes the impetus she receives from Mill and runs with it. First let us seek to elucidate what she means by nature’s capacities, the primary subject of her book:
It is the singular fact that matters to the causal law because that is what causal laws are about. The generic causal claims of science are not reports of regularities but rather ascriptions of capacities, capacities to make things happen, case by case. ‘Aspirins relieve headaches’. This does not say that aspirins always relieve headaches, or always do so if the rest of the world is arranged in a particularly felicitious way, or that they relieve headaches most of the time, or more often than not. Rather it says that aspirins have the capacity to relieve headaches, a relatively enduring and stable capacity that they carry with them from situation to situation; a capacity that may if circumstances are right reveal itself by producing a regularity, but which is just as surely seen in one good single case….My claims, then, are doubly anti-Humean. I take singular causes to be primary, and I endorse capacities. [pp. 2-3]
Where does our knowledge of regularity come from? Cartwright does not herself entertain the genealogical problem of how we come to ascribe capacities to things, but we may speculate. A child through experience of his life-world arrives over the course of several years at an understanding of how typical causes operate, an understanding which is embedded in and expressed by natural language. Thus, we may suppose that the faculty of interpreting the environment in causal terms is affiliated with what Noam Chomsky calls the language faculty, innate in all human beings. Now, what Cartwright refers to as a natural capacity of a thing seems, then, to be a description via natural language of how it tends to operate in the settings in which we encounter it in its environment. It would be fascinating if psychologists specializing in language acquisition were to apply their theories to the problem of concept formation in the sciences! Perhaps they could go on a fact-finding expedition, rather as Andrew Pickering does in treating the occupants of a particle accelerator laboratory as subject of an anthropological investigation, in his controversial Constructing Quarks: A Sociological History of Particle Physics (University of Chicago Press, 1984).
The papers in first half deal with probability theory [pp. 11-140]; the second half unfolds her thesis about natural capacities [pp. 141-250]. One usually says that a factor A causes the outcome B if the presence of A increases the frequency of B occurring. But what about this example of Cartwright’s: does rain cause automobile accidents? For on account of the bad weather fewer people will go outside but, for those who do, the roads will be slipperier. There can also be cases where the effect is brought about through the mediation of more than one cause, which may interfere with one another constructively or destructively. The general method statisticians have come up with for dealing with such cases is that of treatments (analysis of variance and so forth, as will be familiar to those who have ever taken a course in statistics or worked in machine learning). But there are subtleties having to do with precisely what one means by a ceteris paribus clause.
Cartwright discusses the associated problems extensively in the setting of structural models in econometrics. How correlations and conditional probabilities work in path analysis already a complicated matter and Cartwright wants to examine it for exceptional conditions. Among the considerations Cartwright discusses are randomized experiments to control for a factor, singular causes, the meaning of the noise term and causes that operate probabilistically versus deterministically.
Last, Cartwright attends to the problem of how to know when the model includes all relevant causes. For our ordinary concept of causation is based on cases we can analyze where the connections are clear, but what about real-world scenarios where we don’t necessarily know in advance what all the causes may be? Then it’s not after all so clear what we can say about the causal factors; cf. this passage from Keynes quoted by Cartwright:
At any rate, Prof. Tinbergen agrees that the main purpose of his method is to discover, in cases where the economist has correctly analyzed beforehand the qualitative character of the causal relations, with what strength each of them operates….If we already know what the causes are, then (provided all the other conditions given below are satisfied) Prof. Tinbergen, given the statistical facts, claims to be able to attribute to the causes their proper quantitative importance….Am I right in thinking that the method of multiple correlation analysis essentially depends on the economist having furnished, not merely a list of the significant causes, which is correct as far as it goes, but a complete list? [Keynes, cited on p. 15 and 87]
The second half of the present work is devoted to Cartwright’s theory of natural capacities. To start with, she explains why capacities matter to her account of causation:
There are undoubtedly more complicated alternatives one can try. The point is that one needs an account of causal laws that simultaneously provides for a natural connection between the law and the individual case that it is supposed to cover, and also brings order into the methodology that we use to discover the laws. The account in terms of capacities does just that, and it does so by jettisoning regularities. The regularities are in no way ontologically fundamental. They are the consequence of the operation of capacities, and can be turned, when the circumstances are fortuitous, into a powerful epistemological tool. [pp. 139-140]
Another anti-Humean point [p. 128]: to determine what the right equations are with which to model the system depends on a knowledge of its capacities (in this case, where correct coarse-graining of the time series is needed to bring out the effect).
