Studies of categorical induction typically examine how belief in a premise (e.g., Falcons have an ulnar artery) projects on to a conclusion (e.g., Robins have an ulnar artery). We study induction in cases in which the premise is uncertain (e.g., There is an 80% chance that falcons have an ulnar artery). Jeffrey's rule is a normative model for updating beliefs in the face of uncertain evidence. In three studies we tested the descriptive validity of Jeffrey's rule and a related probability (...) theorem, the rule of total probability. Although these rules provided good approximations to mean judgments in some cases, the results from regression and correlation analyses suggest that participants focus on the parts of these rules that are associated with the highest overall probability. We relate our findings to rational models of judgment. (shrink)
Dienes' & Perner's proposals are discussed in relation to the distinction between explicit and implicit systems of thinking. Evans and Over (1996) propose that explicit processing resources are required for hypothetical thinking, in which mental models of possible world states are constructed. Such thinking requires representations in which the individuals' propositional attitudes including relevant beliefs and goals are made fully explicit.
In his commentary, Oaksford makes two main claims: (1) that the externalisation method used by Green, Over, and Pyne (1997) enforces the correlation observed between probability estimates and selection, and (2) that these estimates support the prediction of a downward revision of P(p) when P(p) > P(q). In this reply, we rebut claim 1 by describing the instructions more comprehensively, and claim 2 by reiterating the importance of making certain theoretical distinctions which Oaksford does not make. Our interest is (...) the psychological process of reaching decision: externalisation methods provide a means of exploring this process and of assessing the value of Bayesian approaches. (shrink)
The new paradigm in the psychology of reasoning adopts a Bayesian, or prob- abilistic, model for studying human reasoning. Contrary to the traditional binary approach based on truth functional logic, with its binary values of truth and falsity, a third value that represents uncertainty can be introduced in the new paradigm. A variety of three-valued truth table systems are available in the formal literature, including one proposed by de Finetti. We examine the descriptive adequacy of these systems for natural language (...) indicative condi- tionals and bets on conditionals. Within our framework the so-called “defective” truth table, in which participants choose a third value when the antecedent of the indicative conditional is false, becomes a coherent response. We show that only de Finetti’s system has a good descriptive fit when uncer- tainty is the third value. (shrink)
A study is reported testing two hypotheses about a close parallel relation between indicative conditionals, if A then B , and conditional bets, I bet you that if A then B . The first is that both the indicative conditional and the conditional bet are related to the conditional probability, P(B|A). The second is that de Finetti's three-valued truth table has psychological reality for both types of conditional— true , false , or void for indicative conditionals and win , lose (...) , or void for conditional bets. The participants were presented with an array of chips in two different colours and two different shapes, and an indicative conditional or a conditional bet about a random chip. They had to make judgements in two conditions: either about the chances of making the indicative conditional true or false or about the chances of winning or losing the conditional bet. The observed distributions of responses in the two conditions were generally related to the conditional probability, supporting the first hypothesis. In addition, a majority of participants in further conditions chose the third option, “void”, when the antecedent of the conditional was false, supporting the second hypothesis. (shrink)
The two main psychological theories of the ordinary conditional were designed to account for inferences made from assumptions, but few premises in everyday life can be simply assumed true. Useful premises usually have a probability that is less than certainty. But what is the probability of the ordinary conditional and how is it determined? We argue that people use a two stage Ramsey test that we specify to make probability judgements about indicative conditionals in natural language, and we describe experiments (...) that support this conclusion. Our account can explain why most people give the conditional probability as the probability of the conditional, but also why some give the conjunctive probability. We discuss how our psychological work is related to the analysis of ordinary indicative conditionals in philosophical logic. (shrink)
We investigate how the perceived uncertainty of a conditional affects a person's choice of conclusion. We use a novel procedure to introduce uncertainty by manipulating the conditional probability of the consequent given the antecedent. In Experiment 1, we show first that subjects reduce their choice of valid conclusions when a conditional is followed by an additional premise that makes the major premise uncertain. In this we replicate Byrne. These subjects choose, instead, a qualified conclusion expressing uncertainty. If subjects are given (...) a third statement that qualifies the likelihood of the additional premise, then the uncertainty of the conclusions they choose is systematically related to the suggested uncertainty. Experiment 2 confirms these observations in problems that omit the additional premise and qualify the first premise directly. Experiment 3 shows that the qualifying statement also affects the perceived probability of the consequent given the antecedent of the conditional. Experiment 4 investigates the effect of suggested uncertainty on the fallacies and shows that increases in uncertainty reduce the number of certain conclusions that are chosen while affirming the consequent but have no effect on denying the antecedent. We discuss our results in terms of rule theories and mental models and conclude that the latter give the most natural account of our results. (shrink)
