As someone interested in naturalized epistemology, I have benefited from reading Leech et al.'s target article for it argues that there is a need to study early analogical reasoning in a developmental framework. Although complex analogical reasoning – as observed in adults with proper mental makeup and education – may be explicated in the abstract (Falkenhainer et al. Reference Falkenhainer, Forbus and Gentner1989), a developmental approach requires, more than anything else, psychological plausibility. In one of the better works in the latter regard, Thagard et al. (Reference Thagard, Holyoak, Nelson and Gochfeld1990, p. 290) affirm that the computational model they describe is “intended to be a model of human cognition, so it is essential that it be consistent with the results of psychological experiments.” It is uplifting to watch Leech et al. pay careful attention to present-day cognitive psychology and never let the results of their work drift away from correlation with its accomplishments.
Leaving aside the connectionist implementation for others to comment upon, I think it is fair to say that the core of Leech et al.'s argument is the cognitive apparatus for an “A is to B as C is to …?” (denoted as “A:B::C:?” in what follows) analogy, which is customarily handled thus:
map A onto C
map B onto D (this is the unknown term to occupy the … position)
transfer across the relation between A and B to C and D (so as to correctly determine D)
Their conjecture is that relational priming accomplishes this task neatly. To wit, exposure to A and B primes a relation R that then biases C to show the way to the appropriate D. To give an example from the simple causal domains of childhood, after seeing the triple “cake, slice of cake (i.e., cut cake), pizza,” the analogically appropriate response would be “slice of pizza” (i.e., cut pizza). Here, the terms “cake” and “slice of cake” prime a relation (“cutting”) that then biases “pizza” to produce the appropriate response “slice of pizza.”
Relational priming is a commonsense notion, and its relatives are widespread. Estes and Jones (Reference Estes and Jones2006, p. 89) define relation [sic] priming as a phenomenon in which grasp of a word pair (“plastic spoon”) is facilitated by the past presentation of another (“wooden plate”) that instantiates the same conceptual relation (“made of”). Recanati (Reference Recanati2004, pp. 148–51), inspired by Wittgenstein, elucidates how someone learns a predicate P – a central concern in cognitive linguistics. The learner observes the application of P in a particular context (situation) K and associates P and K. In another context K′, the learner will assume that P applies in case she discerns that K′ is adequately “similar” to K (Akman Reference Akman and Fetzer2007). If her judgment regarding the resemblance of K and K′ is flawed (in other words, K and K′ are similar in a way not pertinent for the application of P), then communal help would come and correct the learner. The learning phase of the learner boils down to noting enough contexts in which P is reasonably applicable. In some sense, we can say that P and K cause a “legitimate context of application” to be primed.
Unfortunately, the notion of relational priming is fairly problematic. It is true that an analogy problem such as “puppy:dog:: kitten:?” can be solved rather easily with relational priming. Basically, exposure to “puppy” and “dog” primes the relation “offspring,” which then biases “kitten” to produce “cat” as the D term. But the question arises: Why not the relation “younger than”? Let me borrow the notation of situation theory for a second (Barwise & Perry Reference Barwise and Perry1983) and say that if R is a binary relation and A, B are objects appropriate for the respective argument places of R, then we shall write <<R, A, B, 1>> to denote the informational item that A, B stand in the relation R. My point is that exposure to “puppy,” “dog” could potentially prime several candidate relations, and it is no easy feat to decide which one of these is to be preferred. (It is a different matter to inquire whether this would affect the correct solution of the analogy problem.) In a nutshell, <<offspring, puppy, dog, 1>> and <<younger than, puppy, dog, 1>>, <<cuter than, puppy, dog, 1>>, and so on, are all possible informational items, not to mention the more theoretical <<isa, puppy, dog, 1>>. Presumably, this problem does not arise in the aforementioned cake example because of the implicit presence of a causal agent (e.g., a knife), but even that is suspect. Surely, the primed relation could have been “larger than” in that example. (Or “more expensive than,” if you truly want to make life difficult for a fan of relational priming.)
It is also crucial to observe that R has two argument roles, yet these “slots” into which appropriate objects can be placed are not ordered in any way – and “certainly not linearly ordered as a finite sequence” (Devlin Reference Devlin1991, p. 116). In the case of the relation “offspring,” the argument roles can be termed as “ascendant” and “descendant.” Accordingly, one apparent objection has to do with the “direction” of the relationship. Maybe “ancestry” (rather than “offspring”) should be the primed relation as it does the job equally well; after all, one of the informational items <<ancestry, ascendant: dog, descendant: puppy, 1>> and <<offspring, descendant: puppy, ascendant: dog, 1>> is redundant given the other. In all likelihood, young children would never use these abstract relations anyway; they would prefer a tangible relation such as “mother of.” At least this is what my 5-year-old consistently does. Whenever she sees a lonely cat in the backyard, she says that the animal is seeking “the mom” (and never “the dad” or “the parents”).
To make things more complicated, it is not clear whether other examples superficially similar to “puppy:dog::kitten:?” can be solved effortlessly. Take “rake:leaves::magnet:?.” In this case, exposure to the first pair should presumably prime the relation “conveniently collects in one place (location).” Then the answer “paper clips” would be apparent. However, I trust that this must be a tough one for a child of five.
Finally, take the celebrated line attributed to Groucho Marx: “Military justice is to justice as military music is to music.” When this is formulated as “military justice:justice::military music:?,” it is straightforward to say that the first two terms prime the theoretical relation “ako” – representing one class being a subset of another – and hence the D term can be trivially worked out as “music.” However, and I say this somewhat hesitantly, the correct understanding here starts from the reverse direction. In other words, what makes the analogy a striking one (one that works) is that we are supposed to know that military music is invariably dreadful as a harmonious experience and that military justice should fail in the same vein. Maybe another Groucho quip is in order: “A child of five would understand this. Send someone to fetch a child of five.”
