Substances as a core domain.

Central to What Babies Know (Spelke, ) is the thesis that infants' understanding is divided into independent modules of core knowledge. As a test case, we consider adding a new domain: core knowledge of substances. Experiments show that infants' understanding of substances meets some criteria of core knowledge, and they raise questions about the relations that hold between core domains.

How do we regard fictional people? How do they regard us?

Readers assume that commonplace properties of the real world also hold in realistic fiction. They believe, for example, that the usual physical laws continue to apply. But controversy exists in theories of fiction about whether real individuals exist in the story's world. Does Queen Victoria exist in the world of Jane Eyre, even though Victoria is not mentioned in it? The experiments we report here find that when participants are prompted to consider the world of a fictional individual ("Consider the world of Jane Eyre . . ."), they are willing to say that a real individual (e.g., Queen Victoria) can exist in the same world. But when participants are prompted to consider the world of a real individual, they are less willing to say that a fictional individual can exist in that world. The asymmetry occurs when we ask participants both if a real person is in the character's world and if the person would appear there. However, the effect is subject to spatial and temporal constraints. When the person and the character share spatial and temporal settings, interchange is more likely to occur. These results shed light on the author's implicit contract with the reader, which can license the reader to augment a fictional world with features that the author only implicates as part of the work's background.

Possible Objects: Topological Approaches to Individuation.

We think of the world around us as divided into physical objects like toasters and daisies, rather than solely as a smear of properties like yellow and smooth. How do we single out these objects? One theory of object concepts uses part-of relations and relations of connectedness. According to this proposal, an object is a connected spatial item of maximal extent: Any other connected item that overlaps (i.e., shares a part with) the object must be a part of that object. This article reports four experiments that test this proposal. Participants see descriptions or diagrams of spatial items that vary across trials in their relative positions. In separate experiments, participants decide whether the items are physical objects, whether they are wholes, or how many objects are present. All experiments find support for connectedness as a contributor to object status, but they find little support for maximality. The results suggest that maximality is not a necessary feature of wholes or of objects.

Concepts of objects and substances in language.

People distinguish objects from the substances that constitute them. Many languages also distinguish count nouns and mass nouns. What is the relation between these two distinctions? The connection between them is complicated by the facts that (a) some mass nouns (e.g., toast) seem to name countable objects; (b) some count and mass nouns (e.g., pots and pottery) seem to name the same objects; (c) nouns for seemingly the same things can be count in one language (English: dishes) but mass in another (French: la vaisselle); (d) count nouns can be used to name substances (There is carrot in the soup) and mass nouns to name portions (She drank three whiskeys); and (e) some languages (e.g., Mandarin) appear to have no count nouns, whereas others (e.g., Yudja) appear to have no mass nouns. All these cases counter a simple object-to-count-noun and substance-to-mass-noun relation, but they provide opportunities to see whether the grammatical distinction affects the referential one. We examine evidence from such cases and find continuity through development: Infants appear to have the conceptual OBJECT/SUBSTANCE distinction very early on. Although this distinction may change with development, the acquisition of count/mass syntax does not appear to be an effective factor for change.

Children's Understanding of the Natural Numbers' Structure.

When young children attempt to locate numbers along a number line, they show logarithmic (or other compressive) placement. For example, the distance between "5" and "10" is larger than the distance between "75" and "80." This has often been explained by assuming that children have a logarithmically scaled mental representation of number (e.g., Berteletti, Lucangeli, Piazza, Dehaene, & Zorzi, ; Siegler & Opfer, ). However, several investigators have questioned this argument (e.g., Barth & Paladino, ; Cantlon, Cordes, Libertus, & Brannon, ; Cohen & Blanc-Goldhammer, ). We show here that children prefer linear number lines over logarithmic lines when they do not have to deal with the meanings of individual numerals (i.e., number symbols, such as "5" or "80"). In Experiments 1 and 2, when 5- and 6-year-olds choose between number lines in a forced-choice task, they prefer linear to logarithmic and exponential displays. However, this preference does not persist when Experiment 3 presents the same lines without reference to numbers, and children simply choose which line they like best. In Experiments 4 and 5, children position beads on a number line to indicate how the integers 1-100 are arranged. The bead placement of 4- and 5-year-olds is better fit by a linear than by a logarithmic model. We argue that previous results from the number-line task may depend on strategies specific to the task.

Five-month-old infants have expectations for the accumulation of nonsolid substances.

