4.1 Object files

Object files are perceptual representations that select individuals, track them across time and space, and store information about them in visual working memory (VWM). This construct is probed via independent, but converging methods, including: Multiple-object tracking (Fig. 2a; Pylyshyn & Storm, Reference Pylyshyn and Storm1988), object-based VWM storage (Fig. 2b; Hollingworth & Rasmussen, Reference Hollingworth and Rasmussen2010), physical reasoning, especially in infants (Fig. 2c; Xu & Carey, Reference Xu and Carey1996), and object-specific preview benefits (Fig. 2d; Kahneman, Treisman, & Gibbs, Reference Kahneman, Treisman and Gibbs1992). These methods cluster around a common underlying representation, standardly taken to be a unified representational kind (Carey, Reference Carey2009; Green & Quilty-Dunn, Reference Green and Quilty-Dunn2021; Scholl & Leslie, Reference Scholl, Leslie, Lepore and Pylyshyn1999; Smortchkova & Murez, Reference Smortchkova, Murez, Smortchkova, Dolega and Schlicht2020). Object files are extremely well-studied, are generated by encapsulated perceptual processes (Mitroff, Scholl, & Wynn, Reference Mitroff, Scholl and Wynn2005; Scholl, Reference Scholl2007) that operate prior to and independently of natural-language-guided cognition (Carey, Reference Carey2009), and are widely believed to have some sort of compositional structure (minimally, object–property bindings), making them an excellent test case for LoTH.

Figure 2. (a) Multiple-object tracking: A subset of visible items (“targets”) is tracked while others (“distractors”) are ignored; reprinted from Pylyshyn (Reference Pylyshyn2004), Figure 1, with permission from Taylor & Francis. (b) Object-based VWM storage: A change detection task demonstrates that color is recalled for each object despite location changes, providing just one example piece of evidence that object-based storage in VWM uses object-file representations; reprinted from Hollingworth and Rasmussen (Reference Hollingworth and Rasmussen2010), Figure 2, with permission from American Psychological Association. (c) Object-based physical reasoning: Objects pop out from behind an occluder, and preverbal infants rely on spatiotemporal information (and featural and categorical information – see section 5) to keep track of the number of objects, as evidenced by their increased looking time when an unexpected number of items is displayed; reprinted from Xu and Carey (Reference Xu and Carey1996), Figure 1, with permission from Elsevier. (d) Object-specific preview benefit: A feature is previewed in each of two visible objects before disappearing, after which the objects move to new locations, and a target feature appears. Subjects show a benefit in reaction time when discriminating the feature if reappears in the same object, illustrating that object-file representations store object properties across spatiotemporal changes; reprinted from Mitroff et al. (Reference Mitroff, Scholl and Wynn2005), Figure 4, with permission from Elsevier.

According to Carey's (Reference Carey2009) seminal theory of core cognition, object files are amodal but iconic in format (cf. Xu, Reference Xu2019). Nonetheless, we believe an LoT-based model is better suited to the data than an iconic model (Green & Quilty-Dunn, Reference Green and Quilty-Dunn2021; Quilty-Dunn, Reference Quilty-Dunn2020a, Reference Quilty-Dunn2020c). As far as we know, the possibility of logical operators in object files hasn't been studied. However, converging evidence suggests that object files have discrete constituents, role-filler independence, predicate–argument structure, and abstract conceptual content. In section 5, we'll explore the inferential promiscuity of object files in physical reasoning.

4.2. Structured relations

We've just argued that perceptual representations of individual objects contain discrete constituents that are organized in a predicate–argument structure and predicate abstract conceptual contents – in other words, they're sentences in the LoT. We'll now describe some LoT-like properties of representations used in the perception of structured relations, both within and between objects.

4.2.1

First, our perceptual systems represent hierarchical part-whole structure. Our perceptual systems don't simply select objects and attribute properties to them. They also break objects down into component parts and represent their part-whole structure. When we perceive a pine tree, we see a branch as part of the tree and a needle as part of the branch, with a sense of the borders between these various parts. Thus the visual system makes use of hierarchical structural descriptions (Fig. 3a; Green, Reference Green2019; Hummel, Reference Hummel and Reisburg2013).

Figure 3. (a) Hierarchical part-whole structural description: Ps = monadic featural properties, horizontal Rs = spatial relations, vertical Rs = mereological relations; reprinted from Green (Reference Green2019), Figure 9, with permission from Wiley. (b) Structural analogy between tree-like structures in natural-language syntax and tree-like perceptual representations of interobject relations; reprinted from Cavanagh (Reference Cavanagh2021), Figure 3, with permission from Sage under CC BY 4.0, cropped and rearranged. (c) Hierarchical structure in scene grammar: Objects are organized relative to “anchors” (relatively large, immobile elements of environments like showers and trees) in phrase-like structural descriptions of normal relative positions; reprinted from Võ, Bettcher, and Draschkow (Reference Võ, Bettcher and Draschkow2019), Figure 2, with permission from Elsevier. (d) Examples of perceived interobject relations; reprinted from Hafri and Firestone (Reference Hafri and Firestone2021), Figure 2, with permission from Elsevier.

