A successive-conditionalization approach to disjunctive and syllogistic reasoning

With p and q each standing for a familiar event, a disjunctive statement, “either p or q”, seems quite different from its material conditional, “if not p then q”. The notions of sufficiency and necessity seem specific to conditional statements. It is surprising, however, to find that perceived sufficiency and necessity affect disjunctive reasoning in the way they affect conditional reasoning. With B and C each standing for a category name, a universal statement, “all B are C”, seems stronger than its logically equivalent conditional statement, “if B then C”. However, the effects of perceived sufficiency or necessity were found to be as pronounced in conditional reasoning as in syllogistic reasoning. Furthermore, two experiments also showed that (a) MP (modus ponens)-comparable disjunctive reasoning was as difficult as MT (modus tollens)-comparable disjunctive reasoning, and that (b) MT-comparable syllogisms were easier to solve than MT problems in conditional reasoning.     

A factor-analytic study of reasoning abilities

A battery of 32 tests was administered to a sample including 144 Air Force Officer Candidates and 139 Air Cadets. The factor analysis, using Thurstone's complete centroid method and Zimmerman's graphic method of orthogonal rotations, revealed 12 interpretable factors. The non-reasoning factors were interpreted asverbal comprehension, numerical facility, perceptual speed, visualization, andspatial orientation. The factors derived from reasoning tests were identified asgeneral reasoning, logical reasoning, education of perceptual relations, education of conceptual relations, education of conceptual patterns, education of correlates, andsymbol substitution. The logical-reasoning factor corresponds to what has been called deduction, but eduction of correlates is perhaps closer to an ability actually to make deductions. The area called induction appears to resolve into three eduction-of-relations factors. Reasoning factors do not appear always to transcend the type of test material used.Under Contract N6onr-23810 with the Office of Naval Research. The views expressed here are not nesessarily shared by the Office of Naval Research. These studies are under the general direction of J. P. Guilford. P. R. Christensen is assistant director. A. L. Comrey was in direct charge of this study during its early stages and R. F. Green during most of its progress.     

A factorial study of the reasoning and closure factors

A battery of 46 tests was given to 237 college men. A factor analysis using the Thurstone technique revealed eight clearly interpretable first-order factors, one dubious factor, and a residual factor. The factors were interpreted as induction, deduction, flexibility of closure, speed of closure, space, verbal comprehension, word fluency, and number. Four second-order factors were abstracted from the matrix of first-order correlations. The presence of induction, deduction, and flexibility of closure on the first second-order factor, interpreted as an analytic factor, confirmed previous indications of relationships between the reasoning and closure factors. A second bipolar factor is interpreted as a speed of association factor. The third factor is interpreted as facility in handling meaningful verbal materials—perhaps an ability to do abstract thinking. The fourth factor is possibly a second-order closure factor—perhaps an ability to do concrete thinking.The author is grateful to Professor L. L. Thurstone for his encouragement and invaluable advice and for permission to use many tests originally prepared in the Psychometric Laboratory of the University of Chicago, to Mr. James Degan for assistance in rotations, and to the Social Science Research Committee of the University of Chicago for a grant to this study.     

Age and probabilistic reasoning: Biases in conjunctive,disjunctive and Bayesian judgements in early and late adulthood

Probabilistic reasoning plays an essential part in many aspects of our daily routine and it has been argued that as we grow older, the need to make judgements under uncertainty becomes increasingly important. Two studies were conducted to establish whether the propensity to commit probabilistic reasoning errors increased with age. Young (aged 16–24), middle aged (25–54), and older persons (55 years and above) were included. Study 1 revealed systematic biases and errors across a range of judgement tasks. However, no evidence of any age effect in Bayesian inference, the incidence of the conjunction fallacy, or in the number of disjunction errors was found. The results obtained in Study 1 were replicated in Study 2, where the potential mediating role of working memory processes and intellectual capacity were explicitly assessed. While some aspects of probabilistic reasoning performance were correlated with measures of intelligence and working memory functioning among young adults, this was much less evident in older persons. The present findings are discussed in relation to the evolution of the dualistic heuristic–analytical system over the adult lifespan. Copyright © 2005 John Wiley & Sons, Ltd.     

