R1. LoT and development

The topic of development arose frequently, raised by Canudas-Grabolosa, Martín-Salguero, & Bonatti (Canudas-Grabolosa et al.); Carey; Cesana-Arlotti; Colombo; Demetriou; Hochmann; Kibbe; Planer; and Xu. Many theories ask difficult, important questions about the specifics of developmental trajectory. For example Carey, Hochmann, and to some extent Canudas-Grabolosa et al. all have varying levels of skepticism about whether certain logical concepts (e.g., OR) or modal concepts (e.g., POSSIBLE) are available for preverbal infants. Before addressing the specifics, we want to stress how healthy this debate is. Regardless of where one comes down on any specific proposal, these criticisms highlight a serious difference between our LoT and Fodor's. For Fodor, there was no role for developmental psychology; LoT was fixed innately, and the substantive empirical questions were largely restricted to facts about the timescale of developmental triggering. By contrast, we make no claims about radical nativism (or triggering vs. availability at birth, for that matter). Although we are inclined to share the Harvard nativist view (e.g., the views of Spelke, Carey, and Xu) of core cognition, we need not agree with Fodor that all lexeme-sized LoT representations are unlearned.

As Kibbe points out, our LoTH framework allows us to ask fine-grained questions about the developing child's shifting representational repertoire. We needn't just ask “does the steady state of adult conceptual mastery exceed the infant's expressive power?” Instead we can also ask which concepts are available prelinguistically, and which ones are acquired through a process of Carey-style bootstrapping; we can discuss stage developments without taking on a Piagetian framework, but while allowing that the innate conceptual endowment needn't be fixed; we can in principle accommodate a full rational constructivist framework (Xu, Reference Xu2019). Moreover, because some core LoT properties are gradable (both individually and as subclusters), some might emerge before others, or more quickly, and with nonmonotonic shifts in expressive power. Our framework therefore allows for distinct LoTs not only across species and systems, but also across different stages of development. As Canudas-Grabolosa et al. write, LoT is “probably a genus, but, we would add, one whose actual species are still barely known.” We agree. The project of uncovering specific LoTs and their expressive powers at various stages of development and evolution is a challenging one. Perhaps negation and disjunction are available prelinguistically, or perhaps they must be acquired through word learning.

This is an exciting time for the study of logical reasoning in infants and animals, and the commentaries on this topic demonstrate how rapidly the field has evolved – including in the time since we submitted our target article. Although we agree with Carey that the debate on baby and animal logic is still open, we are optimistic about the explanatory prospects of LoTH. Carey proposes baboons and children between 17 months and 3 years old sequentially simulate possibilities in three- and four-cup tasks (Leahy, Huemer, Steele, Alderete, & Carey, Reference Leahy, Huemer, Steele, Alderete and Carey2022). This would predict their roughly 50–50 responding, where mental-logic accounts appeal to imperfect performance. However, near-ceiling performance on such tasks can be found in other species (Pepperberg, Gray, Cornero, Mody, & Carey, Reference Pepperberg, Gray, Cornero, Mody and Carey2019), as can the holding of multiple alternatives in mind at once on a task similar to the two-cup task (Engelmann et al., Reference Engelmann, Völter, O'Madagain, Proft, Haun, Rakoczy and Herrmann2021). The latter result is a hurdle for sequential simulation, and the former suggests that genuine disjunction is indeed possible without language.

Carey also notes two-cup task failures for 14- and 15-month olds (Feiman, Mody, & Carey, Reference Feiman, Mody and Carey2022) and suggests that success starts at the same time as negation acquisition in some languages: 17 months. But if success has something to do with natural-language acquisition, it is curious that we should find a 50–50 pattern of results in three-cup tasks for children as old as three, well after even English learners have started producing linguistic negation. Why not near-ceiling performance? There are limits to logical reasoning even here (performance constraints or a preference for suboptimal strategies), and they could be masking competence in younger toddlers and infants. Relatedly, why might negation acquisition induce simulation? The 50–50 responding and negation production both emerge at around 17 months, but if there is an inference to be drawn here, it is that linguistic negation should improve logical reasoning, not that it primes sequential simulation. Why acquiring linguistic negation would improve one's powers of simulation is unclear.

