On a now orthodox view, humans and many other animals possess a “number sense,” or approximate number system, that represents number. Recently, this orthodox view has been subject to numerous critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique – the arguments from congruency, confounds, and imprecision – and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds or exotic substitutes for (...) number, such as “numerosities” or “quanticals,” as critics propose. In so doing, we raise a neglected question: numbers of what kind? Proponents of the orthodox view have been remarkably coy on this issue. But this is unsatisfactory since the predictions of the orthodox view, including the situations in which the ANS is expected to succeed or fail, turn on the kind of number being represented. In response, we propose that the ANS represents not only natural numbers, but also non-natural rational numbers. It does not represent irrational numbers, however, and thereby fails to represent the real numbers more generally. This distances our proposal from existing conjectures, refines our understanding of the ANS, and paves the way for future research. (shrink)

Two experiments were conducted to examine adult learners' ability to extract multiple statistics in simultaneously presented visual and auditory input. Experiment 1 used a cross‐situational learning paradigm to test whether English speakers were able to use co‐occurrences to learn word‐to‐object mappings and concurrently form object categories based on the commonalities across training stimuli. Experiment 2 replicated the first experiment and further examined whether speakers of Mandarin, a language in which final syllables of object names are more predictive of category membership (...) than English, were able to learn words and form object categories when trained with the same type of structures. The results indicate that both groups of learners successfully extracted multiple levels of co‐occurrence and used them to learn words and object categories simultaneously. However, marked individual differences in performance were also found, suggesting possible interference and competition in processing the two concurrent streams of regularities. (shrink)

A symposium on Michael Strevens' book "Tychomancy", concerning the psychological roots and historical significance of physical intuition about probability in physics, biology, and elsewhere.

Children posit unobserved causes when events appear to occur spontaneously. What about when events appear to occur probabilistically? Here toddlers saw arbitrary causal relationships in a fixed, alternating order. The relationships were then changed in one of two ways. In the Deterministic condition, the event order changed ; in the Probabilistic condition, the causal relationships changed. As intended, toddlers looked equally long at both changes. We then introduced a previously unseen candidate cause. Toddlers looked longer at the appearance of a (...) hand and novel agent in the Deterministic than the Probabilistic conditions, but looked equally long at novel non-agents, suggesting that by 2 years of age, toddlers connect probabilistic events with unobserved agents. (shrink)

Much research on cognitive development focuses either on early-emerging domain-specific knowledge or domain-general learning mechanisms. However, little research examines how these sources of knowledge interact. Previous research suggests that young infants can make inferences from samples to populations (Xu & Garcia, 2008) and 11- to 12.5-month-old infants can integrate psychological and physical knowledge in probabilistic reasoning (Teglas, Girotto, Gonzalez, & Bonatti, 2007; Xu & Denison, 2009). Here, we ask whether infants can integrate a physical constraint of immobility into a statistical (...) inference mechanism. Results from three experiments suggest that, first, infants were able to use domain-specific knowledge to override statistical information, reasoning that sometimes a physical constraint is more informative than probabilistic information. Second, we provide the first evidence that infants are capable of applying domain-specific knowledge in probabilistic reasoning by using a physical constraint to exclude one set of objects while computing probabilities over the remaining sets. (shrink)

The present studies tested the hypothesis that strong assumptions about within-category homogeneity impede children’s recognition of the inductive value of diverse samples of evidence. In Study 1a, children (7-year-olds) and adults were randomly assigned to receive a prime emphasizing within-category variability, a prime emphasizing within-category similarities, or to not receive a prime. Only following the variability prime, children demonstrated a reliable preference for evaluating diverse over nondiverse samples to determine whether there is support for a category-wide generalization. Adults demonstrated a (...) robust preference for diverse samples in all conditions. These effects extended beyond the specific categories included in the prime, as well as to multiple types of test questions. Study 1b demonstrated that priming variability leads children to select diverse samples only when doing so is informative for induction. Implications for conceptual development are discussed. (shrink)

It is an old and venerable idea in philosophy that morality is built into us, and this nativist view has seen a resurgence of late. Indeed, the prevailing systematic account of how we acquire complex moral representations is a nativist view inspired by arguments in Chomskyan linguistics. In this article, I review the leading argument for moral nativism – the poverty of the moral stimulus. I defend a systematic empiricist alternative that draws on the resources of statistical learning. Such an (...) empiricist account, I argue, promises to explain much of the complexity of people’s moral and other normative attitudes. (shrink)

