R2.1. The discontinuity in the continuum

Many commentators argued that there is no discontinuity between human and nonhuman minds because the cognitive abilities of human and nonhuman animals exist along a “continuum” (e.g., Burghardt, Hallinan & Kuhlmeier, Herman et al., McGonigle & Chalmers, Pepperberg, Siegal & Varley, Tomlinson & Love, Wasserman). We tried to forestall this objection by clearly defining up front what we meant by the term “discontinuity” in our target article (see Note 1). But it seems our definition of this term got lost in the rush to defend Darwin's honor. We therefore begin this reply by pointing out, once again, that our claim that there is a significant gap (a.k.a. “functional discontinuity”) between the relational abilities of modern humans and those of all other extant nonhuman species is completely consistent with the fact that the relational abilities of all extant species undoubtedly evolved along a multidimensional continuum and can still be distributed along that continuum.

According to the framework laid out in our target article, relational cognitive processes run the gamut from simple conditional discriminations based on the perceptual similarity between objects (e.g., same–different tasks) to systematic inter-domain inferences based on higher-order structural correspondences (e.g., analogical inferences). At the simplest end of the spectrum, relational discriminations can be made by encoding relations into analog measures of perceptual variability. At the most complex end of the spectrum, relational inferences can only be made using explicitly structured representations of roles, relations, and fillers. In both human and nonhuman animals, relational problems at the simplest end of the spectrum are typically solved using “embedded” perception and action routines (see Barrett). Relational problems at the most complex end of the spectrum require increasingly abstract, non-domain-specific representations including, at the limit, extensive linguistic scaffolding (see Bermúdez, Gentner & Christie).

As Clark and Thornton (Reference Clark and Thornton1997) pointed out in this journal a decade ago, relational problems are “rife” in biologically realistic settings, but animals regularly solve them – typically quite well. Therefore, it is apparent that (almost) all biological cognizers are capable of “reasoning” about relations to some degree. Indeed, if every organism that had ever lived on this planet still existed today, there would be no functional discontinuity to speak of and the immense interval between the two ends of this relational spectrum would be filled with “numberless gradations” (Darwin Reference Darwin1871, p. 35). But, based on the available empirical evidence, there appears to be a significant gap between the relational abilities of modern humans and all other extant species – a gap at least as big, we argued, as that between human and nonhuman forms of communication. Among extant species, only humans seem to be able to reason about the higher-order relations among relations in a systematic, structural, and role-based fashion. Ex hypothesi, higher-order, role-based relational reasoning appears to be a uniquely human specialization, or “human cognitive autapomorph[y]” (our thanks to Suddendorf for reminding us of this excellent term; see extended discussion in Povinelli & Eddy Reference Povinelli and Eddy1996, Ch. 1).

R2.2. Is our hypothesis “premature”?

Many commentators claimed that our hypothesis is “premature” (e.g., Emery & Clayton, Hallinan & Kuhlmeier, Lupyan, Pepperberg, Siegal & Varley, Wasserman). Now, it would clearly be premature (indeed daft) to claim that we have definitively refuted all alternative hypotheses, or that our RR hypothesis is the last word on the issue of what makes the human mind human. But it hardly seems premature to postulate the possibility that human cognition is, indeed, unique in certain ways and to make some attempt to specify how and why. In our eyes, postulating plausible, falsifiable hypotheses and then trying to verify those hypotheses empirically is the sine qua non of any experimental science. If our target article serves no other purpose than to motivate our critics to go forth and prove us wrong, our efforts will not have been in vain. We are happy to be hostage to empirical fortune.

R2.3. Same–different relations

Thompson & Flemming cite a list of studies showing that nonhuman animals can acquire a “categorical” understanding of sameness and difference relations. Pepperberg makes a similar claim on behalf of the Grey parrot, Alex. We agree that a “categorical” understanding of perceptual similarity is not a uniquely human capability. We made the same point in our target article. The crucial and persistently overlooked issue, however, is that the kind of cognitive operation required to pass same–different (S/D) and relational match-to-sample (RMTS) tasks is not the same kind of operation required to reason about higher-order relations in a systematic, structural, role-based fashion. The fundamental problem is that the relations at stake in S/D and RMTS tasks involve symmetrical and interchangeable roles and are therefore reducible to analog measures of variability, such as entropy. Therefore, the ability to make a categorical distinction between displays above and below a certain entropy threshold is not evidence for higher-order relational reasoning in the structural or role-based sense posited by our hypothesis.

Gentner & Christie claim that although RMTS tasks involving multiple items per set can be solved by perceptual variability alone, tasks involving only two items per set cannot. This is incorrect. Using the definition of categorical entropy proposed by Young and Wasserman (Reference Young and Wasserman1997), “same” pairs such as AA have an entropy of 0, whereas “different” pairs such as AB have an entropy of 1. The difference in entropy between all-same and all-different displays is certainly smaller in two-item sets than in multiple-item sets; but there is a non-zero difference nonetheless. Training with same–different symbols may improve subjects' ability to pay attention to these small differences in entropy (a form of perceptual learning) or may align the threshold for their responses more closely to that of humans. However, once the possibility that RMTS tasks can be solved using an analog measure of variability is admitted, it must also be admitted the task lacks the power, even in principle, to demonstrate that a subject is reasoning about the kind of higher-order, structurally explicit relations that Gentner and her colleagues have rightfully claimed to be the centerpiece of human cognition (e.g., Gentner Reference Gentner, Gentner and Goldin-Meadow2003).

Thompson & Flemming point out that there is a disparity between the responses of nonhuman apes and monkeys on RMTS tasks. Thompson & Flemming ask why such a disparity exists if (as we argue) the RMTS task is solvable using entropy values.

There are many possible reasons for this disparity. That there is a significant gap between the relational abilities of human and nonhuman subjects does not imply that the relational abilities of all other extant species are identical or even homogeneous. The RMTS task may be more computationally complex than the S/D task for primates. And the two-item RMTS task may require a greater sensitivity to variability than the multi-item RMTS task does. These are all plausible hypotheses that deserve further experimental scrutiny. But the fact that only certain species possess the evolved heuristics and/or processing capacity necessary to solve two-item RMTS tasks does not imply that the RMTS task requires subjects to reason about higher-order structural relations. To make this latter claim, Thompson & Flemming would need to show that the RMTS task requires subjects to reason about higher-order relations in a structurally sensitive fashion. And this, they have not done.

R2.4. Analogical relations

We defined “analogical reasoning” as the ability to draw inferences about a target domain based on systematic, structural similarities between a source domain and the target domain. Importantly, the relevant similarities in analogical inferences are based on the roles various entities play in their respective relations, and on structural similarities between the relations, rather than (and distinct from) perceptual similarities between the entities involved in the relations (Gentner Reference Gentner1983; Gentner & Markman Reference Gentner and Markman1997; Holyoak & Thagard Reference Holyoak and Thagard1995). Like any other form of relational reasoning, analogical inferences vary in their degree of abstraction, structural sophistication, and domain specificity. Even 4-year-old children understand simple analogies involving familiar visuospatial relations – for example, “If a tree had a knee, where would it be?” (Gentner Reference Gentner1977). But it takes quite a bit of linguistic scaffolding, inter-domain mapping, and content-specific enculturation to make sense out of Donald Rumsfeld's assertion that installing democracy in Iraq is like teaching a child to “ride a bike” (Silverstein Reference Silverstein2007). According to our RR hypothesis, reasoning about even the simplest, most modality-specific analogies is a human cognitive autapomorphy.

