The Facticity of Laws of Physics

Banin D. Sukmono

Director and Head of Metaphysics and Science
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A review of Nancy Cartwright’s How the Laws of Physics Lie (1983)

Laws of physics are typically assumed to be true and describe facts of reality. Moreover, it is usually assumed that a nomological generic-specific relation holds between a more fundamental law of physics, such as Maxwell’s equation and Schrödinger equation, and a more specific law of physics, such as Airy’s law. The relationship implies that the truth of a more specific law is contained in the more fundamental law. If a law of physics is categorized as fundamental, not only is the law deemed true and describing what is happening in the real world, but also it is deemed the source of other laws and theories. Those two tenets, following Cartwright, can be called the facticity view of laws and deductive-nomological model of explanations, respectively, and it appears to be a common understanding of nature thought by both positivist and some realist philosophers and physicists.

However, in How the Laws of Physics Lie (1983), Cartwright tried to combat these faiths. Cartwright argued that while some laws of physics, namely phenomenological laws, may describe reality, it is not the case for the fundamental laws. There is a trade-off between truth and explanatory power that makes the fundamental laws not be able to describe reality. Furthermore, Cartwright also stated that the relationships between fundamental and phenomenological laws, which are often considered more specific, are not linear and straightforward. By relying on what happens in the current venerated scientific practices, the deduction of phenomenological laws from fundamental laws is hard to accept. This picture clearly must not delight positivists and some version of realists since although they disagree about the status of some theoretical entities, they often share a view about the well-arranged nature, that nomological orderliness is derived from tidy nature. Cartwright suggested, nevertheless, that it is probably only their image of nature. Scientific practices seem to imply the inverse view.

To begin with, it is a good idea to differentiate between phenomenological and fundamental laws. This distinction is not a distinction between observable and unobservable entities as what realists and anti-realists usually argue for and against. The use of instruments is not the main case because a law can still be phenomenological despite positing electron or superconductivity. By contrast, this distinction is between description and explanation and between directly observed phenomena and indirect inference. A law that focuses on describing the empirical relationship of phenomena without wishing to derive it from or integrate it to other more allegedly fundamental laws or background theories can be categorized as phenomenological laws. On the other hand, a law that mostly functions as a derivation source, and its significance lies in explaining and covering different types of situations and the relationship in the background theory, can be categorized as fundamental laws. Although degree admittedly matters here since a single law that only fulfills one role is doubted, this distinction is not hard to obtain in practice. For example, Cartwright takes Airy’s law of magneto-optical effect as an example of phenomenological law while employment of electron theory by Lorentz as fundamental treatment. The example is taken not because “Lorentz employs the unobservable electron, but rather because the electron theory explains the magneto-optical effect and Airy does not (Cartwright, 1983, p. 2).” Against the definition above, it is not surprising if phenomenological laws are frequently considered inferior to fundamental laws because not only do they intend merely to describe, but the range also not as extensive as fundamental laws.

 However, it is precisely the core of the problem. Cartwright sees that the conclusion regarding fundamental laws drawn by the advocates of facticity view of physicsand deductive-nomological model, or as Cartwright a decade later (1999) called fundamentalists, is unsupported. While fundamentalists believe that explanation is parallel with truth, that the more explanatory a law is, the closer it is from the truth, Cartwright sees that the case should be the inverse, that it should retract the law farther from the truth. The reason is that for a law to be true, it should only limit its range in one component, while to be explanatory, it must expand it to another. Fundamentalists cannot see the problem because Cartwright suspects that they rely on a world view of composition, i.e., “the explanatory laws ‘act’ in combination just as they would ‘act’ separately (Cartwright, 1983, p. 59),” even though resultant in interaction is hardly couched in terms of components. Cartwright exemplified the interaction between Newton’s law of gravity and Coulomb’s law of electrostatics and interaction in the Soret effect as an example. The resultant of the first case laws are neither Newton’s nor Coulomb’s laws, so too with the second case. Linear addition of Fourier’s law, Newton’s law, and Ohm’s law to complement Fick’s law cannot determine the evolution of the process of diffusion and mixture in transport theory of statistical mechanics. Another apposite example maybe is the role of Coulomb’s law in the ground state of a carbon atom that is hardly responsible for the emergence of the five energy level because of spin-orbit coupling. Those examples showed one takeaway, “we have little theory about what happens in the intersection of domains (Cartwright, 1983, p. 50).”

