Mental representation of logical connectives

Logical connectives, such as “AND”, “OR”, “IF . . . THEN”, and “IF AND ONLY IF” are ubiquitous in both language and cognition; however, reasoning with logical connectives is error-prone. We argue that some of these errors may stem from people's tendency to minimize the number of possibilities compatible with logical connectives and to construct a “minimalist” one-possibility representation. As a result, connectives denoting a single possibility (e.g., conjunctions) are likely to be represented correctly, whereas connectives denoting multiple possibilities (e.g., disjunctions or conditionals) are likely to be erroneously represented as conjunctions. These predictions were tested and confirmed in three experiments using different paradigms. In Experiment 1, participants were presented with a multiple-choice task and asked to select all and only those possibilities that would indicate that compound verbal propositions were true versus false. In Experiment 2, a somewhat similar task was used, except that participants were asked later to perform a cued recall of verbal propositions. Finally, Experiment 3 used an old/new recognition paradigm to examine participants' ability to accurately recognize different logical connectives. The results of the three experiments are discussed in relation to theories of representation of possibilities and theories of reasoning.     

Binocular cues in the perception of distance of a point source of light

The ability to make egocentric distance estimates of a single point source of light, seen in darkness and without the cues of changing size and luminance, was investigated in sixteen observers. The attenuation required to maintain constant luminance, when the target was viewed from different distances, was shown to follow the inverse square law providing the angle subtended by the light was less than 20 s arc. Distance changes were also simulated by means of a split mirror which produced vergence cues, or by test lenses to provide accommodation cues. Over the range 0.5 to 9.2 m distance estimates were surprisingly accurate, although there was some overestimation of near and underestimation of far distances. Most observers made good judgements when only convergence cues were varied, whereas no observers made consistently good judgements when only accommodation cues were varied. The difficulties are discussed in terms of the accommodation-convergence link. When distance was simulated by changing convergence and accommodation cues, estimates were not as good as when real distance was changed. Since good estimates were made with brief target exposures, these judgements were not based on subsequent convergence or accommodation changes. It is suggested that the metric or reference against which the apparently absolute judgements were made was the efferent demand signal associated with a 'resting' position of convergence in darkness.