Where do social institutions and phenomena come from? A venerable tradition in economics seeks to explain some of these institutions and phenomena, for example, money, traffic rules, racial segregation and many others, using a concept of invisible hand. Such explanations show a phenomenon to be an unintended outcome of a multitude of actions and interactions of individual persons. In a book based on his doctoral dissertation, Emrah Aydinonat seeks to a) give an account of what sort of social phenomena are susceptible to this sort of explanation, b) evaluate the success of some of the most famous explanations of this type, and along the way, c) draw lessons for philosophical accounts of formal models in economics. In many ways, this book represents philosophy of economics at its finest. It is impeccably informed on the present state of economics, sensitive to the history of the discipline and full of interesting and thoughtful philosophical analysis. A significant problem, however, is that the central notion of the paper – partial potential explanation – does not receive an appropriate articulation. After presenting Aydinonat's views, I explain the problems and why they matter.

What exactly is the explanandum? In the impressive chapter 2, the author offers an analysis of the notion of “unintended consequence” that invisible hand explanations apply to. There are many types of unintended consequences but only some of them are an appropriate target for such explanations. Aydinonat develops an intricate typology of these consequences (19), and isolates the following characteristics as definitive of the phenomenon in question. 1) The consequence is located at social rather than individual level. 2) The consequence was not intended by any of the individuals whose actions caused it. 3) It took many individual actions to produce the phenomenon. 4) All these individuals had intentions aimed at the individual, not the social level. 5) The action of one individual is insufficient to bring about the outcome in question. 6) Individuals do not have the collective intention to bring about the phenomenon in question.

Each of these conditions are necessary for delineating the phenomenon because invisible hand explanations do not apply to unintended consequences of actions of just one individual, nor collectively intended actions, nor actions intended to bring about a social phenomenon, etc. These conditions are of independent interest, but they become especially useful when Aydinonat criticizes Emma Rothschild's contention that the notion of invisible hand is in tension with the rest of Adam Smith's thought. The operation of invisible hand is entirely compatible with individuals being the best judges of their interests and it does not presuppose an all-knowing philosopher who can correctly see what others cannot. This is, among other reasons, because whether or not an action is unintended is orthogonal to whether or not it is unanticipated.

What about the explanantia? Aydinonat discussed two major examples of invisible hand explanations: the origins of money and the origins of segregation.

In the first case, he traces the history of the project from Carl Menger's original articulation of how a medium of exchange could emerge to the contemporary formal models that explore the existence of fiat or commodity money equilibria. Roughly, the attempt is to show that self-interested sellers and buyers who bring saleable and perishable commodities to the market will act in such a way that a medium of exchange will emerge, which itself has no or almost no intrinsic value. Aydinonat deftly explains what such attempts can and cannot provide thus showing which criticisms of this research project are appropriate and which aren't. For example, while it is appropriate to criticize Menger's story for ignoring actual institutional factors which, as a matter of historical fact, led to the emergence of moneys in specific human cultures at specific times, it is not appropriate to argue on this basis that his invisible hand account cannot be explanatory of a different aspect of money, namely its general feature of being a medium of exchange. Since the invisible hand and the anthropological explanations of money may in fact have different explananda and, in addition to that, aim at explanations at different levels of generality, they are not necessarily in conflict.

