Cultural Attractor Theory and Explanation

2.1 Reconstructive Learning

Work in cultural evolution pursues several explanatory aims. These include accounts of human cognitive evolution (Boyd and Richerson 1985; Henrich 2016); the dynamics of cultural transmission (Cavalli-Sforza and Feldman 1981; Boyd and Richerson 1985; Odling-Smee et al. 2003; Henrich 2004; Powell et al. 2009); how cultural traditions change over time (Sperber 1996; Morin 2015); and how such traditions themselves may spread and go extinct across distinct populations (Mace and Holden 2005; Currie and Mace 2014).

Within the cultural evolutionary literature, CAT is distinguished by its account of human learning. As I have said above, the dominant account of learning used in cultural evolutionary models is replicative (e.g. Boyd and Richerson 1985; Odling-Smee et al. 2003; cf. Henrich and Boyd 2002; Henrich 2004). This replicative picture is one where learners reliably acquire whatever behaviours, skills, or pieces of know-how (what I'll call ‘cultural variants’) are currently of interest. Though this learning process might be error-prone and noisy—particularly when what is being learned is complex or when teachers are uncooperative—multiple exposures to learning opportunities can lead to the reliable replication of cultural variants over time.

Yet as CAT theorists note, the replicative picture is metaphorical, and should not be taken too seriously (Sperber 2000). Individuals cannot actually copy things like beliefs or skills, because learners do not have access to beliefs or skills; all that learners have access to are the ways that beliefs or skills are manifest in behaviour. So copying is a misleading picture of the nuts-and-bolts of how learning actually occurs. A more realistic picture takes learning to be reconstructive (Sperber 1996, 2000). On a reconstructive picture, when individuals learn from one another, they construct a variant of their own on the basis of observable evidence. This is what I have elsewhere called reconstructive learning (Buskell 2017).

To be sure, there are many possible causes of the states of affairs that learners observe. When an individual is attempting to learn a particular behaviour, say, how to carry out long-division, then they will have to piece together evidence from a wide variety of sources: textbooks, examples, and whatever help comes from teaching or instruction. Integrating all these sources of evidence involves the learner's inferential capacities. Learning is inferential rather than imitative or replicative.

Unsurprisingly, these inferences can be sensitive to a range of local factors. Learning is not only influenced by background beliefs, but also variations in an individual's affective, cognitive, and axiological state (Sperber 1996). One area where such differences are acute is in politics. Here, local influences can cause the same piece of information to be reconstructed in wildly different ways. Consider a news bulletin announcing the privatisation of public resources by the ruling political party. If I have antecedent beliefs about the effectiveness of the ruling political party, I might understand or integrate such news positively. On the other hand, if I have antecedent beliefs that the ruling political party is acting in their own self-interest, I am likely to view such privatisation more sceptically.

A clear articulation of such inferential biases on reconstructive learning is given by Claidière and Sperber who write:

Reconstructive learning is “influenced by past inputs” (Sperber 1996, 118)—past inputs that might lead one to be a partisan politico, for instance—and these past influences can generate biases in learning. Inferential biases, as I will use the term, consist in the way that beliefs and values, as well as one's cognitive and affective state, impact and influence the inferences made by individuals during learning.

The causal factors that generate such inferential biases are what cultural epidemiologists call factors of attraction. In other work (Buskell 2017), I have shown that cultural epidemiologists appeal to distinct kinds of factors of attraction: factors that bias inferential capacities during learning (inferential biases); factors that motivate the expression of certain cultural variants (motivational factors); and factors that impact the accessibility and availability of information and evidence (ecological factors).

Below I suggest that the central causal-explanatory factors CAT should appeal to are those that bias inferential capacities. As I go on to show, such inferential capacities can be construed as a force impinging upon an otherwise unbiased population of learners. This construal of CAT shows how it can contribute to standard cultural evolutionary theory, and in doing so, improve the realism of their models.