One might wonder whether 50–50 responding is because of a response bias to pick a container from either side half the time. However, Leahy et al. (Reference Leahy, Huemer, Steele, Alderete and Carey2022) report that 3-year olds who are asked to “throw away” one of the containers in a three-cup task picked from the pair 81% of the time. There might be other response biases at play here, however. Humans like symmetry and dislike lopsidedness, and a 3-year old might prefer not to throw away the lone container, instead throwing away one of the containers in the pair, thus leaving one container on each side. One way to substantiate this explanation would be to do a pure throw-away task: For example, with one candy on the left and two candies on the right, does a 3-year old pick a candy to throw away randomly, or is there a preference to throw away one from the pair? If so, that would suggest a response bias can explain the Leahy et al. results.

Recent evidence suggests that easing performance constraints can eliminate 50–50 responding in 3-year olds in otherwise similar tasks. Alderete and Xu (Reference Alderete and Xu2023) developed a task involving transparent gumball machines, one of which might produce the desired gumball and the other of which must. This task places much lighter demands on working memory, and does not require the arguably demanding feat of quantifying over trajectories of balls through Y-shaped tubes as in other recent studies. Alderete and Xu found that 3-year olds select the correct gumball machine roughly 90% of the time. We think these results tentatively support optimism about performance-error-based explanations of earlier findings regarding disjunction (specifically, problems with working-memory-demanding tasks, including tracking hidden locations and anticipating trajectories, and response biases).

Other tasks (Cesana-Arlotti et al., Reference Cesana-Arlotti, Martín, Téglás, Vorobyova, Cetnarski and Bonatti2018; Cesana-Arlotti, Kovács, & Téglás, Reference Cesana-Arlotti, Kovács and Téglás2020) yield higher success rates, even in 12-month olds. As Cesana-Arlotti notes in his commentary, these results, and in particular the pupil dilation results, are difficult to accommodate with simulation. Carey instead appeals to 1–1 mapping of object files to percepts. Because adults show the same pupillometric profile as 12-month olds in such studies, her interpretation suggests adults, like infants, resolve this problem with 1–1 mapping. This is an area for future research that can help us distinguish between 1–1 mapping and logical explanations of these results. Because adults can perform disjunctive syllogism (DS) in Cesana-Arlotti et al.'s task, the 1–1 mapping explanation opens up the intriguing possibility that multiple redundant reasoning processes are carried out by adults. Independent evidence regarding the cognitive mechanism behind the pupillary dilation and eye movements can help shed light on whether 12-month olds are indeed performing DS.

Even in adults, as Lupyan points out, “rule-based reasoning is far more difficult than it should be if such logical operators actually underlie much of our perception and reasoning.” This is an important point that allows us to clarify our view. We agree, of course, that people make systematic errors in reasoning. We have seen ourselves how difficult it can be to teach symbolic logic to undergraduates. But we think the cognitive architecture of belief, rather than its format, explains many deviations from norms of reasoning (Mandelbaum, Reference Mandelbaum2019). Unsurprisingly, the architecture we favor can operate over representations in an LoT (Porot & Mandelbaum, Reference Porot and Mandelbaum2020, Reference Porot, Mandelbaum, Musolino, Sommer and Hemmer2022; Quilty-Dunn & Mandelbaum, Reference Quilty-Dunn and Mandelbaum2018). We do not assume that logical operators of LoTs are just like those of formal or even natural languages; in fact, we agree with Canudas-Grabolosa et al., Cesana-Arlotti, and Wellwood & Hunter, who argue they differ (see also Mandelbaum et al., Reference Mandelbaum, Dunham, Feiman, Firestone, Green, Harris and Quilty-Dunn2022; Porot, Reference Porot2019).

Xu pushes back on our defense of LoT-like effects in the use of object files for physical reasoning in infancy, including research grounded in her landmark work on this topic (especially Xu & Carey, Reference Xu and Carey1996). Xu's commentary makes valuable points about the methodological issues, especially concerning differences in the evidence for abstract representation of a special class of superordinate kinds (e.g., object vs. agent; for related philosophical work, see Murez & Smortchkova, Reference Murez and Smortchkova2014; Westfall, Reference Westfallforthcoming) and ordinary basic-level categories like knife and marker. We are grateful for these points.