However, to accept this fact does not amount to granting success to the invisible hand explanations of money. Aydinonat argues that Menger left us with a story about a possible partial process that may have led to the emergence of a medium of exchange. Note the double weakening: Menger's story is partial, in the sense of describing only some factors that could bring about money, and it is not actual, but merely potentially true. Furthermore, Menger gives us no characterization of the mechanism that would lead sellers and buyers to settle on a medium of exchange. A hundred years later, we have many mathematical models which explore the conditions under which fiat or commodity money will emerge as a result of interaction of idealized agents in idealized settings. These models greatly improve our understanding of the features of that ideal world first imagined by Menger in which money emerges as an unintended consequence of human action. But, as Aydinonat persuasively argues, we are no closer to seeing that this world is our world, and thus are no closer to being justified in thinking that in our world money emerged via such a process. Given the absence of a genuine evaluation of the relation between the model worlds in which money emerges by invisible hand and our world in which money exists, all these exercises yield is, as in the case of Menger, a possibility claim. At times Aydinonat suggests that along with a possibility result we have a plausibility result, that is the models give us reasons to believe that the properties they are exploring have something to do with the emergence of money. But even plausible claims are a long way away from explanations. Thus the project yields much interesting theoretical work which uses different ingenious methodologies from modelling to simulations, but there is no actual explanatory progress.

The situation is similar in the second case study. Thomas Schelling's famous chequerboard model, which attempts to show that mild discriminatory preferences can, by invisible hand, bring about residential segregation, has been a focus of much philosophical attention. First, it is considered to be a good example of a social mechanism. Second, it is considered to be one of the successes of economic theory. Aydinonat helpfully explains the sense in which Schelling's model may be said to provide a mechanism. The parts of the mechanism at the individual level are rules that the individuals on the chequerboard follow (e.g. “if most immediate neighbors are of a different color, then move”). The interaction of this mechanism with components such as preferences and the state of immediate neighbours yields a degree of segregation. Manipulations of the model starting from several different initial states show that segregation can indeed emerge via this mechanism. Unlike in models of emergence of money, this model supplies a precise mechanism alleged to underlie the phenomenon in question. In what sense is the model a success?

Schelling's defence of the model is to point out that since the real-world mechanisms of segregation are unobservable, we need to find the model that best predicts the observable data and then infer, by abductive reasoning, that it provides the best explanation of segregation. Robert Sugden augmented this argument by appealing to the credibility of the postulated mechanisms, where credibility is a function of how much the process proposed in the model coheres with our background knowledge of how the world works (Sugden Reference Sugden2000). Since we've all encountered residential segregation and are familiar with people trying to avoid a minority status, it seems reasonable to grant Schelling's model a Sugdenesque credibility. Luckily Aydinonat puts these arguments in their place: “The chequerboard model may be plausible and interesting, yet it does not tell us whether mild discriminatory preferences bring about segregation in the real world” (64). As in the first case, the theoretical articulation of a credible mechanism of a phenomenon does not amount to its explanation, not even to its partial explanation. Rather it amounts to a potential partial explanation (hereafter PPE). This clarification is particularly important because modellers and model users sometimes appeal merely to plausibility and a similarity of the model as grounds for counting this model as an explanation.

Time has come to look at the philosophical heart of Aydinonat's book – the notion of partial potential explanation. This notion is put forward as 1) an account of what the best current invisible hand explanations provide and b) as a way to unify the existing philosophical attempts at explicating models in economics. However, it only partially succeeds in these aims.

The conditions for a successful invisible hand explanation, according to Aydinonat, are as follows: 1) It needs to show a transformation in the model from the state without the phenomenon present to the state in which it is present. 2) It should give an explicit characterization of the individual-level mechanisms of this transformation. 3) If the representation of the initial state in the model is an inaccurate representation of the initial state in the real world, then at least the mechanisms proposed should be plausible enough to be followed by real individuals. 4) Relevant aspects of the explanandum, given the interests of the explanation, should be correctly stated. 5) The aggregate mechanism proposed should be either novel or a “firmer” formulation of the previous.

Note, first of all, that these conditions are not sufficient for a successful causal or mechanistic explanation of the phenomenon, for there is no requirement that the model states albeit abstractly and incompletely the actual mechanism that brought about the phenomenon in question. Rather, an explanation that satisfies these conditions is a PPE. This indicates that Aydinonat believes that, given the constraints of today's economics and the availability of data and testing, PPEs are all that we should expect the invisible hand stories to provide (90). This is not to say that these stories are of no value. It is no small thing to develop rigorously formulated new hypotheses that open new research programmes. Aydinonat's catchphrase to describe the achievement of our best invisible hand explanations is that they “expand our mental horizon” (51, 66, 90). They do so by opening up new possibilities for approaching familiar phenomena. But to state these requirements as Aydinonat does, underlines the fact that some of the most famous pieces of economic research are empirical at most in their ambitions, not their achievements.