2.2 Explanatory Payoffs

I suggest that CAT can gain explanatory traction on phenomena by adopting what Lewens (2015) calls the kinetic approach to culture. The kinetic approach is aggregative, modelling the downstream outcome of interactions among homogeneously construed individuals. As I hinted at above, in the real world, individuals' inferential capacities are influenced by a number of factors of attraction—some held widely across many human populations, others more locally. Yet to generate tractable models, CAT researchers assume homogeneous populations (or sets of sub-populations) where individuals share sets of inferential biases. Assuming such homogeneity, cultural epidemiologists can model and predict the way in which biases generate populational changes.

The explanatory concept used by cultural epidemiologists to describe and ultimately explain downstream population changes is what they call cultural attractors. Here is Sperber's characterisation of the concept:

Cultural attractors are characterisations of systematic transformation biases within a population that influence how individuals learn. This much is straightforward. But what does Sperber mean what he calls such attractors ‘abstract statistical constructs’? I suggest we take the analogy between transformations and mutations at face value.

In toy models of population genetics, a mutation rate can be modelled as a fixed frequency at which a particular allele mutates into another. Consider an asexual haploid population with two non-fatal alleles, A and a. Further, assume that A mutates into a at some rate μ every generation. Even under situations of strong selection, where the selection coefficient s ≫ μ, there will always be a proportion of the population μ that has the allele a.

An analogous situation holds for CAT. Just as researchers in populations genetics model the rate of one allele mutating into another, so too, I suggest, are cultural epidemiologists modelling the rate of transformation from one cultural variant into another: cultural variant A is transformed into a distinct cultural variant a at a particular rate. More than this however, cultural epidemiologists hold that cultural variants have multiple transformation probabilities. The cultural variant A not only has a transformation rate to transform into a, but distinct rates for transforming into a', or a". It is the aggregate of all various transformation rates that Sperber points to when he calls cultural attractors an abstract statistical construct. Cultural attractors, as I construe them, are an aggregate of transformation rates for a set of cultural variants.

With this characterisation on the table, we can ask how it is that such aggregate transformation rates can explain downstream population outcomes. Here we face some controversy. According to Robert Boyd and Peter Richerson, there are two different characterisations of transformations appealed to by cultural epidemiologists. On the one hand, cultural epidemiologists appeal to “systematic transformations [that] create a new nonselective force that moves the population towards nearby attractors” (Boyd and Richerson 2005, 84). On the other hand, so they allege, cultural epidemiologists write as if “the transformations that occur during social learning are unsystematic, so that people observing the same behaviour infer very different cultural variants; consequently, cultural replication is so noisy and inaccurate that weak selective forces would be swamped” (Boyd and Richerson 2005, 84). According to Boyd and Richerson, reconstructive learning is either directional and systematic or noisy and inaccurate.

While accuracy of this characterisation would no doubt be challenged by cultural epidemiologists, I think it is correct suggesting that CAT can be interpreted so as to make progress on two distinct explanatory endeavours. In what follows I'll suggest that these two distinct kinds of explanatory endeavours recruit the concept of cultural attractors in different ways. First, cultural attractors can explain systematic changes in the frequency distribution of variants and explain insofar as they account for how the transformations made during learning lead to some variant(s) being acquired rather than others. This strategy provides what Godfrey-Smith (2009) calls distribution explanations.

But there is another way in which cultural attractors are recruited in explanations. This occurs when one focuses on how variants are “transformed or distorted to become more similar to a particular form” (Mesoudi and Whiten 2008, 3492). That is, when cultural attractors are employed as part of an explanation for why certain variants have the form that they do. Here, cultural attractors are put forward as explanations for why variants of a particular form are more likely to evolve than others. I call these latter kinds of explanations cultural evolvability explanations.

3.1 Cultural Attractors

As I've suggested, one of CAT's explanatory aims is to provide distribution explanations. Broadly, distribution explanations are those that articulate why a distribution of variants at some initial time has the same or different distribution at some later time. So, for instance, a distribution explanation for different brands of ice-skates would explain why the proportion of skaters wearing ice-skate brands [x,y,z] at distribution [20%, 55%, 25%] at time T₁ changes to a distribution of [60%, 30%, 10%] at time T₂.