Many commentators agree with us that analogical reasoning is a distinctively human capability (e.g., Bermúdez, Gentner & Christie, Hallinan & Kuhlmeier, Markman & Stilwell). Thompson & Flemming, however, argue that at least one chimpanzee, Sarah, is also capable of comprehending some analogies. We have considerable sympathy with their point of view, as one of us (Holyoak) reached similar conclusions at one time (see Holyoak & Thagard Reference Holyoak and Thagard1995). However, more recent findings (i.e., Oden et al. Reference Oden, Thompson, Premack, Gentner, Holyoak and Kokinov2001) have shown that Sarah's performance does not merit this conclusion.

Thompson & Flemming admit that Sarah's performance on Oden et al.'s (Reference Oden, Thompson, Premack, Gentner, Holyoak and Kokinov2001) replication does not qualify as a “material analogy” and acknowledge that Sarah's performance was functionally equivalent to the performance of other primates and birds on S/D tasks. Thompson & Flemming nonetheless claim that Sarah's performance counts as a “formal analogy,” and they find our own definition of analogy “overly exclusive.”

Researchers clearly use the term analogy to refer to a wide variety of relational inferences (see, e.g., Gentner & Christie, Halford et al., Herman et al., Lupyan, Markman & Stilwell). But Thompson & Flemming's definition of a “formal analogy” is exceptionally idiosyncratic. In the philosophical literature (e.g., Hempel Reference Hempel1965), a formal analogy is defined as an isomorphism between systems of relations (e.g., the analogy between groups in algebra and topological manifolds in geometry). Sarah's strategy for solving geometric “analogies” – equating number of featural changes – does not establish an isomorphism, and hence does not exemplify an analogy under any established definition. If the term formal analogy is now to be used to refer to relational tasks that can be solved by comparing analog measures of variation, then indeed Sarah is capable of solving “formal analogies” – but so are many other species, including pigeons (Cook & Wasserman, in press). Thompson & Flemming's change in terminology simply shifts the semantics, not the substance, of the debate.

The substantive debate is not about how to define the term analogy but about whether or not there is a discontinuity in the cognitive mechanisms that human and nonhuman animals employ to make relational inferences. Thompson & Flemming propose that there is a discontinuity between the symbolic-relational abilities of apes and all other species (see also Thompson & Oden Reference Thompson and Oden2000). We believe this “analogical ape” hypothesis fails twice: It severely underestimates the symbolic-relational abilities of other non-primate species (see, e.g., the commentaries by Herman et al. and Pepperberg). And it glosses over the fundamental, qualitative difference between the feature-based strategy employed by Sarah and the non-domain-specific, role-based analogies made universally by modern humans. Even Thompson & Flemming admit that the sole evidence of a nonhuman animal having solved a “material analogy” is Sarah's unreplicated performance on Experiment 3 reported by Gillan et al. (Reference Gillan, Premack and Woodruff1981). As we pointed out in our target article, Sarah's remarkable and unreplicated success in this experiment constitutes exceedingly thin support for the “analogical ape” hypothesis. (See our Appendix [sect. R7] for examples of experimental protocols that could provide evidence for various kinds of analogical reasoning in nonverbal subjects.)

R2.5. Rules

Tetzlaff & Carruthers are right to emphasize the fact that rule learning (or, at least, rule-like learning) can be found among minds as distantly related to humans as those of honeybees and desert ants. We made the same point in our target article. But we hypothesized that only humans possess the ability to learn rules that involve non-perceptual, structural relations among role-based variables. Tetzlaff & Carruthers provide no reason to doubt this hypothesis.

For example, the location of a particular object with respect to specific landmarks is the epitome of a perceptual (i.e., spatial) relation between observable stimuli. Therefore, the fact that honeybees' path integration mechanisms use the distance and angle between arbitrary landmarks is evidence that they can represent these spatial relations in a rule-like fashion; but it hardly counts as evidence that honeybees are able to reason in terms of “non-perceptually-based information” as Tetzlaff & Carruthers claim.

R2.6. Higher-order spatial relations

Hallinan & Kuhlmeier do not challenge our claim that reasoning about higher-order spatial relations is a uniquely human specialization, nor our interpretation of the chimpanzees' performance on Kuhlmeier and Boysen's (2002) scale-model task. Instead, they point out that human children younger than 5 years of age sometimes fail a fully relational version of this task, as well; and they argue that the “continuous” nature of human ontogeny implies a similar continuity in phylogeny.

We will return to question the analogy between ontogenetic and phylogenetic continuity further on. For now, let us simply note just how marked the gap is between human children and all other animals on this planet. All normal 5-year-old children reason about three-dimensional scale models in a systematic fashion, as Hallinan & Kuhlmeier fully admit. Moreover, there is even evidence that children as young as 3 years of age can use distance information from a map to find a point in the real world along a single dimension, and, by 5 years of age, can find objects using a two-dimensional map where the objects are located some distance away from any mapped landmarks (Huttenlocher et al. Reference Huttenlocher, Newcombe and Vasilyeva1999; Vasilyeva & Huttenlocher Reference Vasilyeva and Huttenlocher2004). Needless to say, there is no evidence that any nonhuman animal could use a one- or a two-dimensional map in this fashion (but see the Appendix for a protocol that could be used to test for this ability in nonhuman subjects).

R2.7. Transitive inference

We singled out Lazareva et al.'s (Reference Lazareva, Smirnova, Bagozkaja, Zorina, Rayevsky and Wasserman2004) test of “transitive responding” in hooded crows as a recent example of an experimental protocol that lacks the power, even in principle, of providing evidence for logically underpinned transitive inferences (TI). Notably, Wasserman did not challenge our analysis of these results; instead he claimed that we failed to provide any examples of experimental protocols that could falsify our hypothesis. In the Appendix, we suggest a lab-based protocol that could be used to test for TI in a nonverbal species.

We also criticized two recent “naturalistic” experiments that claimed to have demonstrated TI in male pinyon jays and small African cichlids (Grosenick et al. Reference Grosenick, Clement and Fernald2007; Paz et al. Reference Paz, Bond, Kamil and Balda2004). Pepperberg did not defend the validity of these experiments but instead cited two sets of experiments with great tits (Otter et al. Reference Otter, McGregor, Terry, Burford, Peake and Dabelsteen1999; Peake et al. Reference Peake, Terry, McGregor and Dabelsteen2002) that we had overlooked. These experiments do, indeed, provide additional evidence that the ability to reason about tertiary social relations is not limited to primates (cf. Tomasello & Call Reference Tomasello and Call1997). But they provide no evidence that great tits are capable of TI.

In Otter et al.'s (1999) experiment, for example, it suffices for the female subject to keep track of the dominance relation between her mate and any males she has heard in her current mate's territory and then follow the procedural rule <look for males that have dominated my current mate>. As we explained in our target article, the ability to recognize the social relation among conspecifics based on certain perceptual cues and to rank conspecifics relative to some egocentric benchmark (e.g., my own dominance ranking, my current mate, my matriline) is widely available in the animal kingdom (e.g., Grosenick et al. Reference Grosenick, Clement and Fernald2007; Paz et al. Reference Paz, Bond, Kamil and Balda2004; Silk Reference Silk1999). What appears to be missing among extant nonhuman species is the ability to systematically generalize information about observed relations to unobserved tertiary relations in a transitive fashion. Although neither of the experiments with great tits provides any evidence for this ability, in the Appendix we show how Otter et al.'s (1999) protocol could be adapted to provide a valid test of TI.

