The role of relational reasoning in children's addition concepts

The study addresses the relational reasoning of different‐aged children and how addition reasoning is related to problem‐solving skills within addition and to reasoning skills outside addition. Ninety‐two 5‐ to 8‐year‐olds were asked to solve a series of conceptually related and unrelated addition problems, and the speed and accuracy of all self‐reported strategies were used to monitor their addition performance. Children were also given a series of general relational reasoning tasks to assess their ability to solve problems based on thematic, causal and visual relations. The results revealed that, while children were able to reason about commutativity relations, recognition of relations based on additive composition was rare. Furthermore, children's ability to reason about addition concepts increased with age and problem‐solving proficiency. Reasoning about addition concepts was related to performance on the thematic, causal and visual reasoning tasks for older children but not for younger children. Overall, the findings suggest that while children's early knowledge of addition relations is domain specific, as children develop in their broader reasoning abilities these developments enhance their addition reasoning.     

My Heart Made Me Do It: Children's Essentialist Beliefs About Heart Transplants

Psychological essentialism is a folk theory characterized by the belief that a causal internal essence or force gives rise to the common outward behaviors or attributes of a category's members. In two studies, we investigated whether 4‐ to 7‐year‐old children evidenced essentialist reasoning about heart transplants by asking them to predict whether trading hearts with an individual would cause them to take on the donor's attributes. Control conditions asked children to consider the effects of trading money with an individual. Results indicated that children reasoned according to essentialism, predicting more transfer of attributes in the transplant condition versus the non‐bodily money control. Children also endorsed essentialist transfer of attributes even when they did not believe that a transplant would change the recipient's category membership (e.g., endorsing the idea that a recipient of a pig's heart would act pig‐like, but denying that the recipient would become a pig). This finding runs counter to predictions from a strong interpretation of the “minimalist” position, an alternative to essentialism.     

Causal reasoning

The main focus of this paper is the question as to what it is for an individual to think of her environment in terms of a concept of causation, or causal concepts, in contrast to some more primitive ways in which an individual might pick out or register what are in fact causal phenomena. I show how versions of this question arise in the context of two strands of work on causation, represented by Elizabeth Anscombe and Christopher Hitchcock, respectively. I then describe a central type of reasoning that, I suggest, a subject has to be able to engage in, if we are to credit her with causal concepts. I also point out that this type of reasoning turns on the idea of a physical connection between cause and effect, as articulated in recent singularist approaches of causation.     

Causal reasoning and the diagnostic process

Background: Causal reasoning as a way to make a diagnosis seems convincing. Modern medicine depends on the search for causes of disease and it seems fair to assert that such knowledge is employed in diagnosis. Causal reasoning as it has been presented neglects to some extent the conception of multifactorial disease causes. Goal: The purpose of this paper is to analyze aspects of causation relevant for discussing causal reasoning in a diagnostic context. Procedures: The analysis will discuss different conceptions of causal reasoning in medical diagnosis, discriminating primarily between narrow causal diagnosis and more thorough causal explanation. The theory of causes as non-redundant factors in effective causal complexes is used as an analytical background. Causal explanations are performed according to different causal models. Such models of diagnosis are assumptions concerning structure and mechanisms, which cannot be directly or immediately observed. Conceptions and results of causal search strategies differ, according to the focus of the searcher. Causal reasoning is also seen in diagnosis in a more extensive meaning: the pin-pointing of factors responsible for the condition of the patient at any time during the course of disease. Conclusion: Causal reasoning and diagnosis go well in hand, especially if both concepts are widened. The theory of causes as non-redundant components in effective causal complexes, modulated by what is referred to as the stop problem and causal fields, is valuable for explaining the many aspects of causal reasoning in medical diagnosis.     

Encouraging children to think counterfactually enhances blocking in a causal learning task

According to a higher order reasoning account, inferential reasoning processes underpin the widely observed cue competition effect of blocking in causal learning. The inference required for blocking has been described as modus tollens (if p then q, not q therefore not p). Young children are known to have difficulties with this type of inference, but research with adults suggests that this inference is easier if participants think counterfactually. In this study, 100 children (51 five-year-olds and 49 six- to seven-year-olds) were assigned to two types of pretraining groups. The counterfactual group observed demonstrations of cues paired with outcomes and answered questions about what the outcome would have been if the causal status of cues had been different, whereas the factual group answered factual questions about the same demonstrations. Children then completed a causal learning task. Counterfactual pretraining enhanced levels of blocking as well as modus tollens reasoning but only for the younger children. These findings provide new evidence for an important role for inferential reasoning in causal learning.     