Unfortunately, evaluating CAT's success in providing distribution explanations has been hampered by the multiple accounts of the cultural attractor concept. As discussed above, the cultural attractor concept is statistical. And though I have put forward my own interpretation of this concept above, it is important to note that the CAT literature contains several such interpretations. In other work (Buskell 2017), I've noted that there are four distinct characterisations of this cultural attractor concept. Here I build on this past work and show how the conceptual ambiguity of the cultural attractor concept has explanatory consequences.

We can group the distinct characterisations of the cultural attractor concept into two broad categories: kinetic characterisations and distributional characterisations. Kinetic characterisations follow the strategy discussed above, where one aggregates the effect of a homogeneously construed population of individuals. Distributional characterisations, on the other hand, identify attractors with particular distributional changes. Here I argue that CAT should employ kinetic characterisations—what I call transformation pattern[1]—to the exclusion of the others.

transformation pattern should be familiar. It is the characterisation of cultural attractors I have reconstructed above. On this interpretation, cultural attractors are identified with aggregates of transformation rates (Sperber 1996, 2000; Sperber and Claidière 2008). Under simplifying assumptions, this aggregate can be identified with shared inferential biases that lead to systematic population-level effects.

cluster point, increasing frequency, and equilibrium point, on the other hand, identify attractors with distinct distribution outcomes. cluster point (Sperber 1996, 108–112; Sperber and Claidière 2008, 92) identifies cultural attractors with distributions that change over time to cluster around a particular variant. increasing frequency (Claidière, Scott-Phillips, et al. 2014; Scott-Phillips and Sperber 2015) identifies cultural attractors with distributions where some variant increases in relative frequency over time. Finally, equilibrium frequency (Claidière, Scott-Phillips, et al. 2014) identifies cultural attractors with the distribution that occurs at some equilibrium point.

I will have more to say about the explanatory merits of these various characterisations of the cultural attractor concept in a later section (‘Circularity and Pan-attractivism’). However, before moving on, it is important to emphasise a crucial point. Distributional characterisations of the cultural attractor concept (cluster point, increasing frequency, equilibrium point) identify attractors with subsets of distribution outcomes. For instance, cluster point identifies cultural attractors with distributions that change to cluster around a single variant. But why should one restrict cultural attractors, such that they can only be used to explain a restricted subset of possible outcomes?

Though it might be tempting to assume that such a restriction allows greater scope for predicting or explaining distributions, I am not convinced. Identifying attractors with distribution outcomes seems to rob the concept of any deiive or explanatory power: attractors just end up being whatever distribution actually occurs.

My hunch is that such distributional characterisations are best interpreted as slips of the tongue—a mistaken identification of attractors with outcomes rather than the causal processes that generate such outcomes. The slip between the two is easy to make, particularly if one assumes that aggregate transformation rates can be approximated by smooth functions, with increasing likelihoods of adopting a particular variant clustering around a particular attractor ‘point’ or ‘peak’ (e.g. Sperber 1996; Claidière and Sperber 2007). With such an assumption, transformation rates work to generate distributions of variants with equilibrium distributions that cluster around a central variant that increases in relative frequency.

But this neat and tidy picture is not a conceptual necessity. Transformation rates can be irregularly distributed across many cultural variants, and inferential biases may cause ‘leaps’ from variants across ‘culture-space’. Once one notices that transformation rates can involve variable and jumpy reconstructions, the neat picture articulated above loses its appeal. It is also at this point where the contrast between the kinetic and distributional characterisations of the cultural attractor concept becomes clear: while kinetic characterisations explain how distributions are generated by aggregations of transformation rates, distributional characterisations are identifications of attractors with some mere subset of distributions.

If this analysis is right, then transformation pattern is not only the most inclusive of the cultural attractor characterisations, but also the most explanatory. It can capture the wide variety of possible population outcomes, including those with distributions captured by clustering, increases of relative frequency, and stable equilibria. As a result, I suggest that cultural epidemiologists should reject definitions of cultural attractors that identify the concept with an overly restricted subset of distribution outcomes. To the extent that CAT generates distribution explanations, cultural epidemiologists should understand cultural attractors as a deiion of shared, aggregate transformation rates.

