From Bosons to Markets to Black Holes: New Prospects for Analogical Reasoning

In analogical reasoning, observations about one or more source domains are commonly taken to provide support for a conjecture about a target domain. Recently, it has been argued (Dardashti et al. 2017, Dardashti et al. 2019) that tabletop experiments in analogue gravity can provide particularly strong support – indeed, theoretical confirmation – for the hypothesis of Hawking Radiation in black holes, despite the fact that the target domain (black holes) is inaccessible. Against this, Crowther et al. (2019) have objected that analogue confirmation for a model of, or hypothesis concerning, an inaccessible target is impossible. I believe that the debate about analogue confirmation needs to be broadened. I survey the prospects of analogue confirmation for wholly or partially inaccessible target domains: remote historical phenomena (in archaeology and evolutionary biology) and targets that are ethically off-limits (human subjects for some areas of medicine), as well as astronomically remote phenomena such as black holes. The paper has two main conclusions. First: analogical reasoning in these settings, whether based on observation or experiment, is not different in kind from analogical reasoning about accessible target domains. Second: in each case, the prospects for confirmation must be assessed by attending to the logical structure of the analogical argument.

An internally valid experiment justifies our beliefs about a source system, which is directly manipulated in the experiment. An externally valid experiment justifies our beliefs about a target system, which is not directly manipulated in the experiment. Typically the internal validity of a given experiment is necessary but not sufficient for the external validity of that experiment. What kinds of target systems can we gain knowledge about? And what factors place limits on the strength of this knowledge? In particular, must target systems be, in principle, themselves manipulable? Or should we insist that they are at least accessible, in the sense of being subject to possible observation? In this paper we will argue that the limits of experimental knowledge should not be taken to be circumscribed by the manipulability or accessibility of target systems. There is no, in principle, epistemic barrier to experiments with unmanipulable or inaccessible target systems being externally valid. Experiments in contemporary science can and do allow us to gain knowledge of unmanipulable and inaccessible target systems.

We will argue that the limits of experimental knowledge are in fact set by the mitigation of reasonable doubt -- that is, the application of inductive strategies for internally and externally valid source-target inferences. When reasonable doubt has been partially mitigated, a theory can be said to be well supported, and a scientist is justified to treat the empirical consequences of the theory as likely to be true, in the relevant domain. When reasonable doubt has been almost entirely mitigated a theory can be said to be established, and a scientist is justified to treat the empirical consequences of the theory as true, in the relevant domain. Our key contention is that whether a theory regarding certain phenomena can be well supported or established by experiment is not constrained by the requirement that the target system displaying these phenomena be manipulable or accessible, either in principle or practice. Thus, theories regarding unmanipulable and inaccessible phenomena can in principle become established via experiment. On our view, the limits of experimental knowledge are set by the extent to which strategies for inductive triangulation are available: that is, the validation of the mode of inductive reasoning involved in the source-target inference via appeal to one or more distinct and independent modes of inductive reasoning.

To demarcate the limits of experimental knowledge we will probe the limits of what might be called an experiment. In particular, we will illustrate our arguments by drawing upon experiments in the field of analogue gravity. In particular, we will consider analogue experiments designed to probe the phenomenon of Hawking radiation. There are good reasons to expect the next generation of such analogue experiments to provide genuine knowledge of unmanipulable and inaccessible phenomena such that the relevant theories can be understood as well supported. Furthermore, looking further to the future, inductive triangulation allows for the possibility of analogue experiments to play a role, when combined with appropriate conventional experimental results, in establishing new theories.

Analogies between condensed matter physics and particle physics have played an important heuristic role in the construction of new models for both domains. Prominent examples are (1) the analogy to models of superconductivity in the construction of the Higgs model in particle physics and (2) the analogies between phase transitions and renormalization that led to the development of renormalization group methods and the construction of new models in both condensed matter and particle physics (Fraser and Koberinski 2016; Fraser 2018). In contrast to prior historical examples of analogies used in physics, the analogies in these cases are purely formal: the analogical mappings between models were determined by formal similarities between the mathematical formalism and the mapped elements have substantially different physical interpretations. Extant philosophical accounts of analogies have been informed by the earlier historical case studies, in which formal analogies are accompanied by physical analogies. As a result, these case studies of the successful use of purely formal analogies necessitate a new philosophical account of analogies in physics.


