2.1. Perceptual versus relational similarity

We begin our review of the similarities and differences between human and nonhuman cognition with what William James (Reference James1890/1950) called “the very keel and backbone of our thinking”: sameness. The ability to evaluate the perceptual similarity between stimuli is clearly the sine qua non of biological cognition, subserving nearly every cognitive process from stimulus generalization and Pavlovian conditioning to object recognition, categorization, and inductive reasoning. Humans, however, are not limited to evaluating the similarity between objects based on perceptual regularities alone. Humans not only recognize when two physical stimuli are perceptually similar, they can also recognize that two ideas, two mental states, two grammatical constructions, or two causal-logical relations are similar as well. Even preschool-age children understand that the relation between a bird and its nest is similar to the relation between a dog and its doghouse despite the fact that there is little “surface” or “object” similarity between the relations' constituents (Goswami & Brown Reference Goswami and Brown1989; Reference Goswami and Brown1990). Indeed, as numerous researchers have shown, the propensity to evaluate the similarity between states of affairs based on the causal-logical and structural characteristics of the underlying relations rather than on their shared perceptual features appears quite early and spontaneously in all normal humans – as early as 2–5 years of age, depending on the domain and complexity of the task (Gentner Reference Gentner1977; Goswami Reference Goswami, Gentner, Holyoak and Kokinov2001; Halford Reference Halford1993; Holyoak et al. Reference Holyoak, Junn and Billman1984; Namy & Gentner Reference Namy and Gentner2002; Rattermann & Gentner Reference Rattermann and Gentner1998a; Richland et al. Reference Richland, Morrison and Holyoak2006).

In short, there appear to be at least two kinds of similarity judgments at work in human thought: judgments of perceptual similarity based on the relation between observed features of stimuli; and judgments of non-perceptual relational similarity based on logical, functional, and/or structural similarities between relations and systematic correspondences between the abstract roles that elements play in those relations (Gentner Reference Gentner1983; Gick & Holyoak Reference Gick and Holyoak1980; Reference Gick and Holyoak1983; Goswami Reference Goswami, Gentner, Holyoak and Kokinov2001; Markman & Gentner Reference Markman and Gentner2000). The question we are interested in here is whether or not there is any evidence for non-perceptual relational similarity judgments in nonhuman animals as well.

2.2. Same-different relations

Among comparative researchers, the most widely replicated test of relational concept learning over the last quarter century has been the simultaneous same-different (S/D) task, in which the subject is trained to respond one way if two simultaneously presented stimuli are the same and to respond a different way if the two stimuli are different. In the purportedly more challenging relational match-to-sample (RMTS) task, the subject must select the choice display in which the perceptual similarity among elements in the display is the same as the perceptual similarity among elements in the sample stimulus. For example, presented with a pair of identical objects, AA, as a sample stimulus, the subject should select BB rather than CD; presented with a pair of dissimilar objects, EF, as the sample stimulus, the subject should select GH rather than JJ (see Thompson & Oden Reference Thompson and Oden2000 for a seminal discussion).

Although Premack (Reference Premack1983a; Reference Premack1983b) initially reported that only language-trained chimpanzees passed S/D and RMTS tasks, success on two-item S/D tasks has since been demonstrated in parrots (Pepperberg Reference Pepperberg1987), dolphins (Herman et al. Reference Herman, Pack, Morrel-Samuels, Roitblat, Herman and Nachtigall1993b; Mercado et al. Reference Mercado, Killebrew, Pack, Macha and Herman2000), baboons (Bovet & Vauclair Reference Bovet and Vauclair2001), and pigeons (Blaisdell & Cook Reference Blaisdell and Cook2005; Katz & Wright Reference Katz and Wright2006), among others. Thompson et al. (Reference Thompson, Oden and Boysen1997) showed that language-naive chimpanzees with some exposure to token-based symbol systems are able to pass a two-item RMTS task (cf. Premack Reference Premack and Weiskrantz1988). Vonk (Reference Vonk2003) has reported that three orangutans and one gorilla were able to pass a complex two-item RMTS task without any explicit symbol or language training at all. Fagot et al. (Reference Fagot, Wasserman and Young2001) have shown that language-naïve baboons can pass an RMTS task involving arrays of elements (see discussion below); and Cook and Wasserman (in press) have reported successful results on an array-based RMTS task with pigeons. So passing S/D and RMTS tasks does not appear to be limited to language-trained apes or even primates.

Regardless of which nonhuman species are capable of passing S/D and RMTS tasks, the more critical and largely overlooked point is this: Both of these experimental protocols lack the power, even in principle, of demonstrating that a subject cognizes sameness and difference as abstract, relational concepts which are (1) independent of any particular source of stimulus control, and (2) available to serve in a variety of further higher-order inferences in a systematic fashion. A functional decomposition of the S/D and RMTS protocols reveals that the minimum cognitive capabilities necessary to pass these tests are much more modest.

The fundamental problem is that the same-different relation at stake in the classic S/D task can be reduced to a continuous, analog estimate of the degree of perceptual variability between the elements in each display. Halford et al. (Reference Halford, Wilson and Phillips1998a) refer to this type of cognitive trick as “conceptual chunking.” Chunking reduces the complexity of processing a relation at the cost of losing the original structure and components of the relation itself, but suffices when the task does not require the structure of the relation itself to be taken into account. A cognizer could pass a classic S/D task by calculating an analog estimate of the variability between items in the sample display and then employ a simple conditional discrimination to select the appropriate behavioral response to this chunked result. Hence, success on an S/D task may imply that a subject can generalize a rule-like discrimination beyond any particular feature in the training stimuli; but it cannot be taken as evidence that the subject has understood sameness and difference as structured relations that are mutually exclusive or that can be freely generalized beyond the modality-specific rule the subject used in a particular learning context.

The same deflationary functional analysis applies, mutatis mutandis, to the RMTS task. The apparent relational complexity of the RMTS task can be significantly reduced by segmenting the task into separate chunked operations that are evaluated sequentially. First, the subject can evaluate the variability within the first-order relations by chunking them into analog variables. Second, the subject can employ a straightforward conditional discrimination to select the appropriate choice display: for example, <if the variability of the sample display is low, select the choice display with a low variability>. Although this may qualify as a “higher-order” operation, it does not qualify as a higher-order relational operation since the constituent structures of the first-order relations are no longer relevant or available to the higher-order process (see again, Halford et al. Reference Halford, Wilson and Phillips1998a). At best, the RMTS task demonstrates that nonhuman animals can select the choice display that has the same degree of between-item variability as the sample display. But the task says nothing about nonhuman animals' ability to evaluate the non-perceptual relational similarity between those relations.

The preceding functional decomposition of the S/D and RMTS tasks is not merely a hypothetical possibility. There is now good experimental evidence that chunking and segmentation are precisely the tactics that nonhuman animals employ when they succeed at S/D and RMTS tasks. Wasserman and colleagues, for example, have shown that both pigeons and baboons have much less difficulty passing S/D tasks when there are 16 items in each set than when there are only 2 items in each set (Wasserman et al. Reference Wasserman, Young and Fagot2001; Young & Wasserman Reference Young and Wasserman1997). Wasserman et al. showed that a simple measure of item variability, based on Shannon and Weaver's (Reference Shannon and Weaver1949) measure of informational entropy, nicely captures the functional pattern of nonhuman subjects' discriminations across a variety of experimental conditions (reviewed in Wasserman et al. (Reference Wasserman, Young and Cook2004). Nonhuman animals' performance on S/D tasks differs markedly from the categorical, logical distinction that humans make between sameness and difference. Human subjects' responses to S/D tasks are also influenced by the degree of variability in the stimuli (Castro et al. Reference Castro, Young and Wasserman2007; Young & Wasserman Reference Young and Wasserman2001); but most human subjects exhibit a categorical distinction between displays with no item variability (i.e., same) and those with any item variability at all (i.e., different).

An analogous discontinuity between human and nonhuman judgments of similarity has also been documented on RMTS tasks. Fagot et al. (Reference Fagot, Wasserman and Young2001) presented two adult baboons and two adult human subjects with an RMTS task using arrays of 16 visual icons that were either all alike or all different. Both baboon and human subjects learned to pass the RMTS test and successfully generalized to novel sets of stimuli. When the authors reduced the number of items in the sample set from 16 to 2 icons, the difference between the two species, however, was notable. The impact on the human subjects' responses was insignificant. The baboons' performance, however, fell to chance on different trials, whereas their performance on same trials remained unchanged. This markedly asymmetric effect is exactly what one would expect if the baboons were discriminating between second-order same and different relations by comparing the amount of variability (e.g., entropy) in the two displays. That is, same trials with 2 icons continue to yield zero entropy, but different trials now yield a small entropy value that is more difficult to discriminate from zero.