3.2 The Force of Attraction

Evolutionary theory is often conceived of as a theory of forces (Sober 1993; Stephens 2004, 2010). Such forces drive changes in populational properties in line with the force's strength (or magnitude) and direction (Sober 1993; Stephens 2010). In evolutionary theory, these forces (at least selection, mutation, and migration) can be additive, having a stronger net effect when acting in concert. Or such forces may counteract one another, leaving the distribution of variants in line with whatever ‘zero-force state’ is operative for a particular population.

Understanding evolutionary theory as a theory of forces has some explanatory payoffs.[2] Notably, one can appeal to the direction and magnitude of combined forces to explain why a population could come to have certain distributions of variants. Here I will argue that cultural evolution can also be understood as a theory of forces, and that understanding it in this way demonstrates how cultural attractors can generate distribution explanations.

For Sober (1993) a theory of forces is only conceivable if one is able to determine how a system will act in the absence of forces acting upon it. For single-locus, two-allele organisms with sexual reproduction, this zero-force state is captured by the Hardy-Weinberg equations.[3] The most important feature of such a zero-force state is that once “genotypes have gone to their Hardy-Weinberg equilibrium values, there they stay, in the absence of an evolutionary force” (Sober 1993, 34). Of course, the converse of the claim is not true—one cannot assume from the fact that a population is at Hardy-Weinberg equilibrium that there are no evolutionary forces at work. There may be forces whose net effect cancels each other out.

This has relevance for the discussion of the force of attraction and cultural evolutionary theory. For one requires an analogous articulation of a zero-force state within cultural evolution. This I find in what Peter Richerson, Robert Boyd, and Joseph Henrich call unbiased learning (Boyd and Richerson 1985; Henrich 2001). Unbiased learning occurs when individuals reliably acquire cultural variants from a random member of their population. This is usually cashed out in a generational model, where individuals of a new incoming generation learn from, and then replace, individuals in a previous generation.[4] Under such conditions, the incoming generation reliably replicates the previous generation's distribution of cultural variants.

Actually, the list of idealisations required to generate unbiased learning is somewhat more onerous than mere random copying in non-overlapping generations. To generate unbiased learning one has to assume that cultural variants are exclusive (that is, that one can only hold one variant at a time, akin to alleles at a locus in haploid organisms); that there is no assortative learning or biased sampling of particular individuals; that there is no population structure that would make learning non-random; that there are no frequency-dependent effects; and most importantly for current concerns, that individuals reliably acquire the variants of their models without distortion or deviation. When all of these idealisations are satisfied (and, perhaps, more that have yet to be identified), then subsequent generations will display the characteristic static distributions of unbiased learning.

The force of attraction can impinge on populations characterised by such unbiased learning, and in doing so, explain systematic changes in population-level distributions. To take one example, imagine a scenario where incoming members of a high-school ice-hockey team have to purchase their equipment (hockey sticks, helmets, ice-skates, etc.). Let us assume that this school is highly competitive so that only final-year students make the team (or, in other words, that there are non-overlapping generations). Further, let us assume that incoming members of the team learn from the outgoing members what brands of equipment to purchase. Imagine that this situation is characterised by unbiased learning, where incoming team members are randomly paired up with outgoing members and end up purchasing the same equipment as their model. In such a scenario, year after year, successive generations of hockey teams will end up purchasing the same brands of equipment—the same kinds of hockey sticks, helmets, and ice-skates and in the same proportion.[5]

But if there is a situation where individuals infer that brands with red colouration give a competitive advantage—perhaps in line with the notorious ‘red effect’ on competition (Hill and Barton 2005; though cf. Fortunato and Clauset preprint)—then what was unbiased becomes biased. This can lead to a directional effect, perhaps over successive generations of hockey teams, where individuals purchase more and more red gear.