We grant that the evidence is not decisive about abstract representation of basic-level categories before 12 months, and that careful attention to experimental details is required to make progress on this issue. We add two points here. The first concerns the relevance of the Stavans and Baillargeon (Reference Stavans and Baillargeon2018), Stavans, Lin, Wu, and Baillargeon (Reference Stavans, Lin, Wu and Baillargeon2019), and Lin et al. (Reference Lin, Li, Gertner, Ng, Fisher and Baillargeon2021) results. Children's failures to use basic-level categories for object individuation before 12 months might be because of a performance error. Appeals to performance errors are unhelpful without specifying the relevant performance constraints and the experimental paradigms that might overcome them. We suggest that the aforementioned results implicate “catastrophic individuation failures” (Lin et al., Reference Lin, Stavans and Baillargeon2022), wherein featural and categorical information encoded in the object file system fail to be used in physical reasoning, resulting in disagreement between the two systems about the number of occluded objects and thus no coherent expectation on the infant's part. This account predicts that priming relevant information – including surface features like color or the function of a basic-level artifact category like knife or marker – helps the object file system to make the relevant information accessible to physical reasoning. There is considerable independent evidence from vision science that the object file system makes some encoded properties available for use in object individuation and not others, and that drawing attention to a feature increases the likelihood that it is made available (see Quilty-Dunn & Green, Reference Quilty-Dunn and Green2023). We agree that further work along the lines Xu describes is needed to show decisively that appropriate priming can allow infants to use abstract basic-level categories for object individuation.

Our second point concerns the Nc event-related potential (ERP) used by Pomiechowska and Gliga (Reference Pomiechowska and Gliga2021). In their experiment 2, 12-month-old infants were unfamiliar with labels for a group of basic-level categories (e.g., feather, guitar), as confirmed by their parents and by their insensitivity to the category in experiment 1. Infants in the experimental condition saw multiple instances of two categories sorted by category without a linguistic category label, and those in the control condition were shown the category instances without category-relevant training. They found that “[i]nfants who learned nonverbal categories prior to the EEG task displayed sensitivity to across-category but not to within-category object changes” (Pomiechowska & Gliga, Reference Pomiechowska and Gliga2021, p. 9). This result offers hope that infants represent abstract basic-level categorical information in object files. Questions for future research include: How early can these ERP results be observed? What, if any, role do the representations in this experiment play in the Xu and Carey's (Reference Xu and Carey1996) “is-it-one-or-two” task? Would similar nonverbal category training enable success on that task before 12 months? These questions are experimentally tractable, and we are excited to see the trajectory of developmental research on the format of object representations in the years to come.

R2. Object representations

Many commentators focused on our discussion of object file representations, which was just one component of our discussion of LoT in perception. Some directly rejected our claims (Block; Lupyan; Xu), some worried that the argument overextends (Attah & Machery; Cheng; Roskies & Allen), and some saw opportunity for testable claims about development (Carey; Kibbe; Xu), which we discuss in section 1 of the target article. We are thankful to have such a rich interdisciplinary discussion on the representational format of this core posit of contemporary cognitive science in these commentaries.

Block worries that the object file representations that can be maintained in visual working memory (VWM) are distinct representations with distinct formats from object representations used in online vision. He cites evidence that perception relies on iconic representations of objects, while VWM involves a distinct LoT-like form of object representation. There is a background dispute here regarding the border between perception and cognition, which Block (Reference Block2023) argues is because of format. Two of us (Mandelbaum, Reference Mandelbaum2018; Quilty-Dunn, Reference Quilty-Dunn2020c) argue that format cannot explain the perception–cognition border because there are non-iconic, conceptual, LoT representations in vision. For our purposes, we could concede the “border” issue and limit ourselves to the claim that visual cognition involves LoT-like object files. In fact, however, we think the evidence suggests that the same object files that can be held in VWM are genuinely visual – they underwrite clearly visual phenomena like apparent motion (Odic, Roth, & Flombaum, Reference Odic, Roth and Flombaum2012), multiple-object tracking (Haladjian & Pylyshyn, Reference Haladjian and Pylyshyn2008), and much more (see Green, Reference Green, McLaughlin and Cohen2023, for an overview and reply to Block's apparent motion case). It is possible that some “object-like” phenomena in vision (e.g., some gestalt phenomena, figure-ground segregation) might involve iconic representations of regions of space and their interaction with attention guided by full-blown object files. We are grateful to Block for years of discussion on the structure of perception and look forward to continuing this conversation, hopefully with more and more relevant experimental evidence.

Cheng argues that the case for LoT structures in tactile perception is “at least as good as the object file” case, but that this “generates a potential worry” that our notion of LoTH is too weak. However, we don't agree that Cheng's commentary provides convincing evidence for any of our six LoT properties in tactile perception, nor that this evidence is as strong as the case we provide for LoT structures in object perception. We appreciate the opportunity to demonstrate the rather demanding constraints on positing LoT structures that our six core properties entail.

