Precursors of logical reasoning in preverbal human infants

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Science  16 Mar 2018:
Vol. 359, Issue 6381, pp. 1263-1266
DOI: 10.1126/science.aao3539

The infant as philosopher

Visual behaviors, such as a shift in one's gaze or a prolonged stare, can be diagnostic of internal thoughts. Cesana-Arlotti et al. used these measures to demonstrate that preverbal infants can formulate a logical structure called a disjunctive syllogism (see the Perspective by Halberda). That is, if A or B is true, and A is false, then B must be true. Presenting infants with scenes where the outcome revealed B to be false evoked looks of surprise.

Science, this issue p. 1263; see also p. 1214


Infants are able to entertain hypotheses about complex events and to modify them rationally when faced with inconsistent evidence. These capacities suggest that infants can use elementary logical representations to frame and prune hypotheses. By presenting scenes containing ambiguities about the identity of an object, here we show that 12- and 19-month-old infants look longer at outcomes that are inconsistent with a logical inference necessary to resolve such ambiguities. At the moment of a potential deduction, infants’ pupils dilated, and their eyes moved toward the ambiguous object when inferences could be computed, in contrast to transparent scenes not requiring inferences to identify the object. These oculomotor markers resembled those of adults inspecting similar scenes, suggesting that intuitive and stable logical structures involved in the interpretation of dynamic scenes may be part of the fabric of the human mind.

Fifty years ago, Piaget argued that logic in the mind is the culmination of a long developmental process, extending into adolescence. Forty years ago, Fodor answered that if learning implies testing hypotheses, then learners must possess the representational resources to formulate them, including logical primitives: rule-like combinatorial concepts embedded in a compositional system of representation, or a language of thought (1).

After four decades, we still lack insight into the nature and development of the logical representations, if any, that structure infants’ thinking and problem-solving. Partly, this profound lack of knowledge stems from the widespread belief that infant cognition relies on independent modules, functioning early and efficiently, but not supported or connected by general reasoning (2). Partly, it stems from the assumption that although logical representations are involved in processing language, and hence are present in organisms that master a natural language, it is difficult, perhaps impossible (3), to identify them in nonverbal organisms (4). Acquiring language does improve cognition, perhaps also by creating novel logical representations (5). However, none of these considerations weakens the real force of Fodor’s argument, although its premises need to be reappraised. Although infants possess learning mechanisms that do not require hypotheses [e.g., bottom-up tracking of statistical regularities (6)], flexible and productive hypothesis testing does begin in infancy, with a vengeance. Infants can generate hypotheses about uncertain future events (7), flexibly adapting them to novel, albeit subtle, elements of a situation (8, 9). They measure the evidence in support (10) and test alternative hypotheses when violations occur (11, 12). Such abilities extend far beyond precompiled mechanisms for domain-specific responses, demonstrating a high degree of rationality in several domains. One prominent account of them depicts infants as precocious Bayesian reasoners. However, most Bayesian theories require a logical scaffolding to formulate, test, and modify hypotheses (8, 1315). Thus, characterizing the basic logical representations available to preverbal infants for formulating hypotheses remains fundamental to understanding the very nature of knowledge acquisition (16).

Here we begin investigating the developmental precursors of such scaffolding, looking for behavioral correlates of one simple logical representation and rule: disjunction (either A or B) and disjunctive syllogism (not A, therefore B). Although elementary, this schema grounds one crucial hypothesis-testing strategy: Sherlock Holmes–like case-by-case analysis of different possibilities, excluding alternatives until the culprit is found. Attempts to find clear evidence of disjunctive syllogism in nonhuman animals have so far been inconclusive (4, 17). A related reasoning pattern has been studied in toddlers’ and preschoolers’ word-learning strategies (18, 19), but it is unknown whether it is within the conceptual repertoire of preverbal infants. We first investigate whether infants can frame disjunctive hypotheses and make inferences by logically eliminating alternatives, testing their reactions to outcomes that violate conclusions of this deductive process. Then, we identify markers of inferential activity by examining the dynamics of oculomotor responses during inference making. Last, we explore stability across development by comparing the oculomotor responses of infants, toddlers, and adults passively looking at nonverbal scenes that potentially involve logical inferences.

