New Directions in Law-Based Explanations in the Sciences

Abstract

Complex socio-technical systems are heterogeneous so they cannot be modelled by a single approach (Simon 1962). From a socio-technical systems modelling perspective what is required is a commitment to the possibility that a given model and its relationships with other models can be fictional (Frigg 2010) and that models are effective decision making aids (Eckert and Hillerbrand 2022). The property of potentially being part of multiple subsystems makes complex systems inherently difficult to model with model analysis being affected by decisions about the allocation of parts to models. Epistemologically adequate modelling accounts need to offer a way of addressing such divergences and potentially incommensurability. One approach to modelling this complexity is applied category theory whose basic concept is that many formally describable structures can be described as maps (Mac Lane 1998).

The particular case of complex socio-technical system processes is considered with central concepts including flows, bottlenecks, margins, probability, change propagation and resilience. These concepts can be thought of as frames for concepts rather than concepts in themselves. There is scope for such concepts to have lawlike generalisations which take the form of parameters governing conceptual frames and which are instantiated in particular ways for particular versions of these concepts. In that sense concepts such as flows are candidate lawlike generalisations which are context dependent. Category theory is well suited to representing laws in a given explanation because it is about structural description which is a way of thinking about framing.

References

Addis, M. and Eckert, C. (2026). Explanatory frameworks in complex change and resilience system modelling. Special Issue on Formal Representations in Model-Based Reasoning and Abduction. Logic Journal of the IGPL, 34 (2). https://doi.org/10.1093/jigpal/jzae087.6.

Eckert, C., and Hillerbrand, R. (2022). Models in engineering design as decision-making aids. Engineering Studies, 14 (2), 134-157.

Frigg, R. (2010). Models and fiction. Synthese 172 (2), 251-268.

Mac Lane, S. (1998). Categories for the Working Mathematician. 2nd ed. Springer.

Simon, H.A., (1962). The architecture of complexity. Proceedings of the American Philosophical Society, 106 (6), 467-482.

Abstract

This communication investigates the epistemology of ceteris paribus (CP) laws in experimental and behavioral economics through the example of “social preference” models. We ask two separate questions. First, to what extent is it correct to claim that behavioral models like social preferences express CP laws ? Second, according to which criteria do economists settle a preference between alternative CP laws ?

Social preference models account for the sensitivity of economic agents to the payoff of other individuals. For instance, the inequality aversion model of Fehr and Schmidt (1999) assumes that individuals not only try to increase their own monetary gain but also to reduce the difference between them and others.

At first glance, social preference models seem to possess the formal features commonly attributed to CP laws. Taken literally, these models are lawful in the minimal sense of making counter-factually robust predictions about individuals behavior. The Fehr and Schmidt model, for instance, predicts that an inequality averse individual always accepts to reduce his own payoff by 1 $ if it raises the other payoff by at least (1 - β) / β $ (where β is a structural, free parameter of the model). The lawfulness of the model clearly lies in the parameter “β”, which predict how an individual behavior change under varying budget constraints. On the other hand, social preferences are highly unstable because of their sensitivity to contextual variations : an econometric estimation of β in an experimental setting E1 will not necessarily be valid in another setting E2. This instability motivates the claim that social preferences models express CP laws, whose validity is limited by an implicit and largely unknown CP clause. However, we argue that actual research practices of economists are not always compatible with this reading of their models. The main problem is that structural parameters like β actually do not perfectly fit observed individual decisions, even in the same experimental setting. Strikingly, the experimental estimation of β is more often used as a qualitative tool for classifying individuals into different behavioral “profiles” (“selfish” when β =0, “inequality averse” when 0 < β < 0.5, etc.).

Regarding the second question, we claim that experimental economists face two opposite theoretical strategies to elaborate new social preference models. One strategy consists in eliminating law exceptions by generalizing their models. This requires to integrate the disturbing factors that are part of the CP clause as new functional variables of the model. The other strategy is to independently account for the exceptions that are included in the CP clause. We contend that economists choose between these strategies according to a mixture of epistemic and cognitive criteria. Epistemic criteria relate to the trade-off between the theoretical virtues of empirical accuracy and simplicity. Including new variables in a model makes it more accurate but also more complex, with a higher number of free parameters. Cognitive criteria refer to the intellectual burden placed on individual researchers. Accounting for the exceptions to a CP laws frequently require to study factors that traditionally belongs to other disciplines than economics.

Abstract

The idea that causes can be complete plays an important role in many debates, including those concerning the causal exclusion problem (Kim 2005; Gibb et al. 2013). Consider, for example, the following, simplified, causal exclusion argument.