His argument for discrete constituents in tactile representations is that touch involves “multiple tactile stimuli, each of them exists independent of one another.” This is not evidence for discrete constituents, however. To support the presence of discrete constituents, there would need to be evidence (i) that representations of these stimuli are composed into a complex structure of which they are constituents, and (ii) that the representations remain discrete while being composed (to rule out, e.g., holistic feature composition, tensor products, and other nondiscrete forms of composition). The mere presence of representations of different stimuli that exist independently does not meet these constraints. Compare: One might have a mental map of Brooklyn and a mental map of St. Louis, which exist independently of each other, but that fact by itself does not entail the presence of discrete constituents (cf. Camp, Reference Camp, Grzankowski and Montague2018). Similarly, the fact that tactile stimuli “exhibit different properties at different times” does not demonstrate that they exhibit predicate–argument structure, with a representation of a predicate and a distinct representation of an argument that predicate applies to. And the fact that geometrical properties like lines and triangles are represented in touch does not show that their encoding abstracts away from low-level tactile details, which would be needed to infer abstract conceptual content. We are optimistic that there might be evidence for these LoT properties in tactile perception, but the mere presence of multiple stimuli that can change properties and represent geometrical shapes is insufficient for establishing that fact.

Similarly, Roskies & Allen argue that object files are among the examples “never before conceived of as examples of the LoT” and that our defense of LoT models of object files entails that feature maps as understood in Treisman's feature integration theory are also LoT structures, and thus that “LoTH seems to have been weakened almost to the point of vacuity.” As a historical point, we note that the claim that researchers in the area have never conceived of the idea that object files might be LoT representations is inaccurate. Carey (Reference Carey2011, p. 116) and Xu (Reference Xu2019) have conceived of the idea enough to argue explicitly against it, and Pylyshyn (Reference Pylyshyn2009) and Cavanagh (Reference Cavanagh2021) have argued in favor of it. Furthermore, feature maps in Treisman's theory (which should be distinguished from current-day theories of visual attention, such as Guided Search 6.0; Wolfe, Reference Wolfe2021) do not appear to satisfy any of our six LoT properties. Roskies & Allen say that feature maps represent “discrete features” but cite no evidence that the features are represented discretely (rather than, say, via analog magnitude representations; Clarke, Reference Clarke2022); indeed they mention that a feature map “does not have discrete word-like tokens.” As pointed out in response to Cheng above, the mere presence of two separate representations (e.g., two feature maps) does not provide evidence of discrete constituents. They also assert that feature maps encode “abstract content” but their examples are “color and shape.” As we understand the abstract conceptual content property of LoTs, modality-specific formats representing specific colors and shapes, as feature maps do, are paradigmatic cases of representations that lack abstract conceptual content.

Roskies & Allen appear to conflate feature maps, which represent individual features and not their conjunctions, with the outputs of the feature integration operation. This distinction is important, because for Treisman the outputs of feature integration are the very object file representations at issue (Kahneman, Treisman, & Gibbs, Reference Kahneman, Treisman and Gibbs1992). For example, Roskies & Allen write that “the feature binding can be seen as implementing predicate–argument structure” (emphasis added) and that feature maps provide “a kind of role-filler independence that allows the system to bind the same features to different objects and different features to the same object.” The mere presence of a feature binding operation does not require (i) that the output (i.e., the representation of the feature conjunction) represents the features via discrete constituents rather than holistically; (ii) that the features are predicates applied to an explicitly represented argument rather than in an icon that lacks a discrete constituent that stands for an individual property-bearer; or (iii) that the features obey role-filler independence rather than other forms of composition (e.g., the sort instantiated by deep convolutional neural networks [DCNNs] that encode feature conjunctions; Taylor & Xu, Reference Taylor and Xu2021). All of these are nontrivial empirical claims. Indeed, some forms of feature binding in the visual system seem to be iconic and possess none of these LoT-like properties (Quilty-Dunn, Reference Quilty-Dunn, Mroczko-Wasowicz and Grushforthcoming).

The distinction between the initial detection of separate features (e.g., feature maps) and the way features are represented in the output of a binding operation (e.g., object files) is also relevant to the critique from Attah & Machery. They argue that our six LoT properties are vaguely defined (to a certain extent, we agree; see sect. R5) and that they are “too readily discoverable in cognition.” Their example pertains to role-filler independence and binding features to objects: “even the swapping of visual features to objects (e.g., misattributing the color of one object to another) counts as a demonstration of role-filler independence.”

