Logic of paradox revisited

Conclusion If, to return to the image with which I started this paper we consider the path of papers written on the logical paradoxes, then there is much to be learnt from the more recent additions, those by Chihara, Dowden and Woodruff included. However, the case for the paraconsistent approach to the paradoxes has not been weakened. In fact, it seems to me to have been strengthened. If we consider the path of papers, not as a signle line, but branching according to the approach to the paradoxes advocated, then the Logic of Paradox would, I still submit, be on the right track.     

Inconsistent Models of Arithmetic Part I: Finite Models

The paper concerns interpretations of the paraconsistent logic LP which model theories properly containing all the sentences of first order arithmetic. The paper demonstrates the existence of such models and provides a complete taxonomy of the finite ones.     

On a Paradox of Hilbert and Bernays

The paper is a discussion of a result of Hilbert and Bernays in their Grundlagen der Mathematik. Their interpretation of the result is similar to the standard intepretation of Tarskis Theorem. This and other interpretations are discussed and shown to be inadequate. Instead, it is argued, the result refutes certain versions of Meinongianism. In addition, it poses new problems for classical logic that are solved by dialetheism.     

Psychological Resources in Australasian Correctional Departments

The past and present delivery of psychological services to correctional departments in Australia and New Zealand was surveyed via questionnaires. Responses were received from six of the eight Australian jurisdictions surveyed and the one New Zealand department. Considerable variation in size and range of service was evident. Clinical work, particularly treatment, was the central activity in all cases. Recent developments, such as larger-scale treatment programs for special groups (e.g., sex offenders) and contributions to overall correctional management were repotted by some respondents. The restructuring of psychology sections in some departments had produced problems in relations between psychologists and their employing departments. Similarities in developments and issues in correctional psychology in the United States, England, and Wales were noted.     

To be and not to be: Dialectical tense logic

The paper concerns time, change and contradiction, and is in three parts. The first is an analysis of the problem of the instant of change. It is argued that some changes are such that at the instant of change the system is in both the prior and the posterior state. In particular there are some changes from p being true to p being true where a contradiction is realized. The second part of the paper specifies a formal logic which accommodates this possibility. It is a tense logic based on an underlying paraconsistent prepositional logic, the logic of paradox. (See the author's article of the same name Journal of Philosophical Logic 8 (1979).) Soundness and completeness are established, the latter by the canonical model construction, and extensions of the basic system briefly considered. The final part of the paper discusses Leibniz's principle of continuity: Whatever holds up to the limit holds at the limit. It argues that in the context of physical changes this is a very plausible principle. When it is built into the logic of the previous part, it allows a rigorous proof that change entails contradictions. Finally the relation of this to remarks on dialectics by Hegel and Engels is briefly discussed.     

Seeds of discontent: Expert opinion, mass media messages, and the public image of agricultural biotechnology

Survey data are presented on opinions about agricultural biotechnology and its applications held by agricultural science faculty at highly ranked programs in the United States with and without personal involvement in biotechnology-oriented research. Respondents believed biotech holds much promise, but policy positions vary. These results underscore the relationship between opinion and stakeholder interests in this research, even among scientific experts. Media accounts are often seen as causes, rather than artifacts, of the existence of public controversy; European and now U.S. opposition to food biotechnology is often explained away in terms of such a relationship. The authors argue that where even experts are divided, public opposition cannot reasonably be attributed to poor public understanding or sensationalistic media accounts. Ethical implications for communicating science are explored.     

On Alternative Geometries,Arithmetics, and Logics; a Tribute to Łukasiewicz

The paper discusses the similarity between geometry, arithmetic, and logic, specifically with respect to the question of whether applied theories of each may be revised. It argues that they can - even when the revised logic is a paraconsistent one, or the revised arithmetic is an inconsistent one. Indeed, in the case of logic, it argues that logic is not only revisable, but, during its history, it has been revised. The paper also discusses Quine's well known argument against the possibility of logical deviancy.     

Vasil'Év and Imaginary Logic

This paper is about the ‘Imaginary Logic’ developed by the Russian logician Nicholas Vasil'év between about 1910 and 1913, a logic that is often claimed to be a forerunner of different sorts of modern nonclassical logics. The paper describes the content of that logic (not by trying to interpret it in modern logic, as some commentators have done, but by describing it in its own terms). It then looks at the philosophical underpinnings of the logic. Finally, in the light of the preceding, it discusses Vasil‘év's place in the history of logic.