1. 1. Every physical effect has a complete physical cause (simple closure).
2. 2. There is no overdetermination of physical effects (simple exclusion).
3. 3. Thus, there are no non-physical causes of physical effects.
4. 4. Thus, interactionist dualism is false.

Arguments of this type essentially involve the notion of a complete cause, but there is significant dispute in the exclusion literature about how best to understand what being a complete cause amounts to (Kim 2007; Loewer 2007; Hitchcock 2012; Won 2014; Gibb 2015; Vaassen 2021). A standard move is to hold that a cause is complete if it is sufficient for the relevant effect. However, this standard move is subject to well-known objections, including that it entails the implausible outcome that a complete cause must encompass the entire cross section of the backwards lightcone of the relevant effect (Vaassen 2021: 10343-10344).

I argue that such objections can be responded to successfully by appeal to a version of the causes/background conditions distinction which invokes Maudlin’s notion of a quasi-Newtonian law: i.e. a law which involves a distinction between inertial versus deviant from the inertial behaviour (Maudlin 2007: 155-156). In sum, the proposal is that a complete cause can be understood as that which is, according to our best theory, a non-inertial cause of the effect, whilst also being a proper subset of a minimally sufficient condition of that effect. I discuss the potential benefits of understanding complete causes in this way, especially for those interested in evaluating the soundness of causal exclusion arguments.

References

Gibb, S. C. 2015. ‘The Causal Closure Principle’. The Philosophical Quarterly 65 (261): 626–47. https://doi.org/10.1093/pq/pqv030.

Gibb, S. C., Edward Jonathan Lowe, and Rögnvaldur D. Ingthorsson. 2013. Mental Causation and Ontology. Oxford university press.

Hitchcock, Christopher. 2012. ‘Theories of Causation and the Causal Exclusion Argument’. Journal of Consciousness Studies 19 (5–6): 40–56.

Kim, Jaegwon. 2005. Physicalism, or Something Near Enough. Princeton University Press. https://doi.org/10.1515/9781400840847.

Kim, Jaegwon. 2007. ‘Causation and Mental Causation’. In Contemporary Debates in Philosophy of Mind, edited by Brian P. McLaughlin and Jonathan Cohen. Wiley-Blackwell.

Loewer, Barry M. 2007. ‘Mental Causation, or Something near Enough’. In Contemporary Debates in Philosophy of Mind, edited by Brian P. McLaughlin and Jonathan Cohen. Wiley-Blackwell.

Maudlin, Tim. 2007. The Metaphysics Within Physics. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199218219.001.0001.

Vaassen, Bram. 2021. ‘Causal Exclusion without Causal Sufficiency’. Synthese 198 (11): 10341–53. https://doi.org/10.1007/s11229-020-02723-y.

Won, Chiwook. 2014. ‘Overdetermination, Counterfactuals, and Mental Causation’. Philosophical Review 123 (2): 205–29.

Abstract

Most current explanations in cell biology, as I have argued elsewhere, are mechanistic and could be augmented by the addition of cell-biology-relevant lawlike generalisations (‘laws’ for short). But very few, if any, laws have been established in cell biology, and the question remains how a putative law could be ‘modelled’ when it is first hypothesised. When we consider the development of cell biology since the 1950s, large molecules (i.e. mechanistic parts) were modelled using physical artefacts and later (or concomitantly) using computational simulations. But entire cellular mechanisms (consisting of many parts with interactions and organisations and so on) are often too complex to be amenable to artefactual modelling, and the usual means of modelling them in the field is through repeated revisions of mental maps and different diagrammatic representations. In this talk I will argue for a three-component approach to modelling laws: (i) that a putative cell-biological law can, if scientifically feasible, be examined using artefactual models, among other means; (ii) that such modelling could roughly be thought of as characterising the possible basis of the law or characterising its consequences (with potential overlap); and (iii) that a Giambattista Vico-inspired ‘factum’—‘certum’—‘verum’ framework could be used to assess the modelling progress of different putative laws relative to each other. The three criteria within this framework concern the informal/formal formulation of the law (factum), the empirical evidence supporting the generalisation (certum), and the type of regularities the law could capture or explain (verum). Finally, the principle of cellular synchrony will be used as a test case to illustrate the different stages and potential challenges of this modelling approach.