Models of the force of attraction given by Claidière and Sperber (2007) make this informal example more precise. In their work Claidière and Sperber examine how individuals come to adopt one of thirty-one smoking variants, corresponding to smoking between zero and thirty (whole) cigarettes per day. Two forces influence the number of cigarettes that individuals come to smoke: the force of attraction and the force of cultural selection. The force of attraction is simply the aggregate of transformation rates, as discussed above. The force of cultural selection, as Claidière and Sperber use the term, is one of discriminate sampling, where individuals preferentially learning from particular individuals. Without rehearsing the technical details of this model, Sperber and Claidière show that these two forces can interact in complex ways, generating a wide range of variant distributions. But in one special case, where the force of attraction acts in isolation from other forces, Sperber and Claidière (2007, 94–95) note that the variants become allocated in direct proportion to the strength of the force of attraction. And this is just what one would expect: in the absence of other forces, reconstructive learning ends up shaping population-level distributions in accordance with the strength and direction of the aggregated transformation rates.

Sperber and Claidière's model was not intended as a comprehensive nor a general characterisation of CAT. Nonetheless, I take it to be a useful example in showing how aggregates of transformation rates can factor into distribution explanations. CAT can explain downstream distributions of cultural variants in a population by showing how such distributions result from the force of attraction.

Other benefits come along for free when one understands CAT in this way. To see why, consider the way that forces are employed to explain simple physical phenomena. To explain the trajectory of a billiard ball as it rolls across the table, one need only appeal to a force acting on the ball with a certain magnitude and direction. One does not need to provide a causal interpretation of this force; it might have been caused by a cue striking the ball, but might equally have been the result of a powerful gust of wind, or the final trick in an elaborate Rube Goldberg contraption. In fact, the cause of the force can be explanatorily irrelevant—all that might matter is why the ball went this way with this speed rather than that way with that speed. In precisely the same way, cultural epidemiologists can provide distribution explanations appealing to a force of attraction.

This is a point that is not recognised by cultural epidemiologists despite their occasional use of ‘force talk’. Yet it is important. Positing a force of attraction means that CAT theorists can explain distribution outcomes without having to characterise the complex set of causal factors that generates such a force (contra Sperber 1996). This saves cultural epidemiologists from needing to articulate the nitty-gritty of how inferential biases combine together to jointly change distributions of cultural variants. (I will have more to say about this below.)[6]

6.1 Harmonisation Problems

The first worry concerns the complexity and heterogeneity of the force of attraction. As I showed above, the force of attraction is a composite, where a mix of affective, cognitive, and doxastic factors together combine to influence reconstructive learning. One worry that might be leveraged at the account I have developed here is what Christopher Stephens (2004) calls a harmonisation problem: when one is attempting to describe or characterise the force of attraction, how is one to weigh the various affective, cognitive and doxastic factors? How do they add up? Let us call the problem of ‘adding up’ the various affects on reconstructive learning the problem of intra-force harmonisation.

What does this intra-force harmonisation problem actually problematise? The first thing to note is that this is not a problem for general formalisations or models like those given by Sperber and Claidière (2007). As I have suggested above, forces can be explanatory even if one lacks knowledge about the causal underpinnings of that force. One does not need to know what struck the billiard ball to explain its trajectory towards the corner pocket. Instead, what this intra-force harmonisation problem renders difficult is the application of general formalisations or models to real-world scenarios. Without a clear sense of how various factors impact reconstructive learning and how these factors are to be composed, we lack a way of making predictions, or explaining past scenarios in anything but an ad hoc manner.

But is this really a problem? I am not sure that it is, or at least, that it is a problem unique to the account on offer. Evolution by natural selection also relies on heterogeneous sets of causal processes and complex biological and ecological trade-offs to explain adaptations and evolution (Sober 1993; Sterelny and Griffiths 1999). Evolution by natural selection, too, faces a problem of intra-force harmonisation. And if evolution by natural selection can be successful theory despite providing ad hoc explanations, there does not seem to be a reason why CAT should not be treated in an analogous way.

So there does not seem to be much to worry about with the first kind of harmonisation problem. But there is a second harmonisation problem: How is it that the force of cultural attraction should be combined or integrated with other cultural evolutionary forces? That is, how does the force of attraction work with or against forces that determine who or what one should pay attention to, or the fitness ramifications of adopting particular cultural variants? Let us call this the problem of inter-force harmonisation. It points to the difficulty in combining the various cultural evolutionary forces—for example, the force of attraction, the force of cultural selection, and perhaps some cultural evolutionary analog of drift (Bentley et al. 2004). Is this a problem for this reconstruction of CAT?