The motivation for classic structural-description accounts of object perception was computational: Positing representations of object parts that compose to generate descriptions of part–whole structure allows for successful computational modeling of object perception (Biederman, Reference Biederman1987; Marr & Nishihara, Reference Marr and Nishihara1978). These models operate just as a classical LoT picture demands, exhibiting systematic and productive compositionality of viewpoint-invariant descriptions of parts (Fig. 3b; Cavanagh, Reference Cavanagh2021). Structural descriptions “are compositional – forming complex structures by combining simple elements – and thus meaningfully symbolic” (Saiki & Hummel, Reference Saiki and Hummel1998b, p. 1146).Footnote ⁶

One of the key assumptions of such models is that object-part boundaries are psychologically real, that is, two points will be treated differently by the visual system when they lie on the same part as opposed to two different parts of the same object. This assumption turns out to be true (Green, Reference Green2019). For example, a well-known example of object-based attention is that two stimuli are better discriminated when they lie on the same object than different objects, controlling for distance (Duncan, Reference Duncan1984; Egly, Driver, & Rafal, Reference Egly, Driver and Rafal1994). The same is true within parts of objects: Participants are quicker to discriminate targets if they lie on the same part than if they cross a part-boundary (Barenholtz & Feldman, Reference Barenholtz and Feldman2003). Furthermore, unfamiliar object pairs that share structural descriptions are seen as more similar than object pairs that have a higher degree of overall geometrical similarity but different structural descriptions (Barenholtz & Tarr, Reference Barenholtz and Tarr2008).

Role-filler independence emerges directly from structural description models, often explicitly so (Hummel, Reference Hummel, Dietrich and Markman2000). Some independent evidence comes from Saiki and Hummel (Reference Saiki and Hummel1998a), who found that shapes of parts and their spatial relations are not represented holistically – in other words, the type-identity of each part is represented independently of its particular role in the structural description and vice versa. Similarity judgments are also guided independently by part shapes and their interrelations, suggesting role-filler independence (Goldstone, Medin, & Gentner, Reference Goldstone, Medin and Gentner1991).

We don't deny that the visual system also employs holistic view-based template-like representations (Edelman, Reference Edelman1999; Ullman, Reference Ullman1996) and other formats. Our claims are merely (i) structural descriptions are among the many representations used in visual processing, and (ii) they have an LoT-like format comprising discrete constituents ordered in hierarchical ways that preserve role-filler independence (Fig. 3b).

4.2.2

Second, we perceive structured relations between objects. We don't perceive objects as isolated atoms, as if through a telescope. Instead, we see the glass on the table, the pencils in the cup, and so on.

In a recent review, Hafri and Firestone (Reference Hafri and Firestone2021) survey striking evidence that such relations are recovered rapidly and in abstract form in visual processing (Fig. 3d). For example, the visual system distinguishes containment events (one object disappears inside another) from occlusion events (one disappears behind another) (Strickland & Scholl, Reference Strickland and Scholl2015). A hallmark of categorical perception is greater discrimination across- than within-category boundaries; participants are better at identifying changes in the position of two circles if the change places the circles in a distinct relation (e.g., CONTAIN(X,Y), TOUCH(X,Y), etc.), suggesting categorically perceived interobject relations (Lovett & Franconeri, Reference Lovett and Franconeri2017). When participants are searching for a particular relation like cup-contains-phone, they are more likely to have a “false-alarm” for target images that instantiate the same relation, like pan-contains-egg, but not book-on-table (Hafri, Bonner, Landau, & Firestone, Reference Hafri, Bonner, Landau and Firestone2021).

Like structural descriptions, perceptual representations of abstract relations exhibit role-filler independence. Abstract relations apply independently of the relata, and representations of relata persist once the relation is broken – for example, it's the same ON in ON(CAT,COUNTER) and ON(KETTLE,STOVE), and it's the same CAT once the cat leaps off the counter. Hafri et al.'s (Reference Hafri, Bonner, Landau and Firestone2021) finding is especially relevant: The relation CONTAIN(X,Y) governs similarity judgments independently of the relata, about as clear a demonstration of role-filler independence as one could expect to find.

It would be efficient for the visual system to store frequently represented relations. A fascinating recent literature on “scene grammar” (Fig. 3c; Kaiser, Quek, Cichy, & Peelen, Reference Kaiser, Quek, Cichy and Peelen2019; Võ, Reference Võ2021) details effects of representations of structured relations in visual long-term memory on visual search (Draschkow & Võ, Reference Draschkow and Võ2017), categorization (Bar, Reference Bar2004), consciousness (Stein, Kaiser, & Peelen, Reference Stein, Kaiser and Peelen2015), and gaze duration (Võ & Henderson, Reference Võ and Henderson2009). Relational representations in visual long-term memory (e.g., ON(POT,STOVE) = yes, IN(SPATULA,MICROWAVE) = no) aren't based on associations or statistical summaries over low-level properties. They persist despite changes in position and context (Castelhano & Heaven, Reference Castelhano and Heaven2011), thus abstracting away from overlearned associations. Characteristic scene-grammar effects disappear, however, for upside-down stimuli (Stein et al., Reference Stein, Kaiser and Peelen2015), implicating a categorical rather than low-level format. The effects also appear not to rely on summary-statistical information represented outside focal attention (Võ & Henderson, Reference Võ and Henderson2009). Despite developing independently of natural language (Öhlschläger & Võ, Reference Öhlschläger and Võ2020), structured relations in scene grammar display curious hallmarks of language-like formats. For instance, the P600 ERP increases for syntactic violations in language, and also increases for stimuli that violate visual scene “syntax” (e.g., mouse-on-computer instead of mouse-beside-computer; Võ & Wolfe, Reference Võ and Wolfe2013). It's standard to talk of scene grammar as associative, but its relational components satisfy a handful of our LoT hallmarks (e.g., discrete constituents with role-filler independence that encode abstract contents, including categories and relations, and function as arguments in multiplace predicates as in ABOVE(MIRROR,SINK)). Scene grammar is used directly in controlled behavior (e.g., how to arrange a virtual reality scene; Draschkow & Võ, Reference Draschkow and Võ2017); how broadly it can function in logical inference remains to be explored experimentally.