Children’s causal reasoning: Counterfactual thinking occurs for ‘negative’ outcomes only

Harris, German and Mills (Children’s use of counterfactual thinking in causal reasoning. Cognition, 61 (1996), 223–259), following Mackie, argue that children make explicit use of counterfactual thinking in arriving at causal judgments. They showed that children as young as 3, in explaining simple mishap events, made reference to courses of action that a protagonist had rejected, when that course of action would have prevented the observed outcome. It is hypothesized here that such counterfactual thinking might have been invoked by the ‘negative’ mishaps rather than as part of the causal reasoning process. Although the generation of counterfactuals in explanation was replicated using mishap outcomes such as those used by Harris et al., counterfactual thinking was not evident in children’s explanations of ‘positive’ outcomes. These results undermine the view that a counterfactual thinking process, as indexed by reference to possible actions rejected by a protagonist, is necessary for causal reasoning. Alternative characterizations of the relationship between causals and counterfactuals are discussed.     

The distinct contributions of cause–effect order and reasoning type in judgments of causality

ABSTRACT

People generally perceive a stronger link between smoking and cancer than between cancer and smoking. Generally, prior research on asymmetrical causal reasoning has not distinguished predictive (searching for effects) and diagnostic reasoning (searching for causes) from the order in which causes and effects are presented. Across 6 studies (overall N = 627), we show that order and reasoning have an additive influence on the causality perception: causes, spatially or temporally presented before the effect, strengthen the causality attribution associated to predictive (vs. diagnostic) frames. Moreover, we show that order and reasoning frame are bi-directionally related, as the cause-first order triggers predictive reasoning and vice versa, and people mentally maintain the cause-first order when envisaging a causal relation. Besides its methodological contribution to the causal reasoning literature, this research demonstrates the powerful role of word order in causal reasoning. Implications for the role of word order in communication and risk prevention are discussed.     

Reasoning's relation to bodily action

Recent philosophical work on the relation between reasoning and bodily action is dominated by two views. It is orthodox to have it that bodily actions can be at most causally involved in reasoning. Others have it that reasoning can constitutively involve bodily actions, where this is understood as a matter of non-mental bodily events featuring as constituents of practical reasoning. Reflection on cases of reasoning out-loud suggests a neglected alternative on which both practical and theoretical reasoning can have bodily actions as constituents, where such bodily actions themselves amount to contentful mental events. Furthermore, the natural lines of resistance to this view trade on type-token errors, or on a questionable common-factor assumption.     

Perception Versus Knowledge of Cause and Effect in Children: When Seeing Is Believing

Recent research has shown that even infants have perceptual sensitivity to the causal structure of the world, and it is often claimed that causal knowledge supports many of preschoolers' impressive cognitive achievements. That older children nevertheless can encounter difficulties in causal-reasoning tasks is typically attributed to lack of domain knowledge. A different explanation, however, is that causal structure may appear at more than one level, in perception, as well as in underlying knowledge. Children may make some reasoning errors because they have difficulty coordinating these levels. This article reviews relevant evidence on physical causality: Even infants in their first year perceive the causal structure of simple collision events. This perceptual skill could support rapid causal learning without prior knowledge and thus helps us understand children's precocity preschoolers already reason with the assumption that causes and effects are linked by underlying physical mechanisms. However, what may promote early development may later become a hindrance: When perception and mechanism point to different causes, children may not realize that mechanism is superordinate. Although the components of competent causal reasoning are available early in development, much experience may be required before children learn how to integrate them.     