We studied 12- and 19-month-old infants, two ages at the onset of speech production and language learning but that precede the development of extensive language knowledge. We presented infants with scenes injected with ambiguity about the identity of an object, which could be resolved through disjunctive syllogism. In experiments 1 and 2, two objects different in shape, texture, color, and category, but with identical top parts (say, a dinosaur and a flower), enter a virtual theater (Fig. 1 and fig. S1). An occluder hides them, and a cup scoops one of them from behind it, with only the top part visible. Thus, infants cannot know the identity of the scooped object and may establish a disjunctive representation. Then, the occluder moves downward, revealing one object—say, the dinosaur. We call this moment the “potential deduction phase,” in which infants have evidence to disambiguate the identity of the scooped object by disjunctive syllogism. Last, in the “outcome phase,” the dinosaur leaves the stage, and the cup reveals the second object. Half of the time, the revealed object is consistent with the conclusion suggested by the logical inference (it is the flower), whereas the other half, it is inconsistent (it is the dinosaur). We recorded looking time during the outcome phase in a violation of expectation (VOE) paradigm. Both 12- and 19-month-olds looked longer at the inconsistent outcome, suggesting that they may have derived the identity of the object in the cup through logical inference and were surprised when this conclusion was violated, as revealed by mean looking times, M [experiment 1, 19-month-olds (n = 24), Mconsistent = 7.7 s, Minconsistent = 10.5 s, F1,23 = 5.79, P = 0.025; experiment 2, 12-month-olds (n = 24), Mconsistent = 6.2 s, Minconsistent = 7.6 s, F1,23 = 5.19, P = 0.032; repeated measures analyses of variance (ANOVAs)].

Fig. 1 Infants look longer at outcomes that are inconsistent with a logical deduction.

(A) (i) Two objects with an identical upper part enter the theater. (ii and iii) An occluder hides them, and a cup scoops one from behind, only the top part of which is visible (dinosaur or flower?). (iv and v) The occluder lowers, allowing the observer to infer the identity of the object in the cup (not dinosaur, therefore flower). (vi) The cup reveals its content, which is either consistent (flower) or inconsistent (dinosaur) with the inference. (B) Mean (± SEM) time spent looking at the outcomes (in seconds). Both 19- and 12-month-olds looked longer at the inconsistent outcome. *P < 0.05. Mos, months.

In experiments 1 and 2, in an inconsistent outcome, an object appears twice successively: The occluder lowers, revealing the dinosaur, which exits the stage, and then the cup reveals a dinosaur again (Fig. 1A, vi-2). Conversely, in a consistent outcome, two different objects appear successively: After the dinosaur exits, the cup reveals the flower. Thus, the infants may have reacted not to a logical inconsistency but to the surface aspects of the final sequence, when the same object appeared twice in succession (Fig. 1A, vi-1). In experiments 3 and 4, the logical status of the final object sequence reverses (Fig. 2A). The movies are identical to those of experiments 1 and 2 until the potential deduction phase. There, the occluder never lowers; one object (e.g., a snake) exits from its side, remaining visible for about 1.5 s, then returns behind it. In the outcome phase, the cup never reveals its content. Instead, another object exits the occluder: sometimes the snake again, and sometimes the other object in the pair (in this example, a ball; Fig. 2A, vi). The former outcome is consistent with the logical inference; however, unlike experiments 1 and 2, one single object is seen twice in succession. The latter outcome is inconsistent, but two different objects are seen once in succession. If infants respond to the surface aspects of the final sequence, they should disregard the logical consistency of the outcome and look longer when the single object appears twice, as in experiments 1 and 2. If, instead, their behavior is guided by a logical inference, they should look longer when the outcome is inconsistent with it even if the final sequence reverses that of experiments 1 and 2. Both 19 and 12-month-olds looked longer at the inconsistent outcome (Fig. 2C), suggesting that they reacted to the logical gist of a scene [experiment 3, 19-month-olds (n = 24), Mconsistent = 4.9 s, Minconsistent = 6.2 s, F1,23 = 8.5, P = 0.008; experiment 4, 12-month-olds (n = 24), Mconsistent = 4.2 s, Minconsistent = 6.1 s, F1,23 = 11, P = 0.003; repeated measures ANOVAs]. These results also control for other nonlogical explanations, such as an object’s magical disappearance in the inconsistent outcome of experiments 1 and 2 (no such disappearance occurred in experiments 3 and 4) or its greater featural variability in experiments 3 and 4 (reversed in experiments 1 and 2).