A cross-cultural study of hindsight bias and conditional probabilistic reasoning

Hindsight bias is a mistaken belief that one could have predicted a given outcome once the outcome is known. Choi and Nisbett (2000 Choi, I. and Nisbett, R. E. 2000. Cultural psychology of surprise: Holistic theories and recognition of contradiction. Journal of Personality and Social Psychology, 79: 890–905. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) reported that Koreans showed stronger hindsight bias than Americans, and explained the results using the distinction between analytic cognition (Westerners) and holistic cognition (Easterners). The purpose of the present study was to see whether hindsight bias is stronger among Easterners than among Westerners using a probability judgement task, and to test an “explicit–implicit” hypothesis and a “rule-dialectics” hypothesis. We predicted that the implicit process is more active among Easterners to generate hindsight bias, and that Easterners are more dialectical thinkers, whereas Westerners are more rule-based thinkers. French, British, Japanese, and Korean participants were asked to make probabilistic judgements in a Good Samaritan scenario (Experiment 1) and in a scenario including conditional probabilistic judgement (Experiment 2). In both Experiments, we presume that the implicit revision of causal models is made just by being given unexpected outcome information, and that explicit revision is made by being asked to point out possible factors for an unexpected outcome. In the results Easterners showed greater hindsight bias generally and it was greater in the Good Samaritan scenario. We conclude that the reason why hindsight bias was lower among Westerners is primarily that they tried to follow a rule to suppress the bias.     

Individual differences and reasoning: A study on personality traits

Personality can play a crucial role in how people reason and decide. Identifying individual differences related to how we actively gather information and use evidence could lead to a better comprehension and predictability of human reasoning. Recent findings have shown that some personality traits are related to similar decision‐making patterns showed by people with mental disorders. We performed research with the aim to investigate delusion‐proneness, obsessive‐like personality, anxiety (trait and state), and reasoning styles in individuals from the general population. We introduced personality trait and state anxiety scores in a regression model to explore specific associations with: (1) amount of data‐gathered prior to making a decision; and (2) the use of confirmatory and disconfirmatory evidence. Results showed that all our independent variables were positively or negatively associated with the amount of data collected in order to make simple probabilistic decisions. Anxiety and obsessiveness were the only predictors of the weight attributed to evidence in favour or against a hypothesis. Findings were discussed in relation to theoretical assumptions, predictions, and clinical implications. Personality traits can predict peculiar ways to reason and decide that, in turn, could be involved to some extent in the formation and/or maintenance of psychological disorders.     

Necessity, possibility and belief: A study of syllogistic reasoning

The present study extended the investigation of the belief bias effect in syllogistic reasoning in two ways: (1) The effect was studied under instructions to decide whether conclusions were possible, as well as necessary, given the premises; and (2) the effect was studied for types of syllogism where people rarely endorse the conclusions as well as those (valid and fallacious) where endorsements are common. Three experiments are reported, which show first that there is a marked tendency to reject unbelievable conclusions relative to abstract or neutral controls on all kinds of syllogism and under both types of instruction. There was also significant evidence of positive belief bias (increased acceptance of believable conclusions) and of interactions between belief bias effects and logical form. The results are discussed with particular respect to accounts of belief bias offered by theorists in the mental-model tradition.     

The modulation of disjunctive assertions

The theory of mental models postulates that disjunctions of the sort, A or B, where A and B are sensible everyday clauses, have a core meaning that allows an inclusive interpretation, referring to three possibilities: A and not-B, not-A and B, and A and B. The meaning of the clauses and knowledge can modulate this meaning by blocking the construction of at least one model of a possibility—for example, “Rui is playing tennis or he is surfing” blocks the model of Rui doing both activities. This theory is implemented in a computer program. Three experiments investigated the core interpretation and interpretations in which the contents of the clauses should block the model of A and B (as in the preceding example), the model of A and not-B, or the model of not-A and B. In Experiment 1, the participants listed the possibilities for each of the four sorts of disjunction. The results corroborated the predicted modulations. In Experiment 2, these predicted interpretations governed the conclusions that participants accepted from disjunctions and categorical premises. In Experiment 3, the predicted interpretations yielded reliable effects on the conclusions that the participants drew for themselves. We relate these results to theories of reasoning.     