Consciousness as a logically consistent and prognostic model of reality

The work demonstrates that brain might reflect the external world causal relationships in the form of a logically consistent and prognostic model of reality, which shows up as consciousness. The paper analyses and solves the problem of statistical ambiguity and provides a formal model of causal relationships as probabilistic maximally specific rules. We suppose that brain makes all possible inferences from causal relationships. We prove that the suggested formal model has a property of an unambiguous inference: from consistent premises we infer a consistent conclusion. It enables a set of all inferences to form a consistent model of the perceived world. Causal relationships may create fixed points of cyclic inter-predictable properties. We consider the “natural” classification introduced by John St. Mill and demonstrate that a variety of fixed points of the objects’ attributes forms a “natural” classification of the external world. Then we consider notions of “natural” categories and causal models of categories, introduced by Eleanor Rosch and Bob Rehder and demonstrate that fixed points of causal relationships between objects attributes, which we perceive, formalize these notions. If the “natural” classification describes the objects of the external world, and “natural” concepts the perception of these objects, then the theory of integrated information, introduced by G. Tononi, describes the information processes of the brain for “natural” concepts formation that reflects the “natural” classification. We argue that integrated information provides high accuracy of the objects identification. A computer-based experiment is provided that illustrates fixed points formation for coded digits.     

The cognitive structure of social categories

Support for the prototype theory of categorization was found in a study of the structure of social categories. Though occupational terms such as DOCTOR are socially defined, they do not have the classical structure their clear definitional origins would predict. Conceptions of social categories are richer and more complex than those of physical object categories and subjects agree upon them. Comparison of various instructions for eliciting attributes of categories showed that whether subjects are asked to define a term, give characteristics, or describe ways they recognize members of categories, the attributes they list contribute to a prototype structure. These data provide evidence against the view that prototype structure is relevant only to an identification procedure and not to the core of concepts, as has been suggested.     

The Role of Probability and Intentionality in Preschoolers' Causal Generalizations

Three experiments examined whether preschoolers recognize that the causal properties of objects generalize to new members of the same set given either deterministic or probabilistic data. Experiment 1 found that 3- and 4-year-olds were able to make such a generalization given deterministic data but were at chance when they observed probabilistic information. Five-year-olds reliably generalized in both situations. Experiment 2 found that 4-year-olds could make some probabilistic inferences, particularly when comparing sets that had no efficacy with sets in which some members had efficacy. Children had some difficulty discriminating between completely effective sets and stochastic ones. Experiment 3 examined whether 3- and 4-year-olds could reason about probabilistic data when provided with information about the experimenter's beliefs about causal outcomes. Children who were more successful on standard false-belief measures were more likely to respond as if the data were deterministic. These data suggest that children's probabilistic inferences develop into early elementary school, but preschoolers might have some understanding of probability when reasoning about causal generalization.     

The role of learning data in causal reasoning about observations and interventions

Recent studies have shown that people have the capacity to derive interventional predictions for previously unseen actions from observational knowledge, a finding that challenges associative theories of causal learning and reasoning (e.g., Meder, Hagmayer, & Waldmann, 2008). Although some researchers have claimed that such inferences are based mainly on qualitative reasoning about the structure of a causal system (e.g., Sloman, 2005), we propose that people use both the causal structure and its parameters for their inferences. We here employ an observational trial-by-trial learning paradigm to test this prediction. In Experiment 1, the causal strength of the links within a given causal model was varied, whereas in Experiment 2, base rate information was manipulated while keeping the structure of the model constant. The results show that learners’ causal judgments were strongly affected by the observed learning data despite being presented with identical hypotheses about causal structure. The findings show furthermore that participants correctly distinguished between observations and hypothetical interventions. However, they did not adequately differentiate between hypothetical and counterfactual interventions.     

Asymmetries in predictive and diagnostic reasoning

In this article, we address the apparent discrepancy between causal Bayes net theories of cognition, which posit that judgments of uncertainty are generated from causal beliefs in a way that respects the norms of probability, and evidence that probability judgments based on causal beliefs are systematically in error. One purported source of bias is the ease of reasoning forward from cause to effect (predictive reasoning) versus backward from effect to cause (diagnostic reasoning). Using causal Bayes nets, we developed a normative formulation of how predictive and diagnostic probability judgments should vary with the strength of alternative causes, causal power, and prior probability. This model was tested through two experiments that elicited predictive and diagnostic judgments as well as judgments of the causal parameters for a variety of scenarios that were designed to differ in strength of alternatives. Model predictions fit the diagnostic judgments closely, but predictive judgments displayed systematic neglect of alternative causes, yielding a relatively poor fit. Three additional experiments provided more evidence of the neglect of alternative causes in predictive reasoning and ruled out pragmatic explanations. We conclude that people use causal structure to generate probability judgments in a sophisticated but not entirely veridical way.     