The claim I am going to develop in this chapter is that the concept of general sui generis causal truths—general causal truths not reducible to associations—separates naturally into two distinct concepts, one at a far higher level of generality than the other: at the lower we have the concept of a causal law; at the higher, the concept of capacity. I speak of levels of generality, but it would be more accurate to speak of levels of modality, and for all the conventional reasons: the claims at both levels are supposed to be universal in space and through time, they support counterfactuals, license inferences, and so forth. The level of capacities is ‘higher’ not only because the generalizations involved are broader in scope but also because the inferences that they allow are far stronger and, correlatively, the amount of metaphysics assumed in their use is far greater. [p. 142]
In an aside, she notes that the concept of laws of nature should be objectionable to a radical empiricist, for:
Capacities are peculiar, from a radical empiricist point of view, in exactly the same way as laws, only one level up. Just as laws constrain relations between matters of fact, capacities constrain relations among laws. [p. 146]
Strength that flows from this:
If you are committed to the assumption that all the internal properties of electrons are essential, this makes science a lot easier for you. You can measure the charge or mass on one, and you know it on all the others. [p. 146]
Something similar holds with the universal quantifier in her Principle CC:
That means that, where capacities are at work, one can reason as above: one can infer from one causal law directly to another, without ever having to do more tests. [p. 146]
By the end of the present work, Cartwright is headed towards a radical proposal to eliminate laws leaving only capacities (to be developed fully in her late work, The Dappled World: A Study of the Boundaries of Science, Cambridge University Press, 1999):
Return for a moment to my conclusions about causality. In the end I present a structure with three tiers. At the bottom we have individual singular causings. At the top we have general causal claims, which I render as statements associating capacities with properties….In between stands the phenomenal content of the capacity claim—a vast matrix of detailed, complicated, causal laws. These causal laws, which stand at level two, provide no new obstacles for the Humean beyond those that already appear at the bottom level. For these are just laws, universal or probabilistic, about what singular causings occur in what circumstances what percentage of the time….Yet there is a good reason for the Humean to be wary, at least the modern-day Humean who believes in laws but not in causes. For if the program of section 4.6 succeeds, this treasured layer of laws will be eliminated altogether from our fundamental scientific picture. All that remains would be capacities and the causing for which they are responsible. The laws—even causal laws—would no longer play any basic role; and the pretence that nature is full of regularities could be dropped….For I hope it becomes clear that what are taken as the fundamental laws of, say, physics are not laws at all in the empiricist’s sense, but abstractions. [pp. 228-229]
The argumentative flow is somewhat piecemeal, not a fully rounded theoretical account like one would get from John Maynard Keynes (see our review of the latter’s A Treatise on Probability (Cambridge University Press, 1920), here). In general, Cartwright’s discussions can get somewhat technical and presuppose knowledge of the literature; i.e., she does not develop the theory from scratch. Rather than undertake a systematic exposition, she prefers to stake out her own positions in stages through close commentary on the work of others.
The reader may well wonder, how solid is Cartwright’s evaluation of path analysis here? For the sake of comparison, one will want to consult Judea Pearl’s (roughly contemporaneous) monograph Causality: Models, Reasoning and Inference (Cambridge University Press, 2009, second edition, 2013). Here, one will find a systematic presentation of the highly developed path analysis technique of probabilistic inference to causation which is subjected to repeated criticism in the present book. The substance of what Cartwright has to say comes down, not to a claim that statistical inference cannot work (she acknowledges that, in the right hands, it often does in practice), but to the contention that its theoretical presuppositions remain somewhat obscure and one can contrive cases where they could be expected to fail.
What about the objection that her capacities are tantamount to the much-derided scholastic occult qualities? Fundamentally, they are the same thing, but hers lend themselves better to mathematization, whether in models of physics or of economics.
