Understanding the mechanism underlying analogy is a notoriously difficult problem. As argued by French (Reference French2002, p. 204): “The lessons of almost 40 years of research in the computational modeling of analogy-making have, more than anything else, shown us just how hard the problem is.” Analogy involves using one situation for understanding another situation, and often the only commonality across the two situations is a common relation among the constituent elements. Given that the base and the target relation (or relations) is the only commonality, most approaches have posited that analogy requires explicit representation of relations. However, several findings could be potentially problematic for this idea. Most importantly, there is evidence that organisms whose ability to represent relations explicitly is unclear (such as nonhuman primates and very young children), can perform analogy (Chen et al. Reference Chen, Sanchez and Campbell1997; Thompson et al. Reference Thompson, Oden and Boysen1997; see also Goswami Reference Goswami, Holyoak, Gentner and Kokinov2001, for a review). The target article attempts to attack the problem head-on: that is, by considering alternatives to the idea that analogy requires explicit representation of relations. This is a laudable attempt – providing a low-level explanation of a process that has been traditionally explained by invoking higher-level processes would be an important contribution.

The target article's proposal has three components: (a) analogy could be a host of phenomena, rather than a unitary phenomenon; (b) relations are construed as transformations between states rather than as explicit symbols; and (c) analogy is the priming of a target relation by a base relation. In this commentary, I focus on each of these components. While I am very sympathetic with the search for alternatives to explicit representation of relations, I am not convinced that the proposed account solves the problem.

The construal of analogy as a set of disparate phenomena is a potentially interesting idea, which attempts to simplify the problem by suggesting a “divide and conquer” approach to analogy. In particular, if analogies performed by nonhuman primates, human infants, and adults are in fact different phenomena, then there is no need to develop a unified account of analogy, or to explain how “analogy as priming” gives rise to more complex forms of analogical reasoning. However, a potential downside of this approach is that in the absence of a clear taxonomy of these putatively disparate phenomena (what these phenomena are, how they are interrelated, and how they differ), it is not clear what the theory of analogy purports to explain. In my view, it remains to be seen whether the idea is truly productive, or whether it offers more “divide” than “conquer” in the study of analogy.

The idea of relation-as-transformation, although promising, seems to cover only a small set of situations, such as some of the tasks described by Goswami and Brown (Reference Goswami and Brown1989). At the same time, even early in development, there are multiple situations where the relation-as-transformation construal is less obvious. These examples include the “animal-habitat” relation, such as “bird to nest as dog to doghouse” (Goswami & Brown Reference Goswami and Brown1990); the class inclusion relation (Goswami & Pauen Reference Goswami and Pauen2005); spatial relations, such as “in the middle” (Lowenstein & Gentner 2005); quantitative relations, such as “monotonic increase” (Kotovsky & Gentner Reference Kotovsky and Gentner1996); and identity relations (Thompson et al. Reference Thompson, Oden and Boysen1997). The fact that young children (and even nonhuman primates) successfully perform analogies based on relations that are difficult to construe as transformations suggests that the construal of relations-as-transformations is at least unnecessary to account for the early analogy. In addition, even if some relations could be construed as transformations, surprisingly little is said by Leech et al. about how relations-as-transformations could be learned. At the same time, learning of relations is a nontrivial problem: It has been argued that different instances of the same relation lack statistical density, and, as a result, it is difficult to learn the categories implicitly, without some sort of supervision (Kloos & Sloutsky Reference Kloos and Sloutsky2008).

The third major component of the proposed account is relational priming. Whereas priming is a relatively basic phenomenon, relations that are putatively primed are not. Therefore, it is critically important to understand how relations are represented. Leech et al. suggest that a key to representations of relations (which are construed as transformations) is the causal agent that is responsible for the transformation. For example, the relation “cutting” could be accessed by “knife” as a putative causal agent. However, whereas this idea is relatively clear for “cutting” it is less clear for “melting,” which depends on an invisible causal agent (i.e., heat), or for “breaking,” which could be implemented by multiple causal agents. If a causal agent is critical for construing relations as transformations, then analogies with more obvious causal agents (e.g., “knife”) should be substantially easier than analogies with invisible causal agents (e.g., “heat”), or those with multiple causal agents (e.g., “breaking”). However, there is little evidence in the literature supporting such differential difficulty (cf. Goswami & Brown Reference Goswami and Brown1989).

It is also unclear where constraints on priming come from. Objects can enter in multiple relations, each of which could be primed. In addition, a set of entities semantically associated with these objects could be primed as well. Consider the following problem: Falcon is to Pigeon as Human is to what (Canary, Chimp, or Chicken)? In addition to Canary (which could be primed by both falcon and pigeon), the Falcon-Pigeon pair can also prime several relations: (1) Larger (in which case Canary or Chicken could be selected); (2) Similar Animal (in which case Chimp could be selected); or (3) Predate (in which case Chicken could be selected). Given that priming does not lead to an unambiguous response, response selection becomes a nontrivial problem; however, the proposed account does not offer an obvious way of addressing this problem.

There are also important developmental questions associated with the proposed account. How do children learn that transformations are important? How do they encode, store, and retrieve relations-as-transformations in the absence of an obvious causal agent? Do relations-as-transformation undergo developmental change, or do they remain the same throughout development? And most importantly, how do people acquire the ability to perform analogy when relations cannot be construed as transformations? Overall, while the target article makes a promising proposal, it also provides further evidence of “how hard the problem of analogy is.”