This description is not quite right. One might have parallel systems for detecting individual features (as in Treisman & Gelade, Reference Treisman and Gelade1980) and then a binding operation that constructs representations of objects and their features without role-filler independence (e.g., because conjoined features are represented in a final holistic map without discrete constituents for each feature). This system could generate illusory conjunctions (Treisman & Schmidt, Reference Treisman and Schmidt1982), where a blue square and red circle are misperceived as a blue circle and red square because of errors in the binding operation, without role-filler independence. The evidence we discuss in our perception section, crucially, concerns how features are represented after being encoded in object files; that is, after the compositional operation of binding is completed. Without illusory conjunctions in the initial encoding of feature conjunctions, individual features (including not only color and shape but also more abstract properties like the openness or closedness of a book) are represented discretely enough that they can be swapped from one item to another in VWM. Thus the object file representation must compose various features while allowing that these representations can easily be separated from one another and swapped to different objects. This kind of format is a nontrivial instance of role-filler independence.

This evidence could have turned out differently. Object files could have encoded feature conjunctions without preserving discrete representations of features that incur their own individual memory costs, as was originally thought to be the case in research on object-based VWM storage (Luck & Vogel, Reference Luck and Vogel1997). It could have turned out that feature representations, once encoded into object files, tend to degrade together in VWM rather than feature-by-feature, as an LoT model predicts – and so on for the other properties of object file representations detailed in the target article. If the evidence had differed in these ways, then there would be no support for LoT models of object files.

Despite our disagreements, we thank Cheng, Roskies & Allen, and Attah & Machery for raising these objections. The specific examples of tactile perception, feature maps, and illusory conjunctions allow us to illustrate in detail how our defense of LoT structures in the object file system does not trivially apply to these other cases.

R3. LoTH and natural language

Our target article focuses on sources of evidence for LoTH other than natural language. But natural language is of course deeply linked to the LoTH and the relation is not merely evidential. Many of the commentaries discuss promising avenues of research on LoT and natural language.

Canudas-Grabolosa et al. claim that “rather than regarding [natural languages] as the origin of logical abilities in thought, one could look at their semantics as crystalized repositories of thought primitives.” We very much agree, and much could be done to better understand both the process by which this “crystallization” occurs and the precise lessons it offers for the structure of individual LoTs. But as Cesana-Arlotti and Wellwood & Hunter point out, natural language cannot be taken as a simple blueprint for mental syntax. LoTs of particular cognitive systems and (especially) those of nonhuman LoTs might differ syntactically from any known natural or formal languages. Similarly, perhaps some syntactic features of natural language differ from those of prelinguistic LoT(s), and as Dupre suggests, such structures might scaffold human-specific cognitive abilities. Xu argues that this scaffolding from natural language might extend to LoT structures in core cognition, including object file representations (though see sect. R1 for our reply). Until we know more about the syntactic features and representational primitives of actual LoTs, we cannot know very much for sure how close or far they are from natural language.

These are the very early beginnings of an expansive research program that seems to open as many questions as it settles. For example, a programmatic approach to understanding the syntactic and representational primitives of thought would allow us to type cognitive systems, stages of development, and even minds themselves (across species) with remarkable fineness of grain. This in turn would raise new questions about the origins of each of those LoTs. Fishes can have the same fin shape despite sharing no ancestor that has it, because there are only a few good ways to swim when one has a spine. Similarly, perhaps certain syntactic features, such as predicate–argument structure or logical connectives, are the products of convergent evolution, having reemerged repeatedly because of their usefulness to biological organisms faced with similar constraints and problems to solve. Relatedly, if there are very many possible LoTs, how many are not worth considering when testing between alternatives? In this regard, principles of natural and formal languages can be a useful (if imperfect) starting point for understanding the fundamental properties of an LoT.

