Exploitable similarity as causally relevant similarity
It is usually recognized that the mere existence of structural similarity between two entities is by no means sufficient to confer on one of those entities the status of representation. S-representations only come into play when a cognitive system depends, in some nontrivial sense, on the relation of similarity in its engagements with its representational targets. As Godfrey-Smith (1996) and Shea (2007, 2014) put this, the correspondence (here, the structural similarity) between representation and its target should be understood as “fuel for success” or a resource that enables organisms to “get things done” in the world. In other words, similarity should be understood as a relation that is exploitable for some larger representation-using system. We now want to address the question of what it means exactly for structural similarity to be exploitable. In particular, we will try to clarify this idea in the context of purely subpersonal S-representations of the sort that we could find inside a mechanical system such as a human brain.
Let us start by taking a closer look at the basic, commonsense intuition that underlies the notion of exploitable similarity. Consider an external, artifactual S-representation such as a cartographic map. We can at least sometimes explain someone’s success at navigating a particular territory by pointing to the fact that the person in question used an accurate map of this territory (and vice versa, we can explain someone’s navigational failure by citing the fact that the person in question used an inaccurate map). Users of cartographic maps owe their success to the similarity that holds between the spatial structure of the representation and the spatial structure of the territory it represents (analogously, the failures can be due to the lack of similarity between the representation and what is represented). This link between similarity and success generalizes to all S-representations, including, we claim, the ones that do not require interpretation by a human being.
On the view we are proposing, explanations of success that invoke the similarity between the representation and its target can be true in virtue of similarity being causally relevant to success. That is, the structural correspondence can quite literally cause the representation-user to be successful at whatever she (or it) is using the representation for, and lack of structural correspondence can cause the user to fail at whatever she (or it) is using the representation for. Explanations that invoke S-representations should thus be construed as causal explanations that feature facts regarding similarity as an explanans and success or failure as an explanandum. To exploit structural similarity in this sense is to use a strategy whose success is causally dependent on structural similarity between the representational vehicleFootnote 2 and what is represented.
Our treatment invokes two concepts that are in need of clarification, especially when applied to internal, subpersonal representations: the notion of success/failure (for which similarity is causally responsible), and the notion of causal relevance. We will now concentrate on each of these notions in turn. Let us start with success and failure.
The idea that human agents can succeed or fail at whatever they use S-representations for seems straightforward enough and we will not dwell on it here. But how to understand success/failure in the case of internal, subpersonal representations of the sort that are of interest to us here? We propose to look at the problem through the lens of the prominent neomechanistic theory of explanation, as applied to cognitive-scientific explanation (Boone and Piccinini 2015; Bechtel 2008; Craver 2007; Miłkowski 2013). Neomechanists see the cognitive system as a collection of mechanisms. A mechanism is a set of organized components and component operations which jointly enable the larger system to exhibit a certain phenomenon (often understood as a capacity of this system). Mechanisms in this sense are at least partly individuated functionally, that is, by reference to the phenomenon that they give rise to—they are essentially mechanisms of this or that cognitive function (mindreading, motor control, attention, perceptual categorization, spatial navigation, etc.). Components and operations derive their functional characterization from the function of the larger mechanism they are embedded in. That is, the function of a component is determined by an operation such that it is through the performance of this particular operation that the component in question contributes to a phenomenon for which the larger mechanism is responsible (see Craver 2007). This is why, say, the function of the heart as a component of a mechanism responsible for blood circulation lies in its pumping blood, and not in its emitting rhythmic sounds; it is the former, and not the latter operation through which the heart contributes to blood circulation.
The vehicles of internal S-representations can be treated as components of cognitive mechanisms, and are targets of various cognitive operations. Each mechanism equipped with an S-representation as its component part underlies a certain phenomenon, i.e., some cognitive capacity. S-representations construed as mechanism components owe their functional characterization to how they contribute to the phenomenon that the larger mechanism is responsible for. What we mean by this is, essentially, that structural similarity between the representation and what it represents is what contributes toward the mechanism’s proper functioning. To put it more precisely, any mechanism responsible for some capacity C which includes an S-representation as its component can fail to realize or enable C as a result of the fact that the component in question is not (sufficiently) structurally similar to the representational target; and analogously, when the mechanism succeeds at realizing or enabling C, this is at least in part due to the fact that this component is (sufficiently) structurally similar to the target. So structural similarity is causally relevant to success/failure because the ability of any S-representation-involving mechanism to perform its function depends on the degree of structural similarity between the representational vehicle and the target. Success and failure are treated here as success or failure at contributing to some function or capacity of a mechanism.
