The approximate number system (ANS) enables organisms to represent the approximate number of items in an observed collection, quickly and independently of natural language. Recently, it has been proposed that the ANS goes beyond representing natural numbers by extracting and representing rational numbers (Clarke & Beck, 2021a). Prior work demonstrates that adults and children discriminate ratios in an approximate and ratio-dependent manner, consistent with the hallmarks of the ANS. Here, we use a well-known “connectedness illusion” to provide evidence that these (...) ratio-dependent ratio discriminations are (a) based on the perceived number of items in seen displays (and not just non-numerical confounds), (b) are not dependent on verbal working memory, or explicit counting routines, and (c) involve representations with a part-whole (or subset-superset) format, like a fraction, rather than a part-part format, like a ratio. These results vindicate key predictions of the hypothesis that the ANS represents rational numbers. (shrink)

According to agent-causal accounts of free will, agents have the capacity to cause actions, and for a given action, an agent could have done otherwise. This paper uses existing results and presents experimental evidence to argue that young children deploy a notion of agent-causation. If young children do have such a notion, however, it remains quite unclear how they acquire it. Several possible acquisition stories are canvassed, including the possibility that the notion of agent-causation develops from a prior notion of (...) obligation. Finally, the paper sets out how this work might illuminate the philosophical problem of free will. (shrink)

A number of theoretical positions in psychology—including variants of case‐based reasoning, instance‐based analogy, and connectionist models—maintain that abstract rules are not involved in human reasoning, or at best play a minor role. Other views hold that the use of abstract rules is a core aspect of human reasoning. We propose eight criteria for determining whether or not people use abstract rules in reasoning, and examine evidence relevant to each criterion for several rule systems. We argue that there is substantial evidence (...) that several different inferential rules, including modus ponens, contractual rules, causal rules, and the law of large numbers, are used in solving everyday problems. We discuss the implications for various theoretical positions and consider hybrid mechanisms that combine aspects of instance and rule models. (shrink)

Previous research suggests that children can infer causal relations from patterns of events. However, what appear to be cases of causal inference may simply reduce to children recognizing relevant associations among events, and responding based on those associations. To examine this claim, in Experiments 1 and 2, children were introduced to a “blicket detector,” a machine that lit up and played music when certain objects were placed upon it. Children observed patterns of contingency between objects and the machine's activation that (...) required them to use indirect evidence to make causal inferences. Critically, associative models either made no predictions, or made incorrect predictions about these inferences. In general, children were able to make these inferences, but some developmental differences between 3- and 4-year-olds were found. We suggest that children's causal inferences are not based on recognizing associations, but rather that children develop a mechanism for Bayesian structure learning. Experiment 3 explicitly tests a prediction of this account. Children were asked to make an inference about ambiguous data based on the base rate of certain events occurring. Four-year-olds, but not 3-year-olds were able to make this inference. (shrink)

This paper examines the strengths and weaknesses of one of science's most pervasive and flexible metaprinciples;optimalityis used to explain utility maximization in economics, least effort principles in physics, entropy in chemistry, and survival of the fittest in biology. Fermat's principle of least time involves both teleological and causal considerations, two distinct modes of explanation resting on poorly understood psychological primitives. The rationality heuristic in economics provides an example from social science of the potential biases arising from the extreme flexibility of (...) optimality considerations, including selective search for confirming vidence, ex post rationalization, and the confusion of prediction with explanation. Commentators are asked to reflect on the extent to which optimality is an organizing principle of nature, a set of relatively unconnected techniques of science, a normative principle for rational choice and social organization, a metaphysical way of looking at the world, or something else still. (shrink)

Previous research suggests that children can infer causal relations from patterns of events. However, what appear to be cases of causal inference may simply reduce to children recognizing relevant associations among events, and responding based on those associations. To examine this claim, in Experiments 1 and 2, children were introduced to a “blicket detector”, a machine that lit up and played music when certain objects were placed upon it. Children observed patterns of contingency between objects and the machine’s activation that (...) required them to use indirect evidence to make causal inferences. Critically, associative models either made no predictions, or made incorrect predictions about these inferences. In general, children were able to make these inferences, but some developmental differences between 3- and 4- year-olds were found. We suggest that children’s causal inferences are not based on recognizing associations, but rather that children develop a mechanism for Bayesian structure learning. Experiment 3 explicitly tests a prediction of this account. Children were asked to make an inference about ambiguous data based on the base-rate of certain events occurring. Fouryear-olds, but not 3-year-olds were able to make this inference. (shrink)

People are adept at inferring novel causal relations, even from only a few observations. Prior knowledge about the probability of encountering causal relations of various types and the nature of the mechanisms relating causes and effects plays a crucial role in these inferences. We test a formal account of how this knowledge can be used and acquired, based on analyzing causal induction as Bayesian inference. Five studies explored the predictions of this account with adults and 4-year-olds, using tasks in which (...) participants learned about the causal properties of a set of objects. The studies varied the two factors that our Bayesian approach predicted should be relevant to causal induction: the prior probability with which causal relations exist, and the assumption of a deterministic or a probabilistic relation between cause and effect. Adults’ judgments (Experiments 1, 2, and 4) were in close correspondence with the quantitative predictions of the model, and children’s judgments (Experiments 3 and 5) agreed qualitatively with this account. (shrink)