R2.8. Hierarchical relations

Reasoning about hierarchical relations is a universal feature of human cognition and, as Shatz points out, well within the repertoire of toddlers. Contrary to persistent claims by comparative researchers over the years (e.g., Bergman et al. Reference Bergman, Beehner, Cheney and Seyfarth2003; Greenfield Reference Greenfield1991; Matsuzawa Reference Matsuzawa, McGrew, Marchant and Nishida1996; Pepperberg Reference Pepperberg2002), we argued that reasoning about hierarchical relations is outside the scope of the capabilities of any extant nonhuman species. None of our commentators directly challenged our analysis of this evidence.

Instead, Pepperberg mentions an experiment by T. Q. Gentner et al. (Reference Gentner, Fenn, Margoliash and Nusbaum2006) that purports to show that European starlings can learn a recursive, center-embedded grammar. But it is far from clear that the particular grammar mastered by the starlings in this experiment requires a hierarchical or recursive computation (see Corballis Reference Corballis2007a). In addition, there is no evidence that starlings can generalize the patterns they did learn to novel vocabularies – the essential feature of cognizing hierarchical relations in a language-like fashion (Marcus Reference Marcus2006). It is worth noting that even Herman et al.'s dolphins never demonstrated the ability to process sentences involving hierarchically embedded constructions. Herman et al. (Reference Herman, Richards and Wolz1984) once claimed that the dolphins responded appropriately to “recursive forms including conjoined constituents and conjoined sentences” (p. 188); however, the tests given were, at best, examples of “tail recursion” and therefore did not involve embedded structures or hierarchical relations.

McGonigle & Chalmers cite an experiment (McGonigle et al. Reference McGonigle, Chalmers and Dickinson2003) purporting to show evidence for “hierarchical classification” in monkeys and claim that this experiment sheds light on the “genesis” of human thought and language. In the cited experiment, McGonigle et al. (Reference McGonigle, Chalmers and Dickinson2003) presented four capuchin monkeys with nine icons that were to be selected on a touch screen in a predefined order: for example, first by shape and then in order of increasing size. After thousands of trials, the capuchin monkeys succeeded in selecting the nine icons in the correct order at least 75% of the time over 20 consecutive trials. McGonigle et al. (Reference McGonigle, Chalmers and Dickinson2003) interpret these results as “evidence for hierarchical processing based on branching procedures.” Indeed, McGonigle et al. (Reference McGonigle, Chalmers and Dickinson2003) claim that the monkeys acquired rules “similar to those operating in a phrase structure grammar,” and they explicitly challenge Hauser et al.'s (2002a) hypothesis that hierarchical and recursive computations are uniquely human.

Given the exhaustive task-specific training McGonigle et al. (Reference McGonigle, Chalmers and Dickinson2003) employed, it is hard to interpret the cognitive significance of these results. But one thing is clear: The manifest behavior of the capuchin monkeys in this experiment has very little bearing on whether or not they are capable of reasoning about hierarchical relations in a human-like fashion. What makes hierarchical and recursive operations such a powerful component of the human language faculty is that they enable human subjects to generatively combine a finite number of linguistic elements into an unlimited range of novel combinations. McGonigle et al. (Reference McGonigle, Chalmers and Dickinson2003) provide no evidence that capuchin monkeys are able to recombine hierarchically organized sequences in a systematic or generative fashion. For example, there is no evidence that the monkeys would be able to switch from sorting on the basis of shape and then size, to sorting on the basis of size and then shape, without learning the entire sequence over from scratch. If it took human language learners thousands of trials to acquire a single invariant sentence, human language would be of little interest.

R2.9. Causal relations

A key claim in our target article is that the ability to reason about unobservable causal mechanisms is a uniquely human capability (see also Penn & Povinelli Reference Penn and Povinelli2007a; Povinelli Reference Povinelli2000; Vonk & Povinelli Reference Vonk, Povinelli, Zentall and Wasserman2006). We interpreted Seed et al.'s (2006) results as further evidence for this hypothesis. Emery & Clayton claim that we were guilty of “misinterpretations, absences, and misrepresentations” in our portrayal of Seed et al.'s (2006) experiment. What is “at issue,” Emery & Clayton write, is the performance of a single rook, Guillem, which passed the crucial transfer test.

We fail to see where the alleged “misrepresentations” are to be found. Indeed, our interpretation of Guillem's singular behavior is the same as that proposed by the authors of the original paper:

We certainly agree that Guillem's behavior deserves “further attention,” but Tebbich et al. (Reference Tebbich, Seed, Emery and Clayton2007) subsequently replicated the same task on seven new rooks and found that only three out of seven passed the perceptual transfer task, and none of them passed the crucial nonperceptual transfer task. In the Abstract to this paper, Tebbich et al. (Reference Tebbich, Seed, Emery and Clayton2007) write:

If anything, our interpretation of Seed et al.'s (2006) results seems to be more generous than that of the original authors: Contra Tebbich et al. (Reference Tebbich, Seed, Emery and Clayton2007), we posit that rooks as well as other nonhuman animals do, indeed, have a “mental representation of physical problems” and a “causal understanding of the trap-tube problem” – albeit not one that involves unobservable causal mechanisms (see again Penn & Povinelli Reference Penn and Povinelli2007a; Povinelli Reference Povinelli2000).

Emery & Clayton also argue that the rooks' performance on the two-tube task could not be due to “domain-specific expectations” because rooks do not use tools in the wild. Here, we suspect that both we and Emery & Clayton were tripped up by the protean term “domain-specific.” Emery & Clayton interpreted our use of the term as meaning “tool-specific.” We meant the term to refer to the domain of physical causal reasoning in general, not tools in particular. Many cognitive psychologists believe that human subjects reason about the physical world using formal and substantive assumptions such as temporal priority, causal directionality, and Michottean perceptual causal principles that are specific to the domain of physical causality, but not specific to tool use per se (see Gopnik et al. Reference Gopnik, Glymour, Sobel, Schulz, Kushnir and Danks2004; Lagnado et al. Reference Lagnado, Waldmann, Hagmayer, Sloman, Gopnik and Schultz2005). There is abundant evidence that nonhuman animals make many of the same causal assumptions as humans (see Penn & Povinelli Reference Penn and Povinelli2007a for a review). In our view, the fact that a non-tool-using species such as rooks was able to quickly master the initial version of Seed et al.'s (2006) task is compelling evidence that at least some nonhuman animals are able to reason about novel tool-use tasks using knowledge and expectations that are specific to physical causal relations but not to tool use per se (see also Santos et al. Reference Santos, Pearson, Spaepen, Tsao and Hauser2006).

R2.10. Theory of mind

In our target article, we criticized Dally et al.'s (2006) experiment with scrub-jays as providing no new positive evidence for theory of mind (ToM) abilities. Emery & Clayton did not challenge our interpretation of Dally et al. (Reference Dally, Emery and Clayton2006). Instead, they reasserted that scrub-jays are capable of “experience projection” based on evidence reported by Emery and Clayton (Reference Emery and Clayton2001).