Fig. 2 Infants’ logical reasoning does not depend on how the scene is physically realized.

(A) (i to iii) Inference condition: The identity of the object in the cup cannot be determined before the potential deduction phase. (B) (i to iii) No-inference condition: The cup scoops the object in full view, so its identity is known. (iv and v) Potential deduction phase [common to (A) and (B)]: Only in the inference condition is a deduction needed to determine the cup content. Note that the physical realization of this phase is very different from that of experiments 1 and 2. (vi-1 and vi-2) Outcome phase [common to (A) and (B)]: An object exits the occluder, yielding a consistent or inconsistent outcome. (C) Mean (± SEM) time spent looking at the outcomes (in seconds). Both 12- and 19-month-olds looked longer at the inconsistent outcome. *P < 0.05; **P < 0.01; ***P < 0.001.

VOE only measures a response post hoc, after a conclusion has been reached (20). Adults reasoning with language make disjunctive inferences as early as they have the relevant evidence (21, 22). The data reported so far do not characterize the unfolding of an inference in the infant mind. To explore this, we analyzed oculomotor responses during the potential deduction phase. We created novel scenes identical to experiments 3 and 4 in the potential deduction and outcome phases, but requiring no inference to identify the object in the cup (experiments 5 and 6; Fig. 2B). We did this by showing the cup scooping one object in full view before occlusion. Thus, unlike experiments 3 and 4, in experiments 5 and 6, infants already know which object is in the cup before the potential deduction phase. As expected at these ages (23), infants looked longer at an outcome inconsistent with the identity of the (known) object in the cup [experiment 5, 19-month-olds (n = 24), Mconsistent = 3.8 s, Minconsistent = 8.3 s, F1,23 = 26.1, P = 0.0001; experiment 6, 12-month-olds (n =24), Mconsistent = 4.9 s, Minconsistent = 6.2 s, F1,23 = 4.9, P = 0.037; repeated measures ANOVAs]. But our focus here is the temporal course of oculomotor responses during the potential deduction phase, which we expected to be modulated by the need for an inference. Cluster-based permutation tests (24, 25) revealed that at several points during the potential deduction phase, the infants’ pupils dilated more when the scene licensed an inference than when it did not, suggesting increased cognitive activity possibly due to inference-making. By the end of this phase, infants also displaced their eyes toward the cup more markedly (Fig. 3, B and C, and supplementary materials) and switched their focus from the visible object to the cup in more trials (Minference = 71%, Mno_inference = 50%, F1,88 = 10.4, P = 0.002, two-way ANOVA; fig. S2 and supplementary materials) when a deduction was needed than when it was not.

Fig. 3 Pupil dilation and eye position during the potential deduction phase may signal online logical inferences.

(A) Subcomponents of the potential deduction phase, time-adjusted to participants’ ages and color-coded in indigo shades. (iv-a) An object exits the occluder. (iv-b) It stops by the cup containing a second object whose identity is either known (no-inference condition) or ambiguous (inference condition). In the inference condition, this is the first moment in which participants have evidence available that disambiguates the cup content. (v-a) The visible object returns behind the occluder. (v-b) The object remains hidden inside the cup, onstage. (B to D) Temporal course of pupil dilation changes (in millimeters) from baseline and mean x gaze positions for (B) 12-month-olds, (C) 19-month-olds, and (D) adults in the inference (blue) or no-inference (red) condition. Conditions were distributed between participants for infants and within participants for adults. Data are plotted starting when the mean x coordinates of the two conditions converged on the object emerging from the occluder. Error bars are SEM for infants and 95% within-participants confidence intervals for adults. Yellow bars indicate regions of potential differences in the two conditions (supplementary materials, fig. S7). During the potential deduction phase, at all ages, participants who had to perform a logical inference to identify the cup content had pupils that were more dilated and gazed more toward the cup.

Only when the potential deduction phase afforded an inference did higher pupil dilation and visible object-to-cup shifts contribute to predicting success at identifying inconsistencies in the later outcome phase. No such predictive relation occurred absent the need for an inference (fig. S3 and supplementary materials). The fact that this relation occurred only when an inference may have been involved suggests that oculomotor markers in the potential deduction phase are not simply due to memory of past event structures but are tied to some kind of mental inference about the identity of the object in the cup, drawn soon after infants acquire the disambiguating evidence.