Four experiments investigated uncertainty about a premise in a deductive argument as a function of the expertise of the speaker and of the conversational context. The procedure mimicked everyday reasoning in that participants were not told that the premises were to be treated as certain. The results showed that the perceived likelihood of a conclusion was greater when the major or the minor premise was uttered by an expert rather than a novice (Experiment 1). The results also showed that uncertainty (...) about the conclusion was higher when the major premise was uttered by a novice and an alternative premise by an expert, compared to when the major premise was uttered by an expert and the alternative by a novice (Experiment 2). Similarly, the believability of a conclusion was considerably lower when the minor premise was uttered by a novice and denied by an expert, as opposed to when an expert uttered the minor premise and a novice denied it (Experiment 3). Experiment 4 showed that the nature of the uncertainty induced by a denial of the minor premise depended on whether or not the context was a conversation. These results pose difficult problems for current theories of reasoning, as current theories are based on the results of experiments in which the premises are treated as certain. Our discussion of the results emphasises the importance of pragmatics in reasoning, namely, the role of general knowledge about the world in assessing the probability of a premise uttered by an expert or a novice and the role of interpretations of the premise based on pragmatic inferences in revising these initial probabilities. (shrink)
Psychological research on people’s understanding of natural language connectives has traditionally used truth table tasks, in which participants evaluate the truth or falsity of a compound sentence given the truth or falsity of its components in the framework of propositional logic. One perplexing result concerned the indicative conditional if A then C which was often evaluated as true when A and C are true, false when A is true and C is false but irrelevant“ (devoid of value) when A is (...) false (whatever the value of C). This was called the “psychological defective table of the conditional.” Here we show that far from being anomalous the “defective” table pattern reveals a coherent semantics for the basic connectives of natural language in a trivalent framework. This was done by establishing participants’ truth tables for negation, conjunction, disjunction, conditional, and biconditional, when they were presented with statements that could be certainly true, certainly false, or neither. We review systems of three-valued tables from logic, linguistics, foundations of quantum mechanics, philosophical logic, and artificial intelligence, to see whether one of these systems adequately describes people’s interpretations of natural language connectives. We find that de Finetti’s (1936/1995) three-valued system is the best approximation to participants’ truth tables. (shrink)
M. Oaksford and N. Chater presented a Bayesian analysis of the Wason selection task in which they proposed that people choose cards in order to maximize expected information gain as measured by reduction in uncertainty in the Shannon-Weaver information theory sense. It is argued that the EIG measure is both psychologically implausible and normatively inadequate as a measure of epistemic utility. The article is also concerned with the descriptive account of findings in the selection task literature offered by Oaksford and (...) Chater. First, it is shown that their analysis data reported in the recent article of K. N. Kirby is unsound; second, an EIG analysis is presented of the experiments of P. Pollard and J. St. B. T. Evans that provides a strong empirical disconfirmation of the theory. (shrink)
Iterated conditionals of the form If p, then if q, r are an important topic in philosophical logic. In recent years, psychologists have gained much knowledge about how people understand simple conditionals, but there are virtually no published psychological studies of iterated conditionals. This paper presents experimental evidence from a study comparing the iterated form, If p, then if q, r with the “imported,” noniterated form, If p and q, then r, using a probability evaluation task and a truth-table task, (...) and taking into account qualitative individual differences. This allows us to critically contrast philosophical and psychological approaches that make diverging predictions regarding the interpretation of these forms. The results strongly support the probabilistic Adams conditional and the “new paradigm” that takes this conditional as a starting point. (shrink)
Two experiments using a realistic version of the selection task examined the relationship between participants' probability estimates of finding a counter example and their selections. Experiment 1 used everyday categories in the context of a scenario to determine whether or not the number of instances in a category affected the estimated probability of a counter-example. Experiment 2 modified the scenario in order to alter participants' estimates of finding a specific counter-example. Unlike Kirby 1994a, but consistent with his proposals, both studies (...) showed that probability estimates significantly predicted selection. Overall results point to the value of understanding selections in terms of their subjective expected utility. (shrink)
Oaksford & Chater (O&C) begin in the halfway Bayesian house of assuming that minor premises in conditional inferences are certain. We demonstrate that this assumption is a serious limitation. They additionally suggest that appealing to Jeffrey's rule could make their approach more general. We present evidence that this rule is not limited enough to account for actual probability judgements.
