Online research in philosophy

We report the results of three experiments designed to assess the role of suppositions in human reasoning. Theories of reasoning based on formal rules propose that the ability to make suppositions is central to deductive reasoning. Our first experiment compared two types of problem that could be solved by a suppositional strategy. Our results showed no difference in difficulty between problems requiring affirmative or negative suppositions and very low logical solution rates throughout. Further analysis of the error data showed a pattern of responses, which suggested that participants reason from a superficial representation of the premises in these arguments and this drives their choice of conclusion. Our second experiment employed a different set of suppositional problems but with extremely similar proofs in terms of the rules applied and number of inferential steps required. As predicted by our interpretation of reasoning strategies employed in Experiment 1, logical performance was very much higher on these problems. Our third experiment showed that problems that could be solved by constructing an initial representation of the premises were easier than problems in which this representation was not sufficient. This effect was independent of the suppositional structure of the problems. We discuss the implications of this research for theories of reasoning based on mental models and inference rules.

This article reports on a study of children's deductive reasoning in solving novel relational problems. Detailed protocols were obtained from 264 children (aged 9- 12 years) who verbalised their thinking as they solved the problems. The study included the development of a three-phase theory based on Johnson-Laird and Byrne's mental models perspective, but with some distinct modifications. These include a focus on the relational complexity entailed in model construction and in premise integration, and the advancement of four reasoning principles that are applied throughout problem solution (in contrast to Johnson-Laird's falsification processes as the hallmark of deductive reasoning). The reported case studies and the results of statistical analyses supported predictions arising from the proposed theory, including the key role of the reasoning principles. The results also showed that problem difficulty is a function of relational complexity, not of the number of models to be constructed, as argued by Johnson-Laird and Byrne.

Relatively little is known about those who consistently produce the valid response to Modus Tollens (MT) problems. In two studies, people who responded correctly to MT problems indicated how “convinced” they were by proofs of conditional reasoning conclusions. The first experiment showed that MT competent reasoners found accurate proofs of MT reasoning more convincing than similar “proofs” of invalid reasoning. Similarly, there was a tendency for MT competent reasoners to find an initial counterfactual supposition more convincing than did people who were less competent in MT. The second experiment showed that when individuals produced the correct MT response, and found correct MT proofs to be more convincing than “bogus” proofs, they were also less likely to find the conclusions to Denying the Antecedent, or Affirming the Consequent problems valid, compared to individuals who could not discriminate between valid and bogus MT proofs. These findings are discussed in terms of both their implications for the mental logic and mental models positions, and individual differences in System 1 and System 2 reasoning.

In this paper, I examine an account of instrumental reasoning recently put forth by John Broome. His key suggestion is that anyone who engages in reasoning about his intentions also believes that he will do what he intends to do and that combined with a belief about necessary means this creates rational pressure towards believing that one will take the necessary means. I argue that Broome’s model has three significant problems; his key premise is false—the sincere expression of an intention does not entail the belief that one will successfully execute that intention; his account yields a model of instrumental reasoning that is uncomfortably reflective; he seems unable to explain the rational pressure towards taking necessary means that arises directly from having an end and an instrumental belief. All three problems, I argue, are a consequence of Broome’s inadequate position on what it is to intend to do something.

This paper reports four experiments investigating whether model construction of linear reasoning problems is open to strategic decisions. A reversed choice/nochoice paradigm was used in which reasoners first had to apply two model construction strategies (acronym and rehearsal strategy) to two problem sets. Next, they could choose freely among the two strategies to apply to a new problem set. Experiment 1 showed that reasoners selected the strategy that they experienced as the most accurate one in the no-choice phase. Moreover, in Experiment 2, it was found that reasoners adapted their strategy choice to changing problem features, to use the most suitable strategy for premise encoding. Experiments 3 and 4 generalised these findings to more complex linear reasoning problems with a mixed sentence frame and a semi-continuous presentation of the premises, and to two-model problems. On the basis of these results, we argue that strategic decisions influence model construction in linear reasoning.