In these experiments, Emery & Clayton investigated the propensity of scrub-jays to re-cache food that they had previously cached in front of a conspecific, and found that scrub-jays only re-cached food when they had had prior experience stealing another bird's caches. “This result raises the exciting possibility,” Emery (Reference Emery and Watanabe2004, p. 21) wrote, “that birds with pilfering experience can project their own experience of being a thief onto the observing bird, and so counter what they would predict a thief would do in relation to their hidden food” (see also Emery & Clayton Reference Emery and Clayton2004b).

As noted by Penn and Povinelli (Reference Penn and Povinelli2007b), this may be an “exciting possibility”; but it is certainly not the only, or even the most cogent, explanation. Unfortunately, the existing evidence sheds almost no light on the internal mental representations or cognitive processes being employed by the birds in question. For example, all of the birds involved in this experiment had had previous experience being pilfered (see discussion in Emery & Clayton, in press). But Emery & Clayton do not explain how scrub-jays could have the cognitive prowess necessary to reason by analogy to their own subjective experience as pilferers but not have the cognitive wherewithal to realize they should start caching once they have been victims of pilferage themselves. Indeed, Emery & Clayton do not explain why a species with the ability to reason by analogy cannot understand, prior to pilfering another's cache, that caching food from potential competitors might be a good idea.

To make matters worse, the existing evidence has not ruled out the obvious possibility that pilfering changes the subjects' motivation to cache their own food rather than change their cognitive understanding of the functional value of caching per se. This is the point of our analogy to redirected aggression in primates (see Penn & Povinelli Reference Penn and Povinelli2007b): after conflicts, monkeys sometimes behave more aggressively towards groupmates not involved in the original conflict. This evolved behavior seems to be adaptive, both because it reduces monkeys' stress hormones and because it lessens their chance of being victims of further harassment (Silk Reference Silk2002b). But there is no reason to conclude that monkeys are reasoning by analogy to their own subjective experience as “victims.” The same evolutionary and ecological analysis, mutatis mutandis, might shed some light on why scrub-jays only cache their food once they have had experience pilfering. In the meantime, the claim that scrub-jays are capable of “experience projection” would seem to require considerably more empirical support before this “exciting possibility” could be qualified as anything more than that (see our Appendix [sect. R7] for an example of how such evidence might be produced).

Herman et al. cite the example of bottlenosed dolphins responding to “tandem+create” commands as an example of “collaboration.” In fact, as Herman (Reference Herman, Hurley and Nudds2006) himself acknowledges, responding to the “tandem+create” command need not require explicit collaboration or intentional communication. It suffices for one of the two dolphins in the pair to understand that the command requires it to mimic the behavior of the other dolphin. To be sure, this is no mean cognitive feat; and we know of no other nonhuman subject that has ever manifested this degree of symbolic-relational sophistication. At the very least, one of the dolphins on each trial interpreted the argument “create” in the context of a “tandem” command in a radically different manner than it had in the past. But the available evidence is still a long way from demonstrating that dolphins understand each other's roles in a collaborative fashion or are capable of intentional communication. In the Appendix, we propose a modified version of Herman et al.'s “tandem+create” command that could provide definitive evidence for role-based collaboration and intentional communication among dolphins, as well as a nonverbal “false belief” task that could provide positive evidence, at least in principle, that there is another species on this planet that possesses a ToM.

R2.11. A LoT for every species

After reviewing the comparative evidence across a variety of domains, we (like Bermúdez) concluded that extant nonhuman species do, in fact, possess representational systems that are “syntactically structured,” “functionally compositional,” and “featurally systematic” to some degree (we thank Bermúdez for suggesting this last term). Therefore, as we pointed out, our RR hypothesis should not be reduced to the claim that human minds alone approximate a language of thought (LoT), whereas nonhuman minds do not. Quoting Bloom (Reference Bloom2000), we argued that “every species gets the syntax it deserves.”

Notwithstanding our efforts to forestall this very misunderstanding, Tetzlaff & Carruthers make the same point as if they are disagreeing with us: “[E]ven the thought capacities of a very simple mind could approximate one LoT-based system to the same extent as a human's could approximate another.” To reiterate: We believe that minds as “simple” (sensu Carruthers) as those of honeybees employ internal mental representations that are syntactically structured, functionally compositional, and featurally systematic to some degree. Because human minds are by no means unique in approximating a LoT, the real issue is what distinguishes the human species of LoT from all the others that remain on this planet. Carruthers has argued elsewhere (see Carruthers Reference Carruthers2002; Reference Carruthers, Carruthers, Laurence and Stich2005a) that there are certain features of human thought – particularly our ToM and faculty for language – that are distinctively human. So it would seem that Tetzlaff & Carruthers would have to agree with us that there is something uniquely human about the modern human LoT. Unfortunately, Tetzlaff & Carruthers do not suggest what this might be.

Wasserman finds our claim that there is a difference in “kind” between the manifest cognitive abilities of human and nonhuman animals to be inconsistent with our claim that there is a difference in “degree” between human and nonhuman animals' ability to approximate the relational capabilities of a PSS. The problem here is not an “anomaly” in our logic – the problem is that Wasserman does not acknowledge the difference between a functional-level and a representational-level analysis (Marr Reference Marr1982). In our target article, we use the construct of a PSS as a heuristic framework for decomposing the relational operations manifested by biological cognizers at a functional level of analysis into distinct representational-level components (i.e., symbols, compositionality, types and tokens, etc.). As we point out, different species approximate these multifarious features of a PSS to varying degrees. Ex hypothesi, the difference in degree to which various species approximate the features of a PSS at a representational level produces a difference in the kinds of relational reasoning these species manifest in their cognitive behaviors. In particular, although all biological cognitive architectures approximate the features of a PSS to some degree, only those cognizers that closely approximate the higher-order, structural properties of a PSS manifest the kinds of relational reasoning that are characteristic of human cognition (e.g., ToM, analogical inferences, hierarchically structured languages, reasoning about unobservable causal mechanisms).

Halford et al. propose that dynamic binding to a coordinate system in working memory is the fundamental prerequisite for any form of relational reasoning. We agree. And, in our view, Halford et al.'s proposal provides a more plausible and cogent framework for understanding the LoT-like abilities of honeybees and desert ants than does the classical version of a LoT espoused by Tetzlaff & Carruthers. Halford et al.'s proposal also puts a hard lower limit on the kinds of computational architectures that constitute plausible models of animal cognition (cf. Lupyan).

Halford et al. propose two protocols for testing the compositionality and systematicity of nonhuman mental representations, using a delayed response task and “generativity tests” based on learned relational schemas. Our prediction is that nonhuman animals of many taxa will pass both of these tasks but that many connectionist-style models will have great difficulty with them. Of course, it is important to keep in mind that Halford et al.'s proposed tasks test only whether a subject can form implicitly structured relations by binding an object to a “slot” in working memory. This is a necessary prerequisite for functionally compositional and syntactically structured representations (Horgan & Tienson Reference Horgan and Tienson1996). But Halford et al.'s tasks do not test the capacity to reason about higher-order relations or relational roles in the fashion that we have posited is unique to modern humans. In their past research, Halford and colleagues have employed a wide variety of protocols to test higher-order, role-based relational capabilities in human subjects (e.g., Andrews & Halford Reference Andrews and Halford2002; Andrews et al. Reference Andrews, Halford, Bunch, Bowden and Jones2003; Halford Reference Halford1984; Halford et al. Reference Halford, Baker, McCredden and Bain2005; Halford & Busby Reference Halford and Busby2007). Many of these protocols can (and should) be adapted to probe the similarities and differences between human and nonhuman LoTs (see our Appendix for examples).