4.3 Vision and DNNs

In sum, our perceptual capacities to identify and track objects, grasp their characteristic structures, and perceive and store their relations with one another, appear to rely on LoT-like representations.

A major source of contemporary skepticism about LoTH is the rise of DNNs. Apart from large language models like GPT-3, nowhere are DNNs more visible as models of human cognitive capacities than in visual perception. Given their successes at image classification and apparent similarities to biological vision, one might wonder whether the subsymbolic network structure of DNNs obviates the need to posit LoT-like structures.

The DNNs that have been most touted as models of biological vision are deep convolutional neural networks (DCNNs) trained to classify images (Kriegeskorte, Reference Kriegeskorte2015; Yamins & DiCarlo, Reference Yamins and DiCarlo2016). After training on large data sets like ImageNet, DCNNs exhibit remarkable levels of performance on image classification. It is important to evaluate comparisons to human vision not simply in terms of performance, but primarily in terms of underlying competence (Chomsky, Reference Chomsky1965). Just as differences in performance need not entail differences in competence (Firestone, Reference Firestone2020), human-like performance on a limited range of tasks need not entail human-like underlying competence. In other words, DCNNs may accomplish image classification while lacking key structural features of human vision, including those relevant to LoTH.

DCNNs have been argued to resemble primate vision in competence as well as performance by appeal to metrics of similarity such as “Representational Similarity Analysis” (Khaligh-Razavi & Kriegeskorte, Reference Khaligh-Razavi and Kriegeskorte2014) and “Brain-Score” (Schrimpf et al., Reference Schrimpf, Kubilius, Hong, Majaj, Rajalingham, Issa and DiCarlo2018). However, there are shortcomings both to earlier findings of high similarity using these metrics and to the metrics themselves. For example, Xu and Vaziri-Pashkam (Reference Xu and Vaziri-Pashkam2021b) used higher quality fMRI data for their representational similarity analysis and found that, contra Khaligh-Razavi and Kriegeskorte's earlier findings, high-performing DCNNs (both feedforward and recurrent) show large-scale dissimilarities to human vision. Brain-Score has been criticized for insufficient sensitivity to architectural distinctions (e.g., feedforward vs. recurrent models): “either the Brain-Score metric or the methodology with which a model is evaluated on it fails to distinguish among what we would think of as fundamentally different types of model architectures” (Lonnqvist, Bornet, Doerig, & Herzog, Reference Lonnqvist, Bornet, Doerig and Herzog2021, p. 3). Furthermore, although Schrimpf et al. (Reference Schrimpf, Kubilius, Hong, Majaj, Rajalingham, Issa and DiCarlo2018) found that Brain-Score positively correlates with image classification performance, it fails to capture the crucially hierarchical structure of human vision. Nonaka, Majima, Aoki, and Kamitani (Reference Nonaka, Majima, Aoki and Kamitani2021) thus developed a “Brain Hierarchy Score” that measures similarities between hierarchical structures, applied it to 29 DNNs, and found a negative correlation between image classification performance and similarity to human vision. This finding provides a striking illustration of how DNNs can excel in performance while veering apart from human competence (see also Fel, Felipe, Linsley, & Serre, Reference Fel, Felipe, Linsley and Serre2022).

Our case for LoT in vision is limited to certain domains: Objects, relations between parts and wholes, and relations between objects. It is not a coincidence, in our view, that DNNs that succeed at image classification exhibit little to no competence in these domains. As Peters and Kriegeskorte write about feedforward DCNNs, “the representations in these models remain tethered to the input and lack any concept of an object. They represent things as stuff” (2021, p. 1128).Footnote ⁷ It is also not clear that DCNNs are capable of representing global shape, let alone the relation between global shape and object parts (Baker & Elder, Reference Baker and Elder2022). Baker, Lu, Erlikhman, and Kellman (Reference Baker, Lu, Erlikhman and Kellman2020) trained AlexNet, VGG-19, and ResNet-50 to classify circles and squares, but found that these DCNNs relied only on local contour information; circles made of jagged local edges were classified as squares, and squares made of round local curves were classified as circles. The same models (and several others) also could not distinguish possible from impossible shapes, which requires relating local contour information to global shape (Heinke, Wachman, van Zoest, & Leek, Reference Heinke, Wachman, van Zoest and Leek2021). Failures at processing relations hold not only for DNNs that map images to labels, but also those that map labels to images: Conwell and Ullman (Reference Conwell and Ullman2022) fed the text-guided image-generation model DALL-E 2 a set of interobject relations (including those used by Hafri et al., Reference Hafri, Bonner, Landau and Firestone2021) and found that it failed reliably to distinguish, for example, “a spoon in a cup” from “a cup on a spoon.”