A potentially more instructive tack to pursue would be to inquire about the epistemic role her natural capacities have to play in relation to theory construction. Cartwright’s capacities function in a manner akin to Kant’s schemata which connect the categories of pure reason to anticipations of experience in time and space; for capacities allow us to go from general laws to a model of the mechanism for a given experimental situation. For instance, if we posit that electric charges (have the capacity to) exert forces on one another as described by Coulomb’s law, we know that we have to solve Poisson’s equation for the potential in the given geometry.
How to differentiate capacities from physical principles? Perhaps as follows: principles are yet one level up from capacities. The analysis discloses first the pertinent capacities of the entities participating in a given experimental set-up, then comparing across many arrangements one may arrive at general principles governing them all. But the distinction so sketched does not seem to be hard and fast.
The salient point is just that, contra Russell, we do not get the supposed laws of nature in a vacuum or handed down to us from on high, from which we may then proceed to a differential equation to solve without the intermediary of any background knowledge as to what kinds of models are likely to be applicable. Cartwright’s natural capacities are intuitive guides to the formulation of specific models that have a fair chance of being correct. They describe how actual practicing scientists reason—one does not just try out candidate equations of motion at random, guessing in the dark, but adheres to general rules of theory construction. For instance, the Lagrangian should ordinarily be a difference between a kinetic term and a potential term. The kinetic term is often a quadratic form in the velocities of the bodies in motion, while the potential may involve combinations of known force laws or may be constrained by reason of symmetry to be parametrized in a certain way etc.
Four stars: the blurbs on the back cover overstate the importance of this work, although it is indeed very provocative for the serious philosopher of science to ponder. In our judgment, Cartwright’s analysis itself in the present book isn’t as refined as it gets to be in her last work, entitled The Dappled World: A Study of the Boundaries of Science (1999), which we are about to review in a moment (see our forthcoming review here).
Russell’s radicalization of David Hume’s celebrated skeptical position on causation in A Treatise of Human Nature (1739) appeals to many observers in our day, no doubt. Yet Cartwright will not have any of it. Why? Cartwright’s strategy is to play off J.S. Mill’s logic against Humean empiricism. J.S. Mill, in his trend-setting System of Logic (first published in 1843) anticipates her capacities, calling them ‘tendencies’. Mill was motivated by the intractability of calculations in the usual hypothetico-deductive method so another method is required in the social sciences. As Cartwright puts it:
Mill proposes, then, that political economy should be modeled on mechanics and not on geometry [seeing that the former allows for interference of effects as in Newton’s parallelogram of forces]….But his view of mechanics is peculiar from the standpoint of a modern empiricist, who will construct mechanics itself on the model of geometry. [p. 173]
Thus, Mill. As an original philosopher of science, however, Cartwright takes the impetus she receives from Mill and runs with it. First let us seek to elucidate what she means by nature’s capacities, the primary subject of her book:
It is the singular fact that matters to the causal law because that is what causal laws are about. The generic causal claims of science are not reports of regularities but rather ascriptions of capacities, capacities to make things happen, case by case. ‘Aspirins relieve headaches’. This does not say that aspirins always relieve headaches, or always do so if the rest of the world is arranged in a particularly felicitious way, or that they relieve headaches most of the time, or more often than not. Rather it says that aspirins have the capacity to relieve headaches, a relatively enduring and stable capacity that they carry with them from situation to situation; a capacity that may if circumstances are right reveal itself by producing a regularity, but which is just as surely seen in one good single case….My claims, then, are doubly anti-Humean. I take singular causes to be primary, and I endorse capacities. [pp. 2-3]
Where does our knowledge of regularity come from? Cartwright does not herself entertain the genealogical problem of how we come to ascribe capacities to things, but we may speculate. A child through experience of his life-world arrives over the course of several years at an understanding of how typical causes operate, an understanding which is embedded in and expressed by natural language. Thus, we may suppose that the faculty of interpreting the environment in causal terms is affiliated with what Noam Chomsky calls the language faculty, innate in all human beings. Now, what Cartwright refers to as a natural capacity of a thing seems, then, to be a description via natural language of how it tends to operate in the settings in which we encounter it in its environment. It would be fascinating if psychologists specializing in language acquisition were to apply their theories to the problem of concept formation in the sciences! Perhaps they could go on a fact-finding expedition, rather as Andrew Pickering does in treating the occupants of a particle accelerator laboratory as subject of an anthropological investigation, in his controversial Constructing Quarks: A Sociological History of Particle Physics (University of Chicago Press, 1984).
