Creative reasoning in formal discussion

Systems of formal dialectics articulate methods of conflict resolution. To this end they provide norms to regulate verbal exchanges between the Proponent of a thesis and an Opponent. These regulated exchanges constitute what are known as formal discussions.One may ask what moves, if any, in formal discusions correspond to arguing for or against the thesis. It is claimed that certain moves of the Proponent's are properly designated as arguing for the thesis, and that certain moves of the Opponent purport to criticize the tenability or the relevance of the reasons advanced. Thus the usefulness of formal dialectic systems as models for reasonable argument is vindicated.It is then proposed to make these systems more realistic by incorporating in them a norm of Creative Reasoning that removes the severe restrictions to which the Proponent's arguing was hitherto subject. As a consequence, a certain type of irrelevant reason is no longer automatically excluded. Therefore, it is proposed to extend the Opponent's rights to exert relevance criticism. The new dialectic systems are shown to be strategically equivalent to the original ones. Finally, it is stressed that the Opponent's criticism should not be designated as arguing against the thesis. The Opponent criticizes, but does not argue.     

The four-card problem and the generality of formal reasoning

Three experiments were designed to investigate the failure of intelligent adults to solve an apparently simple problem of formal reasoning devised by Wason. Both the mode of presentation and the type of material reduced the difficulty of the problem, while retaining its essential form. However, success on the original problem remained at a low level, even when subjects had attempted an easier version and had been given an explanation.

These results enable one to reject a “strong” formulation of Piaget's theory of formal reasoning. A “weaker” formulation is suggested as a basis for further research.     

Developmental and content effects in reasoning with causal conditionals

Two predictions derived from Markovits and Barrouillet's (2001) developmental model of conditional reasoning were tested in a study in which 72 twelve-year-olds, 80 fifteen-year-olds, and 104 adults received a paper-and-pencil test of conditional reasoning with causal premises ("if cause P then effect Q"). First, we predicted that conditional premises would induce more correct uncertainty responses to the Affirmation of the consequent and Denial of the antecedent forms when the antecedent term is weakly associated to the consequent than when the two are strongly associated and that this effect would decrease with age. Second, uncertainty responding to the Denial of the antecedent form ("P is not true") should be easier when the formulation of the minor premise invites retrieval of alternate antecedents ("if something other than P is true"). The results were consistent with the hypotheses and indicate the importance of retrieval processes in understanding developmental patterns in conditional reasoning with familiar premises.     

The belief-bias effect in formal reasoning: The influence of knowledge on logic

The present study examines the applicability of a rational model of categorical inference (e.g., Revlis, 1975b) to account for the apparently irrational decisions students reach on categorical syllogisms. In Experiment 1, students judged the logical validity of emotionally neutral conclusions to controversial premises. Of the reasoners’ decisions, 80% can be accounted for by the application of rational rules to their idiosyncratic encoding of the syllogistic premises. In Experiment 2, students were asked to solve syllogisms whose conclusions varied in truth value. When asked to reason about controversial, if not emotional, material, students do not suspend rational choice, but rather, their decisions are judicious ones, flowing logically from their idiosyncratic understanding of the materials reasoned about. When errors do occur, they result from an interrupt to rational processes and reflect conflict between competing goals rather than a switch to irrational decision processes.     

The adolescent personality, formal reasoning, and values

This study examined the relationship between levels of Piagetian formal reasoning ability and values preferences derived from the Rokeach Value Survey. The subjects were 448 secondary school students (mean age = 16.25 years). The results of the study were consistent with predictions about the likely changes in value rankings as formal reasoning ability develops. Subjects with high scores on formal reasoning ranked terminal values representing abstract notions with long-term implications higher than those focusing on immediate gratification. They also favored the instrumental values of self-reliance, competence, and independence. Low scorers on formal reasoning showed a preference for value groupings which were personal, hedonistic, and involved immediate gratification and social approval.     