To be clear, we make no claims about in-principle limitations of DNNs. The machine-learning literature is extremely fast-moving, and we do not pretend to know what it will look like in even 1 year's time. Moreover, different DNN architectures might better capture the visual processes discussed here. Although convolutional architectures might privilege local image features, perhaps nonconvolutional architectures like vision transformers (Vaswani et al., Reference Vaswani, Shazeer, Parmar, Uszkoreit, Jones, Gomez and Polosukhin2017) are better suited to avoid these limitations and will supersede DCNNs as models of human vision (Tuli, Dasgupta, Grant, & Griffiths, Reference Tuli, Dasgupta, Grant and Griffiths2021). Because DCNNs have accumulated enormous publicity despite apparently lacking basic elements of biological vision like global shape and objecthood, future DNN–human comparisons should be approached with caution. Finally, as was noted long ago, neural-network architectures might be able to implement an LoT architecture (Fodor & Pylyshyn, Reference Fodor and Pylyshyn1988). Indeed, some recent work on DNNs explores implementations of variable binding (Webb, Sinha, & Cohen, Reference Webb, Sinha and Cohen2021; though see Gröndahl & Asokan, Reference Gröndahl and Asokan2022; Miller, Naderi, Mullinax, & Phillips, Reference Miller, Naderi, Mullinax and Phillips2022), a classic example of LoT-like symbolic computation (Gallistel & King, Reference Gallistel and King2011; Green & Quilty-Dunn, Reference Green and Quilty-Dunn2021; Marcus, Reference Marcus2001; Quilty-Dunn, Reference Quilty-Dunn2021). Our six core LoT properties help specify a cluster of features that such an implementation should aim for.

DNNs are marvels of contemporary engineering. It does not follow that they recapitulate architectural aspects of human vision. We agree with Bowers et al.'s (Reference Bowers, Malhotra, Dujmović, Montero, Tsvetkov, Biscione and Blything2022) recent complaint that research on DNNs as models of biological vision is overly focused on performance benchmarks and insufficiently guided by experimental perceptual psychology. Given that DNNs are universal function approximators, and given the vast resources being poured into their development, they will only get closer to human performance over time. But this performance will not reflect core competences of the human visual system unless the relevant models incorporate LoT-like representations of objects and relations.

5.1 Abstract content and physical reasoning

Considerable evidence suggests infants use object files to reason about the identity, location, and numerosity of hidden objects (Carey, Reference Carey2009; Spelke, Reference Spelke1990). However, in a foundational study, Xu and Carey (Reference Xu and Carey1996) found that, although 12-month olds who see a duck and then a ball pop out from behind an occluder expect two objects to be present, 10-month olds don't. This failure might seem to suggest that abstract conceptual content is not usable for physical reasoning in young infants, potentially undermining LoT-based models of infant reasoning (Xu, Reference Xu2019).

However, 10-month olds do succeed for socially significant categories (Bonatti, Frot, Zangl, & Mehler, Reference Bonatti, Frot, Zangl and Mehler2002; Surian & Caldi, Reference Surian and Caldi2010) and objects that are made communicatively salient (Futo, Teglas, Csibra, & Gergely, Reference Futo, Teglas, Csibra and Gergely2010; Xu, Reference Xu2019, p. 843). There is also evidence that priming can allow infants to use information in physical reasoning many months earlier than they would otherwise appear to. Lin et al. (Reference Lin, Li, Gertner, Ng, Fisher and Baillargeon2021) made features (e.g., color) salient by first showing an array of objects that differed along the relevant dimension (e.g., all different colors). This nonverbal priming allowed infants to use information in object files to reason about the individuation of hidden objects 6 months earlier than other methods had detected (e.g., while infants had not shown surprise at a lop-sided object balancing on a ledge until 13 months, Lin et al.'s nonverbal priming of lop-sidedness caused 7-month olds to show the effect).

Infants should therefore be able to use conceptual categories for Xu and Carey's individuation task long before 12 months if the right information is primed first: For example, the relevance of the category's function, a key aspect of artifact concepts (Kelemen & Carey, Reference Kelemen, Carey, Margolis and Laurence2007; cf. Bloom, Reference Bloom1996). Stavans and Baillargeon (Reference Stavans and Baillargeon2018) demonstrated objects' characteristic functions before hiding (Fig. 4a) and found 4-month olds succeeded at Xu and Carey's individuation task, looking longer when only one object was revealed. These results show two key LoT-like features – abstract content and inferential promiscuity – in extremely young preverbal infants. Thus the earlier failures seem to be explained by performance constraints (Stavans, Lin, Wu, & Baillargeon, Reference Stavans, Lin, Wu and Baillargeon2019).

Figure 4. (a) Function demonstrations aid object individuation: In a modification of Xu and Carey's (Reference Xu and Carey1996) paradigm, infants first see the characteristic function of an object demonstrated (e.g., a marker drawing, a knife cutting), and this demonstration primes them to use categorical and featural information about the objects to expect two objects in the test trials (i.e., increased looking time when only one object appears); reprinted from Stavans and Baillargeon (Reference Stavans and Baillargeon2018), Figures 4 and 5, with permission from Wiley. (b) View-invariant information extracted by newborn chicks: Chicks are shown a highly limited set of viewpoints on an object and form an abstract, view-invariant representation; reprinted from Wood and Wood (Reference Wood and Wood2020), Figure 1, with permission from Elsevier.

