Does the law of excluded middle require bivalence?

Determining whether the law of excluded middle requires bivalence depends upon whether we are talking about sentences or propositions. If we are talking about sentences, neither side has a decisive case. If we are talking of propositions, there is a strong argument on the side of those who say the excluded middle does require bivalence. I argue that all challenges to this argument can be met.     

Intuitionistic modal logics incompatible with the law of the excluded middle

In this paper, intuitionistic modal logics which do not admit the law of the excluded middle are studied. The main result is that there exista a continuum of such logics.     

A cut-free gentzen-type system for the logic of the weak law of excluded middle

The logic of the weak law of excluded middleKC _p is obtained by adding the formula A A as an axiom scheme to Heyting's intuitionistic logicH _p . A cut-free sequent calculus for this logic is given. As the consequences of the cut-elimination theorem, we get the decidability of the propositional part of this calculus, its separability, equality of the negationless fragments ofKC _p andH _p , interpolation theorems and so on. From the proof-theoretical point of view, the formulation presented in this paper makes clearer the relations betweenKC _p ,H _p , and the classical logic. In the end, an interpretation of classical propositional logic in the propositional part ofKC _p is given.     

Normalization and excluded middle. I

The usual rule used to obtain natural deduction formulations of classical logic from intuitionistic logic, namely is stronger then necessary, and will give classical logic when added to minimal logic. A rule which is precisely strong enough to give classical logic from intuitionistic logic, and which is thus exactly equivalent to the law of the excluded middle, is It is a special case of a version of Peirce's law: In this paper it is shown how to normalize logics defined using these last two rules. Part I deals with propositional logics and first order predicate logics. Part II will deal with first order arithmetic and second order logics. This research was supported in part by grants EQ1648, EQ2908, and CE 110 of the program Fonds pour la Formation de Chercheurs et l'aide à la Recherche (F.C.A.R.) of the Quèbec Ministry of Education.     

The principle of excluded middle in quantum logic

The principle of excluded middle is the logical interpretation of the law V A v in an orthocomplemented lattice and, hence, in the lattice of the subspaces of a Hilbert space which correspond to quantum mechanical propositions. We use the dialogic approach to logic in order to show that, in addition to the already established laws of effective quantum logic, the principle of excluded middle can also be founded. The dialogic approach is based on the very conditions under which propositions can be confirmed by measurements. From the fact that the principle of excluded middle can be confirmed for elementary propositions which are proved by quantum mechanical measurements, we conclude that this principle is inherited by all finite compound propositions. For this proof it is essential that, in the dialog-game about a connective, a finite confirmation strategy for the mutual commensurability of the subpropositions is used.     

Fate,Fiction and the Future

Abstract

Some fictions, it seems, represent the future as closed, in the sense that some future-tensed propositions are true in those fictions. Yet it is surprisingly difficult to accommodate this plausible thesis within an account of truth in fiction. A number of putative examples of closed fictional futures are discussed (Macbeth, Oedipus, Time and the Conways, The Time Machine) and the problems encountered in reconciling them with various accounts of truth in fiction (David Lewis', Gregory Currie's, Alex Byrne's) elaborated. Connections are drawn between metaphysical views on time and theories of fiction, and an attempt is made to show how the tenseless theory of time (roughly, the denial that time flows) can illuminate accounts of fictional truth, and in particular the issue of how there can be true beliefs about what will happen in a fiction.     

Changing the Past,Present, and Future

Abstract

There has recently been a growing movement within psychology toward placing a greater emphasis on the positive aspects of human nature. This movement, known as positive psychology, focuses on the scientific study of human strengths and virtues as well as the variables that promote positive traits, emotions, and institutions. The purpose of this article is to discuss selected topics of research in positive psychology and the potential psychotherapeutic application of this research for children and youth, particularly in school settings. Interventions are presented for altering and enhancing children's and adolescents' perspectives regarding their past, their experience of the present, and their hopes for the future.     

Prayer, Process, and the Future of Medicine

The wall of separation between spirituality and medicine is crumbling. Physicians are discovering the importance of prayer, spirituality, and religious participation in enhancing physical and mental health and responding to stressful life circumstances. A new metaphysical model is needed to replace the dualistic Cartesian-Newtonian model that has undergirded modern biomedicine. The process-relational metaphysics, influenced by the seminal thought of Alfred North Whitehead, is a fruitful alternative model for the future partnership of spirituality and medicine. A process-relational metaphysic supports this new partnership through its affirmation of (1) the relational nature of life, (2) the essential relatedness of mind, body, and spirit, (3) the multifactorial nature of causation in terms of health and illness, and (4) the affirmation of creativity and the redefinition of divine and human power in terms of partnership. This new metaphysical foundation provides a basis for including spiritual concerns in the care of patients, the education of physicians, and in professional self-care. Physicians are called to be partners with their patients, nurturing their own spiritual well-being even as they care for the spiritual well-being of their patients.     

Jungian Psychology, the Body, and the Future

Impressive reaffirmation of Jung's archetypal hypothesis has come from developments in behavioural biology (Tinbergen 1951; Cosmides 1985), psycholinguistics (Chomsky 1965), structural anthropology (Lévi-Strauss 1967), developmental psychology (Bowlby 1969), dream research (Jouvet 1975). neuroscience (MacLean 1976), sociobiology (Wilson 1978), and evolutionary psychiatry (Gardner 1988; Gilbert 1989). A close correspondence exists between Jungian theories of dreaming in human beings and modern biological theories of dreaming in animals. A paradigm shift is under way in the direction of a growing cross-disciplinary awareness that all human sciences are about archetypal manifestations and that these apply as much to the body as to the mind. Jungian psychology must keep abreast of these developments if it is not to be sidelined and superseded by less humane therapeutic philosophies.     

Choice, experience, and the generalized matching law

Five pigeons were exposed to different pairs of concurrent variable-interval, variable-interval schedules on nine experimental conditions of 30 sessions each. For every session, the parameters of the generalized matching equation were computed for the first five, six, seven, eight, and nine experimental conditions. The exponent a, both for response and time distribution, tended to decrease with increases in number of experimental conditions and to increase with number of sessions per condition, but values of k (bias) varied unsystematically. When the subjects were exposed to five new pairs of schedules, with 55 sessions per condition, the findings were confirmed. Data from the literature on the generalized matching law suggest that the variability of exponent values may be explained in part by the use of naive or experienced subjects in different investigations and by the variability in number of experimental conditions and in number of sessions per condition.