The consistency of disjunctive assertions

In two experiments, we established a new phenomenon in reasoning from disjunctions of the grammatical form either A or else B, where A and B are clauses. When individuals have to assess whether pairs of assertions can be true at the same time, they tend to focus on the truth of each clause of an exclusive disjunction (and ignore the concurrent falsity of the other clause). Hence, they succumb to illusions of consistency and of inconsistency with pairs consisting of a disjunction and a conjunction (Experiment 1), and with simpler problems consisting of pairs of disjunctions, such as eIther there is a pie or else there is a cake and Either there isn't a pie or else there is a cake (Experiment 2), that appear to be consistent with one another, but in fact are not. These results corroborate the theory that reasoning depends on envisaging models of possibilities.     

In defense of the disjunctive

Are there any disjunctive properties—features of things such as being either red or round, or Nelson Goodman’s infamous example of being grue (i.e. either green if observed on or before 2500 A.D. or blue otherwise)? As esoteric as the question may seem at first, central issues about the metaphysics of properties hinge upon its answer, such as whether reductive views about special science properties can handle the phenomenon of multiple realizability. A familiar argument for a negative answer is that disjunctive properties fail to guarantee that their instances are similar in some genuine respect. In this paper, I respond to a novel, sophisticated version of this argument developed in recent work by Paul Audi. Along the way, I develop two new accounts of what it is for a property to be disjunctive—which rely on important recent work on the nature of essence and analysis—and clarify what one is committed to in believing that there are any disjunctive properties at all.     

A three-factor model of syllogistic reasoning: The study of isolable stages

Computer models of the syllogistic reasoning process are constructed. The models are used to determine the influence of three factors—the misinterpretation of the premises, the limited capacity of working memory, and the operation of the deductive strategy—on subjects’ behavior. Evidence from Experiments 1, 2, and 3 suggests that all three factors play important roles in the production of errors when “possibly true” and “necessarily false” are the two response categories. This conclusion does not agree with earlier analyses that had singled out one particular factor as crucial. Evidence from Experiment 4 suggests that the influence of the first two factors remains strong when “necessarily true” is used as an additional response category. However, the third factor appears to interact with task demands. Some concluding analyses suggest that the models offer alternative explanations for certain well established results.     

Strength theories of disjunctive visual detection

Zero, 1, 2, or 3 black dots are tachistoscopically presented on a white field. There are two alternative tasks: (a) to decide on the presence of each of the left, middle, and right dots (multiple detection) or (b) to decide whether any of the dots was present (disjunctive detection), The results indicate that in disjunctive detection, Ss do not add together thestrengths of the three dot positions and compare this sum to a criterion. Rather they combine theirdecisions about each dot, responding “yes” to the array, if and only if they decide “yes” to any one dot. Strength distributions appear to be invariant with respect to irrelevant stimuli. Invariance with respect to report order holds approximately. However, dots reported on first are slightly more detectable. This suggests a successive scanning process, whose rate is independent of whether a stimulus is present or absent at the position scanned.     

Majority and minority influence in inductive reasoning: A preliminary study

Ninety-three students were exposed to majority and minority influence in an inductive reasoning task. The former induced convergent thinking processes, though its effects were not reducible to mere compliance. The latter activated more divergent constructive processes, supporting the predictions of Conversion Theory.     

A hullian reasoning situation

An experiment on a well-known but little-investigated situation proposed by Hull, is reported. The results are inconclusive.     

A logical expression of reasoning

A non-monotonic logic, the Logic of Plausible Reasoning (LPR), capable of coping with the demands of what we call complex reasoning, is introduced. It is argued that creative complex reasoning is the way of reasoning required in many instances of scientific thought, professional practice and common life decision taking. For managing the simultaneous consideration of multiple scenarios inherent in these activities, two new modalities, weak and strong plausibility, are introduced as part of the Logic of Plausible Deduction (LPD), a deductive logic specially designed to serve as the monotonic support for LPR. Axiomatics and semantics for LPD, together with a completeness proof, are provided. Once LPD has been given, LPR may be defined via a concept of extension over LPD. Although the construction of LPR extensions is first presented in standard style, for the sake of comparison with existing non-monotonic formalisms, alternative more elegant and intuitive ways for constructing non-monotonic LPR extensions are also given and proofs of their equivalence are presented.