This paper provides an account of the developmental origins of our belief in free will based on research from a range of ages—infants, preschoolers, older children, and adults—and across cultures. The foundations of free will beliefs are in infants' understanding of intentional action—their ability to use context to infer when agents are free to “do otherwise” and when they are constrained. In early childhood, new knowledge about causes of action leads to new abilities to imagine constraints on action. Moreover, unlike (...) adults, young children tend to view psychological causes (i.e., desires) and social causes (i.e., following rules or group norms, being kind or fair) of action as constraints on free will. But these beliefs change, and also diverge across cultures, corresponding to differences between Eastern and Western philosophies of mind, self, and action. Finally, new evidence shows developmentally early, culturally dependent links between free will beliefs and behavior, in particular when choice‐making requires self‐control. (shrink)

Three experiments with preschool- and young school-aged children (N = 75 and 53) explored the kinds of relations children detect in samples of instances (descriptive problem) and how they generalize those relations to new instances (inferential problem). Each experiment initially presented a perfect biconditional relation between two features (e.g., all and only frogs are blue). Additional examples undermined one of the component conditional relations (not all frogs are blue) but supported another (only frogs are blue). Preschool-aged children did not distinguish (...) between supported and undermined relations. Older children did show the distinction, at least when the test instances were clearly drawn from the same population as the training instances. Results suggest that younger children’s difficulties may stem from the demands of using imperfect correlations for predictions. Older children seemed sensitive to the inferential problem of using samples to make predictions about populations. (shrink)

If folk science means individuals having well worked out mechanistic theories of the workings of the world, then it is not feasible. Laypeople’s explanatory understandings are remarkably coarse, full of gaps, and often full of inconsistencies. Even worse, most people overestimate their own understandings. Yet recent views suggest that formal scientists may not be so different. In spite of these limitations, science somehow works and its success offers hope for the feasibility of folk science as well. The success of science (...) arises from the ways in which scientists learn to leverage understandings in other minds and to outsource explanatory work through sophisticated methods of deference and simplification of complex systems. Three studies ask whether analogous processes might be present not only in laypeople but also in young children and thereby form a foundation for supplementing explanatory understandings almost from the start of our first attempts to make sense of the world. (shrink)

This paper discusses recent evidence that violations of core knowledge offer special learning opportunities for infants and young children. Children make predictions about the world from the youngest ages. When their fail to match observed data, they show an enhanced drive to seek and retain new information about entities that violated their expectations. Finally, the authors draw comparisons between children and adults, and with other species, to explore how surprise shapes thought more broadly.

This paper considers how 5- to 11-year-olds’ verbal reasoning about the causality underlying extended, dynamic natural processes links to various facets of their statistical thinking. Such continuous processes typically do not provide perceptually distinct causes and effect, and previous work suggests that spatial–temporal analysis, the ability to analyze spatial configurations that change over time, is a crucial predictor of reasoning about causal mechanism in such situations. Work in the Humean tradition to causality has long emphasized on the importance of statistical (...) thinking for inferring causal links between distinct cause and effect events, but here we assess whether this is also viable for causal thinking about continuous processes. Controlling for verbal and non-verbal ability, two studies administered a battery of covariation, probability, spatial–temporal, and causal measures. Results indicated that spatial–temporal analysis was the best predictor of causal thinking across both studies, but statistical thinking supported and informed spatial–temporal analysis: covariation assessment potentially assists with the identification of variables, while simple probability judgment potentially assists with thinking about unseen mechanisms. We conclude that the ability to find out patterns in data is even more widely important for causal analysis than commonly assumed, from childhood, having a role to play not just when causally linking already distinct events but also when analyzing the causal process underlying extended dynamic events without perceptually distinct components. (shrink)

Much research supports the existence of an Approximate Number System (ANS) that is recruited by infants, children, adults, and non-human animals to generate coarse, non-symbolic representations of number. This system supports simple arithmetic operations such as addition, subtraction, and ordering of amounts. The current study tests whether an intuition of a more complex calculation, division, exists in an indigene group in the Amazon, the Mundurucu, whose language includes no words for large numbers. Mundurucu children were presented with a video event (...) depicting a division transformation of halving, in which pairs of objects turned into single objects, reducing the array's numerical magnitude. Then they were tested on their ability to calculate the outcome of this division transformation with other large-number arrays. The Mundurucu children effected this transformation even when non-numerical variables were controlled, performed above chance levels on the very first set of test trials, and exhibited performance similar to urban children who had access to precise number words and a surrounding symbolic culture. We conclude that a halving calculation is part of the suite of intuitive operations supported by the ANS. (shrink)