Entropy is certainly not the only factor modulating nonhuman subjects' judgments of sameness and difference. Stimulus oddity as well as spatial organization and degree of similarity also play an important role (see Cook & Wasserman (Reference Cook, Wasserman, Wasserman and Zentall2006 for an important review). Vonk (Reference Vonk2003) has shown that language-naive apes can judge variability along specific perceptual dimensions (e.g., color rather than size or shape). And Bovet and Vauclair (Reference Bovet and Vauclair2001) have shown that baboons can pass a “conceptual” S/D task in which pairs of objects are to be treated as same if they share a similar learning history or biological significance (e.g., objects-I-have-eaten vs. objects-I-have-not-eaten). These results demonstrate that nonhuman animals – and not just language-trained chimpanzees – are capable of learning novel, sophisticated, rule-governed discriminations that generalize beyond any specific perceptual cue. But in all of the results reported to date, the relevant discriminations are bound to a particular source of stimulus control (e.g., entropy, oddity, edibility). There is no evidence that nonhuman animals understand what “sameness” in one task has in common with “sameness” in another. For example, after passing a “perceptual” S/D task and having been trained to categorize objects as either “food” or “not food,” the baboons in Bovet and Vauclair's (2001) study nevertheless required an average of 14,576 additional trials on the “conceptual” S/D task before their responses were correct 80% of the time on trials involving novel pairs of objects.

The available evidence therefore suggests that the formative discontinuity in same-different reasoning lies not between monkeys and apes, as Thompson and Oden (Reference Thompson and Oden2000) proposed, but between nonhumans and humans. Chimpanzees and other nonhuman apes can pass RMTS tasks with only 2 items in the sample display (e.g., Thompson et al. Reference Thompson, Oden and Boysen1997; Vonk Reference Vonk2003). Baboons can pass RMTS tasks with as few as 3–4 items in each sample (Fagot et al. Reference Fagot, Wasserman and Young2001); and pigeons can pass RMTS tasks with 16 items in each sample (Cook & Wasserman, in press). The difference between the performance of language-naive pigeons and language-trained chimps on these tasks often comes down to a question of the number of items in each set and the number of trials necessary to reach criterion. As Katz and colleagues point out (see Katz & Wright Reference Katz and Wright2006; Katz et al. Reference Katz, Wright and Bachevalier2002), this strongly suggests that there is a difference in degree between various nonhuman species' sensitivity to similarity discriminations (influenced by training regimen), not a difference in kind between their conceptual abilities to predicate same-different relations.

The performance of human subjects, on the other hand, contrasts sharply with the performance of all other animal species. Humans manifest an abrupt, categorical distinction between displays in which there is no variability and displays in which there is any variability at all (Cook & Wasserman Reference Cook, Wasserman, Wasserman and Zentall2006; Wasserman et al. Reference Wasserman, Young and Cook2004). More importantly, contra Castro et al. (Reference Castro, Young and Wasserman2007), we believe that human subjects possess a qualitatively distinct system for reinterpreting sameness and difference in a logical and abstract fashion that generalizes beyond any particular source of stimulus control. In short, even with respect to the most basic and ubiquitous of all cognitive phenomena – judgments of similarity – there is already a distinctive seam between human and nonhuman minds.

2.3. Analogical relations

Premack (Reference Premack1983a, p. 357) suggested that the RMTS task is an implicit form of analogy and claimed that “animals that can make same/different judgments should be able to do analogies.” Indeed, it is still widely accepted that the ability to pass an RMTS task is the “cognitive primitive” for analogical reasoning (see, e.g., Thompson & Oden Reference Thompson and Oden2000, p. 378). We disagree. While recognizing perceptual similarities is certainly a necessary condition for making analogical inferences (inter alia), there is a qualitative difference between the kind of cognitive processes necessary to pass an S/D or RMTS task and the kind of cognitive processes necessary to reason in an analogical fashion. The relations at issue in S/D and RMTS tasks are based solely on the perceptual features of the constituents; and the constituents play undifferentiated and symmetrical roles in those relations (e.g., two objects are symmetrically either the same or different).

Most true analogies, on the other hand, are based on relations in which the constituents play asymmetrical, causal-logical roles (e.g., the role that John plays in forming the relation, John loves Mary, is not equivalent to the role that Mary plays, perhaps to John's dismay). Furthermore, genuine analogical inferences are made by finding systematic structural similarities between perceptually disparate relations, allowing the cognizer to draw novel inferences about the target domain independently from the perceptual similarity between the relations' constituents (Gentner Reference Gentner1983; Gentner & Markman Reference Gentner and Markman1997; Holyoak & Thagard Reference Holyoak and Thagard1995). Accordingly, analogical relations sensu stricto cannot be reduced via chunking and segmentation, but require the cognizer to evaluate the abstract, higher-order relations at stake in a structurally systematic and inferentially productive fashion.

Analogical reasoning is a fundamental and ubiquitous aspect of human thought. It is at the core of creative problem solving, scientific heuristics, causal reasoning, and poetic metaphor (Gentner Reference Gentner, Gentner and Goldin-Meadow2003; Gentner et al. Reference Gentner, Holyoak and Kokinov2001; Holyoak & Thagard Reference Holyoak and Thagard1995; Reference Holyoak and Thagard1997; Lien & Cheng Reference Lien and Cheng2000). And it is also central to the more prosaic ways that typical human children learn about the world and each other (Goswami Reference Goswami1992; Reference Goswami, Gentner, Holyoak and Kokinov2001; Halford Reference Halford1993; Holyoak et al. Reference Holyoak, Junn and Billman1984). To date, however, the only evidence that any nonhuman animal is capable of analogical reasoning sensu stricto comes from the unreplicated feats of a single chimpanzee, Sarah, reported more than 25 years ago by Gillan et al. (Reference Gillan, Premack and Woodruff1981). Sarah reportedly constructed and completed two distinct kinds of analogies. The first was based on judging whether or not two geometric relationships were the same or different (e.g., large blue triangle is to small blue triangle as large yellow crescent is to small yellow crescent). The second was based on judging the similarity between two “functional” relationships (e.g., padlock is to key as tin can is to can opener). Gillan et al. (Reference Gillan, Premack and Woodruff1981) reported that Sarah was successful on both tests.

Savage-Rumbaugh was the first to point out that Sarah's performance on the geometric version of the original tests could have been the result of a simple, feature-matching heuristic (cited by Oden et al. (Reference Oden, Thompson, Premack, Gentner, Holyoak and Kokinov2001). In response, Oden et al. (Reference Oden, Thompson, Premack, Gentner, Holyoak and Kokinov2001) followed up Gillan et al.'s original experiment on geometric analogies with a series of more carefully constructed tests designed to flesh out Sarah's actual cognitive strategy. These new experiments used geometric forms that varied along one or more featural dimensions (e.g., size, color, shape, and/or fill). After extensive testing, Oden et al. showed that Sarah was actually tracking the number of within-pair featural differences rather than the kind of relation between pairs of figures. For example, whereas a human would see a color plus a shape change as differing from a size plus a fill change, Sarah saw these two transformations as equivalent because they both entailed two featural changes.

Oden et al. (Reference Oden, Thompson, Premack, Gentner, Holyoak and Kokinov2001) argued that this strategy still demonstrates Sarah's ability to reason about the “relation between relations.” But there is a profound difference between the feature-based heuristic Sarah apparently adopted and the role-based structural operations that are the basis of analogical inference sensu stricto. To be sure, keeping track of the number of within-pair featural changes certainly requires quite sophisticated representational processes. But the fact that Sarah apparently ignored the structure of the relation between pairs of figures suggests that she represented any featural change as an undifferentiated chunk for the purposes of this task. Therefore, her strategy on this task appears to be computationally equivalent to the kind of chunking and segmentation strategies other nonhuman primates use to solve RMTS tasks. According to Oden et al.'s (2001) own analysis, Sarah failed to demonstrate a systematic sensitivity to the higher-order structural relation between relations. It is this systematic sensitivity to higher-order structural relations which is, as Gentner (Reference Gentner1983) has long argued, the hallmark of analogical reasoning in humans.