Human cognition requires coping with a complex and uncertain world. This suggests that dealing with uncertainty may be the central challenge for human reasoning. In Bayesian Rationality we argue that probability theory, the calculus of uncertainty, is the right framework in which to understand everyday reasoning. We also argue that probability theory explains behavior, even on experimental tasks that have been designed to probe people's logical reasoning abilities. Most commentators agree on the centrality of uncertainty; some suggest that there is (...) a residual role for logic in understanding reasoning; and others put forward alternative formalisms for uncertain reasoning, or raise specific technical, methodological, or empirical challenges. In responding to these points, we aim to clarify the scope and limits of probability and logic in cognitive science; explore the meaning of the explanation of cognition; and re-evaluate the empirical case for Bayesian rationality. (shrink)

How do human children come up to carve up and think of the world around them in its most general and abstract structure? And to which degree are these general forms of viewing the world shared by other animals, notably by non-human primates? In response to these questions of what could be called comparative metaphysics, this paper discusses new evidence from developmental and comparative research to argue for the following picture: human children and non-human primates share a basic framework of (...) natural ontology: they think about their natural surroundings in essentialist ways in terms of natural kind objects constituted by their essential properties, and in generic terms as governed by general descriptive regularities. In contrast, there is a great divide when it comes to how human children and non-human primates carve up their social environment: only human children then go on to use their essentialist and generic thinking for developing a distinctively social ontology, to conceive of their surrounding in terms of socially constituted objects governed by general prescriptive norms. (shrink)

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)

Notes on Contributors • Preface • Christopher Peacocke, Introduction: The Issues and their Further Development I OBJECTIVE THOUGHT • John Campbell, Objects and Objectivity Commentaries • Bill Brewer, Thoughts about Objects, Places and Times • John O'Keefe, Cognitive Maps, Time and Causality II OBJECTIVITY AND THE UNITY OF CONSCIOUSNESS • Susan Hurley, Unity and Objectivity Commentaries • Anthony Marcel, What is Relevant to the Unity of Consciousness? • Michael Lockwood, Issues of Unity and Objectivity III UNDERSTANDING THE MENTAL:THEORY OR SIMULATION (...) • MARTIN DAVIES, The Mental Simulation Debate Commentaries • Jane Heal, Simulation vs. Theory Theory: What is at Issue? • Josef Perner, The Necessity and Impossibility of Simulation. (shrink)

is normative in the sense that it aims to make recommendations for improving human judgment; it aims to have a practical impact on morally and politically significant human decisions and actions; and it studies normative, rational judgment qua rational judgment. These nonstandard ways of understanding ACP as normative collectively suggest a new interpretation of the strong replacement thesis that does not call for replacing normative epistemic concepts, relations, and inquiries with descriptive, causal ones. Rather, it calls for recognizing that the (...) aims and normative inquiries of epistemology and normative psychology have become intermutual in nature. Key Words: Heuristics and biases • applied cognitive psychology • normative psychology • rationality • naturalized epistemology • Epistemics • Applied Naturalized Epistemology • strong replacement • strategic reliabilism • ameliorative psychology. (shrink)

A comment on Paul Schoemaker's target article in Behavioral and Brain Sciences, 14 (1991), p. 205-215, "The Quest for Optimality: A Positive Heuristic of Science?" (https://doi.org/10.1017/S0140525X00066140). This comment argues that the optimizing model of decision leads to an infinite regress, once internal costs of decision (i.e., information and computation costs) are duly taken into account.

This study examined students' reasoning about simple repeated choices. Each choice involved ''betting'' on two events, differing in probability. We asked subjects to generate or evaluate alternative strategies such as betting on the most likely event on every trial, betting on it on almost every trial, or employing a ''probability matching'' strategy. Almost half of the college students did not generate or rank strategies according to their expected value, but few subjects preferred a strategy of strict probability matching. High-school students (...) showed greater deviations from expected value than college students. Similar misunderstandings were observed in a choice task involving real (not hypothetical) repeated trials. Large gender differences in prediction strategies and in related computational skills were observed. Subjects who understand the optimal strategy usually do so in terms of independence of successive trials rather than calculation. Some subjects understand the concept of independence but fail to bring it to bear, thinking it can be overridden by intuition or local balancing (representativeness). (shrink)

The examples and concepts that Shoemaker cites are rather heterogeneous. Some distinctions need to be drawn. An optimality thesis involves not just an ordering of options, but a value judgment about them. So let us begin by distinguishing minimality from optimality. And the concept of minimality can play a variety of roles, among which I distinguish between extremum descriptions, statements hypothesizing an optimizing process, and methodological recommendations. Finally, I consider how the three categories relate to Shoemaker’s question that “Who is (...) optimizing: the scientist or nature?” . (shrink)

Rationality in decision making is commonly assessed by comparing choice performance against normative standards. We argue that such a performance-centered approach blurs the distinction between rational choice and adaptive behavior. Instead, rational choice should be assessed with regard to the way individuals make analytic decisions. We suggest that analytic decisions can be made in two different modes in which control processes are directed at different levels. In a RUN mode, thought is directed at controlling the operation of a decision strategy. (...) In the JUMP mode, the individual analyses the interpretation of the decision situation as well as the appropriateness of alternative strategies. We suggest that a decision should be considered “rational” when an individual is able to switch between these modes and balance their interaction. (shrink)

Yunier Broche-Pérez y Denisse Cruz-López Universidad Central “Marta Abreu” de Las Villas, Villa Clara, Cuba Hospital … Read More →.