We now turn to the question of what it means for similarity to be causally relevant to success (or failure) thus understood. Here we aim to make use of James Woodward’s (2003, 2008) popular interventionist theory of causal relevance.Footnote 3 It is beyond the scope of the present discussion to present Woodward’s theory in detail so a rough sketch will have to suffice. The core idea behind the interventionist view is that claims of causal relevance connect two variables, say, X and Y.Footnote 4 What it takes for X to be causally relevant to Y is that appropriate interventions into X (i.e., interventions that change the value of X) are associated with changes in Y (i.e., the values of Y):
(M) X causes Y if and only if there are background circumstances B such that if some (single) intervention that changes the value of X (and no other variable) were to occur in B, then Y would change. (see Woodward 2003, 2008)
The intervention in question can be helpfully understood as an experimental manipulation of X in controlled settings, although Woodward’s theory does not require human agency to be involved in establishing causal relations—any change of the value of X could potentially count as an intervention, even one that is not dependent at all on human action. Importantly, there are certain conditions that an intervention must meet in order to establish a causal connection between X and Y. For example, the intervention must not change the value of Y through any causal route except the one that leads through X (e.g., it must not change the value of Y directly or by directly changing the value of a variable that mediates causally between X and Y) and it must not be correlated with any causes of Y other than X or those that lie on the causal route from X to Y.
By employing the interventionist view, we can now understand the causal relevance of similarity for success in the following way. The structural similarity between the representational vehicle and the target is causally relevant for success by virtue of the fact that interventions in similarity would be associated with changes in the success of whatever capacity that is based on, or guided by the representation in question. That is, manipulations on similarity would also be manipulations on the ability of the representation-user—be it a human being or some internal cognitive mechanism—to be successful at whatever she or it is employing the representation for.
To make this proposal more precise, let us apply (M) to the similarity-success relation. The variable X corresponds to similarity between the vehicle and what is represented. It would probably be a gross simplification if we treated X as a binary variable, with one value corresponding to the existence, and the other to the lack of similarity. Luckily, structural similarity can be easily construed as a gradable relation, depending on the degree to which the structure of one relatum actually preserves the structure of the another relatum (see note 1; for another account that explicitly defines similarity as coming in degrees, see: Tversky 1977; Weisberg 2013). This way we can treat X as capable of taking a range of values {X1, X2,…, Xn}, where each increasing value corresponds to an increased degree of similarity between the vehicle and the target. Therefore, between the lack of any similarity and a complete structural indistinguishability, there is a range of intermediate possibilities.
What about Y, the variable that corresponds to success/failure? As far as we can see, S-representations could turn out to feature in a diverse set of mechanisms which give rise to a diverse set of cognitive functions, like motor control and motor planning, perceptual categorization, mindreading, decision making, etc. Now, cognitive systems can be more or less effective at realizing each such function: they can perform better or worse at motor control and planning, perceptually categorizing objects, attributing mental states, making decisions, etc. In this sense, we can treat the variable Y as corresponding to degrees of success of the mechanism in question at enabling an effective performance of a given capacity. Increasing values of Y = {Y1, Y2,…, Yn} would correspond to increasing degrees of success thus understood. But what sorts of values can we have in mind exactly? Here we want to remain as open as possible. Any scientifically respectable way of measuring success can do. For example, the success could be measured by the average frequency of instances of a certain level of performance at some cognitive task, or the probability of a certain level of performance at some task, or a distribution of probabilities of possible levels of performance at some task, etc. The details will always depend on the sort of function in question, as well as on the experimental paradigm used to test or measure it.
We may now formulate our thesis as follows. For similarity to cause success, interventions into the value of X (which corresponds to the degree of structural similarity between the representational vehicle and what it represents) should result in systematic changes in the value of Y (which corresponds to the degree of success of the mechanism that makes use of an S-representation in performing its mechanistic function or capacity). In particular, by intervening in X so that its value increases, we should increase the value of Y; and by intervening in X so that its value decreases, we should decrease the value of Y.