The use of abstract content in physical reasoning is arguably present throughout the animal kingdom, and is well-studied in primates (e.g., Flombaum et al., Reference Flombaum, Kundey, Santons and Scholl2004) and even some arthropods. Loukola, Perry, Coscos, and Chittka (Reference Loukola, Perry, Coscos and Chittka2017) trained bumblebees through social learning (using a dummy bee) to roll a ball – an unusual behavior for bumblebees in the wild – into the center of a platform for a sucrose reward. When the platform was later rearranged with several balls at various locations that the bees could push into that central area, the bees opted to push balls closest to the center of the platform, even if they differed in color or location from the one they had seen pushed initially. This suggests bumblebees are sensitive to shape in a way that is dissociable from color and location, in contrast to many model-free learning accounts but just as one would expect if shape type is encoded in an LoT. In a similar vein, Solvi, Al-Khudhairy, and Chittka (Reference Solvi, Al-Khudhairy and Chittka2020) found that bumblebees could recognize objects under full light that they had previously encountered only in darkness, suggesting they can transfer shape representations stored through touch to a visual task. Bumblebees therefore appear to represent shape in a way that is dissociable from modality-specific low-level features. These representations figure in practical inferences (thereby displaying inferential promiscuity), and that guides recognition across modalities (thereby displaying abstract content). Furthermore, honeybees trained on a fewer-than relation (e.g., 2 < 5) were able to generalize to cases involving zero items (e.g., 0 < 6) without any zero-item training, implicating an abstract symbolic representation of zero that guides inferential generalization and logico-mathematical reasoning (Howard, Avargues-Weber, Garcia, Greentree, & Dyer, Reference Howard, Avargues-Weber, Garcia, Greentree and Dyer2018; cf. Vasas & Chittka, Reference Vasas and Chittka2019; see Weise, Ortiz, & Tibbetts, Reference Weise, Ortiz and Tibbetts2022, for abstract contents of same and different). Similarly, bees' navigational inferences have been used as an argument for a bee LoT because of their computational complexity (Gallistel, Reference Gallistel2011).

Much of our discussion in sections 4 and 5.1 has concerned abstract (e.g., amodal or view-invariant) object representations, and one might wonder whether these effects are really because of associations between low-level features acquired gradually during development. One might therefore wonder whether DNNs could therefore provide a better explanation for these effects. However, Wood and Wood (Reference Wood and Wood2020) found that newborn chicks showed one-shot learning of abstract object representations (Fig. 4b). Shortly after birth, having been reared in an environment with no movable-object-like stimuli, chicks were shown a virtual three-dimensional (3D)-object rotating either fully 360 degrees, or just 11.25 degrees; later, the chicks successfully recognized the objects from arbitrary viewpoints (equally well under both conditions) and moved toward them. Given the paucity of relevant input, this experiment points away from DNN-based explanations of abstract object representations.

Similarly, Ayzenberg and Lourenco (Reference Ayzenberg and Lourenco2021) showed preverbal infants a single view of 60 degrees of an unfamiliar object; using a looking-time measure, they found that the infants formed an abstract, categorical representation, recognizing the object even when viewpoint and salient surface features had drastically changed. The infants' one-shot category learning outperformed DCNNs trained on millions of labeled images. This divergence between DCNN and human performance echoes independent evidence that DCNNs fail to encode human-like transformation-invariant object representations (Xu & Vaziri-Pashkam, Reference Xu and Vaziri-Pashkam2021a).

5.2 Logical inference

Proponents of LoTH have long held up its ability to explain logical inference in preverbal children and nonhuman animals as a virtue (Cheney & Seyfarth, Reference Cheney and Seyfarth2008; Fodor, Reference Fodor1983; Fodor & Pylyshyn, Reference Fodor and Pylyshyn1988; Gallistel, Reference Gallistel2011; cf. Bermudez, Reference Bermudez2003; Camp, Reference Camp2007, Reference Camp2009; Gauker, Reference Gauker2011). Recent evidence suggests infants and animals may use logical operators in logical inferences.

Consider the growing body of work on disjunctive syllogistic (DS) reasoning. A standard means of testing for this capacity is Call's (Reference Call2004) two-cup task. The task involves placing a reward in one of the two cups behind an occluder. Once the cups are brought back into plain view, the participant is shown that one is empty, and can then choose which of the two cups to select from. Typically, researchers are interested in whether the participant selects the unrevealed cup more often than the revealed one, and whether they choose it without inspecting it first. Such behavior is often taken as evidence that the participant can reason through DS, because there's definitely a reward, and one of the two cups is empty, guaranteeing the location of the reward by DS. A surprising number of animals succeed at this task, as well as children as young as two (Call, Reference Call, Hurley and Nudds2006).

Mody and Carey (Reference Mody and Carey2016) argue that there is a confound in such tasks. Participants could rely on a nonlogical strategy involving modal operators: They could form two unrelated beliefs, MAYBE THERE IS A REWARD IN CUP A and MAYBE THERE IS A REWARD IN CUP B. On this strategy, once shown that cup A is empty, participants simply ignore the possibility that there may be a reward there; left only with the belief that there may be a reward in cup B, they then select cup B. So the authors modified this task, using two rewards and four cups (Fig. 5a). Although children as young as 2.5 succeed at the two-cup task, only 3- and 5-year olds succeed at this four-cup task, with 5-year olds performing best.

Figure 5. (a) Four-cup task: A reward is placed behind an occluder and into one of the two cups, and again for another reward and pair of cups. Then one cup is shown to be empty, and participants who perform disjunctive syllogism can infer that a reward is certain to be in the other cup in that pair; reprinted from Mody and Carey (Reference Mody and Carey2016), Figure 1, with permission from Elsevier. (b) Alternatives in chimps: A reward is placed in one of the two boxes, and chimps pull a string to open the box and reveal the reward. The chimps pull both boxes when they are opaque, suggesting simultaneous representation of two possibilities; reprinted from Engelmann et al. (Reference Engelmann, Völter, O'Madagain, Proft, Haun, Rakoczy and Herrmann2021), Figure 1, with permission from Elsevier. (c) Success on four-cup task by baboons, reprinted from Ferrigno et al. (Reference Ferrigno, Huang and Cantlon2021), Figure 1, Sage.

