Lance Rips

Traditional theories of how children learn the positive integers start from infants' abilities in detecting the quantity of physical objects. Our target article examined this view and found no plausible accounts of such development. Most of our commentators appear to agree that no adequate developmental theory is presently available, but they attempt to hold onto a role for early enumeration. Although some defend the traditional theories, others introduce new basic quantitative abilities, new methods of transformation, or new types of end states. A survey of these proposals, however, shows that they do not succeed in bridging the gap to knowledge of the integers. We suggest that a better theory depends on starting with primitives that are inherently structural and mathematical

A current and very influential theory in psychology holds that infants have innate, perceptually informed systems that endow them with surprisingly high-level concepts—for example, concepts of cardinality and causality. Proponents of core cognition hold that these initial concepts then provide the building blocks for later adult ideas within these domains. This paper reviews the evidence for core cognition and argues that these systems aren’t sufficient to explain how children learn their way to adult thoughts about language, number, or cause.

This interdisciplinary work is a collection of major essays on reasoning: deductive, inductive, abductive, belief revision, defeasible, cross cultural, conversational, and argumentative. They are each oriented toward contemporary empirical studies. The book focuses on foundational issues, including paradoxes, fallacies, and debates about the nature of rationality, the traditional modes of reasoning, as well as counterfactual and causal reasoning. It also includes chapters on the interface between reasoning and other forms of thought. In general, this last set of essays represents growth points in reasoning research, drawing connections to pragmatics, cross-cultural studies, emotion and evolution.

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.

Conditional perfection is the phenomenon in which conditionals are strengthened to biconditionals. In some contexts, “If A, B” is understood as if it meant “A if and only if B.” We present and discuss a series of experiments designed to test one of the most promising pragmatic accounts of conditional perfection. This is the idea that conditional perfection is a form of exhaustification—that is a strengthening to an exhaustive reading, triggered by a question that the conditional answers. If a speaker is asked how B comes about, then the answer “If A, B” is interpreted exhaustively to meaning that A is the only way to bring about B. Hence, “A if and only if B.” We uncover evidence that conditional perfection is a form of exhaustification, but not that it is triggered by a relationship to a salient question.

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, 2010; Siegler & Opfer, 2003). However, several investigators have questioned this argument (e.g., Barth & Paladino, 2011; Cantlon, Cordes, Libertus, & Brannon, 2009; Cohen & Blanc-Goldhammer, 2011). 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.

This article considers how people judge the identity of objects (e.g., how people decide that a description of an object at one time, t₀, belongs to the same object as a description of it at another time, t₁). The authors propose a causal continuer model for these judgments, based on an earlier theory by Nozick (1981). According to this model, the 2 descriptions belong to the same object if (a) the object at t₁ is among those that are causally close enough to be genuine continuers of the original and (b) it is the closest of these close-enough contenders. A quantitative version of the model makes accurate predictions about judgments of which a pair of objects is identical to an original (Experiments 1 and 2). The model makes correct qualitative predictions about identity across radical disassembly (Experiment 1) as well as more ordinary transformations (Experiments 2 and 3).

Sortal terms, such as table or horse, are count nouns (akin to a 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 horse at one time is the same horse 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. Experiments 4-5 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.

If people believe that one activity is a kind of another, they also tend to believe that the second activity is a part of the first. For example, they assert that deciding is a kind of thinking and that thinking is a part of deciding. C. Fellbaum and G. A. Miller's (see record 1991-03356-001) explanation for this phenomenon is based on the idea that people interpret part of in the domain of verbs as a type of logical entailment. Their explanation, however, suffers from at least 2 deficiencies. First, it fails to account for parallel effects with nouns (e.g., a contest is a kind of an activity, and an activity is a part of a contest). Second, it contains a flaw that incorrectly predicts many activities to be parts of each other (e.g., coming is part of going and going part of coming). However, a hypothesis L. J. Rips and F. G. Conrad (see record 1989-24843-001) originally proposed for the kind–part reciprocal effect avoids both of these difficulties.

A central aspect of people's beliefs about the mind is that mental activities—for example, thinking, reasoning, and problem solving—are interrelated, with some activities being kinds or parts of others. In common-sense psychology, reasoning is a kind of thinking and reasoning is part of problem solving. People's conceptions of these mental kinds and parts can furnish clues to the ordinary meaning of these terms and to the differences between folk and scientific psychology. In this article, we use a new technique for deriving partial orders to analyze subjects' decisions about whether one mental activity is a kind or part of another. The resulting taxonomies and partonomies differ from those of common object categories in exhibiting a converse relation in this domain: One mental activity is a part of another if the second is a kind of the first. The derived taxonomies and partonomies also allow us to predict results from further experiments that examine subjects' memory for these activities, their ratings of the activities' importance, and their judgments about whether there could be "possible minds" that possess some of the activities but not others.

First, we describe a psychological experiment in which the participants were asked to determine whether sentences of first-order logic were true or false in finite graphs. Second, we define two proof systems for reasoning about truth and falsity in first-order logic. These proof systems feature explicit models of cognitive resources such as declarative memory, procedural memory, working memory, and sensory memory. Third, we describe a computer program that is used to find the smallest proofs in the aforementioned proof systems when capacity limits are put on the cognitive resources. Finally, we investigate the correlation between a number of mathematical complexity measures defined on graphs and sentences and some psychological complexity measures that were recorded in the experiment