Thus, these oculomotor markers suggest that preverbal infants efficiently deploy logical procedures to process the components of an unfolding scene. To assess developmental stability, we inspected adults’ oculomotor responses during the same potential deduction phase. Adults (experiment 7, n = 30) saw 96 scenes patterned upon those of experiments 1 to 6. Like infants, during the potential deduction phase, adults’ pupils dilated more, and their eyes tended to look more toward the cup, when the scene licensed an inference. Again, this occurred regardless of its physical realization. Adults and infants differed only in the speed of such markers, but not qualitatively (Fig. 3D, figs. S4 and S5, and supplementary materials).

Our data document the early presence of primitive logical abilities. Without instructions or tasks, infants spontaneously reason logically while a scene unfolds. Specific behavioral markers can be used to study the precise temporal course of their reasoning process. Because such markers already appear at ages when language development has barely begun, our data suggest that precursors of logical reasoning are independent of language acquisition. Their stability across ages and spontaneous deployment suggest that some form of elementary logical reasoning may be a primitive property of the logical circuitry in the human brain (26). Explaining our data without invoking deductive inferences has a cost. Bayesian iterative models, which evaluate the most likely of the alternatives first and cycle through them when the first choice is discarded, could mimic deductive syllogism without assuming a logical inference in the potential deduction phase. However, they require that infants represent the space of alternatives (which is equivalent to implementing a disjunctive representation), assign ordered priors to the alternatives, and assess alternative evaluations iteratively. A logical inference requires fewer assumptions. Thus, although not incompatible with Bayesian reasoning, the hypothesis that infants perform a logical inference in the potential deduction phase is a more parsimonious explanation of our results.

In spite of the stability that we document, children begin mastering a verbally expressed disjunction late in development (17). However, a dissociation between spontaneous inferential abilities in nonverbal contexts and their explicit verbal counterparts need not imply the lack of a concept. Instead, it indicates that mapping the spontaneous logical structures of thought onto their verbal counterparts is an extremely intricate process. A deceivingly simple word such as “or” has a very complex semantics (27). Unambiguous evidence for its meaning is hard to come by, a difficulty that affects the acquisition of even simpler abstract words (28). Thus, a consequence of our research is that much work is still needed to understand how the proper alignment between language and thought occurs.

This empirical evidence is directly relevant to the old, yet still fundamental questions debated between Fodor and Piaget. Logical representations that are crucial components of infants’ natural hypothesis-testing attitude are available when infants start projecting and testing hypotheses about the world. Such representations may consist of nonlinguistic but fully language-like structures, or they may piggyback on sophisticated object representations that can track object identities in ambiguous situations. Although further research is needed to clarify their nature, our data suggest that intuitive and stable logical structures involved in the interpretation of dynamic scenes may be essential parts of the fabric of the mind. This does not imply that all logical reasoning is spontaneous or innate, just as spontaneous and innate elementary numerical abilities do not imply that all mathematical knowledge is innate. Reasoning occurs in many different forms and at many different levels of our mental processes, and the gulf separating infant thinking from adult explicit logical reasoning is large. However, the development of reasoning abilities builds on a natural logical foundation, whose profile we are beginning to uncover.

Supplementary Materials

Materials and Methods

Figs. S1 to S6

Table S1

Reference (29)

Movies S1 to S9

References and Notes

Acknowledgments: This paper is dedicated to the memory of Jerry Alan Fodor. We thank J. R. Hochmann, L. Papeo, L. Filippin, E. Parise, R. Feiman, S. Carey, C. Reverberi, J. Gervain, A. Endress, L. Schulz, and K. Clifton for discussions and suggestions. Funding: This research was supported by MINECO [Ministerio de Economía, Industria y Competitividad (Spain)] grant PSI2016-75910-P to L.L.B. and European Research Council starting grant (639840 PreLog) to E.T. Author contributions: N.C.-A. and L.L.B. designed the research and the infant experiments. A.M. designed the adult experiment. N.C.-A., A.M., L.V., and R.C. built the experimental material and performed the research. N.C.-A., A.M., and L.L.B. analyzed the data and wrote the paper. All authors contributed to the conception of the research and approved the paper. Competing interests: The authors declare that they have no competing interests. Data and materials availability: Data are available at
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