Abstract

Aging generates remarkably universal patterns across species, yet the mechanistic origin of this universality remains obscure. Here we show that aging dynamics in complex organisms under very general assumptions reduce to three emergent macroscopic variables: a slow resilience mode, a cumulative damage variable, and physiological noise. This minimal model reproduces core features of aging across species, including the exponential rise in mortality, increasing variability and slower recovery with age, late-life mortality plateaus in short-lived organisms, and a species-specific lifespan limit. The framework unifies molecular, physiological, and demographic observations within a single quantitative theory and predicts that interventions effective in short-lived organisms may have only transient effects in long-lived species such as humans. It further yields a taxonomy of intervention strategies that distinguishes disease-specific therapies from approaches capable of shifting intrinsic lifespan limits.

Abstract

A familiar line of argument in philosophy of biology holds that biological generalizations cannot be explanatory laws because they are highly evolutionarily contingent. A common response grants the contingency but argues that contingent generalizations can nevertheless explain, provided they are sufficiently stable within their domains of application. This paper explores a different possibility: that some biological generalizations, including some that range across widely separated taxa, are not highly contingent after all. I develop this possibility through the case of pregnancy, asking whether there are laws—or at least lawlike generalizations—concerning pregnancy across animals. I consider evidence that these regularities are robust across alternative evolutionary histories, offer an explanation of that robustness in terms of recurrent demands imposed by internal gestation, and briefly consider what this implies for the explanatory role of laws in biology.

Abstract

This paper argues that mechanistic explanation, contrary to a widely accepted view, is fundamentally lawbased. Since the critique of Hempel’s covering-law model—most notably by Salmon—philosophers have tended to reject the explanatory role of laws and instead emphasize causal and constitutive relations within mechanisms. In contemporary accounts, explanatory relevance is often taken to reside in the identification of entities and activities organized to produce a phenomenon.

I argue that this shift overlooks a crucial dimension of mechanistic explanation. Scientific explanations aim not only to identify what produces a phenomenon, but also to answer how it occurs, when and where it takes place, how frequently, and at what rate. These questions concern the spatiotemporal organization of mechanisms, which is essential for explanatory understanding and is shaped by pragmatic constraints on modeling and representation.

Once such organizational demands are taken seriously, mechanistic explanation cannot be grounded in constitutive relevance alone. In many cases, especially when dealing with lower-level or non-manipulable subsystems, direct intervention is not feasible. As a result, the construction of the explanans necessarily relies on theoretical laws and generalizations that capture invariant relations governing the behavior of the system. This is evident in scientific practice: enzyme kinetics in molecular biology are modeled through Michaelis–Menten equations, while neural activity is explained using Hodgkin–Huxley equations and underlying physico-chemical laws of ion dynamics.

I therefore propose that mechanistic and law-based explanations are not competing alternatives but complementary aspects of a unified explanatory framework. Laws play an indispensable role in representing the spatiotemporal organization of mechanisms, particularly in contexts where direct causal manipulation is limited or impossible. Mechanistic explanation, properly understood, should thus be seen as a law-based practice embedded within a broader pragmatic–ontic framework.

Abstract

The mechanistic approach to scientific explanation rejects the idea that phenomena are explained primarily by subsuming them under general laws. Instead, explanation proceeds by analyzing the mechanisms that underlie, realize, or constitute phenomena across multiple levels of organization (cf. Bechtel and Richardson, 1993; Glennan, 1996; Machamer, Darden, and Craver, 2000; Bechtel and Abrahamsen, 2005; Craver, 2007b; Craver and Tabery, 2017). Typically, a phenomenon is first identified and described as an input–output relation. Researchers then decompose it into the entities and activities that produce it at a given level, specifying their behaviors and interactions. These components often become explananda themselves, resulting in multi-level models, where causal and constitutive relations are systematically distinguished.

Building on this framework, a growing philosophical literature has addressed a wide range of issues concerning mechanistic explanation. These include debates over how mechanistic constitution should be defined (Craver, 2007c; Harbecke, 2010; Couch, 2011), whether mechanistic explanations are exclusive or dominant in certain scientific domains (Huneman, 2010; Chirimuuta, 2014), and how constitutive inferences should be regulated (Harbecke, 2015; Gebharter, 2017; Baumgartner and Gebharter, 2016; Baumgartner and Casini, 2017; Baumgartner, Casini, and Krickel, 2018; Craver, 2007c, 2007a; Krickel, 2018). Together, these discussions reflect increasing interest in the epistemic and metaphysical status of constitutive relations within mechanistic models.

This paper contributes to this debate by focusing on the status of constitutive mechanistic propositions. It pursues two closely related questions. First, it investigates whether such propositions exhibit epistemic lawlikeness, that is, whether they function like lawlike connections between variables rather than merely expressing logical or linguistic relations. Second, it examines whether mechanistic constitution can, from a metaphysical perspective, qualify as a natural law.