Barbey & Sloman (B&S) relegate the logical rule of the excluded middle to a footnote. But this logical rule is necessary for natural sampling. Making the rule explicit in a logical tree can make a problem easier to solve. Examples are given of uses of the rule that are non-constructive and not reducible to a domain-specific module.
Causal induction in the real world often has to be quick and efficient as well as accurate. We propose that people use two different frames to achieve these goals. The A-frame consists of heuristic processes that presuppose rarity and can detect causally relevant factors quickly. The B-frame consists of analytic processes that can be highly accurate in detecting actual causes. Our dual frame theory implies that several factors affect whether people use the A-frame or the B-frame in causal induction: among (...) these are symmetrical negation, intervention and commitment. This theory is tested and sustained in two experiments. The results also provide broad support for dual process accounts of human thinking in general. (shrink)
Carruthers’proposals would seem to implicate language in what is known as System 2 thinking (explicit) rather than System 1 thinking (implicit) in contemporary dual process theories of thinking and reasoning. We provide outline description of these theories and show that while Carruthers’characterization of non-verbal processes as domain-specific identifies one critical feature of System 1 thinking, he appears to overlook the fact that much cognition of this type results from domain-general learning processes. We also review cognitive psychological evidence that shows that (...) language and the explicit representations it supports are heavily involved in supporting System 1 thinking, but falls short of supporting his claim that it is the medium in which domain-general thinking occurs. (shrink)
David E. Over is a leading cognitive scientist and, with his firm grounding in philosophical logic, he also exerts a powerful influence on the psychology of reasoning. He is responsible for not only a large body of empirical work and accompanying theory, but for advancing a major shift in thinking about reasoning, commonly known as the ‘new paradigm’ in the psychology of human reasoning. -/- Over’s signature mix of philosophical logic and experimental psychology has inspired generations of (...) researchers, psychologists, and philosophers alike over more than a quarter of a century. The chapters in this volume, written by a leading group of contributors including a number who helped shape the psychology of reasoning as we know it today, each take their starting point from the key themes of Over’s ground-breaking work. The essays in this collection explore a wide range of central topics—such as rationality, bias, dual processes, and dual systems—as well as contemporary psychological and philosophical theories of conditionals. It concludes with an engaging new chapter, authored by David E. Over himself, which details and analyses the new paradigm psychology of reasoning. -/- This book is therefore important reading for scholars, researchers, and advanced students in psychology, philosophy, and the cognitive sciences, including those who are not familiar with Over’s thought already. (shrink)
'If' is one of the most important words in the English language, being used to express hypothetical thought. The use of conditional terms such as 'if' distinguishes human intelligence from that of all other animals. In this volume, Jonathan Evans and DavidOver present a new theoretical approach to understanding conditionals. The book draws on studies from the psychology of judgement and decision making, as well as philosophical logic.
lecting statistics about missing bindings and macros, and other errors. This guides debugging and development eﬀorts, leading to iterative improvements in both the tools and the quality of the converted corpus. The build system thus serves as both a production conversion engine and software test harness. We have now processed the complete arχiv collection through 2006 consisting of more than 400,000 documents (a complete run is a processor-yearsize undertaking), continuously improving our success rate. We are now able to convert more (...) than 90% of these documents to XHTML+MathML. We consider over 60% to be successes, converted with no or minor warnings. While the remaining 30% can also be converted, their quality is doubtful, due to unsupported macros or conversion errors. (shrink)
Partindo das figuras do sábio e do ignorante tal como aparecem na obra de Espinosa, busca-se situá-las, na estratégia de exposição de Espinosa, como modelos ou imagens cujo conceito remete à prática. Com isso, procura-se mostrar o lugar central ocupado pelos conceitos de regra de vida e emenda da vida na concepção espinosana de liberdade.
O artigo procura mostrar, com base no parágrafo 17 do Tratado da Emenda do Intelecto, a centralidade do conceito de vulgo para a interpretação da obra de Espinosa. Para tanto, discute-se a relação entre imagens e conceitos na teoria do conhecimento em Espinosa, bem como a relação entre linguagem e filosofia.
Assunto pouco estudado na obra de Espinosa, o trabalho ocupa centralidade em seu pensamento acerca do direito comum. Através do exame das ocorrências do trabalho nos dois tratados políticos, bem como da observância da correta tradução de _ opera mutua _, procura-se jogar nova luz sobre a história em Espinosa, em particular sobre a gênese do direito comum e sobre as ideias de justiça e injustiça nesse autor.