A possible path that fundamentalists can take is thus to show that problem of errors does not genuinely affect the argument of fundamentalists because it is only the problem of mathematics. If somehow all troublesome but intangible factors can be listed, principally, the cover laws or merely additions (net) are possible. Therefore, passing the challenge to the future possibility of theory progress is frequently taken by most fundamentalists. Nonetheless, for Cartwright, in the context of scientific practice, this reply is flawed, at least in two ways. Firstly, this answer assumes that deduction is nomologically unruffled, and generic-specific reasoning works. Conversely, a strict nomological deduction in physics is limited. Deduction processes in physics are full of emendation and approximation, in which ideal to non-ideal (ab vero) correction is rare. What happens is the non-ideal situation with ad hoc treatment corrects the ideal one (ad verum). In her examination with Jon Nordby, chapter 6, Cartwright challenges the assumption that approximation is ab vero, and, therefore, buttressing deduction. They gave three examples, in T and Hybrid model amplifier, exponential decay, and lamb shift, and in all of those examples, phenomenological treatments and approximations are far more accurate, i.e., fundamental laws are false, and even, as in exponential decay and lamb shift, rigorous derivations are hard to find.  Consequently, as argued by Cartwright, there is a trade-off between explanation and truth. Even though the correction is made from the start by calculating what happens in composition in the non-standard pattern, it will be convoluted and not handy to be counted as a law. But, if it is specific and straightforward, it cannot be used in other domains. Rarely is then the content of phenomenological laws contained in fundamental laws.

Secondly, that reply also assumed cateris paribus laws as elliptical and heuristically can assist science in finding the super covering laws. This is problematic in the sense that this reasoning is mostly based on an unfounded metaphysical assumption instead of reasoning based on scientific consequences, that the world is well-regulated. In fact, it is also probable to think the inverse. Indeed, these (covering) laws and types of explanation cannot be verified or stipulated. For example, this understanding of cateris paribus will be in difficulty to state how weak or complicated, and even how probable, the gap should be determined from the existing theories to the real laws. It is not surprising, according to Cartwright, because, in principle, fundamental laws do not govern laws in reality. They only govern reality in models. The bridge principles are often thought to save this account. However, besides bridge principles are designed rare for not limiting the explanatory power of the fundamental laws, given that there is a process of preparing description and mathematical boundary in the second stage of theory-entry, fitting fact into equation requires a highly idealized fictional object and process that are dictated (distorted) by theories, e.g., box normalization in quantum mechanics. Consequently, for Cartwright, prepared descriptions also do not describe facts. In real practice, a phenomenon is fitted to theories and objects, and not vice versa. Nevertheless, it is necessary for fundamental laws since its aim is not truth but an explanation. Therefore, “we will have to distort the true picture of what happens if we want to fit it into the highly constrained structures of our mathematical theories (Cartwright, 1983, p. 139).”

Cartwright’s account of the relationship between theory and truth is primarily inspired by Bas van Fraassen’s and Pierre Duhem’s criticism of inference to the best explanation. This type of inference is composed of a structure, ‘P explains Q. Q is true. Therefore, P is true.’ For them, this inference is ampliative since the truth of P is not necessarily a consequence of Q is true. Moreover, Q can be explained by other equal systems of explanation. For example, in the laser theory, there are six different equal models and three different equations for one phenomenon that serve different purposes of explanation. This leads to a conclusion that 1) truth is external from explanations, and 2) theoretical explanations are redundant. However, different from Van Frassen and Duhem, Cartwright viewed causal explanation and the entity that holds the causal role as not redundant. By contrast, it is essential to make up a body of explanation and a well-designed experiment. Recalling the laser theory examples, despite having six different models, all refer to only one causal story with real entities that responsible for it: quantum damping due to the emission and absorption of photons. The existence cannot be dispensed with easily. Assume an inference saying that positrons or electrons on the ball caused a change in rate in the fall of a light droplet in an electric field. It suggests that inference from effect to cause matters, and ” the explanation has no sense at all without the direct implication that there are electrons or positrons on the ball (Cartwright, 1983, p. 92).”

Together with the causal reasoning, Cartwright’s account that is founded on the scientific practice accounts for an alternative model of explanation called the simulacrum account of explanation. This account argues that fundamental laws are fiction and only explain objects in models. There is no single model claimed as the only right one, as well as theories, and therefore the more model and theories science has, the merrier (more comprehensive) analyses science can make. However, despite fictitious and not really working in terms of facticity or description of reality, the convenient nature of fundamental laws is productive in organization, unification, and classification works of natural kinds. This is the reason fundamental laws are still held and pursued in scientific works. The equations in cateris paribus situation can be deemed as expressions towards explanatory commitments to back up the predictive and explanatory roles of fundamental laws. Contrary to facticity view, thus, Cartwright stated, fundamental laws of physics “govern has only the appearance of reality” (Cartwright, 1983, p. 162), and not the complex reality itself. Nevertheless, it does not mean that the whole scientific enterprise is fictitious. For the simulacrum account of explanation, the true content of science lies in the phenomenological laws of physics that posit the real properties of entities from low-level causal principles. This incompatible relationship between ad hoc but accurate phenomenological laws and idealized but fictitious fundamental laws makes no real and strict deduction possible.