Conditional reasoning with a spatial content requires visuo-spatial working memory

In previous research, Toms, Morris, and Ward (1993) have shown that conditional reasoning is impaired by a concurrent task calling on executive functions but not by concurrent tasks that load on the slave systems of the working memory system as conceptualised by Baddeley and Hitch (1974). The present article replicates and extends this previous work by studying problems based on spatial as well as nonspatial relations. In the study 42 participants solved 16 types of spatial or nonspatial problems, both in a single-task condition and under concurrent matrix tapping, a task loading the visuo-spatial sketch pad. The findings were consistent with those of Toms et al. (1993) for problems with a nonspatial content. However, when the content was spatial, and only then, a dual-task impairment was observed: processing time of the first premise was lengthened, especially for problems with negations in the antecedent term, the consequent term, or both; moreover, the number of correctly solved problems with negations in both terms was smaller. The implications of these findings for the mental models theory and the mental logic theory are discussed.     

The importance of gesture in children's spatial reasoning

On average, men outperform women on mental rotation tasks. Even boys as young as 4 1/2 perform better than girls on simplified spatial transformation tasks. The goal of our study was to explore ways of improving 5-year-olds' performance on a spatial transformation task and to examine the strategies children use to solve this task. We found that boys performed better than girls before training and that both boys and girls improved with training, whether they were given explicit instruction or just practice. Regardless of training condition, the more children gestured about moving the pieces when asked to explain how they solved the spatial transformation task, the better they performed on the task, with boys gesturing about movement significantly more (and performing better) than girls. Gesture thus provides useful information about children's spatial strategies, raising the possibility that gesture training may be particularly effective in improving children's mental rotation skills.     

Sequential modulations of correspondence effects across spatial dimensions and tasks

In two experiments, we explored sequential modulations of correspondence effects in a prime-target paradigm. In Experiment 1, the participants responded to the direction of target arrows that were preceded by prime arrows with a corresponding or noncorresponding direction. This produced a prime-target correspondence effect that was reduced when the preceding trial contained a noncorresponding prime-target event. This sequential modulation of the correspondence effect was observed even when neither stimuli nor responses were repeated from one trial to the next, ruling out explanations of sequential modulations in terms of stimulus or response repetitions. Experiment 2 combined the prime-target correspondence effect with a Simon-type correspondence effect. Both effects were reduced following noncorrespondence of the same type and, to a lesser extent, following noncorrespondence of the other type. Altogether, these results suggest that part of the sequential modulation of correspondence effects reflects an adaptation to a preceding response conflict independently of the peripheral stimulus events that produced this conflict.     

Reference frame effects on shape perception in two versus three dimensions

Three experiments are reported in which it is tested whether the Gestalt effect of configural orientation on shape perception operates on two-dimensional (2-D) or three-dimensional (3-D) representations of space. It is known that gravitationally defined squares and diamonds take longer to discriminate in diagonal arrays than in horizontal or vertical arrays. In the first experiment it is shown that this interference effect decreases dramatically in magnitude when pictorial depth information is added so that subjects perceive the target shapes in different depth planes. In the second experiment this difference is shown not to be due to relative size of the target shapes or to occlusion of a background plane. It is also shown, in the final experiment, that this difference is not due to linear perspective information or merely to perception of the target figures in a 3-D scene. The overall pattern of results supports the position that this configural reference frame effect arises primarily when the elements of the configuration are coplanar, and that the principal organization underlying it is the structure of the perceived 3-D environment rather than that of the 2-D image. In all three experiments, however, there is also a small interference effect in the noncoplanar 3-D conditions. This might be due either to some aspect of reference frame selection operating on the 2-D image representation or to the failure of subjects to see depth in the 3-D stimuli on some proportion of the trials.     

The effects of presentation and content on syllogistic reasoning by children with and without specific language impairment

This study examines performance at a syllogistic reasoning task for a group of children (age 10 years) with specific language impairment (SLI) along with age- and language-matched controls. The syllogisms were presented either verbally or verbally/pictorially, and contained two types of item: imaginary versus real, both intended not to evoke strong beliefs. Children with SLI performed worse than age-matched controls, and equivalently to language-matched controls. Patterns of performance indicate this may be due to cognitive ability deficits rather than specific language deficits. For all groups, pictorial presentation interfered with reasoning processes. It is suggested that, for syllogisms, this pictorial information contextualises the interpretation of the task, and that in turn either raises working memory load or evokes belief bias. Additionally, these results suggest that caution should be exhibited before using visual aids to help children with SLI in the classroom.     