Infants fail to represent quantities of non-cohesive substances in paradigms where they succeed with solid objects. Some investigators have interpreted these results as evidence that infants do not yet have representations for substances. More recent research, however, shows that 5-month-old infants expect objects and substances to behave and interact in different ways. In the present experiments, we test whether infants have expectations for substances when the outcomes are not simply the opposite of those for objects. In Experiment 1, we find that 5-month-old infants expect that when a cup of sand pours behind a screen, it will accumulate in just one pile rather than two. Similarly, infants expect that when two cups of sand pour in separate streams, two distinct piles will accumulate rather than one. Infants look significantly longer at outcomes with an inconsistent number of piles, providing evidence that infants have expectations for how sand accumulates. To test whether the number of cups or the number of pours guided expectations about accumulation, Experiment 2 placed these cues in conflict. This resulted in chance performance, suggesting that, for infants to build expectations about these outcomes, they need both cues (cup and pour) to converge. These findings offer insight into the nature of infants' representations for non-cohesive substances like sand.

Conditionals, Context, and the Suppression Effect.

Modus ponens is the argument from premises of the form If A, then B and A to the conclusion B (e.g., from If it rained, Alicia got wet and It rained to Alicia got wet). Nearly all participants agree that the modus ponens conclusion logically follows when the argument appears in this Basic form. However, adding a further premise (e.g., If she forgot her umbrella, Alicia got wet) can lower participants' rate of agreement-an effect called suppression. We propose a theory of suppression that draws on contemporary ideas about conditional sentences in linguistics and philosophy. Semantically, the theory assumes that people interpret an indicative conditional as a context-sensitive strict conditional: true if and only if its consequent is true in each of a contextually determined set of situations in which its antecedent is true. Pragmatically, the theory claims that context changes in response to new assertions, including new conditional premises. Thus, the conclusion of a modus ponens argument may no longer be accepted in the changed context. Psychologically, the theory describes people as capable of reasoning about broad classes of possible situations, ordered by typicality, without having to reason about individual possible worlds. The theory accounts for the main suppression phenomena, and it generates some novel predictions that new experiments confirm.

Five-Month-Old Infants Have General Knowledge of How Nonsolid Substances Behave and Interact.

Experience puts people in touch with nonsolid substances, such as water, blood, and milk, which are crucial to survival. People must be able to understand the behavior of these substances and to differentiate their properties from those of solid objects. We investigated whether infants represent nonsolid substances as a conceptual category distinct from solid objects on the basis of differences in cohesiveness. Experiment 1 established that infants can distinguish water from a perceptually matched solid and can correctly predict whether the item will pass through or be trapped by a grid. Experiments 2 and 3 showed that infants extend this knowledge to less familiar granular substances. These experiments indicate that concepts of cohesive and noncohesive material appear early in development, apply across several types of nonsolid substances, and may serve as the basis of later knowledge of physical phases.

Identifying and counting objects: The role of sortal concepts.

Sortal terms, such as table or horse, are nouns akin to basic-level terms. According to some theories, the meaning of sortals provides conditions for telling objects apart (individuating objects, e.g., telling one table from a second) and for identifying objects over time (e.g., determining that a particular table at one time is the same table at another). A number of psychologists have proposed that sortal concepts likewise provide psychologically real conditions for individuating and identifying things. However, this paper reports five experiments that cast doubt on these psychological claims. Experiments 1-3 suggest that sortal concepts do not determine when an object ceases to exist and therefore do not decide when the object can no longer be identical to a later one. Experiments4-5 similarly suggest that sortal concepts do not provide determinate conditions for individuating objects. For example, they do not always decide whether a room contains one table or two. All five experiments feature ordinary objects undergoing ordinary changes.

Divisions of the physical world: Concepts of objects and substances.

Our concepts of the physical world distinguish objects, such as chairs, from substances, such as quantities of wood, that constitute them. A particular chair might consist of a single chunk of wood, yet we think about the chair and the wood in different ways. For example, part of the wood is still wood, but part of the chair is not a chair. In this article we examine the basis of the object/substance distinction. We draw together for the first time relevant experiments widely dispersed in the cognitive literature, and view these findings in the light of theories in linguistics and metaphysics. We outline a framework for the difference between objects and substances, based on earlier ideas about form and matter, describing the psychological evidence surrounding it. The framework suggests that concepts of objects include a relation of unity and organization governing their parts, whereas concepts of substances do not. We propose, as a novel twist on this framework, that unity and organization for objects is a function of causal forces that shape the objects. In agreement with this idea, results on the identification of an item as an object depend on clues about the presence of the shaping relation, clues provided by solidity, repetition of shape, and other factors. We also look at results from human infants about the source of the object/substance distinction and conclude that the data support an early origin for both object and substance knowledge. (PsycINFO Database Record

Do the right thing: the assumption of optimality in lay decision theory and causal judgment.