More specifically, the paper advances two hypotheses. Hypothesis (A) states that, at least in certain well-developed examples from contemporary cognitive science, constitutive mechanistic statements satisfy standard criteria of lawlikeness. Hypothesis (B) claims that, in at least some cases, mechanistic constitution also meets the metaphysical requirements for being a natural law. To support (A), the paper analyzes representative cases from cognitive science in light of prominent theories of mechanistic constitution and widely accepted criteria of lawlikeness. To support (B), it draws on recent accounts of laws of nature, in particular the Better Best System (BBS) approach developed by Loewer (1996, 2007), Cohen and Callender (2009), Albert (2001, 2012), and Frisch (2011). The BBS framework characterizes laws as principles that optimally balance simplicity, informativeness, and empirical fit, even if they are not strictly microphysical.

The talk is planned to proceed as follows. The first part reconstructs three research projects from neuroscience that exemplify the discovery and modeling of constitutive relations in the brain. The second part presents standard criteria for lawlikeness. Thirdly, the talk reviews leading accounts of mechanistic constitution and evaluates them with respect to both scientific practice and lawlikeness. It then argued that, given these results, constitutive mechanistic propositions can enter the BBS in some cases. In the end, a summary of the main findings is offered as well as a selection of open questions for future research.

Abstract

Chemical structure, the arrangement of atoms in three-dimensional space, is a key notion in chemistry and related sciences. Many chemists work to identify the structures of materials, to investigate the relationship between structure and properties or to find ways to make chemicals with particular structures. Chemical structure plays a significant role in explaining and predicting the properties of matter, as well as in understanding chemical synthesis and reaction mechanisms.

One way scientists study chemical structures is by ab initio structure modelling. This method works by starting from known laws of physics, in this case quantum mechanics, and computing the interactions between the different constituents of a given chemical. The modelling results are then compared to experimental findings.

This paper argues that (successful) ab initio modelling provides us with law-based explanations of chemical structures, but with some caveats. To support this claim I start by showing how the Deductive-Nomological (DN) model can be used to construct explanations for some simple chemical structures.

I then consider some challenges for this approach. The first is that it is virtually impossible, for computational and other reasons, to model even moderately complex molecules in full detail. I argue that this difficulty forces scientists to make pragmatic choices that trade off, e.g., accuracy versus speed. And ultimately, the right approach depends on the aims of particular scientists.

The second group of challenges arises for more complex cases, such as giving differential explanations for allotropes or isomers. E.g., why is this diamond and not graphite? In these cases it is not enough to show that a particular structure model is compatible with known laws, as there are often multiple physically possible configurations for a given set of atoms. That means we need additional premises that constrain the explanantia sufficiently to result exclusively in the structure we wish to explain. And in some cases we may need to include pragmatic considerations, e.g., of the intentions of people, for example by using contrast classes.

Abstract

While the mathematical relationship between symmetries and conservations laws is relatively clear, the direction of explanation, if any, is not. This talk argues that we should approach these questions from an epistemic rather than ontic notion of explanation and shows what an answer on an epistemic view might look like.

Abstract

What makes laws usable in scientific explanation? I argue that even the application of exceptionless fundamental physical laws depends on an assumption usually associated only with ceteris paribus generalizations: an assumption of typicality about the state of the world. This reveals a pragmatic dimension of law-based explanation that is often overlooked in discussions of fundamental physics. Laws do not explain on their own; they do so only against a background of typicality assumptions. Importantly, the argument does not depend on rejecting reductionism.

Special science laws are often taken to hold only ceteris paribus: their application presupposes that certain background conditions obtain, even though those conditions are not specified by the laws themselves. Fundamental physical laws, by contrast, are typically regarded as exceptionless and universally valid. I argue that this contrast breaks down at the level of explanatory practice.

The reason is that scientific prediction and confirmation proceed on the basis of partial and coarse-grained information. In principle, the behavior of any subsystem follows from the complete microphysical state of the universe together with the dynamical laws. In practice, however, the fundamental laws alone drastically underdetermine what will happen: given only partial evidence, there are infinitely many microphysically possible evolutions consistent with it, including ones that would yield radically unexpected behavior. Nothing in the microscopic laws—whether classical or quantum—forbids, for example, a dropped cup from veering sideways or disintegrating mid-air. The fundamental dynamical laws permit far more than we ever take seriously.

Yet we routinely use these laws to draw stable, reliable conclusions about subsystems. I argue that this is licensed by an implicit assumption: that the actual microstate of the world is typical among those compatible with our evidence—one that gives rise to the expected behavior of subsystems. Without this assumption, partial information would carry no determinate evidential weight.