Therefore, the claim that nonhuman animals are capable of analogical inferences rests solely on Sarah's performance in the test of functional analogies reported by Gillan et al. (Reference Gillan, Premack and Woodruff1981). There are many reasons to be skeptical of these results as well. For one, Sarah's performance on these analogies has never been replicated either by Sarah herself or by any other nonhuman subject. Second, of the two experiments (3A and 3B) devoted to functional analogies, the authors themselves admit that the first, 3A, is open to an alternative feature-based account. Furthermore, the second experiment, 3B, did not require Sarah to complete or construct analogies. It merely required her to respond to the relation between two pairs of objects with one of two plastic tokens that her experimenters interpreted as meaning same and different. Sarah's extensive prior exposure to the objects used in this experiment, however, makes it very difficult to judge how she learned to cognize the relation between these objects (e.g., how exactly did Sarah understand that the relation between “torn cloth” and “needle and thread” is the same as the relation between “marked, torn paper” and “tape”?). Indeed, the authors themselves admit that Sarah's “unique experimental history” may have contributed to her success on these tasks (Gillan et al. (Reference Gillan, Premack and Woodruff1981, p. 11).

In short, what is sorely needed is a more extensive series of tests, like those carried out by Oden et al. (Reference Oden, Thompson, Premack, Gentner, Holyoak and Kokinov2001), to systematically tease apart the salient parameters in Sarah's cognitive strategy. Until then, Sarah's remarkable and unreplicated success on experiment 3B as reported by Gillan et al. (Reference Gillan, Premack and Woodruff1981) constitutes thin support for claiming that nonhuman animals are capable of analogical reasoning.

5.1. Transitive choices in the lab

For many decades now, the classic comparative test of transitive inference has been a nonverbal five-item task developed by Bryant and Trabasso (Reference Bryant and Trabasso1971) in which subjects are incrementally trained on pairs of stimuli (i.e., A+B-, B+C-, C+D-, D+E-) and then tested on non-adjacent untrained pairs. The discriminative relation between the stimuli used in most of these studies is not, in fact, transitive; it is the subjects' choices that become transitive as a result of the pattern of differential reinforcement: that is, repeated reinforcement of the choice of A over B and of B over C eventually leads to the subject preferring A over C. As Halford et al. (Reference Halford, Wilson and Phillips1998b) pointed out, a subject's preferences can become transitive through incremental reinforcement without there being a transitive relation between the underlying task elements themselves, and therefore without requiring the subject to understand anything about transitivity as a logical property. Indeed, many researchers have shown that successfully selecting B over D in the traditional five-item incremental protocol can be achieved using purely associative operations (De Lillo et al. Reference DeLillo, Floreano and Antinucci2001; Wynne (Reference Wynne1995).

To be sure, reinforcement history cannot be the whole story, as Lazareva et al. (Reference Lazareva, Smirnova, Bagozkaja, Zorina, Rayevsky and Wasserman2004) have recently demonstrated. Lazareva et al. (Reference Lazareva, Smirnova, Bagozkaja, Zorina, Rayevsky and Wasserman2004) trained eight hooded crows in a clever variation on Bryant and Trabasso's five-item protocol. Five colored cards were used to represent the elements in the series, A through E. The color on one side of the card served as the choice stimulus, and a circle of the same color on the underside of the card served as the post-choice feedback stimulus. The crows were asked to choose one of two simultaneously presented cards. Importantly, the colored circles on the underside of the cards were displayed to the crows only after they had selected one of the two choice stimuli. The crows were divided into two experimental groups. In the ordered-feedback group, the diameter of the circles associated with the choice stimuli became progressively smaller from A to E. In the constant-feedback group, the diameter of the feedback circles did not change. After initial training, Lazareva et al. (Reference Lazareva, Smirnova, Bagozkaja, Zorina, Rayevsky and Wasserman2004) overexposed both groups of crows to D+E- pairings. Under traditional associative models, massive overexposure to D+E- pairings should lead to preferentially selecting D over B. Nevertheless, the crows in the ordered-feedback group selected B over D in the BD pairings, whereas the crows in the constant-feedback group either chose at random or preferred D over B.

Lazareva et al.'s (2004) results show that reinforcement history alone cannot account for the emergence of choice transitivity among nonhuman animals. Moreover, we agree with Lazareva et al. (Reference Lazareva, Smirnova, Bagozkaja, Zorina, Rayevsky and Wasserman2004) that these results are consistent with some kind of “spatial representation” hypothesis (Gillan Reference Gillan1981). But what is not often noted by comparative researchers is that evidence for an integrated representation of an ordered series is not in and of itself evidence for transitive reasoning or relational integration in a logical-deductive sense. There is more to making logically underpinned transitive inferences than constructing an ordered representation of one's choices.

As Lazareva et al. (Reference Lazareva, Smirnova, Bagozkaja, Zorina, Rayevsky and Wasserman2004) themselves point out, in order to claim evidence for logically underpinned transitive inferences, one must show that the organism can, in fact, distinguish between transitive and non-transitive relations and that it makes its choices on the basis of this logical relation independently of other non-logical factors such as reinforcement history and training regime (see also Halford et al. Reference Halford, Wilson and Phillips1998a; Wright Reference Wright2001). The results reported by Lazareva et al. (Reference Lazareva, Smirnova, Bagozkaja, Zorina, Rayevsky and Wasserman2004) do not provide evidence for either of these criteria.

In a follow-up experiment, Lazareva and Wasserman (Reference Lazareva and Wasserman2006) showed that pigeons select B over D stimuli in the same protocol employed by Lazareva et al. (Reference Lazareva, Smirnova, Bagozkaja, Zorina, Rayevsky and Wasserman2004) even when the size of the post-choice cues is constant – which demonstrates that the transitive perceptual relation between the post-choice cues is not, in fact, computationally necessary for successfully passing this particular protocol. It is unclear why crows – but not pigeons – were unable to pass the test in the constant-feedback condition. There are many possible explanations. For example, Lazareva et al. (Reference Lazareva, Smirnova, Bagozkaja, Zorina, Rayevsky and Wasserman2004) did not rule out the possibility that it was simply the variability between post-choice cues that encouraged the crows' successful responses rather than their transitivity per se. In any case, in order to warrant the claim that the crows were reasoning on the basis of the logical relation between post-choice stimuli independently of other non-logical factors, it would be necessary to show that the crows could systematically generalize to novel stimuli on a first trial basis: For example, trained to associate a novel choice stimulus, X, with a colored circle of a given diameter, could the crows correctly choose between X and any stimulus from the set, A through E, on a first-trial basis in a systematic manner? To date, there is no evidence that crows, or any other nonhuman animal, could pass such a test.

5.2. Transitive inferences in the wild

Many researchers have argued that animals' full transitive reasoning capabilities are most likely to manifest themselves in inferences involving social relations (e.g., Bond et al. Reference Bond, Kamil and Balda2003; Grosenick et al. Reference Grosenick, Clement and Fernald2007; Kamil Reference Kamil2004; Paz et al. Reference Paz, Bond, Kamil and Balda2004). Much of the early fieldwork focused on nonhuman primates (see Tomasello & Call Reference Tomasello and Call1997 for a review). The strongest evidence to date for transitive social inferences in a nonhuman animal comes not from primates, however, but from birds (see review by Kamil Reference Kamil2004) and fish (see Grosenick et al. Reference Grosenick, Clement and Fernald2007). Paz et al. (Reference Paz, Bond, Kamil and Balda2004), for example, showed that male pinyon jays can anticipate their own subordinance relation to a stranger after having witnessed the stranger win a series of confrontations with a familiar but dominant conspecific. Similarly, Grosenick et al. (Reference Grosenick, Clement and Fernald2007) allowed territorial A. burtoni male fish to observe pairwise fights between five rivals (i.e., AB, BC, CD, DE), with the outcomes implying a dominance ordering of A>B>C>D>E. When subsequently given a choice between B and D, observers preferred to spend more time adjacent to D rather than B.

