P. C. Wason

On the failure to eliminate hypotheses in a conceptual task

This investigation examines the extent to which intelligent young adults seek (i) confirming evidence alone (enumerative induction) or (ii) confirming and discontinuing evidence (eliminative induction), in order to draw conclusions in a simple conceptual task. The experiment is designed so that use of confirming evidence alone will almost certainly lead to erroneous conclusions because (i) the correct concept is entailed by many more obvious ones, and (ii) the universe of possible instances (numbers) is infinite. Six out of 29 subjects reached the correct conclusion without previous incorrect ones, 13 reached one incorrect conclusion, nine reached two or more incorrect conclusions, and one reached no conclusion. The results showed that those subjects, who reached two or more incorrect conclusions, were unable, or unwilling to test their hypotheses. The implications are discussed in relation to scientific thinking.

Reasoning about a rule

Two experiments were carried out to investigate the difficulty of making the contra-positive inference from conditional sentences of the form, “if P then Q.” This inference, that not-P follows from not-Q, requires the transformation of the information presented in the conditional sentence. It is suggested that the difficulty is due to a mental set for expecting a relation of truth, correspondence, or match to hold between sentences and states of affairs. The elicitation of the inference was not facilitated by attempting to induce two kinds of therapy designed to break this set. It is argued that the subjects did not give evidence of having acquired the characteristics of Piagets “formal operational thought.”

NATURAL AND CONTRIVED EXPERIENCE IN A REASONING PROBLEM

This study is concerned with the effects of prior experience on a deceptive reasoning problem. In the first experiment the subjects (students) were presented with the problem after they had experienced its logical structure. This experience was, on the whole, ineffective in allowing subsequent insight to be gained into the problem. In the second experiment the problem was presented in “thematic” form to one group, and in abstract form to the other group. Ten out of 16 subjects solved it in the thematic group, as opposed to 2 out of 16 in the abstract group. Three hypotheses are proposed to account for this result.

The contexts of plausible denial

Summary Two hypotheses were tested about the contexts which facilitate response to negative statements. The same series of stimuli, each stimulus consisting of seven similar items and one dissimilar item, was described by two independent groups in differing terms. The dependent variable was the time taken to complete a statement presented immediately after each stimulus had been described. When the stimuli are described in terms of an exceptional item and a residual class, the response to negative statements is facilitated, if these statements deny that the exceptional item possesses the property of the residual class. On the other hand, when the stimuli are described in terms of a smaller and a larger class, no facilitation of response to the corresponding negative statements is observed. It is hypothesized that the determining factor in these results is the way in which the negated property is coded in the descriptions of the stimuli.

A theoretical analysis of insight into a reasoning task

Abstract An information-processing analysis of insight into a singularly deceptive and difficult deductive problem is presented. Two models are described. The first represents an economical explanation of the Ss initial responses but is difficult to reconcile with their subsequent responses induced by certain remedial procedures. The second model does take account of such responses and shows how insight into the correct solution is correlated with the awareness that tests for falsification are more appropriate than tests for verification. The relevance of the experimental results and the explanatory model are discussed in relation to wider issues.

Dual processes in reasoning

Abstract Previous results have shown that the introduction of negatives into the sentences used in a deductive problem affected behavior in a systematic way which was independent of the logical structure of the problem. In the present investigation, the subjects were asked to justify their responses when reasoning about such sentences. In accordance with previous results, the responses were dominated by the terms in the sentences regardless of whether they were negated. However, the justifications did vary when negatives were introduced in accordance with the logical consequences of the responses. The interpretation of these justifications as causes of behavior seemed implausible. It was suggested that they were rationalizations, or that there was at least some form of dual processing between behavior and conscious thought.

The processing of positive and negative information

An affirmative statement which is known to be false and the complementary negative statement which is known to be true, provide the same information, i.e. that something is not the case. Similarly, an affirmative statement which is known to be true and the complementary negative statement which is known to be false, both imply that something is the case. (If P is false, not-P is true and if P is true, not-P is false.) Hence there are four kinds of statement (“conditions”): true affirmatives, false affirmatives, true negativee and false negatives, but only two kinds of information: positive and negative. This experiment investigates the times taken to process information presented in these ways. The task was to select two alternative words which would make affirmative or negative conjunctive statements agree or conflict with given situations. The four conditions were presented six times in different serial orders, so that each occurred once in every block of four trials. The mean response times were: true affirmatives 8–99 sec, false affirmatives 11 19 sec., true negatives 12–58 sec, false negatives 15–17 sec. This order was the same at each of the six presentations of the conditions, the differences being significant at the 0 001 level in each case. There was a pronounced decline in errors (without knowledge of results) for three of the conditions. These results are discussed in relation to (i) the assumption of a positive set, established through a long learning process; (ii) the inferential nature of negative information in relation to experience; and (iii) the possible emotional effects of negative terms.

Insight into a logical relation

Two experiments are reported which aimed to investigate factors affecting the gain of insight into the logical relation of implication. In the first experiment, subjects had to make a series of inferences about either a conditional sentence or a quantified sentence, both of which had the same underlying logical form. Under one condition the sentences had to be proved true, and under another condition, false. Proving a sentence false facilitated gain of insight, but the linguistic form of the sentence exerted no significant effect on the main dependent variable. In the second experiment, implication was not expressed as a sentence but was inherent in the structure of the task. The experimental material differed in complexity and allowed the cognitive load imposed on the subject to be varied. Results suggested that insight was not all-or-none. It was spontaneously gained when the material was simple, but temporarily lost when it was complex.

Reasoning and mental representation

Four experiments exploring the effects of the coherence of a mental representation of material on reasoning performance are presented. Each employs a simple task that allows most subjects at some stage to solve the problem. We postulate that the crucial factor influencing performance is a unified representation of the material. In Experiment 1 we use an authorization of a kind familiar in daily life, and in Experiments 2, 3 and 4 we use sentences describing simple objects in different ways. In each case performance was enhanced when the material could be given a unified representation.

THOG: The anatomy of a problem

SummaryThree experiments are reported on the attempts to solve a novel hypothetico-deductive problem. Its solution demands both the postulation of hypotheses about its structure and a combinatorial analysis upon the consequences of these hypotheses. The majority of subjects (students) failed to solve the problem because they argued from the properties of stimuli rather than from hypotheses about their conceptual status. The results suggest that a familiarity with the logical structure of the problem and the elicitation of appropriate hypotheses failed to correct this intuitive approach. These findings are discussed in relation to Piagets theory of formal operations, and (very tentatively) in relation to habitual styles of thought.