This assumption, I suggest, is grounded in the probabilistic framework of statistical mechanics, which assigns overwhelmingly low probability to “abnormal” evolutions. The upshot is that both fundamental and special science laws rely, in practice, on typicality assumptions. What underwrites their explanatory power is not just dynamics, but a probabilistic structure that makes the world predictably well-behaved—and thereby makes scientific inquiry possible.

Abstract

This talk argues that the equilibrium concept partakes in a methodology that aims to articulate ceteris paribus claims. As Nancy Cartwright (1995) has notably argued, ceteris paribus clauses help us characterize nomological machines that are productive of laws; bringing equilibrium into the picture also conveniently helps us tie Simon’s notion of near-decomposability in a useful way.

Abstract

The aim of the talk is to sketch an account of explanation in law, and explore what lessons we might draw from it for explanation in the sciences.

Suppose Jones is guilty of murder. What explains this fact? We might think that the answer is straightforward: it is fact that Jones killed with malice aforethought, and it is a legal rule that whoever kills with malice aforethought is guilty of murder. This is an instance of what we might call “law-based legal explanation.” It is an explanation in some sense, yet unsatisfactory in an important respect, due to a difference in how explanation relates to inference in the law and in paradigmatic sciences.

According to a standard story, science deploys inference to the best explanation. Crudely: we start with observed high-level facts E, consider various unobserved (perhaps unobservable) low-level potential explanantia, and infer the truth of the one that explains E best. This is inference to the best explanans of E.

The law, in contrast, deploys inference to the best explanandum. We start with observed low-level facts E: historical facts about what people in certain relevant roles (legislators, judges, government officials) said and wrote and voted on at various points in time. We then consider various unobserved (and indeed unobservable) high-level potential explananda (that Jones is guilty of murder, that Jones is guilty of manslaughter, that Jones is not guilty of a crime, etc), and infer the truth of the one that is best explained by E.

The account given in in the last paragraph is drawing on standard theories about what determines legal facts (Dworkin, 1986; Greenberg, 2014; Hart, 1997), and a recent argument in Greenberg, 2025: that the epistemology of legal facts tracks their metaphysics, and that we can (as a community) only come to know them by inferring them from more the basic facts that determine them. I have substituted ‘explains’ for ‘determines’, and added an explicitly comparative element.

The notion of explanation is the same in inference to the best explanans (IBEans) and inference to the best explanandum (IBEndum); explanation always goes from the lower-level fact to the higher-level facts. What is different is the direction of inference: in IBEans, we typically start with knowledge of the (relatively) higher-level facts; in IBEndum, with knowledge of the (relatively) lower-level facts.

We do not start with knowledge of laws, whether natural or municipal, low-level or high-level. By dint of their generality, laws are not observable, and do not otherwise enjoy epistemic primacy. This is why explanations appealed to in IBEndum, unlike those in IBEans, cannot be law-based explanations; and this is why the explanation of Jones’ guilt cited above is unsatisfactory.

The second part of the talk shall discuss whether IBEndum is a scientific as well as a legal method. The prime candidates where we might find it are sciences whose facts are constitutively tied to intelligibility or rationality, such as psychology and linguistics on a broadly Davidsonian picture.

Abstract

The topics of laws and law-like principles, on the one hand, and mathematical explanations in science, on the other, have largely developed in parallel, with remarkably little interaction between the two literatures. An exception is the work of Marc Lange, who explicitly connects mathematical explanation with laws and necessity, although his discussion focuses mainly on examples from physics and relatively simple mathematical cases, such as the division of apples. In biology, mathematical explanations have been argued to provide counterfactually robust, unificatory, and non-causal explanations. At the same time, they often appear to share important features with law-based and law-like explanations in this discipline. In this talk, I explore the connections between these two kinds of explanation in biology. I argue, first, that paradigmatic examples of mathematical explanation in biology can be characterized as law-like because they depend on being embedded in scientific theories sustained by law-like principles, such as natural selection. Second, I argue that the mathematical component does not explain a biological outcome by making it more necessary than the relevant biological laws or law-like principles alone could make it. Rather, its explanatory force depends on the explanatory and modal strength of the underlying biological principle. Thus, the strength of mathematical explanations in biology may be no greater than that of the law-like principles on which they depend, raising questions about their purportedly distinctive explanatory status and counterfactual robustness.