Secondly, let us focus on the precise sense in which these explanations are partial and potential. Here is where Aydinonat's analysis is weaker than one would hope. In what sense are the explanations these models offer partial? To explicate this idea the author appeals to Hempel's view – an explanation is partial when it fails to account for the explanandum fully even allowing for the fact that an explanatory account can leave out facts and laws implicitly taken for granted for pragmatic reasons (121). However, when explaining the senses in which the models mentioned above offer only partial explanations, Aydinonat switches into a causal mode, not present in Hempel's version of partiality. For example, Schelling's chequerboard model is said to be partial in that it gives only one of the mechanisms that may bring about segregation (62). Other such mechanisms may be racism, economic factors, etc. But that is ambiguous between several different senses of partiality:

• – An explanation may be partial because it does not account for the full effect of a token phenomenon but only for a part of it.

• – An explanation can be partial in that it studies causes that are only responsible for some tokens of the phenomenon and not for others.

Both these senses are at work in different parts of the book, but their difference is not acknowledged. The first sense invokes Galilean idealization, a technique of assuming away or shielding the cause of interest from other possible causes of the phenomenon (e.g. Cartwright Reference Cartwright1989, Maki Reference Maki1992). The second sense concerns the phenomenon at the level of a type, not token, and no shielding or isolation is presupposed. Running these two senses together is unhelpful because some models are partial in the first but not the second sense and the other way around. The PPEs in question in the book are theoretical, that is not explanations of particular phenomena (123). In that case, if the author still wants to argue that models are partial in the first sense, then he needs to reformulate this sense of partiality for type cases.

On to potentiality. This is the notion that is supposed to capture the sense in which models offer possible, not actual, explanations. Aydinonat defines potentiality as the failure of the explanans to be true. Schelling's and Menger's explanantia fail to be true because “the descriptions of the antecedent conditions are rather conjectural or fictional” (122), that is the models in which money or residential segregation emerges assume conditions that are clearly false of our world. But this is not a sufficient characterization of the cases Aydinonat analyses. Sometimes models with premises that are strictly speaking false can be explanatory as in the case of a Newtonian model which represents planets as point masses. This is because we know that the falsity of the assumption in question does not matter. That is not the case in models of economics whose false assumptions, by and large, cannot be relaxed. So a better characterization of potentiality would be that the explanans is false and we do not know whether or not this falsity is significant. But, of course, even that is not a sufficient condition for the model to be a potential explanation. Not just any model with fictional antecedents whose falsity cannot be shown to be irrelevant will qualify as a potential explanation, at least if by “potential explanation” we mean an explanation whose truth isn't merely a logical possibility but something more. A further constraint is needed, for example that the mechanism suggested by the model is plausible given the existing body of knowledge in social sciences. Although, Aydinonat invokes some such conditions elsewhere (134, 138–9) as necessary for explanation, he does not include them as a part of characterization of potentiality of explanations thus leaving this central notion underspecified.

A further distinction between different senses of potentiality of explanations offered by models should be drawn. As Aydinonat is well aware, models such as those he discusses do not always make a prediction about what the modelled actors will do in their situations. It only does so when the game has a unique equilibrium. When the equilibria are multiple, which is most of the time, the model is usually read as showing that such and such outcome is possible because it is an equilibrium. This is one source of potentiality. A different source has nothing to do with the problem of multiple equilibria: if the model's assumptions only partially map on to the real world, then we are not warranted to claim that the mechanism depicted in the model is the mechanism that brings about the phenomenon of interest in the world. But we may be warranted to make a weaker claim – that the model depicts a decent possibility. The latter sense of potentiality is more in line with Aydinonat's explicit account, but, again, an explicit recognition of the different sense of potentialities would have been helpful.