The papers in first half deal with probability theory [pp. 11-140]; the second half unfolds her thesis about natural capacities [pp. 141-250]. One usually says that a factor A causes the outcome B if the presence of A increases the frequency of B occurring. But what about this example of Cartwright’s: does rain cause automobile accidents? For on account of the bad weather fewer people will go outside but, for those who do, the roads will be slipperier. There can also be cases where the effect is brought about through the mediation of more than one cause, which may interfere with one another constructively or destructively. The general method statisticians have come up with for dealing with such cases is that of treatments (analysis of variance and so forth, as will be familiar to those who have ever taken a course in statistics or worked in machine learning). But there are subtleties having to do with precisely what one means by a ceteris paribus clause.
Cartwright discusses the associated problems extensively in the setting of structural models in econometrics. How correlations and conditional probabilities work in path analysis already a complicated matter and Cartwright wants to examine it for exceptional conditions. Among the considerations Cartwright discusses are randomized experiments to control for a factor, singular causes, the meaning of the noise term and causes that operate probabilistically versus deterministically.
Last, Cartwright attends to the problem of how to know when the model includes all relevant causes. For our ordinary concept of causation is based on cases we can analyze where the connections are clear, but what about real-world scenarios where we don’t necessarily know in advance what all the causes may be? Then it’s not after all so clear what we can say about the causal factors; cf. this passage from Keynes quoted by Cartwright:
At any rate, Prof. Tinbergen agrees that the main purpose of his method is to discover, in cases where the economist has correctly analyzed beforehand the qualitative character of the causal relations, with what strength each of them operates….If we already know what the causes are, then (provided all the other conditions given below are satisfied) Prof. Tinbergen, given the statistical facts, claims to be able to attribute to the causes their proper quantitative importance….Am I right in thinking that the method of multiple correlation analysis essentially depends on the economist having furnished, not merely a list of the significant causes, which is correct as far as it goes, but a complete list? [Keynes, cited on p. 15 and 87]
The second half of the present work is devoted to Cartwright’s theory of natural capacities. To start with, she explains why capacities matter to her account of causation:
There are undoubtedly more complicated alternatives one can try. The point is that one needs an account of causal laws that simultaneously provides for a natural connection between the law and the individual case that it is supposed to cover, and also brings order into the methodology that we use to discover the laws. The account in terms of capacities does just that, and it does so by jettisoning regularities. The regularities are in no way ontologically fundamental. They are the consequence of the operation of capacities, and can be turned, when the circumstances are fortuitous, into a powerful epistemological tool. [pp. 139-140]
Another anti-Humean point [p. 128]: to determine what the right equations are with which to model the system depends on a knowledge of its capacities (in this case, where correct coarse-graining of the time series is needed to bring out the effect).
The claim I am going to develop in this chapter is that the concept of general sui generis causal truths—general causal truths not reducible to associations—separates naturally into two distinct concepts, one at a far higher level of generality than the other: at the lower we have the concept of a causal law; at the higher, the concept of capacity. I speak of levels of generality, but it would be more accurate to speak of levels of modality, and for all the conventional reasons: the claims at both levels are supposed to be universal in space and through time, they support counterfactuals, license inferences, and so forth. The level of capacities is ‘higher’ not only because the generalizations involved are broader in scope but also because the inferences that they allow are far stronger and, correlatively, the amount of metaphysics assumed in their use is far greater. [p. 142]
In an aside, she notes that the concept of laws of nature should be objectionable to a radical empiricist, for:
Capacities are peculiar, from a radical empiricist point of view, in exactly the same way as laws, only one level up. Just as laws constrain relations between matters of fact, capacities constrain relations among laws. [p. 146]
Strength that flows from this:
If you are committed to the assumption that all the internal properties of electrons are essential, this makes science a lot easier for you. You can measure the charge or mass on one, and you know it on all the others. [p. 146]
Something similar holds with the universal quantifier in her Principle CC:
That means that, where capacities are at work, one can reason as above: one can infer from one causal law directly to another, without ever having to do more tests. [p. 146]
By the end of the present work, Cartwright is headed towards a radical proposal to eliminate laws leaving only capacities (to be developed fully in her late work, The Dappled World: A Study of the Boundaries of Science, Cambridge University Press, 1999):