Pepperberg, Gray, Cornero, Mody, and Carey (Reference Pepperberg, Gray, Cornero, Mody and Carey2019) found that an African gray parrot, Griffin, succeeded at a modified version of the four-cup task. Remarkably, Griffin selected the cup that contained reward (a cashew) on nearly every trial (chance, in this case, was 33%), besting human 5-year olds (whose success is surprisingly variable; Gautam, Suddendorf, & Redshaw, Reference Gautam, Suddendorf and Redshaw2021). More moderate success at the four-cup task has also been achieved with olive baboons (Fig. 5c; Ferrigno, Huang, & Cantlon, Reference Ferrigno, Huang and Cantlon2021).

A straightforward way of understanding these results is to accept that at least some nonhuman animals are competent with DS. To execute that inference, one needs two sentential connectives, NOT and OR. These must be combined, syntactically, with representations of states of affairs.

The failure of younger kids at Mody and Carey's four-cup task at first looks like bad news for LoTH. However, it might only reflect a failure with using negation, rather than with logical inference more broadly (Feiman, Mody, & Carey, Reference Feiman, Mody and Carey2022). Moreover, as with Xu's (Reference Xu2019) arguments against LoT-like format in object files, the possibility of performance demands masking an underlying LoT-based competence is plausible. The four-cup task requires kids to track four cups divided into two pairs and two occluded stickers, which is demanding on VWM; indeed, animals that outperform children tend to have superior VWM capacity (Pepperberg et al., Reference Pepperberg, Gray, Cornero, Mody and Carey2019, p. 417; cf. Cheng & Kibbe, Reference Cheng and Kibbe2021). As Pepperberg et al. point out, younger children also act more impulsively than older ones, sometimes ignoring relevant knowledge in demanding tasks. Thus we should look for less demanding tasks before ruling out LoT-like logical inference in children. For example, we could look for independent psychophysical signatures of DS as performed by adults and see whether those signatures are present in children in simpler tasks.

Cesana-Arlotti et al. (Reference Cesana-Arlotti, Martín, Téglás, Vorobyova, Cetnarski and Bonatti2018) showed 12-month olds and adults two objects hidden behind occluders (e.g., a snake and ball); they saw one placed in a cup without knowing which, and finally the unmoved object (e.g., snake) popped out, allowing subjects to infer the identity of the cup-hidden object (ball). When the cup-hidden object was revealed, infants' looking time showed they expected it to be the yet-unseen object (ball). This finding is compatible with nonlogic-based explanations. However, Cesana-Arlotti et al. found that adults performing DS showed an oculomotor signature: During inference, their pupils dilated and eyes darted to the still-hidden object. This same signature was found in the infants, implicating the same underlying computations.

Genuine DS should be domain-general. Cesana-Arlotti, Kovács, and Téglás (Reference Cesana-Arlotti, Kovács and Téglás2020) used a similar paradigm to test DS in 12-month olds, this time relying on their knowledge of others' preferences. Participants learned an agent's preference among objects (ball vs. car); the nonpreferred object then briefly popped out from behind its occluder, after which the agent reached behind one of the occluders. Twelve-month olds looked longer when the nonpreferred object was reached for. Cesana-Arlotti and Halberda (Reference Cesana-Arlotti and Halberda2022) also found that 2.5-year olds, who fail the four-cup task, nonetheless reason by exclusion across word-learning, social-learning, and explicit negation with a common saccade pattern: They saccade to the to-be-excluded item, return to the target item, and fail to show “redundant” saccades – evidence of low confidence – after target selection. This pattern suggests a domain-general inferential mechanism that delivers high-confidence conclusions, a functional profile one should expect if children perform DS.

Leahy and Carey (Reference Leahy and Carey2020) provide an alternative, non-DS-based explanation of successful reasoning by exclusion via sequentially simulating alternative possibilities. However, chimpanzees, at least, are able to represent distinct possible states of affairs simultaneously. Engelmann et al. (Reference Engelmann, Völter, O'Madagain, Proft, Haun, Rakoczy and Herrmann2021) used a modified two-cup task in which the empty cup was not revealed. Chimps could pull ropes for both cups, or pull just one rope for one cup, causing the second cup to fall out of reach. Overwhelmingly they expended extra energy to pull both ropes when the cups were opaque, but pulled just one when the cups were transparent (Fig. 5b).Footnote ⁸ Pulling two ropes is hedging under uncertainty, suggesting chimps simultaneously represent two locations as possibly reward-laden.

Furthermore, 12-month olds seem to use the same computations adults do to reason by exclusion, as measured by oculomotor signatures (Cesana-Arlotti et al., Reference Cesana-Arlotti, Martín, Téglás, Vorobyova, Cetnarski and Bonatti2018). It's possible that adults do both DS and simulation-based or icon-based reasoning in these tasks. But given independent reasons to think these tasks run on LoT-like object representations in VWM and adults' capacity for DS, and the relative lack of evidence for multiple redundant reasoning processes underlying task performance, our working hypothesis is that infant's oculomotor behavior is evidence for LoT-based DS.

Logical inference without language is a rapidly developing research area, and central contributors to this research such as Carey are skeptical of the “thicker” interpretations of the data we defend. Although we anticipate further plot twists will emerge in study of infant and nonhuman inference, we take the current state of the literature to favor an LoT-based account of DS in infants and animals and to bear promise for many LoTH-based lines of research in the development of logical operators.