Results such as these demonstrate that the ability to keep track of the dominance relations between tertiary dyads is not limited to nonhuman primates or even to mammals (cf. Tomasello & Call (Reference Tomasello and Call1997). Furthermore, fish and birds, in addition to nonhuman primates, can apparently use this information to make rational (i.e., ecologically adaptive) choices about how to respond to potential rivals (see also Bergman et al. (Reference Bergman, Beehner, Cheney and Seyfarth2003; Bond et al. Reference Bond, Kamil and Balda2003; Hogue et al. Reference Hogue, Beaugrand and Lague1996; Silk Reference Silk1999). The accumulated evidence therefore rules out a traditional associative explanation and strongly supports a more complex, information-processing account of how nonhuman animals keep track of and respond to dominance relations among conspecifics.

But none of the available comparative evidence suggests that nonhuman animals are able to process transitive inferences in a systematic or logical fashion, even in the social domain. The experiments reported by Paz et al. (Reference Paz, Bond, Kamil and Balda2004) and Grosenick et al. (Reference Grosenick, Clement and Fernald2007) provide evidence for only one particular kind of transitive inference: an inference from watching a series of agonistic interactions between conspecifics to an egocentric prediction about how to respond to a potentially dominant rival. Neither experiment provides any evidence that these subjects would also be able to systematically predict the relation between unobserved third-party dyads or could use their own interactions with a conspecific to predict that conspecific's relation to other rivals – let alone answer the kind of omni-directional queries of which humans are manifestly capable: For example, what individuals are dominant to B? What is the relation between C and A? Is A dominant to C to a greater or lesser extent than B is dominant to C? (Goodwin & Johnson-Laird Reference Goodwin and Johnson-Laird2005; Halford et al. Reference Halford, Wilson and Phillips1998a).

In short, whereas at least some nonhuman animals clearly are able to make transitive inferences about their own relation to potential rivals to a degree that rules out purely associative learning mechanisms, the comparative evidence accumulated to date is nevertheless consistent with the hypothesis that nonhuman animals' understanding of transitive relations is punctate, egocentric, non-logical, and context-specific.

6.1. Seriated cups and hierarchical reasoning

A number of comparative researchers have reinterpreted the behavior of nonhuman animals in hierarchical terms (e.g., Byrne & Russon Reference Byrne and Russon1998; Greenfield Reference Greenfield1991; Matsuzawa Reference Matsuzawa, McGrew, Marchant and Nishida1996). In each of these cases, however, there is no evidence that the nonhuman animals themselves cognized the task in hierarchical terms or employed hierarchically structured mental representations to do so. The most widely cited case of hierarchical reasoning among nonhuman animals, for example, has come from experiments involving seriated cups. It has been claimed that “subassembly” (i.e., combining two or more cups as a subunit with one or more other cups) requires the subject to represent these nested relations in a combinatorial and “reversible” fashion (Greenfield Reference Greenfield1991; Westergaard & Suomi Reference Westergaard and Suomi1994). Indeed, Greenfield (Reference Greenfield1991) argued that children's ability to nest cups develops in parallel with their ability to employ hierarchical phonological and grammatical constructions, and therefore, that the ability of nonhuman primates to seriate cups is the precursor to comprehending hierarchical grammars (see Matsuzawa Reference Matsuzawa, McGrew, Marchant and Nishida1996 for claims of a similar “isomorphism” between tool and symbol use).

But is it actually necessary to cognize hierarchically structured relations in order to assemble nested cups? To date, Johnson-Pynn, Fragaszy, and colleagues have provided the most convincing evidence that a nonhuman animal can use subassembly to assemble seriated cups (Fragaszy et al. Reference Fragaszy, Galloway, Johnson-Pynn and Brakke2002; Johnson-Pynn & Fragaszy Reference Johnson-Pynn and Fragaszy2001; Johnson-Pynn et al. Reference Johnson-Pynn, Fragaszy, Hirsh, Brakke and Greenfield1999). Yet, Johnson-Pynn and Fragaszy themselves dispute the claim that this behavior requires hierarchical relational operations of the kind suggested by Greenfield (Reference Greenfield1991).

Fragaszy et al. (Reference Fragaszy, Galloway, Johnson-Pynn and Brakke2002), for example, presented seriated cups to adult capuchin monkeys, chimpanzees, and 11-, 16-, and 21-month-old children. Children of all three ages created five-cup sets less consistently than the nonhuman subjects did, and they were rarely able to place a sixth cup into a seriated set. Bizarrely, at least for a purely relational interpretation of the results, monkeys were more successful than either apes or human children on the more challenging six-cup trials, yet were also the most inefficient (in terms of number of moves) of the three populations.

Fragaszy et al.'s (2002) explanation for these anomalous results is quite sensible (see also Fragaszy & Cummins-Sebree Reference Fragaszy and Cummins-Sebree2005): They hypothesize that the seriation task does not, in fact, require the subject to reason about combinatorial, hierarchical relations per se, but depends more simply on situated, embodied sensory-motor skills that are experientially, rather than conceptually, driven. Apes and monkeys do better than children because they are more physically adept than 11- to 21-month-old children are – not because they have a more sophisticated representation of the combinatorial and hierarchical relations involved. Although subassembly may be a more physically “complex” strategy than other methods of seriation, it does not necessarily require the subject to cognize the spatial-physical relations involved as hierarchical; and therefore there is no reason to claim an isomorphism between the embodied manipulation of nested cups and the cognitive manipulation of symbolic-relational representations (cf. Greenfield Reference Greenfield1991; Matsuzawa Reference Matsuzawa, McGrew, Marchant and Nishida1996).

6.2. Hierarchical relations in the wild

The strongest evidence to date in support of the claim that nonhuman animals can reason about hierarchically structured relations in the social domain comes from Bergman et al.'s (2003) study of free-ranging baboons. Bergman et al. designed an elegant playback experiment in which female baboons heard a sequence of recorded calls mimicking a fight between two other females. Mock agonistic confrontations were created by playing the “threat-grunt” of one individual followed by the subordinate screams of another. On separate days, the same subject heard one of three different call sequences: (1) an anomalous sequence mimicking a rank reversal between members of the same matrilineal family (i.e., sisters, mothers, daughters, or nieces); (2) an anomalous sequence mimicking a between-family rank reversal (i.e., between members of two different matrilineal families in which one of the families is dominant to the other); or (3) a control sequence replicating an existing dominant-subordinate relationship (i.e., no rank reversal) using between-family or within-family dyads. As predicted, there was a significant difference in the focal subjects' responses to the three different kinds of call sequences. Subjects looked longest at between-family rank reversals. There was no significant difference between within-family reversals and no-reversal control sequences. According to Bergman et al., the reason the baboons responded more strongly to between-family rank reversals than within-family sequences is because the baboons recognized that the former imply a superordinate reorganization of matrilineal subgroups. Bergman et al. (Reference Bergman, Beehner, Cheney and Seyfarth2003, p. 1236) conclude: “Our results suggest that baboons organize their companions into a hierarchical, rule-governed structure based simultaneously on kinship and rank” (see also Seyfarth et al. Reference Seyfarth, Cheney and Bergman2005).

In our view, the evidence reported by Bergman et al. (Reference Bergman, Beehner, Cheney and Seyfarth2003) does not support this conclusion. Even if baboons do make a categorical distinction between kin and non-kin dyads based on interaction history, familiarity, spatial proximity, phenotypic cues, or some other observable regularity (see Silk Reference Silk2002a for a review of the possibilities), this does not necessarily mean that they represent the entire matrilineal social structure as an integrated relational schema in which non-kin relations are logically superordinate to between-kin relations. As Bergman et al. (Reference Bergman, Beehner, Cheney and Seyfarth2003) themselves point out, between-family rank reversals are much more disruptive to baboon social life than within-family rank reversals. Therefore, Bergman et al.'s (Reference Bergman, Beehner, Cheney and Seyfarth2003) results are consistent with the hypothesis that female baboons have learned that rank reversals among non-kin are more salient (i.e., associated with greater social turmoil and personal risk) than are within-kin rank reversals occurring in someone else's family (notably, Bergman et al. did not test rank reversals within the focal subject's own family). While baboons clearly recognize particular conspecifics' vocalizations and represent dominance and kin relations in a combinatorial manner, there is nothing in Bergman et al.'s data that remotely suggests a higher-order, hierarchical relation among these representations.