We agree with Oved, Krishnaswamy, Pustejovsky, & Hartshorne (Oved et al.) that eventually LoT will need to be understood as a single element among a broader system in which it is embedded. In particular, questions that Fodor thought of as exotica – for example, how LoTs interact with images, analog magnitudes, motor intentions (Mylopoulos, Pacherie, & Shepherd, Reference Mylopoulos, Pacherie and ShepherdMS; Shepherd, Reference Shepherd2019), and various formats useful for reasoning, categorization, and interacting with the world – will have to be reckoned with. We think a major area for research in the coming years will be how different formats interact and coexist, such as dual codes in perception (Quilty-Dunn, Reference Quilty-Dunn2020c). However, we hesitate to endorse all of Oved et al.'s recommendations. Although we can agree that concepts like CAT are “tied to recognition procedures,” we doubt that constituents of an LoT sentence are “reified abstractions” over these recognition procedures or distributions of worldly features.Footnote ¹ Instead, we suspect LoT concepts are genuine atoms of thought, not composed of features; we distinguish between concepts and the features that trigger their deployment, as Fodor did (Fodor, Reference Fodor1998). This is an in-house dispute, however; LoTH itself is compatible with the more pragmatist approach adopted by Oved et al. as well as the antipragmatist view we are drawn to.

Oved et al. also raise the problem of polysemy, that is, the flexibility of reference observed in many ordinary words, such as “bottle” in “Mary drank the bottle” and “Mary smashed the bottle” (Pustejovsky, Reference Pustejovsky1995, is a locus classicus; see also Vicente, Reference Vicente2018). Fodor dismissed polysemy as either nonexistent or an uninteresting instance of homonymy, as when “bank” can refer to a financial institution or land alongside a river (Fodor & Lepore, Reference Fodor and Lepore1998). Our defense of LoTH in the target article is officially neutral on this issue, but in fact we take the issue seriously. Unlike homonymy, polysemy allows for flexibility in anaphoric reference (“Parched and belligerent, Mary drank the bottle and then smashed it”) and copredication (“Lunch was delicious and informative”) (Murphy, Reference Murphy2021). Unlike homonymy, forms of so-called “regular” (i.e., systematic and rule-governed) polysemy – like, for example, using a word for a container or its contents as in “bottle,” or for an animal and the meat from that animal as in “chicken,” or for an aperture and the object that fills it as in “window” – show up robustly across languages (Srinivasan & Rabagliati, Reference Srinivasan and Rabagliati2015).

So what do we say about an LoT concept like BOTTLE? One option, as Oved et al. note, is to insist that each referent has a distinct LoT concept, and therefore to allow one word in the thinker's lexicon to address many concepts (Carston, Reference Carston2012; Pietroski, Reference Pietroski2018). Another option is to drop Fodor's referentialist requirement on LoT symbols, and allow one concept BOTTLE to function as a pointer to a memory location where diverse bodies of information can be retrieved to resolve polysemy inherent in the concept itself (Quilty-Dunn, Reference Quilty-Dunn2021). Yet another option posits large nonatomic concepts, pieces of which can be deployed on different occasions (Ortega-Andrés & Vicente, Reference Ortega-Andrés and Vicente2019) – though this option perhaps plays least well with LoTH. We take the issue of polysemy and LoT concepts to be largely open and amenable to empirical investigation. As with many questions about the way trains of thought unfold, the answer likely lies in the interaction of many representational formats, organized in nontrivial ways by LoTs.

Much discussion of natural language in the commentaries presupposed that some LoTs might predate it, including in animals. Kaufmann & Newen sum up our target article by saying that we propose LoTH can “explain all animal cognition” and that we “suggest understanding all communication and reasoning through language-like structures in a wide sense, to justify compositionality.” They point to orangutan long calls, which can be explained with non-LoT representations. As we say in the target article, however, we did not intend to suggest that LoT is the “only game in town,” nor did we make any claims about communication, in orangutans or any other creature (including humans); indeed we explicitly denied that all cognition in human or nonhuman animals is explicable through LoT-like formats. Instead, we pointed to evidence for LoTs in many corners of the animal kingdom, focusing on specific experimental paradigms and cognitive domains such as cup tasks and physical reasoning. Because Kaufmann & Newen did not discuss these paradigms or domains, we are left wondering which aspects of our application of LoTH to nonhuman animals they find implausible. In any case, there is a rich research program ahead exploring how LoTs and other formats divide the mind's labor, including in nonhuman animals.