6.1 Logic, load, and LoT

Failures of syllogistic reasoning are commonplace and well-publicized. In particular, belief biases – cases where people mistakenly use the truth of a conclusion in judging an argument's validity, ignoring logical form – are legion (Markovits & Nantel, Reference Markovits and Nantel1989). Even outside of the belief bias people are forever affirming-the-consequent, denying the antecedent, and confusing validity and truth.

Difficulties in reasoning are prima facie problematic for LoTH. The more errors we make in reasoning, the less it seems like we need an inferential apparatus to explain people's thinking. LoT is tailor-made to explain formal reasoning – that is, reasoning based on the structure, rather than the content, of one's premises (Fodor & Pylyshyn, Reference Fodor and Pylyshyn1988; Quilty-Dunn & Mandelbaum, Reference Quilty-Dunn and Mandelbaum2018a, Reference Quilty-Dunn and Mandelbaum2018b). So, failures in reasoning – traditionally seen as because of heuristic S1 processing – are seen as reasons for believing that S1 is associative rather than LoT-like (see, e.g., Gawronski & Bodenhausen, Reference Gawronski and Bodenhausen2006; Rydell & McConnell, Reference Rydell and McConnell2006; Sloman, Reference Sloman1996). However, a closer look at the data shows evidence for nonassociative, LoT-like, logic-sensitive reasoning in S1.

“Conflict problems” are cases where validity and believability conflict, that is, valid syllogisms with unbelievable conclusions or invalid syllogisms with believable conclusions. All other problems (valid/believable; invalid/unbelievable) are “nonconflict.” Some examples:

• (Conflict: Valid/Unbelievable)

• P1: All birds fly

• P2: Penguins are birds

• C: Penguins fly

• (Conflict: Invalid/Believable)

• P1: All birds fly

• P2: Penguins are birds

• C: Penguins swim

• (No Conflict: Valid/Believable)

• P1: All birds have feathers

• P2: Penguins are birds

• C: Penguins have feathers

• (No Conflict: Invalid/Unbelievable)

• P1: All birds have feathers

• P2: Penguins are birds

• C: Penguins fly

If S1 is not logic-sensitive, then conflict problems should not hamper believability judgments, because belief bias is driven by nonlogical factors. Yet logic-sensitive judgments occur even when subjects are explicitly instructed to focus on believability, and even under extreme cognitive load. Logical responses thus seem to be generated automatically. People are less confident and slower on conflict problems than nonconflict problems regardless of whether they are judging belief or logic (Handley & Trippas, Reference Handley and Trippas2015; Howarth, Handley, & Polito, Reference Howarth, Handley and Polito2021; Trippas, Thompson, & Handley, Reference Trippas, Thompson and Handley2017). That is, they'll be slower to judge that “Penguins fly” is false if it is a conclusion of a valid argument than a conclusion of an invalid one. Moreover, those who correctly solve syllogism validity questions in conflict problems do so even under intense time pressure and additional memory load, ensuring the shutdown of system-2 processes (Bago & De Neys, Reference Bago and De Neys2017). That is, correct responding happens right away; giving participants additional time to think adds little accuracy.

Just as the believability of a conclusion can interfere with validity judgments, so too can the logical form of an argument affect believability judgments. In fact, there is evidence that logical responding is more automatic than belief-based responding; derailing logical responding impedes belief-based responding more than vice versa (Handley, Newstead, & Trippas, Reference Handley, Newstead and Trippas2011; Howarth, Handley, & Walsh, Reference Howarth, Handley and Walsh2016; Trippas et al., Reference Trippas, Thompson and Handley2017). For example, in Trippas et al. (Reference Trippas, Thompson and Handley2017), conflict impeded believability judgments more than validity judgments for modus ponens. Sensitivity to logical form persists whether subjects are under load or not (and whether asked to evaluate validity or not), showing that the relevant differences are because of S1 processing (Trippas, Handley, Verde, & Morsanyi, Reference Trippas, Handley, Verde and Morsanyi2016). Even when asked to respond randomly, participants still show implicit sensitivity to logical form (Howarth et al., Reference Howarth, Handley and Polito2021). Automatic logical sensitivity also has very little individual difference between subjects, suggesting it reflects fundamental architectural features of cognition (Ghasemi, Handley, & Howarth, Reference Ghasemi, Handley and Howarth2021). Logical inferences are also made automatically during reading (Dabkowski & Feiman, Reference Dabkowski and Feiman2021; Lea, Reference Lea1995; Lea, Mulligan, & Walton, Reference Lea, Mulligan and Walton2005). As one would expect if logic was intuitive, subliminally presented premises trigger modus ponens inferences (Reverberi, Pischedda, Burigo, & Cherubini, Reference Reverberi, Pischedda, Burigo and Cherubini2012).

Far from undermining LoTH, dual-process architectures vindicate LoTH. They demonstrate abstract logic-based inferential promiscuity outside controlled, conscious cognition using discrete symbols that maintain role-filler independence (e.g., P must be the same symbol in P → Q).

6.2 The logic of implicit attitudes

Implicit attitudes are typically assumed to be associative. However, Mandelbaum (Reference Mandelbaum2016) and De Houwer (Reference De Houwer2019) documented the effects of “logical interventions” on implicit attitudes, that is, cases where one can change implicit attitudes not by counterconditioning or extinction, as would be expected if they had associative structure, but instead by merely changing the logically pertinent evidence. Logical (or “propositional”) interventions on attitudes are only possible given that we have predicate–argument structure, logical operators, and inferential promiscuity.