Abstract

Nancy Cartwright famously argued that the laws of physics lie; that is, laws hold only in highly idealized systems where certain criteria are met and interfering factors are absent. Laws are always ceteris paribus laws. Her position is thus naturally congenial to the powers-based (or dispositional) account of laws, which takes them to be properties (or to flow from the properties) of things rather than brute regularities (like the Humeans) or primitive governing facts (like the primitivists) or contingent necessitation relations between universals (like Armstrong-Dretske-Tooley).

Conservation laws, however, create a unique problem for dispositionalists: they seem to hold always and everywhere, with no exceptions. That is, because they do not seem to be about any particular thing, no single thing’s nature or properties or powers seems capable of grounding them. Conservation of energy, for instance, does not seem to flow from any particular particle or system, but every particle or system seems subject to it. In attempting to solve this problem for dispositionalists, Kimpton-Nye (2022) has recently proposed what he calls the “Powers-BSA account”, according to which conservation laws are the best systematic description of how all powers are possibly distributed.

In this presentation, we shall argue that while Kimpton-Nye’s account represents a step forward in a dispositionalist accommodation of conservation laws, it wrongly treats conservation laws as a uniform class of global constraints. We propose instead that there is a physically significant distinction that has been overlooked in the philosophy of laws debate.

We know from the work of Emmy Noether that conservation laws are always the product of some mathematical symmetry in a theory. But Noether’s theorem applies to two distinct types of symmetry: 1) conservation laws derived from external spacetime symmetries and 2) conservation laws derived from internal gauge symmetries (independent of spacetime geometry). Conservation laws are not a mysterious rule applied to all objects. They derive from distinct invariances of a system.

As such, the conservation laws most people refer to (that is, conservation of energy and momentum) are not present in systems that lack time-translation invariance or space-translation invariance respectively. Given general relativity, our universe is one such system, since it does not exist in a flat, static spacetime, but rather in a dynamic, curved spacetime, leading to a loss of global conservation of energy and momentum (which can be seen concretely with the phenomena of redshifting).

So, we propose that global conservation laws are a product of spacetime—namely, properties of spacetime configurations that possess the appropriate symmetry structure. And although there still seem to be other conservation laws that hold locally or independently of spacetime geometry (those derived from internal gauge symmetries), these do not determine physical outcomes, only what interactions are possible.

By drawing a distinction between these two kinds of conservation laws, we show that the apparent counterexample to Cartwright’s position dissolves and that, in fact, there is a plausible dispositionalist avenue for understanding conservation laws.

References

Bird, A. (2005). The Dispositionalist Conception of Laws. Foundations of Science, 10(4), pp.353–370. doi:https://doi.org/10.1007/s10699-004-5259-9.

Bird, A. (2009). Nature’s metaphysics : laws and properties. Oxford: Clarendon Press.

Cartwright, N. (1983). How the Laws of Physics Lie. Oxford University Press.

Cartwright, N. (1999). The Dappled World. Cambridge University Press.

Chalmers, A. (1993). So the laws of physics needn’t lie. Australasian Journal of Philosophy, 71(2), pp.196–205. doi:https://doi.org/10.1080/00048409312345202.

Corry, R. (2011). Can Dispositional Essences Ground the Laws of Nature? Australasian Journal of Philosophy, 89(2), pp.263–275. doi:https://doi.org/10.1080/00048401003660325.

De Haro, S. (2021). Noether’s Theorems and Energy in General Relativity. [online] arXiv.org. Available at: https://arxiv.org/abs/2103.17160 [Accessed 31 Mar. 2026].

Einstein, A. (1916). The foundation of the general theory of relativity.. Annalen Phys., 49(7), 769–822.

Hirèche, S. (2021). Varieties of dispositional essentialism about natural laws. European Journal for Philosophy of Science, 11(3). doi:https://doi.org/10.1007/s13194-021-00375-4.

Jaag, S. (2014). Dispositional essentialism and the grounding of natural modality . Philosophers’ Imprint , 14.

Kimpton-Nye, S. (2021). Laws of Nature: Necessary and Contingent. The Philosophical Quarterly, 72(4). doi:https://doi.org/10.1093/pq/pqab062.

Kimpton‐Nye, S. (2022). How to be a powers theorist about functional laws, conservation laws and symmetries. Philosophical Studies, 180(1), pp.317–332. doi:https://doi.org/10.1007/s11098-022-01903-5.

Livanios, V. (2009). Symmetries, dispositions and essences. Philosophical Studies, 148(2), pp.295–305. doi:https://doi.org/10.1007/s11098-008-9328-8.

Maudlin, T. (2007). The Metaphysics Within Physics. Oxford Oxford University Press -04-19.