Here too, I would suggest that it is not. Or, at least, is not a problem that uniquely bedevils CAT. As Sober writes, each theory of forces “must discover how to combine the forces it describes [...], there being no antecedent recipe that is guaranteed to work for all cases” (Sober 1993, 31–32). This second harmonisation problem is one for cultural evolutionary theory as a whole, not specifically for CAT.

6.2 CAT and Human Psychology

Is CAT wedded to a particular view of human psychology? In reading work by cultural epidemiologists, one might reasonably think so. CAT seem to be wedded to a speculative picture of massively modular minds (e.g. Sperber 1996; Sperber and Hirschfeld 2004). Why might this be the case? Here is one plausible reason: shared aggregate transformation rates allow for modelling the “convergence of [one's] affective and cognitive processes with those of many people toward some psychologically attractive type” (Sperber 1996, 106). But why should we expect such convergence?

Cultural epidemiologists have long defended populational ‘convergence’ as being the result of “evolved domain- or task-specific autonomous devices or ‘modules” ’(Sperber and Hirschfeld 2004, 40). Indeed, Sperber (1996, 2006; Sperber and Hirschfeld 2004, 2007) has long maintained an idiosyncratic version of the massive modularity thesis (cf. Fodor 1983; Sterelny 2001), where ‘modules’ are special-purpose evolved psychological mechanisms that have been selected for robust processing stimuli. According to Sperber, assuming massive modularity can ground the assumption that human beings will have broad similarities in their cognitive and affective biases.

We do not need to go further into the details of Sperber's account of modularity here. All I seek to argue for here is that one can be agnostic about an appeal to “a modular organization of human cognitive abilities” (Sperber and Hirschfeld 2004, 45). One does not need to ‘go modular’ to ground the assumption that individuals in population can share inferential biases.

Consider here Cecilia Heyes and Chris Frith's (2014) recent argument that capacities for mind reading (capacities for predicting, explaining and manipulating the behaviour of others) are culturally inherited in a manner analogous to print reading. Marshalling a wide range of cross-cultural evidence, Heyes and Frith show that there exists widespread variation in the ontogeny of such capacities. Children in western countries like Australia and the United States seem first to grasp the fact that individuals have beliefs and may vary in their beliefs before they attribute ignorance or knowledge to individuals. By contrast, in countries such as China and Iran, children seem to acquire these capacities in precisely the opposite order: understanding first that individuals can be ignorant or knowledgeable before grasping that individuals may have diverse beliefs (Heyes and Frith 2014, 1243091–2). Heyes and Frith's suggestion here is that such cross-cultural variation can be explained by positing an innate capacity for implicit mind reading that is developed and bootstrapped in distinct ways in different cultures into explicit mind reading capabilities.

Implicit mind reading is a mechanism or set of mechanisms that enables automatic, fast and fluid tracking of other's behaviour. Using an ingenious experiment, Santiesteban and colleagues (2014) showed that adults quickly and automatically take perspectival information of others into account. This automatic incorporation of other's perspective occurs even when the ‘other’ is a non-human stimulus with orienting features (e.g. an arrow-shaped avatar). This suggests a quite general mechanism that quickly and implicit takes orienting information into account (cf. Apperly 2011; Heyes 2014). According to Heyes and Frith (2015; cf. Heyes 2012), this implicit mechanism is then exapted or bootstrapped by various local cultural traditions and practices into more familiar explicit mind reading, exemplified in folk psychology.

This account relies on an innate capacity for implicit mind reading: a mechanism that orients one towards and incorporates the viewpoints of others. To the extent that Heyes and Frith appeal to an innate capacity, then, one might think there is little light between their account and Sperber's. But there are deep disagreements here. For Heyes and Frith, what explains explicit mind reading are cultural practices: variation in mind-reading development results from variation in early childhood environments. This is in comparison to Sperber's (1996; Sperber and Hirschfeld 2004), where such explicit mind reading capacities are universal and innate.