Once again, there is not simply an absence of evidence; there is evidence of an absence. Bergman et al. (Reference Bergman, Beehner, Cheney and Seyfarth2003) note that the subjects' responses to apparent rank reversals were unrelated to the rank distance separating the two signalers: that is, subjects paid as much attention to mock rank reversals involving closely ranked opponents as those involving more distantly ranked opponents. Bergman et al. use this fact to rebut the hypothesis that the baboons were responding more strongly to between-family rank reversals simply because the individuals involved had more disparate ranks. However, the data cut both ways: If the baboons did cognize the relation between female conspecifics as an integrated matrilineal dominance hierarchy, ceteris paribus, they should have been more surprised at a rank reversal between a very low ranking and a very high ranking individual than by a rank reversal between two individuals of adjacent ranks. Ironically, Bergman et al.'s results provide some of the strongest evidence to date that female baboons do not, in fact, cognize the structure of their conspecifics' matrilineal social relationships in a systematic or hierarchical fashion.

9.1. The massive modularity hypothesis

A “modular” explanation for the evolution of human cognition is popular among many evolutionary-minded theorists (e.g., Barkow et al. Reference Barkow, Cosmides and Tooby1992). Certainly, many central cognitive processes – including almost all of the cognitive mechanisms we share with nonhuman animals – are at least moderately modular once the notion of modularity has been defined in a purely functional sense (see Barrett Reference Barrett and Kurzban2006). But the modular story alone does not provide a satisfying explanation for the disparity between human and nonhuman minds.

As we have seen in our review of the comparative evidence, the pattern of similarities and differences between human and nonhuman relational reasoning is remarkably consistent across every domain of cognition, from same-different reasoning and spatial relations to tool use and ToM. Therefore, it seems highly implausible that the disparities in each domain are the result of independent, module-specific adaptations. It seems much more likely (not to mention, parsimonious) that a common set of specializations – perhaps in some more general “supermodule” – is responsible for augmenting the relational capabilities of all of the cognitive modules we inherited from our nonhuman ancestors. Unfortunately, the two most popular supermodules that have been proposed to date – ToM and language – do not do a good job of accounting for the comparative evidence.

9.2. The ToM hypothesis

A number of comparative researchers believe that the discontinuity between human and nonhuman minds can be traced back to some limitation in nonhuman animals' social-cognitive abilities (e.g., Cheney & Seyfarth Reference Cheney, Seyfarth and Peterson1998; Terrace Reference Terrace, Terrace and Metcalfe2005a; Tomasello et al. Reference Tomasello, Carpenter, Call, Behne and Moll2005). Although we certainly agree that nonhuman animals do not appear to possess anything remotely resembling a ToM, the hypothesis that some aspect of our ToM alone is responsible for the disparity between human and nonhuman cognition seems difficult to sustain. For example, it is very hard to see how a discontinuity in social-cognitive abilities alone could explain the profound differences between human and nonhuman animals' abilities to reason about causal relations in the physical world or nonhuman animals' inability to reason about higher-order spatial relations. Even Tomasello and his colleagues have admitted that trying to explain all the differences between human and nonhuman cognition in terms of a difference in ToM skills is “highly speculative” at best (Tomasello & Call Reference Tomasello and Call1997, p. 418). Indeed, in a different context, Tomasello has himself argued (e.g., Tomasello Reference Tomasello2000) that human language learners rely on cognitive capacities – such as analogical reasoning and abstract rule learning – that are independent from ToM and absent in nonhuman animals. So while our ability to participate in collaborative activities and to take each others' mental states into account may be a distinctive feature of the human lineage, it is clearly not the only or even the most basic one.

9.3. The language-only hypothesis

The oldest and still most popular explanation for the wide-ranging disparity between human and nonhuman animals' cognitive abilities is language (for recent examples of this venerable argument, see Bermudez Reference Bermúdez2003; Carruthers Reference Carruthers2002; Clark Reference Clark2006). Dennett (Reference Dennett1996, p. 17) described the extreme version of this hypothesis in characteristically pithy terms: “Perhaps the kind of mind you get when you add language to it is so different from the kind of mind you can have without language that calling them both minds is a mistake.”

To be sure, language clearly plays an enormous and crucial role in subserving the differences between human and nonhuman cognition. But we believe that language alone is not sufficient to account for the discontinuity between human and nonhuman minds. In order to make our case, we need to distinguish between three distinct versions of the language-only hypothesis: (1) that verbalized (or imaged) natural language sentences are responsible for the disparity between human and nonhuman cognition; (2) that some aspect of our internal “language faculty” is responsible for the disparity; and (3) that the communicative and/or cognitive function of language served as the prime mover in the evolution of the uniquely human features of the human mind.

10.1. The PSS hypothesis

The classical school of thought in cognitive psychology has insisted for more than three decades that both human and nonhuman minds are the product of a physical symbol system (Fodor Reference Fodor1975; Reference Fodor1997; Fodor & McLaughlin Reference Fodor and McLaughlin1990; Fodor & Pylyshyn Reference Fodor and Pylyshyn1988; Newell Reference Newell1980; Reference Newell1990; Newell & Simon Reference Newell and Simon1976; Pinker & Prince Reference Pinker and Prince1988). According to the now familiar tenets of the physical symbol system (PSS) hypothesis, mental representations are composed of discrete, symbolic tokens, which can be combined into complex representations by forming syntactically structured relations of various types. Cognitive processes, according to the classical view, are rule-governed algorithms that operate over the formal structure of these mental representations in a truth-preserving fashion. The classic defense of the PSS hypothesis is that it provides a computational account for several of the most spectacular aspects of human thought, including our abilities to generalize rule-like relations over abstract categorical variables, to reason in an inferentially coherent fashion, and to use the artificial symbols of a natural language in a systematic, recursive, and generative manner (Fodor & Pylyshyn (Reference Fodor and Pylyshyn1988; Marcus Reference Marcus2001; Newell Reference Newell1980; Pinker & Prince Reference Pinker and Prince1988).

The PSS hypothesis is certainly not the “only game in town” (Fodor Reference Fodor1975). Indeed, the PSS hypothesis has been roundly criticized for a variety of reasons, ranging from its biological implausibility to its inability to deal with the graded semantic flexibility of many cognitive processes (e.g., Barsalou (Reference Barsalou1999; Clark Reference Clark1997; Rumelhart & McClelland Reference Rumelhart and McClelland1986; van Gelder Reference van Gelder1998). However, even among those who see the PSS hypothesis as fundamentally misguided, most would agree that human subjects are often able to approximate the systematic, higher-order, relational capabilities putatively associated with a PSS, at least in their linguistically mediated behavior. Smolensky (Reference Smolensky1999) calls this the “Symbolic Approximation” hypothesis: that is, the hypothesis that some – though certainly not all – aspects of human mental representations admit of abstract, higher-level descriptions that are closely approximated by the kinds of discrete, abstract structures posited by symbolic, linguistic theory.

In our view, the Symbolic Approximation hypothesis defines an essential and irreducible benchmark for any viable model of human cognition, far beyond the confines of linguistically mediated processes and symbolic, linguistic theory (Holyoak & Hummel Reference Holyoak, Hummel, Dietrich and Markman2000; Reference Holyoak, Hummel, Gentner, Holyoak and Kokinov2001; Hummel & Holyoak Reference Hummel and Holyoak2003; Reference Hummel and Holyoak2005). Although the classical version of the PSS hypothesis appears dead as a model of biological cognition in general, there are compelling reasons to believe that something closely approximating the functionality of a PSS is necessary in order to subserve the systematic, higher-order relational inferences of which human subjects are manifestly capable (Gentner Reference Gentner, Gentner and Goldin-Meadow2003; Goodwin & Johnson-Laird Reference Goodwin and Johnson-Laird2005; Halford et al. Reference Halford, Wilson and Phillips1998a; Holyoak & Thagard Reference Holyoak and Thagard1995). Indeed, all of the most successful neurally inspired computational models of relational reasoning employ – or at least try to approximate the capabilities of – a PSS (e.g., Eliasmith & Thagard Reference Eliasmith and Thagard2001; Hummel & Holyoak Reference Hummel and Holyoak2003; Plate Reference Plate2000; Wilson et al. Reference Wilson, Halford, Gray, Phillips, Gentner, Holyoak and Kokinov2001). In our view, the operational question for researchers interested in modeling the human mind should no longer be whether the human mind implements a PSS, but rather how the higher-order relational capabilities of a PSS can be combined with the associative and generalization capabilities of a nonclassical system in a neurally plausible cognitive architecture (for similar views but alternative answers to this question, see Eliasmith & Thagard Reference Eliasmith and Thagard2001; Marcus Reference Marcus2001; Plate Reference Plate2000; Pollack Reference Pollack1990; Shastri & Ajjanagadde Reference Shastri and Ajjanagadde1993; Smolensky Reference Smolensky1990; Reference Smolensky1999; Wilson et al. Reference Wilson, Halford, Gray, Phillips, Gentner, Holyoak and Kokinov2001).