Noether, E. (1971). "Invariant Variation Problems." Translation by M.A. Tavel, Transport Theory and Statistical Physics, 1(3), 186-207.

Abstract

Physicists have developed a standard dogma that the laws of physics stand in a hierarchy, with ‘meta-laws’ governing symmetry playing a more general and more fundamental than others. Philosophers of physics have demurred, arguing that inter-derivability and multi-realisability flatten or reverse the hierarchy. I defend the standard dogma, in the following sense: certain laws of symmetry (like time translation invariance and gauge invariance) are more general and more fundamental than local dynamical laws like Newton’s laws and the Schrödinger equation. I give a precise argument for this defence, and then reflect on some examples of laws whose position in the hierarchy is not yet clear.

Abstract

Many people explain the lack of strong law-based explanations in psychiatry by pointing to the complexity and diversity of what it studies. While this is partly true, it does not tell the whole story. This paper argues that the challenge of creating laws in psychiatry also comes from the ways evidence is gathered, judged, and combined. It examines how both the evidence hierarchy in evidence-based medicine (EBM) and newer pluralist approaches do not create the practical conditions needed to support stable scientific laws.

The EBM framework, described in key texts (e.g., Guyatt et al., 1992; Sackett et al., 1996), ranks randomized controlled trials (RCTs) and systematic reviews as the best evidence. However, as many have noted (Cartwright, 2007; Deaton & Cartwright, 2018; Worrall, 2007), RCTs mostly show causal effects for specific groups and do not easily support broader claims. Because of this, they are not well suited to back up the kind of stable, universal generalizations that scientific laws require. Instead of helping to find such laws, EBM tends to create a patchwork of evidence based on context-specific patterns.

Evidential pluralism developed in response to these problems, encouraging the use of different types of evidence, such as knowledge about mechanisms (Russo & Williamson, 2007; Williamson, 2019; Shan & Williamson, 2023). While this approach values the role of mechanisms, it brings a new problem: there are no clear rules for combining different kinds of evidence. This diversity, while helpful for understanding, makes it harder to achieve the stability and generality needed for scientific laws.

Based on this analysis, the paper introduces the idea of pragmatic conditions of nomologization, meaning the set of knowledge and method rules that allow a field to support law-like generalizations. Psychiatry does not meet these conditions, not just because its subjects are varied, but also because its methods of gathering evidence—shaped by both EBM and pluralist approaches—favor local results, context-awareness, and diverse evidence over broad, stable laws. In other words, the pragmatic conditions of nomologization that I want to present aim to account for why law-based explanations do not emerge in psychiatry. I argue that current evidence frameworks—both hierarchical and pluralistic—systematically privilege local validity and heterogeneity over the stability necessary for laws. This shift of the debate, from ontology to epistemology and the pragmatics of evidence, aims to shed light on the problem.

This leads to moderate skepticism about psychiatric laws. Strong laws are unlikely, and any possible “laws” should be seen as weak, limited, and dependent on certain conditions. This finding affects how we think about law-based explanations in sciences that lack strong laws and suggests that we should rethink how evidence, explanation, and understanding relate to one another.

Abstract

What counts as a law in medicine? It is generally agreed that we do not have universal and fundamental laws in medicine, but evidence-based medicine (EBM), the prevailing paradigm of modern medicine, treats statistical population-level regularities as the closest substitute for medical laws. These statistical laws have successfully led to a range of reliable diagnostic strategies and treatment regimes. However, I contend that these so-called laws fail when it comes to precision medicine. Drawing on a complex-systems analysis, I show why and how EBM-based generalisations break down at the granularity precision medicine demands. I then suggest that narrative reasoning is the most promising approach to precision medicine and, given EBM's failure at this granularity, a superior replacement for it in this domain. In narrative precision medicine, a tailored and unique narrative is constructed for each medical case, and through it both diagnosis and treatment are tailored to the particular patient. This approach faces an apparent caveat: if every patient requires an individualised narrative, narrative precision medicine seems to be inherently case by case and thus unable to produce a cumulative body of precision medicine knowledge. I resolve this by drawing on the structural parallel between narrative reasoning and simulations of complex systems, and show that each of these yields robust coarse-grained and higher-level patterns despite transience and unpredictability at the fine-grained level. Although each narrative is built for an individual case, a bird's-eye view across many narratives reveals general patterns, discoverable by weak induction. These narrative regularities constitute a distinct, under-recognised class of law-like generalisation that is neither EBM's frequency-based regularities nor physics-style laws, but rather the kind of pragmatic, ceteris-paribus generality characteristic of complex sciences. Although developed for precision medicine, the framework generalises to other complex-systems sciences where strict law-discovery has stalled, and offers a new direction in law-based explanation for sciences that deal with complexity.