Culture and Causal Cognition

East Asian and American causal reasoning differs significantly. East Asians understand behavior in terms of complex interactions between dispositions of the person or other object and contextual factors, whereas Americans often view social behavior primarily as the direct unfolding of dispositions. These culturally differing causal theories seem to be rooted in more pervasive, culture-specific mentalities in East Asia and the West. The Western mentality is analytic, focusing attention on the object, categorizing it by reference to its attributes, and ascribing causality based on rules about it. The East Asian mentality is holistic, focusing attention on the field in which the object is located and ascribing causality by reference to the relationship between the object and the field.     

3~4岁儿童规则因果推理能力的训练研究

学前期是儿童多种推理能力产生和发展的重要时期。本研究(以64名3岁儿童为被试,采用Frye和Zelazo等所设计的“二进二出”装置,通过对3岁儿童的规则因果推理能力进行训练,从而探索儿童规则因果推理的内在机制。在本研究条件下,结果发现:1.年龄与训练的交互效应不显著,各年龄组儿童经过训练后,成绩的提高没有显著差异;2.规则与训练的交互效应显著,竖直规则下,儿童通过训练后提高的成绩不显著,但在交叉规则下前测后测成绩差异极其显著;3.训练效应显著,暴露因果机制,给予及时反馈和阐述规则时附加手势这些信息能促进年幼儿童对高级规则的掌握。     

'DEMONSTRATIVE' COLOUR CONCEPTS: RECOGNITION VERSUS PRESERVATION

Arguments for and against the existence of demonstrative concepts of shades and shapes turn on the assumption that demonstrative concepts must be recognitional capacities. The standard argument for this assumption is based on the widely held view that concepts are those constituents of propositional attitudes that account for an attitude's inferential potential. Only if demonstrative concepts of shades are recognitional capacities, the standard argument goes, can they account for the inferential potential of demonstrative judgements about shades. Shades are conceived as colour universals. Shade a is different from shade b iff it is possible to distinguish a from b visually. In this paper I will argue that the standard argument is based on a mistaken view of inference. We can correctly draw inferences from a demonstrative judgement about something x , even if we are not able to recognise or re-identify the previously demonstrated x during our reasoning. We are prima facie entitled to rely on our preservative memory as retaining our initial demonstrative apprehension of x . The fact that preservative memory entitles us to assume sameness of referent over time is linguistically manifest in the use of anaphoric pronouns: if we can no longer recognise and demonstrate our original demonstratum, we can use anaphoric expressions to pick it up, thereby ensuring sameness of reference. ('That is a nice bird. Now it has vanished. So there is a nice bird that has just vanished.') Since preservation of the initial episode of apprehending x grounds our reasoning from demonstrative judgements, there is no longer a reason to require demonstrative concepts to be recognitional capacities. The standard argument does not get off the ground. ¹     

Causal essentialism in kinds

The current study examines causal essentialism, derived from psychological essentialism of concepts. We examine whether people believe that members of a category share some underlying essence that is both necessary and sufficient for category membership and that also causes surface features. The main claim is that causal essentialism is restricted to categories that correspond to our intuitive notions of existing kinds and hence is more attenuated for categories that are based on arbitrary criteria. Experiments 1 and 3 found that people overtly endorse causal essences in nonarbitrary kinds but are less likely to do so for arbitrary categories. Experiments 2 and 4 found that people were more willing to generalize a member's known causal relations (or lack thereof) when dealing with a kind than when dealing with an arbitrary category. These differences between kinds and arbitrary categories were found across various domains—not only for categories of living things, but also for artefacts. These findings have certain real-world implications, including how people make sense of mental disorders that are treated as real kinds.     

特征相似性、类别标签与因果关系在归纳推理中的作用

采用人工材料,比较类别标签、特征相似性与因果关系对归纳推理强度的影响。包括两个实验,实验1比较类别标签与特征相似性对归纳推理的影响,结果表明,当类别标签对归纳推理的影响显著强于特征相似性时,不能将类别标签等同于一个相似性特征。实验2进一步探讨类别标签与因果关系对归纳推理的作用,结果表明,因果关系作用明显强于类别标签的作用。综合两个实验的结果并整合前人相关研究,提出了不同关系影响归纳推理的强度假想。