Mental model theory has been used to explain many differing phenomena in adult reasoning, including the extensively studied case of conditional reasoning. However, the current theory makes predictions about the development of conditional reasoning that are not consistent with data. In this article, young children's performance on conditional reasoning problems and the justifications given are analysed. A mental model account of conditional reasoning is proposed that assumes that (1) young children can reason with two models and (2) the fleshing out of conditionals involves activation of information in semantic memory that uses the minor premise as a retrieval cue.

Two experiments investigated the mental representation of spatial and nonspatial two-dimensional problems. The experiments were designed to contrast opposite predictions of the model theory of reasoning and the formal rules of inference theories. Half of the problems required more inferential steps but only one model, whereas the other half required fewer inferential steps but two models. According to the inference rules, theory problems that require more inferential steps should be harder, whereas the model-based theory predicts that problems that require two models should be harder. In Experiments 1a and 1b we measured the problem solving time and the percentage of errors. In Experiments 2a and 2b the problems were presented segmented in two different displays. We measured the comprehension time for each display, the question answering times, and the percentage of errors. The results of all experiments supported the model theory predictions in both spatial and nonspatial domains.

Johnson-Laird (1983) has argued that spatial reasoning is based on the construction and manipulation of mental models in memory. The present article addresses the question of whether reasoning about time relations is constrained by the same factors as reasoning about spatial relations. An experiment is reported that explored the similarities and the differences in the performance of subjects in comparable spatial and temporal reasoning tasks. The results indicated that, in both the temporal and the spatial content domains, the data were in agreement with the view that subjects solved problems by constructing models in memory rather than with a logical rule conceptualisation of reasoning. An analysis of the premise-reading times on the basis of premise-linking order provided support for an on-line process of mental models construction, and offered an explanation for the finding that spatial problems that did require an inference of transitivity were easier than problems that did not. No essential differences in processing and performance were observed across the two content domains, although in the time domain the correctness data were in agreement with both the mental models theory and the logical rules view. The results are discussed with respect to the mental models theory and the structural characteristics of the problems.

According to the mental models theory, reasoning performance is primarily influenced by the number of models of a problem that can be constructed. This study investigates whether the content of the model may also influence performance. Linear reasoning problems were devised that either described a believable (script-consistent) or an unbelievable (script-inconsistent) order of actions. The results of two experiments showed that conclusions were inferred more slowly and less accurately on the basis of an unbelievable model than on a believable one. Experiment 2 revealed that script knowledge facilitated as well as impeded reasoning performance. Conclusion evaluation was faster and more accurately for script-consistent problems than for neutral problems, whereas model construction and conclusion evaluation occurred respectively more slowly and less accurately for script-inconsistent problems than for neutral problems. These results show that the content of the model is a noteworthy factor influencing reasoning performance.

This paper reports three studies of temporal reasoning. A problem of the following sort, where the letters denote common everyday events: A happens before B. C happens before B. D happens while B. E happens while C. What is the relation between D and EEfficacylls for at least two alternative models to be constructed in order to give the right answer for the right reason (D happens after E). However, the first premise is irrelevant to this answer, and so if reasoners were to ignore it, then they would need to construct only one model. Experiment 1 showed that one-model problems were answered faster and more accurately than multiple-model problems. When the question preceded the premises in the statement of the multiple-model problems there was a slight tendency for the latencies of response to speed up in the predicted way. Experiment 2 modified the procedure, in part by using practice problems with many irrelevant premises, so that reasoners might grasp the advantage of ignoring them. Its results showed that when the premises preceded the question, the multiple-model problems were significantly harder than one-model problems. But when the question was presented first, the difference was significantly reduced in line with the theory's prediction. Experiment 3 used only problems with valid conclusions (i.e., one-model problems and multiple-model problems), and so the construction of multiple models was never necessary. However, there was still a significant difference between one-model problems and multiple-model problems.