The situation with respect to nonhuman minds, however, is quite different. In the following subsections, we evaluate the degree to which nonhuman minds approximate the defining features of a PSS. As will become quickly apparent, the comparative evidence does not support the all-or-nothing position taken by the orthodox version of the PSS hypothesis (e.g., Fodor & Pylyshyn Reference Fodor and Pylyshyn1988). Unlike the PSS hypothesis, however, the Symbolic Approximation hypothesis invites the possibility that different cognitive organisms may approximate different features of a PSS to varying degrees or even, pace Fodor and Pylyshyn (Reference Fodor and Pylyshyn1988), in a punctate and content-specific manner. And, in fact, this is exactly what the comparative evidence suggests is the case.

10.2. Symbols

The PPS hypothesis is often construed as the claim that mental representations are symbolic. The problem with this construal is that there is little consensus among cognitive researchers on what it means for a representation to be “symbolic” (see discussion by Marcus Reference Marcus2001). Therefore, to sidestep the nettlesome issue of what counts as a “symbol” sensu stricto, we will start with a generic definition of a “mental representation” sensu largo and then ask which, if any, of the additional symbolic abilities postulated by the PSS hypothesis are found in the cognitive behavior of nonhuman animals.

Markman and Dietrich (Reference Markman and Dietrich2000) propose a sensible, minimalist definition of a mental representation as any internal information-carrying state that mediates a cognitive system's furtherance of its goals. We will not pretend that this definition puts to rest the entire – or even a small part – of the controversy surrounding what counts as a mental representation. But we nevertheless propose to stipulate without further argument that nonhuman animals employ “representations” in this minimalist sense, as even the most bare-boned associationist theory of animal learning agrees on the causal relevance of information-carrying mediating states, as well as the explanatory need for these states within comparative research.

The additional claim that nonhuman mental representations carry information about particular states of affairs and that these same representations can subsequently be used off-line in a productive fashion is slightly more controversial, but it should not be. It seems unarguable that nonhuman animals are capable of forming internal representations about discrete states of affairs that endure beyond the sensory-motor inputs giving rise to them. Honey-bees may not be capable of constructing full-fledged cognitive maps, but they are manifestly capable of keeping track of information associated with multiple landmarks they have encountered in the past and then using these representations of absent states of affairs in order to find their way home (e.g., Menzel et al. Reference Menzel, Greggers, Smith, Berger, Brandt, Brunke, Bundrock, Hülse, Plümpe, Schaupp, Schüttler, Stach, Stindt, Stollhoff and Watzl2005). Scrub-jays may not have a theory of mind; but they are manifestly capable of remembering the “what,” “when,” and “where” information associated with tens of thousands of independent cache sites, and they can keep track of “who saw what when” for the purposes of protecting those sites from potential pilferers (Emery Reference Emery and Watanabe2004; Emery & Clayton Reference Emery and Clayton2004b). Bermudez (Reference Bermúdez2003), following Strawson (Reference Strawson1959), calls these “particular-involving” representations; and we feel that it is indisputable that nonhuman animals represent the world in particular-involving ways.

Moreover, nonhuman animals apparently have the ability to update representations associated with a particular state of affairs – for example, where and when one particular piece of food was cached – without catastrophically affecting representations associated with other similar states of affairs – for example, where all the other pieces of food were cached. And they are able to update these representations in response to a single exposure (see, e.g., Clayton et al. Reference Clayton, Bussey and Dickinson2003). For reasons cogently set forth by Blackmon et al. (Reference Blackmon, Byrd, Cummins, Poirier and Roth2004), this means that the nonhuman animals are atomistic learners and that at least some of their internal representations are functionally discrete.

10.3. Compositionality

Perhaps the single most contentious claim of the PSS hypothesis is that mental representations are compositional – that is, complex mental representations are formed by combining discrete representational states into more complex structures such that different combinations of simpler representations can be used to represent different states of affairs in a combinatorial fashion. Few dispute the fact that human thought can approximate the functional effects of compositionality (cf. Prinz & Clark Reference Prinz and Clark2004). The purported compositionality of nonhuman animals' mental representations, on the other hand, has been the object of innumerable, hard-fought battles, particularly between the “associationist” and “symbolic” theoretical camps that have dominated comparative debate for many decades. In our view, the comparative evidence accumulated over the past quarter-century comes down firmly in favor of neither of these venerable theoretical alternatives. Instead, the available comparative evidence suggests that compositionality is a ubiquitous feature of animal cognition, albeit not necessarily the kind of compositionality posited by the PSS hypothesis or “symbolic” accounts of nonhuman cognition.

The PSS hypothesis argues not only that mental representations are compositional but also that they are compositional in a specific fashion: Complex compositional representations in a PSS are formed by concatenation, thereby retaining the identity of the original constituents, rather than by some other conjunctive mechanism that sacrifices the integrity of the original constituents (see discussions by Aydede Reference Aydede1997; Horgan & Tienson Reference Horgan and Tienson1996; van Gelder Reference van Gelder1990). Van Gelder (Reference van Gelder1990) has suggested that any cognitive system should be considered “functionally compositional” if it possesses generally reliable and effective mechanisms for (1) producing a complex representation given its constituents, and (2) decomposing a complex representation back into those constituents – regardless of whether these complex representations are formed by concatenation or by some other means.

As we see it, the comparative evidence leaves no doubt that the nonhuman mind employs enduring, functionally discrete, particular-involving mental representations that are at least functionally compositional in van Gelder's agnostic sense. As Horgan and Tienson (Reference Horgan and Tienson1996) point out, the complexity of social relationships among nonhuman animals would be literally unthinkable without the ability to represent novel dyadic relations by combining discrete representations associated with each individual in a combinatorial fashion. More generally, the well-documented ability of nonhuman animals to keep track of means-ends contingencies and predicate-argument relationships in a combinatorial fashion implies that they possess some generally reliable and productive mechanism for encoding the relation between particular constituents. Such a mechanism is necessary in order to ensure that when multiple relations predicate the same property, the fact that it is the same property in each case is somehow manifest in the structural similarity between the representations. Horgan and Tienson (Reference Horgan and Tienson1996) argue that this is all it should take in order for a representational system to qualify as “syntactically structured”; and therefore one must conclude, they argue, that nonhuman animals employ syntactically structured mental representations, albeit not necessarily in the concatenative sense posited by the PSS hypothesis.

We agree. And this conclusion rules out most traditional associative and distributed connectionist models as plausible accounts of the nonhuman mind (see again Marcus Reference Marcus2001). However, any number of researchers have proposed nonclassical connectionist architectures that are functionally discrete, particular-involving, and syntactically structured without being concatenatively compositional in the sense postulated by the PSS hypothesis (e.g., Plate Reference Plate, Mylopoulos and Reiter1991; Pollack Reference Pollack1990; Smolensky Reference Smolensky1990; van Gelder Reference van Gelder1990; Wilson et al. Reference Wilson, Halford, Gray, Phillips, Gentner, Holyoak and Kokinov2001). Many of these proposals can account for the kind of compositionality manifested by nonhuman animals. Therefore, none of the comparative evidence available to date warrants the widespread assumption among comparative cognitive researchers (e.g., Gallistel Reference Gallistel, Jing, Rosenzweig, d'Ydewalle, Zhang, Chen and Zhang2006) that nonhuman animals necessarily form compositional representations in the concatenative fashion proposed by the PSS hypothesis.

Indeed, as we will see below, nonhuman animals do not even come close to approximating any of the other, more distinctive, higher-order features of a PSS. Therefore, at least in biological organisms, the various representational capabilities putatively associated with a PSS are not a package deal as a matter of nomological necessity (see Hadley Reference Hadley1997).