Return for a moment to my conclusions about causality. In the end I present a structure with three tiers. At the bottom we have individual singular causings. At the top we have general causal claims, which I render as statements associating capacities with properties….In between stands the phenomenal content of the capacity claim—a vast matrix of detailed, complicated, causal laws. These causal laws, which stand at level two, provide no new obstacles for the Humean beyond those that already appear at the bottom level. For these are just laws, universal or probabilistic, about what singular causings occur in what circumstances what percentage of the time….Yet there is a good reason for the Humean to be wary, at least the modern-day Humean who believes in laws but not in causes. For if the program of section 4.6 succeeds, this treasured layer of laws will be eliminated altogether from our fundamental scientific picture. All that remains would be capacities and the causing for which they are responsible. The laws—even causal laws—would no longer play any basic role; and the pretence that nature is full of regularities could be dropped….For I hope it becomes clear that what are taken as the fundamental laws of, say, physics are not laws at all in the empiricist’s sense, but abstractions. [pp. 228-229]
The argumentative flow is somewhat piecemeal, not a fully rounded theoretical account like one would get from John Maynard Keynes (see our review of the latter’s A Treatise on Probability (Cambridge University Press, 1920), here). In general, Cartwright’s discussions can get somewhat technical and presuppose knowledge of the literature; i.e., she does not develop the theory from scratch. Rather than undertake a systematic exposition, she prefers to stake out her own positions in stages through close commentary on the work of others.
The reader may well wonder, how solid is Cartwright’s evaluation of path analysis here? For the sake of comparison, one will want to consult Judea Pearl’s (roughly contemporaneous) monograph Causality: Models, Reasoning and Inference (Cambridge University Press, 2009, second edition, 2013). Here, one will find a systematic presentation of the highly developed path analysis technique of probabilistic inference to causation which is subjected to repeated criticism in the present book. The substance of what Cartwright has to say comes down, not to a claim that statistical inference cannot work (she acknowledges that, in the right hands, it often does in practice), but to the contention that its theoretical presuppositions remain somewhat obscure and one can contrive cases where they could be expected to fail.
What about the objection that her capacities are tantamount to the much-derided scholastic occult qualities? Fundamentally, they are the same thing, but hers lend themselves better to mathematization, whether in models of physics or of economics.
A potentially more instructive tack to pursue would be to inquire about the epistemic role her natural capacities have to play in relation to theory construction. Cartwright’s capacities function in a manner akin to Kant’s schemata which connect the categories of pure reason to anticipations of experience in time and space; for capacities allow us to go from general laws to a model of the mechanism for a given experimental situation. For instance, if we posit that electric charges (have the capacity to) exert forces on one another as described by Coulomb’s law, we know that we have to solve Poisson’s equation for the potential in the given geometry.
How to differentiate capacities from physical principles? Perhaps as follows: principles are yet one level up from capacities. The analysis discloses first the pertinent capacities of the entities participating in a given experimental set-up, then comparing across many arrangements one may arrive at general principles governing them all. But the distinction so sketched does not seem to be hard and fast.
The salient point is just that, contra Russell, we do not get the supposed laws of nature in a vacuum or handed down to us from on high, from which we may then proceed to a differential equation to solve without the intermediary of any background knowledge as to what kinds of models are likely to be applicable. Cartwright’s natural capacities are intuitive guides to the formulation of specific models that have a fair chance of being correct. They describe how actual practicing scientists reason—one does not just try out candidate equations of motion at random, guessing in the dark, but adheres to general rules of theory construction. For instance, the Lagrangian should ordinarily be a difference between a kinetic term and a potential term. The kinetic term is often a quadratic form in the velocities of the bodies in motion, while the potential may involve combinations of known force laws or may be constrained by reason of symmetry to be parametrized in a certain way etc.
Four stars: the blurbs on the back cover overstate the importance of this work, although it is indeed very provocative for the serious philosopher of science to ponder. In our judgment, Cartwright’s analysis itself in the present book isn’t as refined as it gets to be in her last work, entitled The Dappled World: A Study of the Boundaries of Science (1999), which we are about to review in a moment (see our forthcoming review here).
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