I begin with my first question: Why is apple:cut apple :: bread:cut bread an analogy and not a simple categorization? After all, they are both from the food domain. If I show a child a paradigmatic dog – for example, a beagle – and then show that child an unusual dog – for example, a hairless Chinese Crested – then if the child correctly identifies the Chinese Crested as a dog, we would say that the child has categorized the Crested, not that the child has made an analogy. Presumably then, what makes an analogy is mapping relational structure. (I am happy to grant this, but it is a gift, since, for all we know, most concepts have relational structure. So, appealing to such mapping, even mapping systems of structures, may not actually distinguish categorization from analogy.) But is any relational categorization an analogy? Perhaps relational mapping isn't all there is to analogy. Though the notion is hard to define experimentally or even theoretically, the “semantical distance” between the two analogue domains is also important: the greater the distance, the deeper the analogy (Leech et al. make some interesting comments related to this in sect. 5.1.2). So, now my second question: Could Leech et al.'s connectionist network make an analogy (with appropriate changes) between apple:cut apple and team:cut from the team, or cut of a deck of cards? Or, since the result in their examples of cutting an apple and a loaf of bread is a slice, could their network be trained in such a way as to make an analogy with slice of life?

Admittedly, analogies between cutting an apple and being cut from a team are more complex, “adult-level” analogies, and Leech et al. admit that their model has a ways to go before it can make adult analogies; yet, though they do an admirable job of arguing that their model can be extended to make such analogies, one still wonders whether their three central notions of pattern completion, relational priming, and implicit representations are up to the task. This leads to my third question: Can their implicit relational representations account for both the abstraction and conscious knowledge seen in adult analogies? This third question is really comprised of three, more specific, questions, to which I now turn.

Two crucial aspects of adult analogies are that they create abstractions on the fly (the relational structures of the two analogues are abstracted; this is sometimes called “relational change”; see Dietrich et. al 2003) and they bring to consciousness the fact that the two analogues are indeed analogous (one can always say, “X is like Y' or ‘X reminds me of Y’; see Dietrich Reference Dietrich, Dietrich and Markman2000; and cf. Leech et al., sect. 5.2, first para.). Rutherford's crucial analogy between the deflected trajectories of alpha particles and the orbital paths of comets is a classic example of the sort of abstraction that I mean (the abstraction is due in part to the fact that deflected trajectories are by no means orbits – Rutherford Reference Rutherford1911; also see “Rutherford Scattering” and “Gold Foil Experiment” in Wikipedia). This analogy (not the data behind it) doomed the reigning plum-pudding model of the atom and led eventually to the better Bohr model of the atom. Science is rife with such examples.

It is hard to see how these two aspects of analogy could be realized in Leech et al.'s model. How can a relational structure be abstracted if it's only implicitly represented as a state transformation? That would seem to require abstracting the states. Is that possible on their model? And how can the knowledge of something be brought to consciousness if it is not explicitly represented?

Models of analogy that use explicit, discrete representations seem to be able to handle these two aspects. Structure-mapping theory (Gentner Reference Gentner1983) is a good example. However, structure-mapping theory is not the final word on analogy, as everyone, including Gentner, admits (though, of course, there is disagreement on why it is not the final word). It is clear that Leech et al.'s developmental model of analogy brings important new insights to the table. What is not clear is how to have one model that does justice to the developmental data, the obvious constraint that analogy would seem to have to arise from simpler mechanisms such as priming, and the fact that analogies produce abstractions to which we have conscious access (as we do to the analogies themselves). This problem of different, incompatible models explaining different aspects of a single cognitive phenomenon is quite common in cognitive science. This takes me to my final question.

In their Gulf War/World War II model, Leech et al. use the exact same relations in each domain (see Table 3 in sect. 4.1.2). This seems to weaken their case that their relational priming model could be extended to adult-level analogies, for it is very unlikely that the exact same relations would obtain in different domains. It is even very unlikely that the same labels (names) would obtain in different domains. This problem is related to a problem within structure-mapping theory (SMT). According to SMT, analogies are isomorphisms between high-level structures. In an important sense, the analogous concepts simply share one structure that funds their being analogous. Furthermore, SMT assumes that these isomorphisms obtain before a given analogy is made (indeed, the isomorphisms explain why the analogy was made). The probability that such isomorphisms obtain before an analogy is made is very low – too low to account for the quantity of analogies an individual produces (Dietrich Reference Dietrich, Dietrich and Markman2000). Therefore, on any SMT-like model, the relevant representations in an analogy have to change at the time of retrieval in order to forge the needed isomorphism (Dietrich et al. Reference Dietrich, Markman, Winkley, Ohsawa and McBurney2003). Perhaps relational priming could solve this problem without invoking retrieval-based change.

It seems as though the best extension of Leech et al.'s system for handling adult-level analogies would be a system combining their insights regarding relational priming, a process for rendering explicit some implicit relational representations, together with a process for abstracting those explicit representations so that semantically distant analogies can be made. Is such an extension compatible with how Leech et al. see their future work unfolding?