Before we move on, it needs to be noted that the relationship between similarity and success is nuanced in the following way. Good S-representations resemble relevant parts of the world only partially. Maps never mirror the territory in all its detail; instead, they are intentionally simplified, selective, and even distorted. The same applies to subpersonal S-representations. There are at least two reasons to think that. First, S-representations that resemble the target too much become excessively complex themselves. We should then expect there to be a trade-off between a representation’s structural complexity and the temporal or computational resources (costs) that real-life cognitive systems have at their disposal. It is doubtful that limited agents could generate S-representations that come even close to mirroring the structural complexities of the world. Second, in a world as complex as ours, generating maximally accurate S-representations tends to result in overfitting the data, which decreases the representation’s predictive value (this latter point applies to S-representations that are statistical models of the environment).
This general observation can be expressed using our preferred interventionist framework. Suppose that increasing values of variable X correspond to increasing structural similarity between the vehicle and what is represented, and the increasing values of variable Y correspond to increasing success. Now, to accommodate our point, we may say that although in real-life cases of S-representation, there is a positive causal relation between X and Y, it only holds within a limited range of values of X. For simplicity, we may suppose that the relation holds from the lowest value of X to some specific larger value, but it disappears when X exceeds this value. That is, once the value of X exceeds a certain level, then (e.g. due to low cost-effectiveness or overfitting) its relationship to Y breaks down, e.g. increasing the value of X may begin to decrease the value of Y. Crucially, the lesson to be drawn here is not that similarity is functionally irrelevant, but simply that too much similarity can render the S-representation inefficient at serving its purpose. Our proposal is therefore that structural similarity is causally relevant only in a certain range, and the exact range depends on the overall structural trade-offs of the similarity-based system.
The following empirical illustration should illuminate our view. In the philosophical literature, hippocampal spatial maps in rats have been proposed as a good example of an internal S-representation (Ramsey 2016; Rescorla 2009; Shea 2014). The rat’s hippocampus is thought to implement an internal map of the spatial layout of the environment, encoded in a Cartesian coordinate system. According to this hypothesis, the co-activation patterns of so-called place cells in the hippocampus correspond to the spatial structure of the rat’s environment (Shea 2014). That is, the pattern of co-activation relationships between place cells (roughly, the tendency of particular cells to show joint activity) resembles the structure of metric relations between locations within the environment.Footnote 5 This hippocampal map constitutes a component of a cognitive mechanism which underlies the ability to navigate the environment (Craver 2007). The rat’s capacity to find its way within the environment, even in the absence of external cues or landmarks, depends on the fact that it has an internal mechanism equipped with a map of the terrain. This capacity for navigation is usually tested by verifying the rat’s ability to find a reward (food) within a maze in which the animal has no reliable access to external orientation points (see Craver 2007; Redish 1999 for reviews).
As has been already argued in the literature, spatial navigation using hippocampal maps is an instance in which the structural similarity between the map and the territory is being actively exploited by the organism (Shea 2014). Similarity serves as a resource that the rat depends on in its dealings with problems that require spatial navigation. Our proposal provides what we think is a clear and precise interpretation of this claim. The map-world similarity is causally relevant to the rat’s success at finding its way in the environment. This means that we could manipulate the rat’s capacity to navigate in space by intervening in the degree to which its internal map resembles structurally (the relevant part of) the environment. We know, for example, that rats are quite efficient at constructing and storing separate maps for particular mazes (Alme et al. 2014). We may imagine an experiment in which we place the rat in a previously-learned maze and then intervene on the co-activation structure of place cells in a way that distorts (i.e., decreases) the structural correspondence between the map and the maze to a particular degree. If the similarity is really being exploited, then intervention of this sort should decrease the rat’s ability to navigate the particular territory, and we should be able to observe and measure this decrease by investigating the change in the rat’s performance at finding rewards in the maze. What is more, the rat’s navigational capacity (variable Y) should be reduced to a degree which is in proportion to the degree to which we decreased similarity (X) between its internal map and the spatial structure of the maze. And crucially, our intervention should change the rat’s performance only insofar as it constitutes an intervention on similarity as such.
Is similarity really causally relevant?