R3.1. Nature and nurture (and more nature)

Many of our commentators (e.g., Hallinan & Kuhlmeier, Lupyan, McGonigle & Chalmers, Siegal & Varley, Wasserman) assumed that because we postulated an “innate” or “genetic” basis for the discontinuity between human and nonhuman cognition, we were necessarily denying the importance of ontogeny, environment, language, enculturation, and everything else. For example, Wasserman acknowledges that the neural systems of humans may differ from those of nonhumans but asks, “Do these systems merely mature as the child approaches adulthood? Or must these systems be carefully cultivated by enriching experiences to fully flower?”

Wasserman's rhetorical question poses a false dilemma. There is no either/or when it comes to nature and nurture. No biological system, least of all a neural one, “merely” matures on its own. The ontogeny of any biological system is substantially modulated by its environment. But this does not mean that genetic factors play no role in shaping an organism's ontogeny. There is a complex, nonlinear, epigenetic relationship between genes and the environment that plays out over the entire lifespan of an organism – even an enculturated organism.

R3.2. Does primate phylogeny recapitulate human ontogeny?

Hallinan & Kuhlmeier argue that there would be a true cognitive discontinuity between human and nonhuman minds only if the behavior evident in the first stages of human development looked strikingly different from the capacities we see in other species. But the fact that nonhuman primates perform as well as 3-year-old children on some (but not other) tasks has little bearing on our claim that there is a fundamental discontinuity between human and nonhuman minds. The monumental fact of the matter – a fact which Hallinan & Kuhlmeier do not deny – is that the ontogenetic trajectory of one particular primate species' relational abilities distinguishes itself from that of all other extant species on the planet. As Shatz points out, by the second year of life, the cognitive differences between humans and other primates are unmistakable. And by age 5, the functional discontinuity is so enormous that even the most generous comparative psychologist cannot deny the disparity.

Hallinan & Kuhlmeier end up proposing a theoretical account for the disparity between human and nonhuman relational cognition that appears to be the same as our own. Citing Povinelli (Reference Povinelli, Malle, Baldwin and Moses2001), they postulate that humans possess “an additional system that sits side by side with evolutionarily older systems” and that this additional system allows for analogical reasoning that is “not constrained by superficial or context-specific correspondences.” To our ears, that sounds a lot like our hypothesis (see also Povinelli Reference Povinelli2000; Povinelli & Bering Reference Povinelli and Bering2002; Povinelli et al. Reference Povinelli, Bering and Giambrone2000). Like Hallinan & Kuhlmeier, we believe that our uniquely human system for higher-order, role-based relational reasoning continues to interact with cognitive systems that are evolutionarily more ancient and that come on-line earlier in normal human ontogeny (the second ‘R’ in our RR hypothesis stands for “reinterpretation,” not “replacement”). But Hallinan & Kuhlmeier are mistaken, in our opinion, to believe that our “reinterpretation” hypothesis is inconsistent with the claim that there is a fundamental discontinuity between human and nonhuman minds. Both we and Hallinan & Kuhlmeier postulate that there is an “additional system” responsible for subserving our uniquely human ability to reason about higher-order relations and that the emergence of this additional system is unique to the ontogeny of members of our species. Unless Hallinan & Kuhlmeier want to argue that the profound disparity between the cognitive ontogenies of human and nonhuman primates is solely the result of environmental factors, there must be something unique about the potential of the human mental architecture from day one.

R3.3. Constructing the human mind

Lupyan seems to believe that we consider the human mind to be “innately symbolic and propositional.” Our RR hypothesis could not be farther from this strawman. We explicitly denounced the classical view of the mind as biologically implausible and functionally impoverished. To argue that humans and nonhumans differ in their potential for symbolic-relational cognition from conception forward does not entail – or even suggest – that the human cognitive architecture is born with its adult-state symbolic-relational abilities all wired up and ready to go. Our claim is that the human genotype has the unique potential to produce a neural architecture capable of higher-order relational reasoning. Without the appropriate internal and external inputs, however, this genetic potential is sure to be thwarted.

Lupyan goes on to point out that some of the authors we cited on the subject of human language learning do not support the view that adult syntactic competence is prewired into the human brain (e.g., Gomez & Gerken Reference Gomez and Gerken2000; Tomasello Reference Tomasello2000). We cited these authors for a reason: Unlike a Chomskyan view of language, our RR hypothesis does not posit that human beings are born with adult syntactic competence. Again, our claim is simply that there must be something different about the human cognitive architecture in order to explain why only human children have the potential to learn grammatically-structured languages, develop a ToM, participate in collaborative activities, acquire culturally-transmitted knowledge, and employ external symbol systems to scaffold their cognitive achievements.

R3.4. Equal opportunity for pigeons?

Gardner objects to comparative researchers' tradition of “nondiscoveries” of “noncontinuity” based on “nonexperiments.” Gardner is right to remind readers that comparative psychology has been guilty of some rather embarrassing methodological blunders in its short history. Gardner is also certainly correct that differences in rearing conditions and training procedures have a significant impact on the cognitive performance of both human and nonhuman animals. But the claim that human cognitive uniqueness is solely and merely the product of human enculturation is difficult to sustain. The research cited by Herman et al. and Pepperberg are notable examples both of what nonhuman species can achieve with intensive training – and also of how vast a functional discrepancy there is between even the most highly enculturated nonhuman animal and the average human subject. Wasserman's plea to withhold judgment on the cognitive abilities of pigeons until a member of that species has been given the same cultural opportunities as those provided to human children strikes us as particularly extreme. Unless pigeons harbor some heretofore unrealized potential for relational reasoning that surpasses that of chimpanzees, bottlenosed dolphins, and African grey parrots, we doubt the discontinuity between human and nonhuman minds will be challenged by an enculturated pigeon.

R4.1. Are we just the “massively lucky” species?

Tetzlaff & Carruthers, for example, disagree with our claim that higher-order relational reasoning lies at the core of the many uniquely human forms of cognition. Instead, they argue that there are “many distinctively human learning mechanisms.”

To our eyes, it seems wildly implausible that one species happened to be the only one lucky enough to have evolved separate and independent “learning mechanisms” for each distinctively human form of cognition (in a few million years to boot), whereas no other species evolved any of them. Moreover, as we argued in our target article, the massively modular explanation for human cognitive uniqueness is undermined by the fact that each distinctively human cognitive ability seems to rely on a common set of relational competences. Suddendorf acknowledges that we might be on the right track in looking for deep structural similarities across domains. Tetzlaff & Carruthers, however, flatly deny that there are any such “commonalities.”