A further problem with Aydinonat's articulation of the central notions of his account is a lack of proper positioning of his view with respect to the other existing views on the topic. For example, Aydinonat explicates potentiality of model explanations by appeal to the notion of tendency as it appears in Nancy Cartwright's account of models (Cartwright Reference Cartwright1989). He endorses the idea that models explore the operation of tendencies in isolation from other factors, tendencies that continue to hold when the model's assumptions are not satisfied (136–9). In the case of economics these tendencies describe familiar entities such as individuals with plausible preferences, but models also show that under certain conditions these tendencies can aggregate in surprising and novel ways. What is surprising is that Aydinonat takes this view to be compatible and in fact very similar to his account of models as partial potential explanations. But that is, at most, a very unorthodox interpretation of Cartwright's account. If models really made tendency or capacity claims, as the term is used by Cartwright, they would not be merely potential explanations. A capacity is defined to have stability, that is it exercises its power outside the narrow constraints of a model or a controlled experiment (Cartwright Reference Cartwright, Davis, Hands and Mäki1998). If Schelling's model is to be interpreted in this way, then we would have to say that preferences not to be a minority in its own neighbourhood cause residential segregation even in the presence of other preferences. They don't just may cause it, as would be the case on the partial potential view. Of course, there is no evidence that Schelling's model supports such a strong claim. In fact, in a series of recent papers Cartwright argues that economic models are a poor guide to capacity or tendency claims (e.g. Cartwright Reference Cartwright2009), that is that the story above, which may faithfully describe the intentions of economic modellers, does not describe correctly the fruits of their labour. Aydinonat's insistence on mere potentiality of models as explanations is more in line with this recent sceptical development of Cartwright's view. But to endorse both the view that models should be read as providing tendency claims and, at the same time, to maintain that models only tell us how the world may be, amounts to either a reinterpretation of the notion of a tendency or a mistaken attempt to fit a number of conflicting philosophical views under one roof.

The same problem appears in the discussion of Sugden's view of models as credible worlds. Aydinonat seems to endorse some of it, while at the same time pointing out helpfully that a credible explanation is merely a first step to an actual one. But he does not explain how the PPE view is or is not different from Sugden's account. Are models that function as PPEs necessarily Sugden-credible, so to speak? Does the implication hold the other way around?

The existing views on how strong a claim can be read from a model seem to fall along a spectrum from “not at all strong” to “very strong”. The weakest reading of models appears to be expressed by Daniel Hausman – models are mere explorations of concepts, they study relations between ideas without concern with their relation to the world (Hausman Reference Hausman1992). The strongest reading can be made on the basis of Cartwright's and Uskali Maki's view – models make claims about stable causal forces that operate on their own. Sugden's credible worlds view appears to fall in between (Sugden Reference Sugden2009). Where, on this spectrum, does the PPE view fall?

For these reasons, I prefer to view Aydinonat's philosophical discussion of the status of models as a promissory note rather than a fully developed and properly articulated account. This is not to downplay the book's other achievements. Aydinonat produced an analysis of a research project central to the discipline of economics. Yet this analysis reverberates beyond this project. When a model offers a partial potential explanation, what exactly are we warranted to do with it? Are we justified in issuing policy advice on its basis? Is a model-based PPE better than a PPE developed on the basis of, say, ethnographic data? Why do economists only focus on very specific sorts of PPEs, i.e. those associated with rational choice, given that there are so many others? Is that legitimate? How do we characterize the progressiveness of a research programme in the business of producing PPEs, given that the standard Lakatosian criteria seem too strong? These are not questions one should expect this book to answer, but this book is what allows us to pose these questions and in this way undoubtedly moves forward the debate.