Antony points to applications of LoT to person-level phenomena involving beliefs and other propositional attitudes. We wholeheartedly agree. Although our aim was to focus on explanatory successes of LoTH in areas more remote from explicit thought, we think some of the strongest evidence for LoTH remains its utility in explaining the structure of belief. We also concur that dispositionalism and antirepresentationalism about belief struggle to explain familiar phenomena like opacity (why we can believe that p under one description but not another) and the enormous conceptual gap between belief and behavior (how the belief that p can cause us to engage in incompatible behaviors depending on the other attitudes we use in inference). In other projects, all three of us have argued for a full-throated representationalism about belief (Mandelbaum, Reference Mandelbaum2014, Reference Mandelbaum2016; Porot & Mandelbaum, Reference Porot and Mandelbaum2020; Quilty-Dunn & Mandelbaum, Reference Quilty-Dunn and Mandelbaum2018). We are thankful to Antony for bringing these classic issues to the fore, and we are optimistic that LoTH will continue to prove useful in solving problems from the structure of bee cognition up to Frege's puzzle.

Antony's comments on belief can be extended to implicit cognition, which we did in section 6 of the target article. We just here note that applying LoT and belief to the study of implicit attitudes has been an enormously fruitful paradigm, as can be seen by the groundbreaking work of Benedek Kurdi and De Houwer. We note this as it's easy to take for granted how quickly the study of implicit attitudes has changed. Ten years ago, associationism for understanding attitudes still reigned. As Madva implies, our view has now mostly become the accepted backdrop in the experimental implicit bias literature. The recent history of implicit attitude research thus exemplifies the serious power of LoTH.

R4. What is LoTH committed to?

De Houwer suggests that the six properties we describe may reduce to a single feature, relations. Merely encoding relational contents is largely format-neutral – just as a smoke detector can encode propositions about the presence of smoke, an unstructured symbol like a lantern could, if embedded in the right sort of system, encode a proposition with relational content like <The British are approaching the shore of Massachusetts>. Of course we don't think this is what De Houwer has in mind by “relational content.” De Houwer's pathbreaking work provides some of the strongest reasons for detecting LoT representations in implicit attitudes and “associative” learning (Mitchell, De Houwer, & Lovibond, Reference Mitchell, De Houwer and Lovibond2009), and it's this sort of explicit representation of relations that implicates LoT structure. But we suspect that spelling out the notion of explicit relational content (beyond the mere representation of a relation) will require appealing to independently specified LoT properties – for example, predicate–argument structure (explicitly represented relations require multiple argument places) and role-filler independence (representing the same relations across distinct relata and vice versa). Thus we are skeptical that relational content is a more fundamental feature of LoT representations than those we specify or can play a role in grounding these other LoT properties that seem to us more fundamental. The hypothesis that relational contents qua multiplace predicates might constitute an important developmental and/or evolutionary advance in LoTs is an intriguing one, however, and we are grateful to De Houwer for raising the issue here.

Some commentators worried about the inference from LoT-like models to LoT-like structures in the mind. Griffiths, Kumar, & McCoy object that we “cross levels of analysis,” and take LoT models at the Marrian computational level to support LoT structures at the Marrian algorithmic level (see also Roskies & Allen). They point out that deep neural networks (DNNs) can capture the inductive biases of Bayesian models without LoT structures. We agree that the successes of Bayesian models do not entail that the underlying mental representations share formal properties with the models. However, we draw no such inference in the target article. We do discuss computational models, but we do this (i) to point out that some computational models exploit LoT programs, and this undermines claims that the rise of DNN computational models has not made symbolic LoT approaches obsolete, and (ii) to note that the evidence that reaction time and error rates in encoding and searching for geometrical shapes tracks minimal description length in the probabilistic language-of-thought (PLoT), suggesting that the underlying algorithm implements this specific formal property (viz., description length; Sablé-Meyer, Ellis, Tenenbaum, & Dehaene, Reference Sablé-Meyer, Ellis, Tenenbaum and Dehaene2021a). We don't take the modeling evidence to be decisive – instead, we use hundreds of experimental results to draw explanatory inferences about algorithmic-level representational structure. Therefore, although we grant the general point about the looseness between model and reality, we believe the target article takes pains to get at the underlying mental structures themselves.

McGrath, Russin, Pavlick, & Feiman (McGrath et al.) raise an important concern about the relationship between our six LoT properties and the LoT format itself. They are correct that we were unclear in our target article about whether these core properties are criterial or diagnostic of a deeper single cause. Our unclarity on this issue was not accidental – we are indeed unsure about the right answer. We have wondered whether LoT properties cluster together merely because that is what it is to be a language (in a general, cognitively relevant sense). In other moods, we have been drawn to views where these properties cluster because they all subserve efficiency in domain-general reasoning, and perhaps are even necessary for domain-general computational systemsFootnote ²; we have also, in dark moods, been drawn to the idea that recursion is the true core of LoTH. However, in the end we just don't know what we think. Our working hypothesis has been that these properties are diagnostic rather than standard and there is a deeper reason why they cluster across systems and species.