Tetzlaff & Carruthers' assertion that our human ToM, language faculty, and “intuitive physics” have “nothing to do with relations among relations” runs counter to a large body of existing research and theory (as well as the points of view of many of our other commentators; see, e.g., Bermúdez, Gentner & Christie, Halford et al., Markman & Stilwell, and Suddendorf). Numerous researchers have demonstrated a compelling empirical relationship between higher-order relational reasoning and ToM performance (e.g., Andrews et al. Reference Andrews, Halford, Bunch, Bowden and Jones2003; Zelazo et al. Reference Zelazo, Jacques, Burack and Frye2002) and most theoretical models of ToM require some degree of higher-order, role-based relational reasoning (see, e.g., the theories proposed in Carruthers & Smith Reference Carruthers and Smith1996). With respect to causal reasoning, the one point on which most contemporary researchers agree is that the ability to recognize and reason about the network of relations among causes and effects in a systematic and allocentric fashion is the bedrock of human causal cognition (e.g., Gopnik et al. Reference Gopnik, Glymour, Sobel, Schulz, Kushnir and Danks2004; Lagnado et al. Reference Lagnado, Waldmann, Hagmayer, Sloman, Gopnik and Schultz2005; Tenenbaum et al. Reference Tenenbaum, Griffiths and Kemp2006). Tetzlaff & Carruthers even claim that transitive inferences are not about the relations amongst relations, dismissing a long tradition arguing exactly the contrary (e.g., Halford et al. Reference Halford, Wilson and Phillips1998a; Inhelder & Piaget Reference Inhelder and Piaget1964). Ditto for language (e.g., Gomez & Gerken Reference Gomez and Gerken2000; Hauser et al. Reference Hauser, Chomsky and Fitch2002a; Pinker & Jackendoff Reference Pinker and Jackendoff2005).

Perhaps everybody else is wrong. We would certainly be the last ones to claim that a “consensus” (no matter how large) is any guarantor of truth. But at the very least, it seems incumbent on Tetzlaff & Carruthers to provide a far more substantive and convincing refutation of our argument that ToM, causal reasoning, transitive inference, and language all involve higher-order relational reasoning of various kinds before dismissing it out of hand.

To clarify our own position: We never claimed (contrary to what Tetzlaff & Carruthers write) that “there is just one” mechanism that distinguishes human and nonhuman learning mechanisms. Reasoning about the relation between relations is not sufficient to account for any of our human cognitive capabilities. Additional cognitive and morphological adaptations are also necessary to subserve our distinctively human capabilities in ToM, language, and abstract causal reasoning. Nor are we arguing against the functional modularity of human cognition (Barrett & Kurzban Reference Barrett and Kurzban2006). We are merely arguing that higher-order, role-based relational reasoning is one core component of all of these distinctively human capabilities, and that the functional supermodule that subserves this form of reasoning in humans is necessary (but not sufficient) to enable these capabilities.

R4.2. Is there a discontinuity in executive functioning?

After producing a seminal body of research showing that many distinctively human forms of thought are preserved despite severe linguistic impairments (e.g., Siegal et al. Reference Siegal, Varley and Want2001; Varley et al. Reference Varley, Klessinger, Romanowski and Siegal2005; Varley & Siegal Reference Varley and Siegal2000), Siegal & Varley nevertheless make the surprising suggestion that the differences between human and nonhuman cognition may be solely the result of a difference in “executive functioning” rather than a “radical restructuring” of human thinking and reasoning.

We are grateful that Siegal & Varley raised the issue of executive functioning. Variations in executive functioning clearly have a direct impact on the kind and quality of relational reasoning a subject can perform (Andrews et al. Reference Andrews, Halford, Bunch, Bowden and Jones2003; Halford et al. Reference Halford, Wilson and Phillips1998a; Robin & Holyoak Reference Robin, Holyoak and Gazzaniga1995; Waltz et al. Reference Waltz, Knowlton, Holyoak, Boone, Back-Madruga, McPherson, Masterman, Chow, Cummings and Miller2004). For example, uniquely human forms of executive control probably subserve the uniquely human forms of planning and practical decision-making highlighted by Bridgeman. And Hadley (Reference Hadley1999) has argued that some form of a classical computational architecture may be necessary to account for the unique patterns of information flow manifested by human reasoners. Therefore, there are undoubtedly significant differences between the executive functioning capabilities of human and nonhuman animals that contribute to the significant difference in degree to which human and nonhuman minds are able to approximate the computational properties of a PSS.

But positing a difference in executive functioning between human and nonhuman subjects does not somehow undermine our RR hypothesis. Rather, it simply points to one more facet of our supermodule for higher-order relational reasoning that may be uniquely human. Unless Siegal & Varley believe that all the distinctively human forms of cognition they have documented in agrammatic subjects can be performed using the same representational structures as those employed by nonhuman animals, they should agree with us that there is something distinctively human about both the architecture of human relational representations and the executive processes that operate over those representations.

R4.3. Is the discontinuity due to language alone?

In our target article, we argued that language is not solely and completely responsible for the differences between human and nonhuman cognition. Many commentators took issue with this argument (e.g., Bermúdez, Bickerton, Lupyan, Gentner & Christie). In some cases, the disagreements are due to a difference of emphasis rather than a difference in substance. Gentner & Christie, for example, agree with us that our “extraordinary relational ability” is a central reason “why we're so smart” (Gentner Reference Gentner, Gentner and Goldin-Meadow2003); yet they believe they are disagreeing with us when they accord “central importance to language and other symbol systems” as well. Not only do we not disagree with Gentner & Christie on this point, we find their description of the relationship between language and higher-order relational reasoning in their commentary to be succinct and eloquent:

In our target article, we freely acknowledged the “instrumental role” that relational language plays in facilitating human learners' sensitivity to relational similarities and potential analogies. We simply focused the bulk of our argument on the other part of the “positive feedback cycle” – that is, the internal cognitive architecture necessary to support relational learning and reasoning to begin with. To borrow and rephrase Gentner & Christie's closing sentence, our claim is that language, culture, and normal human enculturation are required to fully realize our species' potential for higher-order, role-based relational thought; but that humans alone are born with this potential.

We also find Bermúdez's “rewiring hypothesis” to be largely consistent with our own (see also Bermúdez Reference Bermúdez2005). According to this hypothesis, language played a crucial role in “rewiring” the architecture of the human mind during our evolution as a species. We believe Bermúdez's rewiring hypothesis is plausible and cogent. The only point we tried to make in our target article concerning this evolutionary hypothesis was that language may not have been the only factor that played a role in pushing the architecture of the human mind in a relational direction. Given the enormous adaptive value that abstract causal reasoning, ToM, spatial reasoning, and analogical inferences have in the ecological niche occupied by humans, it is at least possible that one or more of these other relational abilities also played a part. We remain agnostic as to the relative importance of these various cognitive abilities. If our RR hypothesis is correct, all of these specializations coevolved with our capacity for higher-order, role-based relational reasoning in such an inextricable and nonlinear fashion that any linear ordering of their relative importance would be both unverifiable and meaningless.

The evolutionary version of the “rewiring” hypothesis championed by Bermúdez should be distinguished from the kind of ontogenetic “rewiring” alluded to by Gentner & Christie and others (e.g., Dennett Reference Dennett1996). We do not doubt that language played and still plays a crucial role in rewiring the human brain in both its evolution and its ontogeny (i.e., both Bermúdez and Gentner & Christie are right). But any “rewiring” that was performed on the human brain over evolutionary time-scales is an entirely different process (both at a representational and at a physical level) than any “rewiring” done during ontogeny. Therefore, it is important to emphasize that the rewiring effects of language learning do not “recapitulate” the rewiring effects of language evolution (i.e., newborn human brains do not start off at the same place as our prelinguistic ancestors or our nonhuman cousins do). We would only have to take issue with Bermúdez and Gentner & Christie if they were to claim that language and cultural learning are the only factors that distinguish modern human minds from those of extant nonhuman species. To our knowledge, they would not make this claim (but see Lupyan or Wasserman for scholars who might).

Our disagreement with Bickerton is more substantial. Bickerton acknowledges the functional discontinuity between human and nonhuman minds and the importance of higher-order relational reasoning in this discontinuity. He even gives us four kudos for confronting the comparative consensus on this contentious issue. But he gives us only a single kudo for our representational-level account of the discontinuity, preferring his own story about how language “rewired” the human brain.

