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. (shrink)

Discussions on the impact and future directions of technology often proceed from an empirical point of view that seems to presume that the ebb and flow of technological developments is beyond the control of humankind, so that all that humanity can do is adjust to it. However, such an approach easily neglects several crucial normative considerations that could enhance the standing of individual human beings and whole communities as rational users of technology rather than its slaves. Besides, more often than (...) not, technological products are designed in ways that neglect the needs of persons with disabilities, thereby perpetuating their exclusion from society. Consequently, this article proposes four normative considerations to guide the initiatives of African societies in their deployment of the technologies of the Fourth Industrial Revolution, namely, inclusiveness to meet the needs of all human beings, affordability to bridge the digital divide, respect for cultural identity to guard against cultural imperialism, and an ethical orientation as the overarching guide to building a truly human society. (shrink)

Semantic Indexicality shows how a simple syntax can be combined with a propositional language at the level of logical analysis. It is the adoption of such a base language which has not been attempted before, and it is this which constitutes the originality of the book. Cresswell's simple and direct style makes this book accessible to a wider audience than the somewhat specialized subject matter might initially suggest.

We consider the desirability, or otherwise, of various forms of induction in the light of certain principles and inductive methods within predicate uncertain reasoning. Our general conclusion is that there remain conflicts within the area whose resolution will require a deeper understanding of the fundamental relationship between individuals and properties.

Over a longer period than I sometimes care to contemplate I have worked on possible-worlds semantics. The earliest work was in modal logic, to which I keep returning, but a sabbatical in 1970 took me to UCLA, there to discover the work of Richard Montague in applying possible-worlds semantics to natural lan guage. My own version of this appeared in Cresswell (1973) and was followed up in a number of articles, most of which were collected in Cresswell (1985b). A central (...) problem for possible worlds semantics is how to accommodate propositional attitudes. This problem was addressed in Cresswell (1985a), and the three books mentioned so far represent a reasonably complete picture of my positive views on formal semantics. I have regarded the presentation of a positive view as more important than the criticism of alternatives, although the works referred to do contain many passages in which I have tried to defend my own views against those of others. But such criticism is important in that a crucial element in establishing the content of a theory is that we be able to evaluate it in relation to its com petitors. It is for that reason that I have collected in this volume a number of articles in which I attempt to defend the positive semantical picture I favour against objections and competing theories. (shrink)

The paper introduces a first-order theory in the language of predicate tense logic which contains a single simple axiom. It is shewn that this theory enables times to be referred to and sentences involving ‘now’ and ‘then’ to be formalised. The paper then compares this way of increasing the expressive capacity of predicate tense logic with other mechanisms, and indicates how to generalise the results to other modal and tense systems.

In celebrating Arthur Prior we celebrate what he gave to the world. Much of this is measured by what others have made of his ideas after his death. The focus of this paper is a little different. It looks at what Prior himself thought he was accomplishing. In particular it considers Prior’s attitude to the semantic metatheory of the logics that he was interested in. The paper sets out some characteristics of the metalogical study of intensional languages in terms of (...) an indexical theory of truth conditions stated in the language of set theory. In examining Prior’s work using these characteristics, it emerges that Prior had serious reservations about this way of studying modal and tense logics. (shrink)

Throughout his life, John Tyler Bonner contributed to major transformations in the fields of developmental and evolutionary biology. He pondered the evolution of complexity and the significance of randomness in evolution, and was instrumental in the formation of evolutionary developmental biology. His contributions were vast, ranging from highly technical scientific articles to numerous books written for a broad audience. This historical vignette gathers reflections by several prominent researchers on the greatness of John Bonner and the implications of his work.

In this note we sketch a decision procedure for S3.51 based on reduction to conjunctive normal form. Using the following theorem of S3.5: and its dual for M over a conjunction, any formula can be reduced by standard methods (as in S52) to a conjunction of disjunctions of the form where Í is (p ⊃ p), 0 is ∼(p ⊃ p) and α — λ are all PC-wffs (i.e. they contain no modal operators).

‘Candida avis’ is usually assumed to be the white stork . T. E. Page, the Loeb editors and others give a footnote to this effect. T. F. Royds in The Beasts, Birds and Bees of Virgil says of ‘Candida avis’: ‘This is by common consent ‘Ciconia alba’, the white stork. It is a migrant in Mediterranean countries…a most useful bird feeding chiefly on snakes and other reptiles’ He then cites Pliny and Juvenal ‘serpente ciconia pullos nutrit’ to confirm the snake-eating (...) propensities of the stork. Virgil's ornithological mystery is not, however, quite so easily resolved. There is another contender for ‘Candida avis’, one more convincing both on a textual and an ornithological basis — Circaetus gallicus, the short-toed eagle. The short-toed eagle is the only European snake eagle, its diet being almost exclusively snakes. Lizards, and much less frequently small mammals or birds, may also be taken. (shrink)