Human decision-making is often characterized as irrational and suboptimal. Here we ask whether people nonetheless assume optimal choices from other decision-makers: Are people intuitive classical economists? In seven experiments, we show that an agent's perceived optimality in choice affects attributions of responsibility and causation for the outcomes of their actions. We use this paradigm to examine several issues in lay decision theory, including how responsibility judgments depend on the efficacy of the agent's actual and counterfactual choices (Experiments 1-3), individual differences in responsibility assignment strategies (Experiment 4), and how people conceptualize decisions involving trade-offs among multiple goals (Experiments 5-6). We also find similar results using everyday decision problems (Experiment 7). Taken together, these experiments show that attributions of responsibility depend not only on what decision-makers do, but also on the quality of the options they choose not to take.

Identity, causality, and pronoun ambiguity.

This article looks at the way people determine the antecedent of a pronoun in sentence pairs, such as: Albert invited Ron to dinner. He spent hours cleaning the house. The experiment reported here is motivated by the idea that such judgments depend on reasoning about identity (e.g., the identity of the he who cleaned the house). Because the identity of an individual over time depends on the causal-historical path connecting the stages of the individual, the correct antecedent will also depend on causal connections. The experiment varied how likely it is that the event of the first sentence (e.g., the invitation) would cause the event of the second (the house cleaning) for each of the two individuals (the likelihood that if Albert invited Ron to dinner, this would cause Albert to clean the house, versus cause Ron to clean the house). Decisions about the antecedent followed causal likelihood. A mathematical model of causal identity accounted for most of the key aspects of the data from the individual sentence pairs.

Possible number systems.

Number systems-such as the natural numbers, integers, rationals, reals, or complex numbers-play a foundational role in mathematics, but these systems can present difficulties for students. In the studies reported here, we probed the boundaries of people's concept of a number system by asking them whether "number lines" of varying shapes qualify as possible number systems. In Experiment 1, participants rated each of a set of number lines as a possible number system, where the number lines differed in their structures (a single straight line, a step-shaped line, a double line, or two branching structures) and in their boundedness (unbounded, bounded below, bounded above, bounded above and below, or circular). Participants also rated each of a group of mathematical properties (e.g., associativity) for its importance to number systems. Relational properties, such as associativity, predicted whether participants believed that particular forms were number systems, as did the forms' ability to support arithmetic operations, such as addition. In Experiment 2, we asked participants to produce properties that were important for number systems. Relational, operation, and use-based properties from this set again predicted ratings of whether the number lines were possible number systems. In Experiment 3, we found similar results when the number lines indicated the positions of the individual numbers. The results suggest that people believe that number systems should be well-behaved with respect to basic arithmetic operations, and that they reject systems for which these operations produce ambiguous answers. People care much less about whether the systems have particular numbers (e.g., 0) or sets of numbers (e.g., the positives).

Can statistical learning bootstrap the integers?

This paper examines Piantadosi, Tenenbaum, and Goodman's (2012) model for how children learn the relation between number words ("one" through "ten") and cardinalities (sizes of sets with one through ten elements). This model shows how statistical learning can induce this relation, reorganizing its procedures as it does so in roughly the way children do. We question, however, Piantadosi et al.'s claim that the model performs "Quinian bootstrapping," in the sense of Carey (2009). Unlike bootstrapping, the concept it learns is not discontinuous with the concepts it starts with. Instead, the model learns by recombining its primitives into hypotheses and confirming them statistically. As such, it accords better with earlier claims (Fodor, 1975, 1981) that learning does not increase expressive power. We also question the relevance of the simulation for children's learning. The model starts with a preselected set of15 primitives, and the procedure it learns differs from children's method. Finally, the partial knowledge of the positive integers that the model attains is consistent with an infinite number of nonstandard meanings-for example, that the integers stop after ten or loop from ten back to one.

Inference and explanation in counterfactual reasoning.

This article reports results from two studies of how people answer counterfactual questions about simple machines. Participants learned about devices that have a specific configuration of components, and they answered questions of the form "If component X had not operated [failed], would component Y have operated?" The data from these studies indicate that participants were sensitive to the way in which the antecedent state is described-whether component X "had not operated" or "had failed." Answers also depended on whether the device is deterministic or probabilistic--whether X's causal parents "always" or only "usually" cause X to operate. Participants' explanations of their answers often invoked non-operation of causally prior components or unreliability of prior connections. They less often mentioned independence from these causal elements.