We are grateful for any kudos we can get. But we believe we deserve an extra point for effort. The point of our target article was not to tell an evolutionary story. The point of our target article was to argue that the modern human brain is quite distinctive in its representational capabilities and that our unique capacity for higher-order relational reasoning is not entirely and solely a function of language or enculturation. Here, Bickerton would seem to be forced to agree with us. He acknowledges in his commentary that once language wrought its rewiring effects on the human brain, human mental representations became qualitatively different from those of other animals and continue to be so today even in the absence of occurrent verbal labels. But Bickerton does not provide a formal description of the representational changes wrought by language, nor does he provide a computational model of how those changes subserve the extra-linguistic cognitive abilities that distinguish modern human from extant nonhuman cognition. We are a long way from providing a complete representational-level account ourselves; but this is where we think we deserve that extra kudo for effort (see also our reply to Bermúdez in sect. R5.3, para. 2, further on).

Ironically, the weakest part of Bickerton's story is his assessment of the cognitive abilities of nonhuman animals. Bickerton claims that “all nonhuman representations are distributed.” And he challenges us to present evidence inconsistent with this proposal. We think Bickerton would do well to consult the commentaries by Emery & Clayton, Herman et al., Pepperberg, Suddendorf, and Tetzlaff & Carruthers. These commentaries provide ample evidence that nonhuman representations are, indeed, functionally compositional and syntactically structured (see also Bermúdez Reference Bermúdez2003; Horgan & Tienson Reference Horgan and Tienson1996). Furthermore, Bickerton's claim that nonhuman representations are tightly coupled to occurrent stimuli flies in the face of abundant comparative evidence to the contrary (see, e.g., Suddendorf & Whiten Reference Suddendorf and Whiten2001).

The problem for Bickerton is that if language is not necessary to subserve “permanent, focused representations” in nonhuman animals, then Bickerton's evolutionary story does little explanatory work. In our view, language had and still has a substantial role in rewiring the human brain; but language's distinct evolutionary and ontogenetic impact on human reasoning falls more along the lines described by Bermúdez and Gentner & Christie, respectively, than that proposed by Bickerton.

R4.4. Are the differences only in our heads?

Barrett concurs with our reassessment of the comparative literature, but takes us to task for neglecting the role of the environment in supporting higher cognition in humans (see also Rendall, Vokey, & Notman [Rendall et al.]). Her point is well-taken. Many human and nonhuman cognitive abilities clearly rely on organisms' ability to make use of their bodies and the world in highly evolved, species-typical ways. For example, early work on the development of analogical problem solving in children called attention to its close parallels with symbolic play using physical objects (Holyoak et al. Reference Holyoak, Junn and Billman1984; see also Shatz). And our discussion of the “seriated cups” test of “hierarchical reasoning” relied heavily on Fragaszy et al.'s (Reference Fragaszy, Galloway, Johnson-Pynn and Brakke2002) demonstration that this task is more a test of subjects' sensorimotor skills in the world than of their ability to reason about hierarchical representations in their heads. If we had given due consideration to all the myriad of ways in which human and nonhuman animals leverage the world and their bodies in order to solve relational problems, our target article would have been considerably longer.

This said, there is reason behind our gloss. The purpose of our target article was to suggest an explanation for why human and nonhuman cognition differ so radically. And here, contrary to Barrett's contention, the answer cannot be solely or even primarily “outside the head.” One obvious problem with an “it's all outside the head” stance is that it does nothing to explain why humans, and no others, are able to leverage the world in their species-unique ways. Clark's (Reference Clark2001) hybrid stance seems more promising: Certain cognitive tasks are, to borrow Clark's apt phrase, more “representation hungry” than others. One class of representation-hungry problems of central importance to all biological cognizers is relational problems (Clark & Thornton Reference Clark and Thornton1997). Figuring out why human cognizers alone are able to use knowledge-rich artifacts and symbol systems to help them solve higher-order relational problems requires figuring out, among other things, what is distinctive about the internal representational processes humans bring to bear on these problems. As Suddendorf puts it, “chances are that humans' cognitive autapomorphies have something to do with our brain autapomorphies.”

R5.1. Computational models that aim too low

Rendall et al. suggest that “associative processes” could, at least in principle, provide sufficient representational power to subserve higher-order relational reasoning (see also Lupyan). We agree. We certainly do not rule out connectionist mechanisms as possible implementations of higher-order relational reasoning in humans. We merely believe that anyone who wishes to model human cognition needs to take Smolensky's (1999) “Symbolic Approximation” hypothesis very seriously. As we reviewed in our target article, connectionist models that fail to acknowledge the necessity of approximating the higher-order, structural properties of a PSS consistently fall short precisely where higher-order relational reasoning is required. And, at least at present, it seems doubtful that traditional “parallel distributed processing” (PDP) connectionist models can approximate the higher-order structural properties of a PSS without the addition of qualitatively new representational processes (see also Doumas & Hummel Reference Doumas, Hummel, Holyoak and Morrison2005; Holyoak & Hummel Reference Holyoak, Hummel, Dietrich and Markman2000; Wilson et al. Reference Wilson, Marcus, Halford, Johanna and Keith2001b).

R5.2. Computational models that aim too high

Tomlinson & Love pose an excellent question: If animals cannot approximate a full-fledged PSS, what kind of computational architecture do they have? There is a conspicuous dearth of biologically plausible, computationally feasible, behaviorally adequate answers to this question. Indeed, there are so few researchers willing to even ask this daunting question that we happily accord two kudos to Tomlinson & Love just for showing up and making the effort.

This said, the BRIDGES (Building Relations through Instance Driven Gradient Error Shifting) model touted by Tomlinson & Love begs the question at issue in our target article. The BRIDGES model solves S/D and RMTS tasks by combining exemplar-based category learning (what we call perceptual relational learning) with structured relational mapping (which we claim is unique to humans). No one doubts, of course, that S/D and RMTS tasks can be solved by structured relational mapping – human subjects may very well solve RMTS tasks in this manner under certain conditions. But the issue at stake in our target article is whether or not there is any evidence that other extant species employ this particular mechanism as well.

Tomlinson & Love point out that an explanation based on sensitivity to categorical entropy alone does not explain the degree to which pigeons are influenced by the featural similarity between the test array and previous arrays the animal has been trained with. We agree. Categorical entropy is certainly inadequate to account for all of the patterns of relational responding manifested by pigeons or any other animal (as Cook and Wasserman [Reference Cook, Wasserman, Wasserman and Zentall2006] themselves point out). But all of the additional influences on pigeons' relational responses, including those documented by Gibson and Wasserman (Reference Gibson and Wasserman2004), are further examples of feature-based relations, not the higher-order structural relations we have argued are unique to humans. And Tomlinson & Love give no reason to believe that pigeons or any other nonhuman animals employ higher-order mappings between structured relations in order to solve S/D or RMTS tasks.

R5.3. Does LISA earn its explanatory keep?

We discussed the LISA (Learning and Inference with Schemas and Analogies) model of analogical reasoning proposed by Hummel and Holyoak (Reference Hummel and Holyoak1997; Reference Hummel and Holyoak2003) as one possible representational-level model for how higher-order relational reasoning might be implemented in a neurally plausible architecture. But Tetzlaff & Carruthers are not unjustified to point out LISA's numerous limitations. To put it bluntly, LISA is a rudimentary, highly stylized model of analogical reasoning that accounts for only a small part of what makes human cognition human (although it is getting better; see Doumas et al. Reference Doumas, Hummel and Sandhofer2008). In our view, LISA is the worst model of higher-order reasoning currently on offer, except for all the others. If Tetzlaff & Carruthers have a better model to suggest, we are all ears.