So while both accounts appeal to specific adaptations or ‘start-up kits’ that predispose human beings to attend to and orient to specific stimuli—they differ in the extent to which these adaptations invariably end up generating specific capacities for mind reading. For Heyes and Frith, implicit mind reading “is radically insufficient for the development of explicit mind reading” and “no amount of individual learning—implicit mind reading, introspection, and watching the behavior of others—would be enough for the development of explicit mind reading” (1243091–5). If Heyes and Frith are right, then while some cognitive structures are needed for explicit mind reading, further scaffolding is needed. And this scaffolding can vary across cultures and shape explicit mind reading in different ways.

Whatever you make of Heyes and Frith's account, it seems a plausible alternative to Sperber's nativist view of the mind. Such accounts are further buttressed by recent work in the philosophy of biology. Kim Sterelny (2003), for instance, has defended an account where social learning accounts for folk psychological capacities. Matteo Mameli (2004), too, has defended the idea that there can be selection for capacities to learn, and that such learning can do the work of reliably acquiring adaptive traits generation after generation. Taken together, this suggests that one can purchase the robust, shared capacities that CAT theorists appeal to without buying into modular minds.

If this is right, then the reconstructed version of CAT on offer here is not strictly beholden to any particular view of the mind. The inferential biases appealed to in CAT models need not say anything about their causal origins. This is a big difference between my reconstruction and the CAT literature—but I see this as a feature, and not a bug.

Still, the abstract character of the force of attraction does raise tricky issues for the causal interpretation of such models. Cultural epidemiologists have long assumed that ‘going modular ’solves what I have called the intra-force harmonisation problem. The default interpretation of CAT models has been that deep cognitive architecture is the most important causal factor in determining the strength and direction of the force of attraction. This default assumption is visible in both CAT theoretical writings (Sperber 1996; Heintz and Claidière 2015) and empirical work (Miton et al. 2015). But if something like Heyes and Frith's account is right, then this assumption needs to be jettisoned. Local cultural variation may be more important than yet recognised.

The issues at hand reflect ongoing empirical and philosophical issues, and here is not the place to settle the debate. Though there seems to be momentum in scientific and philosophical opinion towards accounts like Heyes's or Sterelny's, the pendulum of opinion may swing back to a nativist one in the future. Whatever the long-term outcome, it is important to note that on the reconstruction on offer, CAT is insulated from these debates; one can appeal to and use inferential biases in one's models regardless of their origins in evolutionary history or local cultural context.

6.3 Circularity and Pan-Attractivism

In a recent paper, I argued that CAT sometimes verges on circularity (Buskell 2016). Occasionally, cultural epidemiologists write as though certain variants are attractive because they are prevalent, and are prevalent because they are attractive. Is there anything to this claim?

To see what is at stake, we are well-advised to return to the discussion of cultural attractors. I argued above that we can isolate four characterisations of the cultural attractor concept (transformation pattern, cluster point, increasing frequency, and equilibrium frequency) and that cultural epidemiologists should not restrict themselves to identifying cultural attractors with a sub-set of possible population outcomes. This is because there is a wide variety of possible distribution outcomes that are not well captured by one or all of these distributional characterisations. It is this identification that underpins my criticism. CAT verges on circularity when it identifies attractors with particular distribution outcomes.

To be sure, it can be the case that aggregate transformation rates generate distributions with increasing frequencies of variants, clustering, and equilibria points. But the problem is that forces other than attraction can generate such distributions. A force of cultural selection could also generate clustering, increasing frequency, and stable equilibria. But such distributions result from discriminate sampling and not from inferential biases.

The solution to all of these worries is to recognise the idealisations at work in cultural epidemiological work. In their models and discussions, researchers typically hold an implicit assumption that cultural attraction is the only force at work. Additionally, they hold that the force of attraction will generate distributions where attractive cultural variants both increase in relative frequencies and cluster together (e.g. Claidière and Sperber 2007). But such clustering and increases in relative frequencies can be counteracted by other forces. Indeed, just as a ball need not roll downhill if there is a contravening force pushing it back up; contravening forces in cultural evolution may drive populations to adopt variants that are not attractive—if what ‘attractive’ picks out is the variant that one would have ended up with had no other forces been acting.