How Cartwright approaches the problem of laws by focusing on the real practice of science attracts various responses. One that gives an appreciative gesture, despite some doubts, is Gibbins (1984). In his response, he wrote:

Professor Cartwright’s achievement is not that what she says on each or any issue is correct, but rather that her work will define the field for the next few years. And one cannot ask for more than that from any philosopher. One finds in her book a much-needed shift away from the abstract view of physics one finds in so much of the recent philosophical literature, and towards the nuts and bolts of real-live physics (Gibbins, 1984, p. 401).

Gibbins saw that Cartwright’s approach in prioritizing what is happening in real life science could shed light on the relationship between science, especially physics, with philosophy, which often, at that time, abounds with semantics.

Of course, this appreciative gesture means nothing for the advocates of deductive-nomological models, whether positivists or realists. Of many criticisms, commentary from Allport (1993), Kline and Matheson (1986), Laymon (1989), and Kamminga and Tavakol (1993) are some of the most influential. However, most arguments were not worrying and missed Cartwright’s point. Mostly, the criticism relied on either what physicists commonly think or what fundamental laws can do if some improvements take place. For example, Allport pointed out that the term phenomenological laws for physicists are temporary and expected to be replaced by a more comprehensive theory; alternatively, Kline and Matheson, and Kamming and Tavakol, and Laymon showed how some laws are relatively accurate in its definition. These points missed Cartwright’s argument because Cartwright’s problem is not what happens in the model or a bit distorted model, which is rare. Conversely, how the models are applied in real-life physical problems, i.e., reality. In that case, most fundamental laws’s power are limited, but not phenomenological laws with their ad hoc treatment. These criticisms also actually presuppose Cartwright’s account that fundamental laws aim to organize and predict, and multiple models and theories complement each other. Therefore, it is not a problem if the fundamental laws can provide different insights. 

Probably, criticism that can adequately address Cartwright’s account comes from human capability in devising a new practice in science and the problem of interpreting scientific practices. Scientific practice is the foundation of Cartwright in establishing her system, and therefore, as Ian Hacking (1983) proposal of experimentation, it is vulnerable to changes in human understanding of scientific practice itself. Kline and Matheson showed that potential by saying that the history of scientific practice despite not thoroughly victorious has shown that some laws of interactions are possible, such as the interaction between electricity and magnetism. Although Cartwright argued that the paucity of the laws is prominent, it is not a knock-down argument for the possibility of coincidence covering law. Another problem that may disturb the Cartwright project is different possible practices, especially practice that hardly uses experiments in a strict sense. That is what Gähde (2008) tried to show with his structuralist interpretation of Haley’s comet discovery. Again, similar to the previous objection, Cartwright’s reply to the interpretation of practice is admittedly not a knock-down argument, despite maybe the most probable. The question about how to interpret the practice of finding the laws of physics itself with practical vocabularies may be the field for objecting to Cartwright’s account.

Apart from the criticism, this exposition could not agree more with what Gibbins stated that a practical approach to the philosophy of science is not only functional but also necessary, as necessary as its semantic approach. Philosophers should know what is happening in science and how scientists measure their objects and properties. Only by this, philosophy can be meaningful to scientific development. Cartwright is a strong proponent that science can fulfill the role. She proved it by giving another insight into the problem in physics, as she demonstrates with the problem of measurement in quantum mechanics (chapter 8).  However, this turn necessitates the philosophers of sciences to broaden their expertise to real measurement and statistics that happen in science, from calculus to real mathematical physics. Granted, it would ameliorate the philosophy position before science.


Allport, P. P. (1993). Are the laws of physics ‘economical with the truth’? Synthese, 94(2), 245–290.

Cartwright, N. (1983). How the laws of physics lie. Oxford University Press.

Cartwright, N. (1999). The dappled world: A study of the boundaries of science. Cambridge University Press.

Gähde, U. (2008). Nancy Cartwright on Theories, Models, and their Application to Reality: A Case Study. In Nancy Cartwright’s philosophy of science (pp. 41–64).

Gibbins, P. (1984). Nancy Cartwright’s new philosophy of physics. The British Journal for the Philosophy of Science, 35(4), 390–401.

Hacking, I. (1983). Representing and intervening: Introductory topics in the philosophy of natural science. Cambridge university press.

Kamminga, H., & Tavakol, R. K. (1993). How untidy is God’s mind? A note on the dynamical implications of Nancy Cartwright’s metaphysics. The British Journal for the Philosophy of Science, 44(3), 549–553.

Kline, A. D., & Matheson, C. A. (1986). How the laws of physics don’t even fib. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 33–41.

Laymon, R. (1989). Cartwright and the lying laws of physics. The Journal of Philosophy, 86(7), 353–372.