How many is a zillion? Sources of number distortion.

When young children attempt to locate the positions of numerals on a number line, the positions are often logarithmically rather than linearly distributed. This finding has been taken as evidence that the children represent numbers on a mental number line that is logarithmically calibrated. This article reports a statistical simulation showing that log-like positioning is a consequence of 2 factors: the bounded nature of the number line and greater uncertainty about the meaning of the larger, less frequent number words. Two experiments likewise show that even college students produce log-like placements under the same 2 conditions. In Experiment 1, participants identified positions on a number line for a set that included both conventional and fictitious numbers (e.g., a zillion). In Experiment 2, participants did the same for conventional numbers that included some larger, unfamiliar items (e.g., a nonillion). Both experiments produced results better fit by logarithmic than by linear functions.

Infants make quantity discriminations for substances.

Infants can track small groups of solid objects, and infants can respond when these quantities change. But earlier work is equivocal about whether infants can track continuous substances, such as piles of sand. Experiment 1 (N = 88) used a habituation paradigm to show infants can register changes in the size of piles of sand that they see poured from a container when there is a 1-to-4 ratio. Experiment 2 (N = 82) tested whether infants could discriminate a 1-to-2 ratio. The results demonstrate that females could discriminate the difference but males could not. These findings constitute the youngest evidence of successful quantity discriminations for a noncohesive substance and begin to characterize the nature of the representation for noncohesive entities.

Split identity: intransitive judgments of the identity of objects.

Identity is a transitive relation, according to all standard accounts. Necessarily, if x=y and y=z, then x=z. However, people sometimes say that two objects, x and z, are the same as a third, y, even when x and z have different properties (thus, x=y and y=z, but x≠z). In the present experiments, participants read stories about an iceberg that breaks into two icebergs, one to the east and the other to the west. Many participants (32-54%, in baseline conditions across experiments) decided that both successors were the original iceberg, despite the different spatial locations of the successors. Experiment 1 shows that this tendency is not due to participants failing to understand both to mean both are simultaneously the original. Similarly, Experiment 2 demonstrates that the tendency is not solely due to their interpreting the question to be about properties of the icebergs rather than about the icebergs themselves. Experiments 3 and 4 suggest, instead, that participants may understand Which is the original? to mean Which, in its own right, is entitled to be the original? Emphasizing entitlement increases the number of seemingly intransitive responses, whereas emphasizing the formal properties of identity decreases them.

Causation From Perception.

Beginning with the research of Albert Michotte, investigators have identified simple perceptual events that observers report as causal. For example, suppose a square moves across a screen and comes to a halt when it makes contact with a second square. If the second square then begins moving in the same direction, observers sometimes report that the first square "pushed" the second or "caused it to move." Based on such reports, Michotte claimed that people perceive causality, and a number of psychologists and philosophers have followed his lead. This article examines Michotte's hypothesis by comparing it with its chief rival: Observers possess representations of pushings, pullings, and other events in long-term memory. A Michottean display triggers one of these representations, and the representation classifies the display as an instance of pushing (or pulling, etc.). According to this second explanation, recognizing an event as a pushing is similar to classifying an object as a cup or a dog. Data relevant to this debate come from infant and animal studies, cognitive and neuropsychological dissociation experiments, and studies of context effects and individual differences. However, a review of research in these paradigms finds no reason to prefer Michotte's theory over its competitor.

Psychological connectedness and intertemporal choice.

People tend to attach less value to a good if they know a delay will occur before they obtain it. For example, people value receiving $100 tomorrow more than receiving $100 in 10 years. We explored one reason for this tendency (due to Parfit, 1984): In terms of psychological properties, such as beliefs, values, and goals, the decision maker is more closely linked to the person (his or her future self) receiving $100 tomorrow than to the person receiving $100 in 10 years. For this reason, he or she prefers his or her nearer self to have the $100 rather than his or her more remote self. Studies 1 and 2 showed that the greater the rated psychological connection between 2 parts of a participant's life, the less he or she discounted future monetary and nonmonetary benefits (e.g., good days at work) over that interval. In Studies 3-5, participants read about characters who undergo large life-changing (and connectedness-weakening) events at different points in their lives and then made decisions about the timing of benefits on behalf of these characters. All 5 studies revealed a relation between perceived psychological connectedness and intertemporal choice: Participants preferred benefits to occur before large changes in connectedness but preferred costs to occur after these changes.