We borrow the notion of homeostatic property clusters from philosophy-of-science, where it has been argued that instances of genuine natural kinds oftenFootnote ³ share a common mechanism that explains the clustering of properties (Boyd, Reference Boyd and Wilson1999; Craver, Reference Craver2009). Perhaps, then, there is a mechanism underlying LoT phenomena (e.g., the still basically unknown formal or “syntactic” properties of LoTs), and these underlying mechanisms explain why the properties mentioned in our target article clump together. Nonetheless, facts like this are what you end up with at the end of inquiry, not the beginning. Without deciding between these views at the outset, we think the correct methodology is to search for a deeper fact that yokes these properties together. This is a big tent project and one that needs theorists from across the cognitive science spectrum. If it turns out that some of the properties we characterize are features of underlying cognitive mechanisms (e.g., discrete constituents) and others are emergent phenomena that these mechanisms produce (e.g., inferential promiscuity) then the target article will have missed out on key metaphysical facts about LoTs and the phenomena they generate. Some such possibility seems extremely likely to us. If our target article has outlined a strictly false but empirically useful characterization of an important kind of cognitive mechanism (a common way that science stumbles forward; Colaço, Reference Colaço2022), we would still consider that a success.

We agree with McGrath et al. that this is one of the most pressing questions at the core of the new iteration of LoTH that we offer. However, as they point out, the fate of LoTH as a viable hypothesis does not hang on the answer. It could be that the standard approach is best, and nonclassical architectures like DNNs could implement LoTs without underlying computational mechanisms that look especially symbolic. It could also be true that domain-general computation requires the cluster of LoT properties, such that any process that wanted to reach true formal computational power would have to end up with these properties one way or the other. If, on the contrary, there is some deeper mechanistic fact that causes LoT properties to cluster, a DNN could potentially instantiate them while lacking the underlying computational mechanism and thus be LoT-like, but not an instance of the same natural kind. Whether it is most fruitful to interpret LoTH as characterizing the underlying mechanism or the cluster of properties that can be produced by very distinct mechanisms is an open empirical question, and not one we need to answer in advance of using LoTH as a guiding hypothesis in cognitive science.

Chalmers's response marshals a similar distinction: Although we have argued for LoT representations, he argues, we are noncommittal about the possibility of subsymbolic computation. On our version of LoTH, it is possible that “computational primitives (units) are not representational primitives.”

Whether or not there is subsymbolic computation in biological cognition, there is also computation over LoT symbols. This would be true even if, as he claims, “the quasi-symbolic operations of composition, decomposition, and quasi-logical inference may be available, but they are a tiny subset of the operations one can perform on the relevant distributed representations.” One reason why this is true is simply because compositional operations are ipso facto computations. At least four of the six features we describe concern the way LoT representations combine in thought to yield new representations. This is a form of computation. In this sense evidence for these features just is evidence for LoT-based computation, whether or not such computations can be implemented at the subsymbolic level, and whether or not subsymbolic computation also implements non-LoT operations.

Furthermore, a good deal of the evidence we cite concerns not merely compositional LoT sentences, but the use of those LoT sentences in cognition in real time. For example, the evidence surveyed in section 6 of the target article suggests that the logical form of LoT sentences is computed over automatically in system-1 reasoning; the evidence in section 4 of the target article suggests that the predicate–argument structure of LoT sentences is computed over when tracking objects; the evidence in section 5 of the target article suggests that physical reasoning computes over abstract content represented symbolically in LoT sentences and even logical representation of disjunction. All this evidence suggests that LoT sentences are not simply represented in the mind, but rather are used in computational processes that unfold across time. That is, pace Aronowitz, our evidence does not solely concern LoT representations “in stasis,” but rather illustrates that LoT representations are held in memory stores like VWM and figure in dynamical cognitive processes. And as Antony points out, LoTs are perfectly suited to make sense of reasoning at the personal level, bridging folk conceptions of mentality with a scientific one. We thank these commentators for their commentaries which allow us to foreground questions about the computational aspects of thought, which we agree is one of the most pressing issues in cognitive science.

It should not be surprising that the evidence for LoT structure tends to be evidence for LoT-sensitive computations – what good is an LoT if you can't use it while thinking?

R5. Is LoTH generative?