The following issue might well be raised in the context of our mechanistic-interventionist treatment of the notion of exploitable similarity. One could wonder whether it is really similarity as such that is causally relevant to success. Notice that it is impossible to perform an intervention on the similarity relation in any way other than by intervening in the structure of at least one of its relata (here, the representational vehicle or the represented target). But this invites a worry. Would it not be much more parsimonious to simply state that what is causally relevant for success are structural properties of the vehicle and/or the target? After all, it is by intervening in either of them that we manipulate success. Why bother attributing the causal role to similarity itself? For example, to change a rat’s performance at navigating mazes, it will suffice to intervene on the hippocampal map. Why not simply say that it is the structure of the map (the representational vehicle) that is causally relevant to the rat’s success at spatial navigation? Why treat the relation between the map and the environment as causally relevant?
To reply to this objection, we need to be careful to make the distinction between interventions that change the way some cognitive system acts (behaviorally or cognitively) and interventions that change the success of its actions. The change of action can, but does not have to change the success of the organism at whatever it is doing. If the change in the way the system acts is accompanied by an appropriate change in the external environment, the success can stay at the same level (e.g., we could change the rat’s behavior in a maze without changing its ability to find food if the maze itself changes accordingly). At the same time, the same manipulation of action can change the success of the organism either by increasing it or decreasing it—again, the direction of influence will depend on properties of the environment (e.g., on the structure of the maze that the rat is traversing). So there is no context-free, one-to-one correspondence between action and success. The reason for this is that success and failure in the sense we are using are essentially ecological categories. They co-depend both on what a given system is doing, and on the world within which it is doing it.
Notice now that by concentrating solely on the properties of the representational vehicle, we would completely miss the point just made. Surely, interventions in the structural properties of the vehicle (e.g., the hippocampal map) would change the cognitive system’s actions (e.g., the rat’s behavior when placed in a maze). That much is not debatable. But manipulating actions is not the same as manipulating success. Because of this, the effect that the structure of the vehicle has on action does not imply that the same sort of relationship exists between the vehicle’s structure and success. It is impossible to say how manipulating the vehicle’s structure (and so the organism’s action) will change success independently of facts about the target; or more precisely, independently of the facts regarding structural similarity between the vehicle and the target. In other words, interventions on the vehicle’s structure change the success only insofar as they change the degree of similarity between the vehicle and the target. They increase success if they increase the structural fit between the vehicle and the target. They decrease success only if they decrease the structural fit. And they do not change the success if they do not bring about any change in the structural fit. In any case, what the success depends on is not just the vehicle, but also structural similarity. Of course, again, the only way to intervene on similarity is by manipulating the relata. But it is just wrong to conclude from this that similarity itself is not what is causally relevant here.
Let us formulate our point using some technicalities of Woodward’s account of causal relevance. Suppose that the independent variable X corresponds not to similarity between the vehicle and the target, but to purely vehicular-structural properties of the representation. More precisely, imagine that each value of X corresponds to a different potential structural pattern of the vehicle, regardless of its relationship to anything outside the mechanism. The dependent variable Y remains the same, i.e., it measures the degree of success at realizing some capacity. Now, there are certain constraints that Woodward (2003) puts on any scientifically respectable causal relationships. Two of them are relevant for our present purposes. First, interventions should not simply effect some changes in Y. Rather, the relation between X and Y should be systematic in that we should be able to establish which values of X correspond to which values of Y. Second, the relationship between X and Y should be stable, viz. it should hold across a wide range of different background conditions. But notice that neither of those constraints is met on the interpretation of X and Y that we are now considering. First, because of the reasons we mentioned above, there is no clear mapping from values of X to values of Y, which prevents the relationship between those variables from being systematic in the relevant sense. Setting X at some value could well increase the value of Y, decrease it or even not change it all. Second, the relation between X and Y is by no means stable. In fact, it is fundamentally unstable because of how dependent it is on the states of the environment. It is not possible to say how manipulation of X will change the value of Y independently of the state of the target. Again, the same manipulation of X (e.g., setting the structure of the spatial map in the hippocampus) could bring about drastically different results depending on external circumstances (e.g., depending on the spatial structure of the maze that the rat navigates).
Both Woodward’s constraints are however met if we go back to our original view and consider the variable X to correspond to the degree of similarity between the representational vehicle and the target. The relation between X and Y is then both systematic and stable. It is systematic because we can map increasing values of X onto increasing values of Y. And it is stable at least in the sense that it cannot be broken down by changes in the target. After all, the value of X itself partially depends precisely on properties of the target.Footnote 6 Overall, we think that these considerations provide strong reasons to think that in an S-representational mechanism, what is causally relevant to success is really the relation of structural similarity.