Bermúdez largely concurs with our analysis of the discontinuity between human and nonhuman minds but argues that the LISA model simply “appears to recapitulate” our functional-level description and does not “explain” how this discontinuity evolved in the first place. It is true that we did not provide an “explanation” for how higher-order relational reasoning evolved in the human brain; but simply invoking a story about how language “rewired” the human mind (see also Bickerton) leaves most of the interesting representational-level questions unanswered as well. It is one thing to identify the functional characteristics of the discontinuity between human and nonhuman cognition. It is quite another to explain how the functional abilities specific to human cognition are implemented in the neural matter of the human brain.

Representational-level computational models such as LISA (see also Tomlinson & Love) have an invaluable but undervalued role to play in cognitive science. It is all too common for psychologists and philosophers to create high-level models of a given cognitive behavior without giving due consideration to whether such models are computationally feasible or biologically plausible. Although there are clearly multiple distinct “levels” of explanation in cognitive science, even Marr (Reference Marr1982) did not countenance ignoring all but the highest level of analysis. Working implementations of a cognitive capability have the potential to challenge or support the plausibility and coherence of higher-level specifications, to provide new insights into the operational characteristics of that cognitive capability, and to serve as models bridging the (often quite large) gap between functional-level and neural-level descriptions.

The bulk of our target article focused on identifying the functional characteristics of the discontinuity between human and nonhuman cognition. Developers of symbolic-connectionist computational models such as LISA are trying to understand what kind of rewiring changes are necessary in order to subserve the higher-order relational capabilities that both we and Bermúdez believe are unique to the human mind – including those that are necessary for language itself. LISA, in particular, provides one possible example of how the higher-order relational capabilities of the human mind might be implemented on top of the lower-order, perceptually grounded capabilities of the nonhuman mind. At the very least, then, LISA provides some confirmation that our RR hypothesis is neither computationally infeasible nor neurally implausible.

But LISA's explanatory neck is stuck out a good deal farther. If LISA is correct, the substantive discontinuity between human and nonhuman cognition came about because only the hominid lineage evolved the ability to use synchronized activity among prefrontal neural populations to support dynamic-binding among roles, fillers, and structured relations. Although neural synchrony is used by many species for coding contextual associations of various sorts (see Fries et al. Reference Fries, Nikolic and Singer2007), LISA suggests that co-opting this mechanism for role-based relational coding was responsible for the “Great Move” (Newell Reference Newell1990) in human cognition. Certainly, neural synchrony is not the only possible mechanism by which the human brain might approximate the higher-order properties of a PSS (for other possibilities, see Smolensky Reference Smolensky1999; Wilson et al. Reference Wilson, Halford, Gray, Phillips, Gentner, Holyoak and Kokinov2001a). And the hypothesis that some form of neural synchrony is the critical innovation subserving higher-order human cognition requires much further empirical support before it can be deemed anything more than a plausible possibility (but see Uhlhaas & Singer Reference Uhlhaas and Singer2006 for a start). Nevertheless, Bermúdez is surely mistaken to argue that LISA is merely a “redescription” of the functional-level facts.

Bermúdez challenges us to explain why the ability to represent higher-order relations, abstract roles, and functions is such a rarity among animals. Here again, LISA suggests one possible story that would not have been apparent otherwise: One of the most interesting and provocative findings to arise out of symbolic-connectionist research is that it is, in fact, quite hard to approximate the higher-order features of a PSS in a neurally plausible fashion. Although higher-order relational reasoning may come naturally to modern humans, it does not come naturally to neural networks. By contrast, it is much easier for neural networks to approximate the kinds of perceptual reasoning that characterize nonhuman cognition. Indeed, traditional PDP-style networks are clearly quite good at approximating many of the basic capabilities of animal cognition. And tweaking these models with various task-specific tricks, ploys, and heuristics (Clark & Thornton Reference Clark and Thornton1997) allows these networks to approximate fairly complex relational tasks, as well. But there is no simple “next step” that will transform a clever PDP model into a full-fledged PSS complete with dynamic role-filler binding and higher-order relational structures. To cross the gap between a PDP network and a PSS, LISA suggests that a neural system needs to make a much more fundamental and costly change in its architecture. From an evolutionary point of view, then, LISA suggests that nonhuman cognitive species have evolved into various “local minima” in the space of biological neural systems, and that the cost of moving out of these local minima has been prohibitive for all but one species on this planet.

R7.1. Analogical relations

R7.2. Higher-order spatial relations

R7.3. Transitive inference

The key criteria for demonstrating transitive inference (TI) experimentally are the following: (1) subjects must be given relational information alone (e.g., A>B) without any cues as to the absolute values of the arguments (e.g., A=5, B=3); (2) the relation involved must be logically transitive and the fact that the relation is transitive must be necessary to make the inference; (3) the transitive relation between stimuli must not be inferable from reinforcement or associative history; (4) the transitive inference must be made on a one-shot, first-trial basis (for further details, see Halford Reference Halford1984; Halford et al. Reference Halford, Wilson and Phillips1998a). Below are two examples of a valid test of TI.

R7.4. Rules

R7.5. Hierarchical relations

R7.6. Causal relations

R7.6.1. Experiment 12: Nonhuman primates' understanding of weight

One of us (Povinelli) has already proposed numerous experiments capable of testing a nonhuman primate's ability to reason about unobservable causal mechanisms (see Povinelli Reference Povinelli2000). Here we suggest one further experiment that would be probative.

Nonhuman primates are quite familiar with the effort required to lift objects. Chimpanzees in particular have been shown to use the weight of an object instrumentally. For example, free-ranging chimpanzees learn to use the weight of heavy stones to crack open hard nuts and lighter stones to crack open softer nuts, in a population-specific fashion. The following experiment tests whether nonhuman primates actually reinterpret the effort required to lift objects and the accompanying sensorimotor cues into a causal notion of “weight” (for more details, see Povinelli, in press). First, present subjects with two balls that are visually identical but of radically differing weights (one is heavy, the other is very light). Train the subjects to sort the balls into one of two containers based on the “weight” of the balls (e.g., “heavy” ball goes in the container to the left, “light” ball goes in the container on the right). Separately, allow the subjects to freely play with the ramp apparatus shown in Figure R1, allowing them to launch balls of various weights down the ramp without the reward apple being present. Then, after placing the apple, allow the subjects (a) to dislodge the apple with their hands and (b) to observe trainers launch heavy and light balls down the ramp, thereby letting them see that only some balls, not all, dislodge the apple. Finally, at test, present the subjects with the two visually identical but differentially weighted balls and the ramp/apple apparatus, and observe whether or not the subjects choose the heavier ball on the first trial.

Figure R1.

Ramp apparatus used to determine if chimpanzees understand that a heavy, but not an extremely light projectile (ball) can be used to dislodge a desired reward apple.

One of us (Povinelli) has already run several experiments like the one just described on a group of captive chimpanzees (see Povinelli, in preparation). Subjects chose to use the heavier ball to dislodge the apple at chance levels on the critical test trials – even though they were still able to sort the balls correctly.

R7.7. Theory of mind