Peter Johnson

This paper describes a semantics for modal terms such as can and may that is intended to model the mental representation of their meaning. The basic assumption of the theory is that the evaluation of a modal assertion involves an attempted mental construction of a specified alternative to a given situation rather than the separate evaluation of each member of a set of possible alternatives as would be required by a “possible worlds” semantics. The theory leads to the conclusion that, contrary to what is often assumed, modal auxiliary verbs are unambiguous.

Quantified modal inferences interest logicians, linguists, and computer scientists, but no previous psychological study of them appears to be in the literature. Here is an example of one: All those artists are businessmen. Paulo is possibly one of the artists. What follows?People tend to conclude: Paulo is possibly a businessman (Experiment 1). It seems plausible, and it follows from an intuitive mental model in which Paulo is one of a set of artists who are businessmen. Further deliberation can yield a model of an alternative possibility in which Paulo is not one of the artists, which confirms that the conclusion is only a possibility. The snag is that standard modal logics, which deal with possibilities, cannot yield a particular conclusion to any premises: Infinitely many follow validly (from any premises) but they do not include the present conclusion. Yet, further experiments corroborated a new mental model theory's predictions for various inferences (Experiment 2), for the occurrence of factual conclusions drawn from premises about possibilities (Experiment 3) and for inferences from premises of modal syllogisms (Experiment 4). The theory is therefore plausible, but we explore the feasibility of a cognitive theory based on modifications to modal logic.

The argument of this article is that the Albert Memorial acted as a catalyst for some of Collingwood's most well known ideas in the philosophy of history and aesthetics. It was not, however, the exclusive source of those ideas, and indeed they had philosophical expression elsewhere. One may view his contemplations, then, as work in progress. For example, the logic of question and answer promoted by the Memorial was also prompted by Collingwood's reading of Bacon and Descartes. This was a reflection of his determination to depart from the realism of his philosophical teachers. Similarly, the Memorial directs Collingwood's thought forward. The Memorial acts as a facilitator of his thought on history, which in the course of its formulation undergoes many transformations. The logic of question and answer also finds a place in Collingwood's early thinking about art, but even here it is in the process of constant transition. Collingwood's reaction to the Memorial helps us to conclude that there is nothing ironic about the fact that Collingwood loathed the structure that was also the instigator of one of his most influential philosophical doctrines

The theory of mental models and its computer implementations have led to crucial experiments showing that no standard logic—the sentential calculus and all logics that include it—can underlie human reasoning. The theory replaces the logical concept of validity (the conclusion is true in all cases in which the premises are true) with necessity (conclusions describe no more than possibilities to which the premises refer). Many inferences are both necessary and valid. But experiments show that individuals make necessary inferences that are invalid, e.g., Few people ate steak or sole; therefore, few people ate steak. Other crucial experiments show that individuals reject inferences that are not necessary but valid, e.g., He had the anesthetic or felt pain, but not both; therefore, he had the anesthetic or felt pain, or both. Nothing in logic can justify the rejection of a valid inference: a denial of its conclusion is inconsistent with its premises, and inconsistencies yield valid inferences of any conclusions whatsoever including the one denied. So inconsistencies are catastrophic in logic. In contrast, the model theory treats all inferences as defeasible (nonmonotonic), and inconsistencies have the null model, which yields only the null model in conjunction with any other premises. So inconsistences are local. Which allows truth values in natural languages to be much richer than those that occur in the semantics of standard logics; and individuals verify assertions on the basis of both facts and possibilities that did not occur.

This book is an exploration of human understanding, from the perspectives of psychology, philosophy, biology and theology. The six contributors are among the most internationally eminent in their fields. Though scholarly, the writing is non-technical. No background in psychology, philosophy or theology is presumed. No other interdisciplinary work has undertaken to explore the nature of human understanding. This book is unique, and highly significant for anyone interested in or concerned about the human condition