This seems to be the most charitable way of interpreting many of the claims of cultural epidemiologists. Rather than seeing their claims as circular, one should see them as making—to coin an ugly term—attractionist or pan-attractionist claims. These are claims that hold that in the absence of other forces, the force of attraction will drive populations to particular distribution and equilibrium outcomes.[9]

Adopting an attractionist viewpoint is not a bad thing. After all, adopting an adaptationist perspective allows for useful modelling of a wide variety of traits. But one should be cautious in adopting a pan-attractionist viewpoint: a view that the force of attraction is the most significant of the forces acting on cultures. One should be cautious of such a position not only because analogous pan-adaptationist stances (sensu Lewens 2009) have been widely criticized in evolutionary theory (notably, by Gould and Lewontin (1979), and most recently by Elisabeth Lloyd (2015)), but also because accounts that appeal to discriminate sampling seem to get real traction on cultural evolution and the evolution of human cognition.

Humans are responsive to information gradients in the local environment (Sterelny 2003). Information gradients exist where useful information is unequally distributed among individuals in a population. Given such gradients, natural or cultural selection can produce strategies for navigating these gradients; strategies like learning from the most successful or most prestigious in one's society. Indeed, the most well-developed and robust models within cultural evolutionary theory assume information gradients to explain human capacities for culture (e.g. Boyd and Richerson 1985, 2005). These capacities in turn have been used to explain a variety of cultural phenomena, notably, the differential success of populations in similar environments and why specific individuals are appealed to for help or learning experiences in particular domains of knowledge (Henrich 2001, 2016; Henrich and Henrich 2010).

Nonetheless, much like the issue of massive modularity, we need not settle the issue of pan-attractionism here. Whatever the views of CAT theorists, one can recognise pan-attractionism as a viable modelling strategy. Adopting such a strategy produces models demonstrating what culture would look like if the force of attraction were the only force impinging on a population. But one can adopt this strategy without making the questionable inference that whatever cultural distributions and form one observes in a population is the result of the force of attraction.

6.4 Explanatory Scope

The reconstruction I have offered in this paper employs a range of conceptual tools—notably, ‘force talk’—to show how CAT can contribute to explanatory projects at work in cultural evolutionary theory. As I hope to have shown, this is a reconstruction with a number of positive features. But there are also likely to be a number of negative features, at least from the perspective of practicing cultural epidemiologists.

First, the reconstructed account on offer here is modest about CAT's theoretical potential. It holds that CAT is an enterprise concerned with offering distribution and evolvability explanations. This is in contrast to several cultural epidemiologists who hold the scope of CAT to be much broader than this. Sperber (1996), for instance, argues that CAT is at least partly an account of human cognitive evolution, and Claidière et al. (2014) hold that CAT is general framework for research in cultural evolution. Though both of these claims are contentious (Sterelny 2001; Acerbi and Mesoudi 2015; Buskell 2017), they are legitimate epistemic aims not well represented in this reconstruction.

Second, the account I have reconstructed here does not employ all the explanatory resources that CAT has to offer. In particular, it focuses on inferential biases to the exclusion of motivational and ecological factors of attraction. While I believe that a focus on inferential biases is warranted, many cultural epidemiologists might disagree. Indeed, they might argue that a focus on inferential biases represents an unjustified jettisoning of useful explanatory resources.

Third, the account I offer here might make CAT hard to distinguish from other cultural evolutionary accounts. In particular, understanding inferential biases in terms of a ‘force of attraction’ might undermine its distinctiveness from other kinds of biases that can similarly be construed in terms of a force impinging on cultural population—notably content-based biases, context-based biases, or guided variation (Richerson and Boyd 2005).

Personally, I see this as a positive feature of the current account. One of the main benefits of using ‘force talk’ is to allow the integration of multiple distinct kinds of forces in a single explanatory framework. And this integration can take place without losing the distinctiveness of such forces. I have elsewhere defended reconstructive learning from arguments that identify reconstructive learning with content-based biases and guided variation (Buskell 2017). Nonetheless, because casting CAT in terms of a theory of forces makes it more amenable to modelling work present in other cultural evolutionary work, it does lose some distinctiveness as an independent research programme.