The effects of spatial frequency and temporal waveform on three measures of temporal processing

The effects of spatial frequency and temporal transition of sine-wave grating onset and offset were assessed using measures of reaction time, visual persistence, and temporal order judgements. The stimuli were lateralized fields, separated by 1 degree of visual angle. Slow temporal transition resulted in significantly poorer performance than did abrupt onset and offset, but spatial frequency had a minimal effect. Thus, the latency, temporal resolution, and temporal ordering of events are mediated by a mechanism that is sensitive to abrupt temporal transients. The stimulus conditions employed did not result in a shift in the point of subjective simultaneity.     

Structure mapping in spatial reasoning

Four experiments examined whether spatial reasoning about non-spatial concepts is based on mapping concepts to space according to similarities in relational structure. Six- and 7-year-old children without any prior graphing experience were asked to reason with graph-like diagrams. In Experiments 1 and 2, children were taught to map time and quantity to vertical and horizontal lines, and then were asked to judge the relative value of a second-order variable (rate) or a first-order variable (quantity) represented in a function line. Children’s judgments indicated that they mapped concepts to space by aligning similar relational structures: quantity judgments corresponded to line height, and rate judgments corresponded to line slope. These correspondences entail a mapping of first-order concepts to first-order spatial dimensions and second-order concepts to second-order spatial dimensions. Experiments 3 and 4 investigated the role of context in establishing relational structure. Children were taught to map age and rate (Experiment 3) or age and size (Experiment 4) to vertical and horizontal lines, and were then asked to judge the rate or the size represented by a function line. In this context, both rate and size were first-order variables, and children’s judgments corresponded to line height, also a first-order variable. The results indicate that spatial reasoning involves a structure-sensitive mapping between concepts and space.     

Four-dimensional spatial reasoning in humans

Human subjects practiced navigation in a virtual, computer-generated maze that contained 4 spatial dimensions rather than the usual 3. The subjects were able to learn the spatial geometry of the 4-dimensional maze as measured by their ability to perform path integration, a standard test of spatial ability. They were able to travel down a winding corridor to its end and then point back accurately toward the occluded origin. One interpretation is that the brain substrate for spatial navigation is not a built-in map of the 3-dimensional world. Instead it may be better described as a set of general rules for manipulating spatial information that can be applied with practice to a diversity of spatial frameworks.     

The effects of externalization on syllogistic reasoning

An experiment is reported that investigated the effects of externalization of mental models in syllogistic reasoning. Although there was no evidence that the requirement to “externalize” mental models of syllogisms improved reasoning, an unexpected recognition test demonstrated that subjects' memory for the meaning of the premises was improved by externalization. In particular, where the correct conclusion had been deduced using the externalization procedure, responses in the recognition test reflected an appreciation of the relations between the end terms of the premises.     

The content and processes of autobiographical reasoning in narrative identity

Building on research that focuses on individual differences in the narration of important life events, this study examined the content of self-event connections and thematic coherence in relation to the processes of autobiographical reasoning. Autobiographical reasoning was defined as making connections between the past and the self, the effort reported in making those connections and the emotional evaluation of the connections. Personality differences at the levels of traits and ego development were examined in relation to autobiographical reasoning. One hundred and nineteen younger and older adults completed a self-defining memory interview. Self-event connections reported in the interviews were coded as being about dispositions, values, outlook, and personal growth. Connections were then coded for the degree of cognitive effort required to make the connection and the emotional evaluation of the connection. Finally, the entire interview was coded for the presence or absence of a theme. Results showed that cognitive effort and evaluation differed across type of connection, and ego development and traits moderated some of these results. Further, across connections, there were individual differences in cognitive effort and evaluation, as well as in the reports of a themes across memories. Results are discussed in terms of individual differences in the construction of narrative identity.