10.4. Types and tokens

The distinction between types (e.g., kinds, classes, roles, variables) and tokens (e.g., individuals, instances, fillers, values) is one of the essential characteristics of a genuine PSS. A PSS maintains explicit information about the syntactic type identity of each structural relation it employs and the type identity of its allowable constituents as distinct from the constituents involved in any particular relational instance. For example, in a PSS, the abstract characteristics of the loves relation is explicitly represented and invariant to whether John loves Mary or Mary loves John.

The ability to reason about the relation between types and tokens pervades many aspects of human thought. Role-governed rules appear to be a formative feature of all human languages; and the universal ability of humans to learn novel role-governed rules is evident not only in their mastery of natural human languages but also in their ability to extract the abstract rules of artificial grammars in AGL experiments. “Role-governed categories” (Markman & Stilwell Reference Markman and Stilwell2001) also play a central role in human concept formation far beyond the abstract grammatical structures of language. A human subject is perfectly capable of reasoning about a role-based category such as “lovers” or “mothers” or “tools” without there being any set of perceptual features that all lovers, mothers, or tools have in common. Moreover, the ubiquitous human capacity to find analogical correspondences between perceptually disparate relations appears to require an ability to find systematic correspondences between the roles defined for those relations as distinct from the perceptual similarity between the fillers of these roles (Gentner Reference Gentner1983; Gentner & Markman Reference Gentner and Markman1997; Markman & Gentner Reference Markman and Gentner1993; Reference Markman and Gentner2000). Therefore, analogical inferences – one of the hallmarks of the human mind and a prominent feature of abstract causal reasoning and ToM – seem to require the ability to distinguish between roles and their fillers and to dynamically “bind” one with the other without corrupting the independence of either. Notably, the ability to maintain role-filler independence while dynamically binding roles and fillers to particular relations seems to require the kind of concatenative compositionality posited by the PSS hypothesis (for more extensive discussions of this point, see Doumas & Hummel Reference Doumas, Hummel, Holyoak and Morrison2005; Holyoak & Hummel Reference Holyoak, Hummel, Dietrich and Markman2000; Hummel & Holyoak Reference Hummel and Holyoak2003; Hummel et al. Reference Hummel, Holyoak, Green, Doumas, Devnich, Kittur, Kalar, Levy and Gayler2004).

Whereas an explicit and concatenative relation between types and tokens appears to be necessary to explain human subjects' higher-order relational capabilities, there is no need or evidence for this distinction in nonhuman cognitive behaviors. Nonhuman animals appear to reason on the basis of “feature-based categories” alone (Markman & Stilwell Reference Markman and Stilwell2001) – that is, they appear to represent categories such as “mothers,” “tools,” or “kin” based on particular sets of features shared by members of the category (e.g., gender, perceptual affordances, affiliative behavior) rather than on the abstract role that members play in a given relational schema. Moreover, there is no evidence, as we argued above, that nonhuman animals are able to process analogical relations or role-governed rules in a human-like fashion. Thus, one of the fundamental features of a PSS, the explicit distinction between types and tokens, appears to be absent from the cognitive behavior of nonhuman animals.

10.5. Structural relations

Classical theories posit that there are a wide range of distinct structural relations between content-bearing representations, of which “constituency” is the most prominent example (Fodor & Pylyshyn Reference Fodor and Pylyshyn1988). One of the defining features of a PSS is that it allows cognitive processes to operate over the formal structure of a relation in a truth-preserving fashion independently of the relation's particular constituents. Among other things, this permits the PSS hypothesis to explain how recursive operations over hierarchically structured representations can be both inferentially coherent and computationally feasible.

We have argued earlier that nonhuman mental representations are functionally compositional and syntactically structured. Therefore, the nonhuman cognitive architecture must be capable of operating over a range of structural relations between content-bearing representations as well. The comparative evidence suggests, however, that nonhuman animals are unable to reason about the higher-order structural relation between these relations in a human-like fashion and are unable to perform those kinds of operations – such as recursion and deductive inference – which apply to the formal structure of a relation independently from the semantic or perceptual features of its constituents. Many theorists, for example, have suggested that humans form a “causal model” of the network of causal relations within a given domain and then use this causal network to make novel inferences and plan their interventions in a quasi-experimental fashion (Gopnik et al. Reference Gopnik, Glymour, Sobel, Schulz, Kushnir and Danks2004; Hagmayer et al. Reference Hagmayer, Sloman, Lagnado, Waldmann, Gopnik and Schulz2007; Waldmann & Holyoak Reference Waldmann and Holyoak1992). Nonhuman animals also appear to be implicitly sensitive to the differences between certain basic causal structures (see Blaisdell et al. Reference Blaisdell, Sawa, Leising and Waldmann2006). Unlike humans, however, nonhuman animals appear to be incapable of explicitly reasoning about these causal networks in a diagnostic manner, of recognizing the structural similarities between perceptually disparate causal relations, of generalizing their prior knowledge about causal structures to novel contexts, or of reasoning about the structure of causal relations independently of their particular perceptual features (see our discussion in Penn & Povinelli Reference Penn and Povinelli2007a).

In our review of the comparative evidence for hierarchical representations and transitive inferences, we found that nonhuman animals reason solely in terms of first-order perceptual relations (e.g., rates of affiliation, reinforcement history, and outcomes of dyadic agonistic encounters), rather than in terms of the logical, role-governed, and/or structural aspects of the relations themselves. Although metrics such as “early association,” “familiarity,” and “age similarity” may provide heuristic proxies for the kinship relation between two conspecifics, these metrics reduce a role-based, structured relation to an analog chunk and forgo the ability to reason about the higher-order relation between these relations independently of their particular perceptual characteristics. There is no evidence, for example, that nonhuman animals understand the higher-order relation between the grandmother-of and mother-of relation, or the analogical similarity between the father-of and mother-of relation. Similarly, the performance of nonhuman animals on RMTS tasks suggests that nonhuman animals are chunking these relations into analog measures of variability, rather than reasoning about the structural relation between relations per se. And we came to similar conclusions with respect to nonhuman animals' performance on tests of transitive reasoning.

In short, the comparative evidence suggests that nonhuman mental representations are implicitly structured, but that nonhuman animals are incapable of representing these structural relations explicitly (i.e., of explicitly tokening the relation qua relation) and therefore are incapable of reasoning about the higher-order structural relation between relations in a recursive, systematic, or productive fashion.

10.6. Systematicity

Fodor and Pylyshyn (Reference Fodor and Pylyshyn1988) famously argued that all cognitive organisms capable of understanding aRb must also understand bRa, where a and b are referential entities and R is some relation. An oft-cited example is that any organism that can understand John loves Mary will necessarily understand Mary loves John or any other systematic variant thereof. Fodor and Pylyshyn (Reference Fodor and Pylyshyn1988) called this feature of thought systematicity. They argued that (1) systematicity is a unique effect of a PSS; (2) it is universally observed in all cognitive organisms; and therefore (3) all cognitive organisms must employ a PSS. As Fodor and Pylyshyn (Reference Fodor and Pylyshyn1988, p. 28) put it, “that infraverbal cognition is pretty generally systematic seems, in short, to be about as secure as any empirical premise in this area can be.”

Many critics have pointed out that Fodor and Pylyshyn's formulation of systematicity was not particularly well-defined or operationally tractable (e.g., Doumas & Hummel Reference Doumas, Hummel, Holyoak and Morrison2005; Hadley Reference Hadley1994; Niklasson & van Gelder Reference Niklasson and van Gelder1994). Moreover, it turns out to be relatively easy for clever connectionist models to replicate many of the examples of systematicity cited by Fodor and Pylyshyn without resorting to classically structured representations (e.g., Chalmers Reference Chalmers1990; Niklasson & van Gelder Reference Niklasson and van Gelder1994; Plate Reference Plate, Mylopoulos and Reiter1991; Smolensky Reference Smolensky1990).

The argument from systematicity fares even worse from a comparative point of view. Nonhuman cognition is certainly systematic and productive to some degree, but it does not appear to be systematic in the way or for the reasons postulated by the PSS hypothesis. Certainly, any animal capable of thinking the thought dominates(A, B) is likely to be able to think the thought dominates(B, A) for any arbitrary pair of conspecifics of the appropriate age and gender. And this kind of systematicity is often cited by advocates of the classical school of thought to support extending the PSS hypothesis to nonhuman animals (e.g., Carruthers Reference Carruthers2004; Fodor & Pylyshyn Reference Fodor and Pylyshyn1988). But there is a fundamental difference between the kind of systematicity manifested by nonhuman animals and the kind of systematicity posited by the PSS hypothesis.