Abstract

The relationship in one direction is more interesting than in the other. Using student experimental investigation of stretching springs as an example, I suggest that the relevance of the philosophy of laws to secondary school physics teaching is modest: Teachers could encourage students to see a regularity such as Hooke’s law_OL (the subscript is for Ordinary Language) as being only approximate, limited to some materials, ceteris paribus, and itself in need of explanation. They could contrast it with Newton’s Third law_OL. Some of these ideas are already in a typical English 16-18 syllabus.

More interesting are the philosophical implications of the observation that it was precisely in these school lessons that we philosophers ‘learned the meaning of physical law_OL’, central to this workshop. Why the scare quotes and the subscript? Because this teacher-student process, far from giving us clear conditions for using ‘law_OL’ – the meaning of ‘law_OL’ - instead merely gave us the rough idea of explanatory regularities, which physicists indiscriminately call ‘laws_OL’, ‘principles_OL’, ‘equations_OL’, ‘hypotheses_OL’, and ‘models_OL’. Nonetheless this learning process enabled us to successfully use ‘law_OL’ in the rough-and-ready Ordinary Language (OL) of physicists.

Reflecting on this process should make us extremely careful of our use of language when we are ‘investigating laws_OL’ philosophically. I propose that some of our problems_P (Philosophical problems) are insubstantial pseudo-problems_P generated by us taking the word out of its Ordinary habitat: “What are laws_OL?”. If there are some substantial extraordinary problems_P, we can hope to solve them partly by engineering our own suitable concepts_P.

Abstract

Contemporary linguistics still appeals to various law-like generalisations, concerning language's statistical structure, crosslinguistic patterns, communicative efficiency constraints. Yet their status as genuine laws remains unclear. They are often supported by corpus statistics, typological regularities, or optimization comparisons, yet lack support from counterfactual robustness, mechanistic grounding and derivation from deeper principles. In this talk, I examine the current status of law-like claims in linguistics and argue that evolutionary and agent-based models can strengthen their explanatory value. These models can provide dynamic support by showing how certain regularities emerge, stabilise, and persist and how robust the results are under various conditions. This might be a promising way to develop law-based explanation in a comparatively law-light field such as linguistics.

Abstract

Recent work on scientific explanation emphasizes its theory-relative aspects, especially in physics. Lina Jansson, Marc Lange and others recognize that whether an argument constitutes a genuine scientific explanation depends not just on features of the argument itself, such as its deductive structure or whether it contains a causal generalization, but also on its relation to relevant high-level laws. Jansson has developed a compelling account of explanation that highlights how higher-level laws of nature that are not part of an explanatory argument themselves licence explanatory inferences. For Lange, whether an argument qualifies as explanatory depends on whether properties featured in the explanation are themselves explained by higher-level laws (what he calls “natural properties”). On these theory-relative accounts, what makes an argument explanatory is fully determined by features of the argument itself and its theoretical context.

This talk presents a challenge for the theory-relative approach and shows how pragmatic factors play a role in scientific explanation. I argue that what makes an argument genuinely explanatory depends in part on how well it serves other scientific aims. Disciplinary communities prioritize diverse scientific goals in addition to explanation, including prediction, intervention, representation, realism, and understanding. Communities working with the same scientific models and within the same theoretical framework may legitimately maintain different explanatory standards based on their alignment with other disciplinary goals.

As I show, the challenge for the theory-relative accounts of Jansson and Lange is that high-level theory alone is insufficient to account for what makes explanations successful. Lange uses the case of Archimedes’ principle to articulate and defend his account of explanation (2018, Ch. 11). According to him, in the context of hydrodynamics Archimedes’ principle is not explanatory but in the context of energy conservation it is. This is because a key property in the explanation, the weight of the displaced water, is a natural property in the latter theoretical context but not in the former. I argue against this interpretation: Archimedes' principle gains explanatory power in hydrodynamics not through some theoretical connection to energy conservation but because it aligns with the discipline's goals of intervention and control.

This new pragmatics for law-based explanation shows how explanatory goals are sometimes closely aligned with other disciplinary goals, and whether an argument is a valid explanation may depend in part on how well it serves these other goals. It is a pragmatic dependence that goes beyond the relevant high-level theory. The result is an approach to law-based explanation that aims to capture both the diversity and the normativity of explanatory standards in science. It maintains that explanations track objective features of the world while acknowledging that what renders an argument explanatory depends partly on pragmatic factors including the goals and methods of the local scientific community.