Formal analogical reasoning falls outside of the taxonomy of arguments from analogy introduced in Bartha (2010)'s articulation model. Methodologically novel features of the reasoning employed in the Higgs model case study are illustrated by contrasting it with Bartha's exemplar of abductive-deductive arguments from analogy: Priestley's analogy between hollow spherical shells of mass and charge. The premises of Priestley's analogical argument are the similarities between the shells (hollow, uniform mass or charge), the absence of gravitational and electrical force inside the shells, and the fact that the absence of gravitational force is deducible from the inverse square law of gravity; the conclusion of this argument is that there is also an inverse square law for charge. The Higgs case shares the goal of generating a model that is plausibly consistent with observations (e.g., no massless Goldstone bosons). A key difference between the two cases is that the equations of the Higgs model do not take the same mathematical form as the equations of the superconductivity models, unlike the inverse square equations for gravity and electrostatic attraction. Instead, the formal analogy is a higher-order similarity between properties of the equations in the two models: symmetries and the breaking of the symmetries. As a result, the argument pattern does not rely on a simple deductive relationship between an equation that expresses a law and observational consequences. Instead, there is a more complex relationship between a model constructed for a particular type of system and the general theoretical principles. Formal analogies to models of superconductivity were useful because they helped to bridge the inferential gap between general theoretical principles and particular models. For example, particle physicists mistakenly believed that spontaneously broken symmetry in a gauge theory is necessarily accompanied by massless Goldstone bosons. A final important difference between the scientific examples in Bartha's abductive-deductive category and the quantum theory case studies is that the former analogies employ cause-effect reasoning and the latter do not (Bartha 2010, 209).

The last thirty years has seen an upswell in alternative approaches to economic modeling, many of which have been inspired by analogies with statistical physics. Work in this tradition has come to be known as econophysics, a term coined by Stanley et al. (1999). Despite the apparent empirical successes of some models in econophysics, especially the ones based on renormalization group techniques, the field has not been widely embraced by economists and the few who have engaged have been strongly critical. The arguments offered by the critics of these approaches are mainly based on the physical disanalogies between the type of systems typically studied in statistical mechanics and economic systems. For instance, it has been pointed out that human behavior is not as stable and predictable as physical phenomena (Lo and Mueller 2010). It has been also claimed that economic systems are deprived of ``universal empirical regularities'' of a sort amenable to predictive mathematical modelling (Gallegati et al. 2006). Finally, it has been said that the absence of conserve quantities in economic systems makes the whole project of using statistical mechanics in the context of economics untenable (Gallegati et al. 2006).


In this contribution, we will address these and other similar criticisms focusing on the following econophysics models: the JLS model, Lux-Marchesi's (1999) multi-agent simulation models, Cont-Bouchaud's (2000) percolation model and Farmer et al's (2005) zero-intelligence models of the market, and we will analyze the extent to which a mere formal analogy between the target system (economic system) and the source system (physical system) can suffice to motivate the use of statistical mechanical methods in the context of economics. We will argue that interpreting the relevant analogy as a formal rather than a material analogy can serve to reply to most of the criticisms against the use of econophysics models, but at the same time strongly limits the scope of these models. In particular, it does not allow for these models to be predictive and explanatory on their own. We will argue that in order for these models to fulfil those epistemic roles, the scientist must partake in the modelling process by constructing the material (physical) analogy alongside the formal one. The physical analogy is what allows us to identify the relevant causal factors underlying the behaviors of interest in both the source and target systems. Constructing this physical analogy, however, requires important idealizations about the target system, which need to be justified on a case by case basis.