The kind of systematicity manifested by nonhuman animals is limited to perceptually based relations in which the values that each argument can take on in the relation are constrained only by observable features of the constituents in question (e.g., the gender and age of the conspecific). Feature-based systematicity such as this does not require the cognizer to posit relational roles distinct from the relations' constituents, nor to cognize the fact that certain relations logically imply certain other relations. Not coincidentally, this is also the kind of systematicity that happens to be easily implemented by many nonclassical connectionist models (e.g., Niklasson & van Gelder Reference Niklasson and van Gelder1994). But as Fodor and colleagues have repeatedly argued (e.g., Fodor Reference Fodor1997; Fodor & McLaughlin Reference Fodor and McLaughlin1990), the kind of systematicity posited by the PSS hypothesis is not statistical or accidental or a by-product of domain-specific adaptations; rather, it arises as a matter of nomological necessity from the fact that a PSS defines relations structurally. Classical systematicity entails cognizing the fact that certain relations necessarily imply other relations independently of any particular domain or learning context: for example, for all R, the relations R(a,b) and R(b,c) necessarily imply the relation R(a,c) provided that R is a transitive relation.

There is no evidence for this kind of classical, inferential, role-governed, domain-independent systematicity among nonhuman animals.

11.1. LISA: Relational reasoning in a biological symbol system

We do not by any means have a complete answer to this formidable question; but we can at least point to work that suggests one possible step towards an answer. Hummel and Holyoak (Reference Hummel and Holyoak1997; Reference Hummel and Holyoak2003; Reference Hummel and Holyoak2005) have proposed a hybrid symbolic-connectionist model of relational reasoning – LISA (Learning and Inference with Schemas and Analogies) – which we view as one promising (though partial) approach to implementing our RR hypothesis in a computationally feasible and neurally plausible fashion (see also Holyoak & Hummel Reference Holyoak, Hummel, Dietrich and Markman2000; Reference Holyoak, Hummel, Gentner, Holyoak and Kokinov2001; Morrison et al. Reference Morrison, Krawczyk, Holyoak, Hummel, Chow, Miller and Knowlton2004). LISA combines the syntactic strengths of a PSS with the semantic flexibility and generalization capabilities of a distributed connectionist system by using temporal synchrony to approximate the dynamic role-filler binding capabilities of a PSS within a connectionist architecture. Notably, LISA implements the distinctive higher-order relational capabilities of a PSS via an additional representational system that has been grafted onto a simpler system of conjunctive representations used for long-term storage. This simpler system provides conjunctive representations that are functionally, but not concatenatively, compositional and therefore is arguably sufficient to approximate the representational capabilities of nonhuman animals but insufficient to approximate the higher-order relational capabilities of humans.

LISA provides an existence proof that the higher-order relational capabilities of a PSS can, in fact, be grafted onto a neurally plausible, distributed connectionist architecture. At the same time, LISA shows that it is quite hard to approximate the higher-order relational capabilities of a PSS within a neural network – particularly to achieve both role-filler independence and dynamic role-filler binding. In other words, LISA suggests that approximating the higher-order, role-governed features of a PSS is not likely to be an ability that evolved by accident or as a by-product of increased brain size, greater neural plasticity, or larger processing capacity alone. There must be other substantive differences between human and nonhuman primate brains waiting to be discovered (Preuss Reference Preuss and Gazzaniga2004).

If LISA is broadly correct, the substantive difference between human and nonhuman brains will be found in the prefrontal cortices, and specifically in synchronized activity among prefrontal neural populations that support working memory, as well as among neural populations in the frontal and posterior cortical areas (see Lu et al. Reference Lu, Morrison, Hummel and Holyoak2006; Morrison et al. Reference Morrison, Krawczyk, Holyoak, Hummel, Chow, Miller and Knowlton2004; Robin & Holyoak Reference Robin, Holyoak and Gazzaniga1995; Waltz et al. Reference Waltz, Knowlton, Holyoak, Boone, Mishkin, Santos, Thomas and Miller1999; Reference Waltz, Knowlton, Holyoak, Boone, Back-Madruga, McPherson, Masterman, Chow, Cummings and Miller2004). Of course, we are not suggesting that temporal synchrony among prefrontal neural populations is the only possible neural-level explanation for the functional differences between human and nonhuman relational cognition, nor that it provides a full explanation (see, e.g., Jung & Haier Reference Jung and Haier2007). We are simply suggesting that computational models of biological cognition such as LISA provide an important tool for comparative researchers wishing to formulate biologically plausible, representational-level hypotheses concerning the similarities and differences between human and nonhuman minds.

11.2. Moving forward

Admittedly, our RR hypothesis has a number of substantial holes. With respect to the empirical evidence, we have not directly addressed a number of important cognitive domains. In some cases – for example, numeracy, cooperation, and mental time travel – others have already proposed analyses of the functional discontinuity between human and nonhuman animals' capabilities that are largely consistent with the hypothesis defended in the present article (see, e.g., Dehaene Reference Dehaene1997; McElreath et al. Reference McElreath, Clutton-Brock, Fehr, Fessler, Hagen, Hammerstein, Kosfeld, Milinski, Silk, Tooby, Wilson and Hammerstein2003; Suddendorf & Corballis Reference Suddendorf and Corballis2007a). In other cases – for example, empathy and metacognition – the discontinuity between human and nonhuman minds continues to be challenged (cf. Preston & de Waal Reference Preston and de Waal2002; Smith et al. Reference Smith, Shields and Washburn2003). We believe our analysis and hypothesis can (and should) be extended to these latter domains as well. Indeed, we believe that our RR hypothesis offers a powerful framework for explaining what all these disparate cases – from cooperation and mental time travel to numeracy and metacognition – have in common. But we acknowledge that we have not had the space to extend our analysis to these other domains herein.

With respect to our representational-level claims, we have not specified how our proposed symbolic-relational supermodule combines inputs from such a motley collection of perceptual and conceptual modules in a computationally feasible fashion. Fodor (Reference Fodor2000) has argued that this problem is unsolvable, and therefore that the human mind cannot, in the end, be entirely computational. We do not have a complete solution to Fodor's challenge; but, like many others, we do not believe it is in principle unsolvable (Barrett Reference Barrett2005; Carruthers Reference Carruthers and Stainton2005b; Pinker Reference Pinker2005). Hybrid symbolic-connectionist architectures such as LISA provide one possible solution that Fodor has not considered.

The most glaring weakness in our hypothesis is that we have no complete, biologically plausible model of nonhuman cognition to propose. Many who have adopted some form of the Symbolic Approximation hypothesis have taken on the ambitious goal of trying to determine how the unique symbolic capabilities of the human mind might be implemented in a neurally plausible architecture (e.g., Holyoak Reference Holyoak, Ericsson and Smith1991; Hummel & Holyoak Reference Hummel and Holyoak2003; Marcus Reference Marcus2001; Plate Reference Plate, Mylopoulos and Reiter1991; Pollack Reference Pollack1990; Shastri & Ajjanagadde Reference Shastri and Ajjanagadde1993; Smolensky Reference Smolensky1990; Reference Smolensky1999; Wilson et al. Reference Wilson, Halford, Gray, Phillips, Gentner, Holyoak and Kokinov2001). Although we applaud the efforts of these researchers and believe that they are already shedding new light on our species' unique relational capacities, relatively little effort has been invested in modeling the relational abilities of other cognitively sophisticated animals. In our view, the entire field of cognitive science – not just our particular hypothesis – would benefit if more effort were focused on constructing biologically plausible, behaviorally accurate, computationally feasible models of the cognitive abilities of honeybees, corvids, and chimpanzees, in addition to the cognitive abilities of enculturated, language-wielding humans.Footnote ⁵

Fortunately, the fate of our RR hypothesis does not ride on the success or failure of any particular computational proposal. Our most important claim in this target article is simply that whatever “good trick” (Dennett Reference Dennett1996) was responsible for the advent of human beings' ability to reinterpret the world in a symbolic-relational fashion, it evolved in only one lineage – ours. Nonhuman animals didn't (and still don't) get it.

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