Peter Johnson

This paper describes Peirce's systems of logic diagrams, focusing on the so-called ''existential'' graphs, which are equivalent to the first-order predicate calculus. It analyses their implications for the nature of mental representations, particularly mental models with which they have many characteristics in common. The graphs are intended to be iconic, i.e., to have a structure analogous to the structure of what they represent. They have emergent logical consequences and a single graph can capture all the different ways in which a possibility can occur. Mental models share these properties. But, as the graphs show, certain aspects of propositions cannot be represented in an iconic or visualisable way. They include negation, and the representation of possibilities qua possibilities, which both require representations that do not depend on a perceptual modality. Peirce took his graphs to reveal the fundamental operations of reasoning, and the paper concludes with an analysis of different hypotheses about these operations.

This paper outlines a theory and computer implementation of causal meanings and reasoning. The meanings depend on possibilities, and there are four weak causal relations: A causes B, A prevents B, A allows B, and A allows not‐B, and two stronger relations of cause and prevention. Thus, A causes B corresponds to three possibilities: A and B, not‐A and B, and not‐A and not‐B, with the temporal constraint that B does not precede A; and the stronger relation conveys only the first and last of these possibilities. Individuals represent these relations in mental models of what is true in the various possibilities. The theory predicts a number of phenomena, and, contrary to many accounts, it implies that the meaning of causation is not probabilistic, differs from the meaning of enabling conditions, and does not depend on causal powers or mechanisms. The theory also implies that causal deductions do not depend on schemas or rules.

Two experiments were carried out to investigate the role of referential continuity in understanding discourse. In experiment 1, a group of university students listened to stories and descriptive passages presented in three different versions: the original passages, versions in which the sentences occured in a random order, and randomised versions in which referential continuity had been restored primarily by replacing pronouns and other terms with fuller and more appropriate noun phrases. The original stories were remembered better, and rated as more comprehensible, than the random versions, but the restoration of referential continuity ameliorated the effects of randomisation. The descriptive passages had little referential continuity from one sentence to the next, and as expected the effects of randomisation on comprehensibility and memory were negligible. In experiment 2, a group of skilled comprehenders and a group of less skilled comprehenders were selected from a population of 7–8-year-old children. The difference between the groups was known to be largely their inferential ability in reading texts. Both groups read a series of short stories presented in the same three versions as used in the previous experiment. As predicted, the ameliorating effects on memory of restoring referential continuity in a randomised story were confined to the skilled group. The results are discussed in relation to the theories of story grammar, text microstructure, and mental models of discourse.