Take Kurdi and Dunham (Reference Kurdi and Dunham2021). Their basic paradigm consisted of a learning and testing phase. In a learning phase participants saw sentences of the form: “If you see a green circle, you can conclude that Ibbonif is trustworthy; if you see a purple pentagon, you can conclude that Ibbonif is malicious.” This design cleverly pits associative versus propositional (i.e., LoT) processes against each other: If the implicit attitude processor is associative then Ibbonif should come out as neutral as Ibbonif is being associated with both positive (trustworthy) and negative (malicious) adjectives. If the processor is sensitive to propositional values however, then the implicit attitude acquired should be dependent on which conditional's antecedent was satisfied (i.e., which shape appears). Participants then moved onto the testing phase which consisted of explicit and implicit attitude testing (via the IAT). Results showed that participant attitudes tracked the logical form of the stimuli during the testing phase. So, using the sample text above, if participants saw a purple pentagon they would conclude that Ibbonif (and the group that he was from, the Niffites, denoted from the suffix on the name) was negatively valenced.

Kurdi and Dunham had ample variations in the paradigm all showing similar LoT-based effects on implicit attitudes. Importantly, LoT-based inferences can be seen even when the response is normatively inappropriate, as in an affirming-the-consequent syllogism (study 3). In the learning phase, participants saw sentences such as “If you see a green circle, you can conclude that Ibbonif is malicious”; however, instead of seeing a green circle, they would then see an, for example, orange square. Thus the correct inference to make is that nothing can be inferred from the setup. If implicit attitudes are updated only by an associative processor, then the valence of the predicate in the consequent should dictate the participants' responses. If instead attitudes are sensitive to the logical form of the inventions, then one of the two things should happen: For those subjects who correctly realize that this is an affirming-the-consequent argument they should form no opinion about the person or group in question. However, the subset of people who incorrectly affirm the consequent should make the wrong inference and infer that the consequent accurately describes the person or group in question. Participants were given a control question to see if they were apt to explicitly affirm the consequent. Those who did also changed their implicit attitudes in line with the affirming-the-consequent stimuli they would later see in the experiment; the implicit attitudes of those who rejected the affirming-the-consequent control question, on the contrary, correctly tracked the logical implications of the stimuli by failing to update at all (similar results hold for denying the antecedent). Given a sufficiently creative setup, one can infer logical processes at play even in the absence of inference, or during misinference (Quilty-Dunn & Mandelbaum, Reference Quilty-Dunn and Mandelbaum2018a).

Similar variations abound. If the associative account were correct then merely giving a major premise that is clearly valenced should set the associative value of the target: Giving participants sentences such as “If you see a purple pentagon, you can conclude that Ibbonif is malicious” should make one associate IBBONIF and negative valence via “malicious.” Except that isn't what happens – if subjects are given the conditional premise with no follow-up they withhold forming any valenced implicit attitudes, unlike what associative theory would predict.Footnote ¹⁰ The concept IBBONIF needs to be linked with the attribute MALICIOUS in a way that is impervious to associative factors, but sensitive to counterevidence. A predicate–argument structure with MALICIOUS as predicate and IBBONIF as argument predicts just this functional profile.

The Kurdi and Dunham is just one of a near-deluge of recent studies showing the efficacy of logical interventions compared to the impotence of associative interventions (Cone & Ferguson, Reference Cone and Ferguson2015; De Houwer, Reference De Houwer2006; Gast & De Houwer, Reference Gast and De Houwer2013; Mann & Ferguson, Reference Mann and Ferguson2015, Reference Mann and Ferguson2017; Mann, Cone, Heggeseth, & Ferguson, Reference Mann, Cone, Heggeseth and Ferguson2019; Van Dessel, De Houwer, Gast, Smith, & De Schryver, Reference Van Dessel, De Houwer, Gast, Smith and De Schryver2016; Van Dessel, Gawronski, Smith, & De Houwer, Reference Van Dessel, Gawronski, Smith and De Houwer2017a; Van Dessel, Mertens, Smith, & De Houwer, Reference Van Dessel, Mertens, Smith and De Houwer2017b; Van Dessel, Ye, & De Houwer, Reference Van Dessel, Ye and De Houwer2019). Telling participants that they will see a pairing of a group with pictures of pleasant (or unpleasant) things is much more effective at fixing implicit attitudes than repeatedly pairing the group and the pleasant/unpleasant things. One-shot learning trumps 37 associative pairings. Even when associative and one-shot propositional learning are combined, the associative trials add no detectable valence to the implicit attitude formed from the one-shot propositional trial (Kurdi & Banaji, Reference Kurdi and Banaji2017). That is, direct exposure to associative pairings isn't necessary or sufficient for forming or changing implicit attitudes, and its effect on attitudes doesn't compare to a single exposure to a sentence. Even when repeated exposure causes some mental representation of the categories to be formed, just telling participants whether the stimuli are diagnostic modulates learning (e.g., if told the data aren't diagnostic, learning is inhibited, and if told the data are diagnostic, learning is increased). This suggests that the representations acquired are being used as beliefs (Quilty-Dunn & Mandelbaum, Reference Quilty-Dunn and Mandelbaum2018b), and updated in a logical, inferentially promiscuous way (Kurdi & Banaji, Reference Kurdi and Banaji2019). The primacy of diagnostic information over repeated exposure is a consistent finding, showing the inadequacies of associative models (e.g., Mann et al., Reference Mann, Cone, Heggeseth and Ferguson2019; Mann & Ferguson, Reference Mann and Ferguson2015, Reference Mann and Ferguson2017).

In short, implicit attitudes – far from being a problem area for LoT – instead demand evidence-sensitive, inferentially promiscuous predicate–argument structures that incorporate abstract logical operators.