Algebras of Intervals and a Logic of Conditional Assertions

Intervals in boolean algebras enter into the study of conditional assertions (or events) in two ways: directly, either from intuitive arguments or from Goodman, Nguyen and Walker's representation theorem, as suitable mathematical entities to bear conditional probabilities, or indirectly, via a representation theorem for the family of algebras associated with de Finetti's three-valued logic of conditional assertions/events. Further representation theorems forge a connection with rough sets. The representation theorems and an equivalent of the boolean prime ideal theorem yield an algebraic completeness theorem for the three-valued logic. This in turn leads to a Henkin-style completeness theorem. Adequacy with respect to a family of Kripke models for de Finetti's logic, ukasiewicz's three-valued logic and Priest's Logic of Paradox is demonstrated. The extension to first-order yields a short proof of adequacy for Körner's logic of inexact predicates.     

On Modal μ-Calculus and Non-Well-Founded Set Theory

A finitary characterization for non-well-founded sets with finite transitive closure is established in terms of a greatest fixpoint formula of the modal -calculus. This generalizes the standard result in the literature where a finitary modal characterization is provided only for wellfounded sets with finite transitive closure. The proof relies on the concept of automaton, leading then to new interlinks between automata theory and non-well-founded sets.     

The Suspended Aesthetic: Slavoj Žižek on Eastern European Film

Slavoj iek's writings on Krzysztof Kies´lowski and Andrej Tarkovskij represent direct challenges to the Central and Eastern European tradition of spiritual art and to dominant aesthetic concepts as such. He refuses to separate the solemn films of Kies´lowski and Tarkovskij from popular culture and stresses their import as ethical statements by their directors. Despite this ethical emphasis, iek makes an important contribution to philosophical aesthetics. He implicitly defines art as a suspension of reality which reveals time in its fragility and potentiality. Defining iek's aesthetics in terms of suspension helps to explain his partiality for Kies´lowski and Tarkovskij and bears comparison to the Russian tradition of philosophical aesthetics, in particular Aleksej Losev and Alexander Bakshy.     

Free Łukasiewicz and Hoop Residuation Algebras

Hoop residuation algebras are the {, 1}-subreducts of hoops; they include Hilbert algebras and the {, 1}-reducts of MV-algebras (also known as Wajsberg algebras). The paper investigates the structure and cardinality of finitely generated free algebras in varieties of k-potent hoop residuation algebras. The assumption of k-potency guarantees local finiteness of the varieties considered. It is shown that the free algebra on n generators in any of these varieties can be represented as a union of n subalgebras, each of which is a copy of the {, 1}-reduct of the same finite MV-algebra, i.e., of the same finite product of linearly ordered (simple) algebras. The cardinality of the product can be determined in principle, and an inclusion-exclusion type argument yields the cardinality of the free algebra. The methods are illustrated by applying them to various cases, both known (varieties generated by a finite linearly ordered Hilbert algebra) and new (residuation reducts of MV-algebras and of hoops).     

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.     

Bocheński and Balance: System and History in Analytic Philosophy

Using the work of Józef Bocheski as apositive example, this paper sets out the casefor a balanced use of historical knowledge indoing analytic philosophy. Between the twoextremes of relativizing historicism, whichdenies absolute truth, and arrogant scientism,which denies any constructive role for thehistory of ideas in philosophy, lies a viamedia in which historical reflection onconcepts and their history is placed at theservice of the system of cognitive philosophy.Knowledge of the history of philosophy, whilenot a sine qua non, can empower analyticphilosophy to push forward to new and moresatisfactory solutions to old and new problems.Examples are adduced from Bocheski's oeuvreand from the author's own experience.     

Function word repetitions emerge when speakers are operantly conditioned to reduce frequency of silent pauses

Beattie and Bradbury (1979) reported a study in which, in one condition, they punished speakers when they produced silent pauses (by lighting a light they were supposed to keep switched off). They found speakers were able to reduce silent pauses and that this was not achieved at the expense of reduced overall speech rate. They reported an unexpected increase in word repetition rate. A recent theory proposed by Howell, Au-Yeung, and Sackin (1999) predicts that the change in word repetition rate will occur on function, not content words. This hypothesis is tested and confirmed. The results are used to assess the theory and to consider practical applications of this conditioning procedure.     

Living with Contradictions: The Taken-for-Granted in Israeli Political Discourse

Two apparently contradictory ideas are closely linked in Israeli political discourse: Israel is powerful and independent and Israel is vulnerable and dependent. This study used content analysis and focus groups, as well as existing survey data analyzed by others, to explore how this paradox has been reflected in newspapers and conversations during six different time periods from 1948 to 1996. The goal was not to explain the paradox but to examine its consequences for Israeli perceptions of U.S. policy in the Middle East—and, in the process, to explore Israeli self-images. The nature of U.S. strategic interests was originally treated as problematic and in need of political discussion, but in the past 25 years these interests have become taken for granted. Surprisingly, even after the end of the Cold War, a critical discourse moment in which a reexamination of U.S. interests in the Middle East would seem inevitable, the U.S. role remains taken for granted and largely unexamined. The strong/vulnerable paradox explains this absence of discussion: Examining U.S. interests too closely upsets the delicate balance that keeps the sense of vulnerability in check.     

Betrayal And Paranoia: The Psychotherapist's Function as an Intermediary

We present an approach to the problem of structuring a therapeutic alliance with patients presenting paranoid symptoms, using both psychoanalytical and cognitive techniques. Initially, we focused on one of the main aspects of the paranoid worldview: the fear of being betrayed and the tendency to betray. This is a defense maneuver, through which patients deny their passivity, and the impotence in the relationship with their own internal needs and with the significant people in the external world, including the therapist. In our experience to build up a working relationship, both a psychoanalytical interpretation of unconscious conflicts and the cognitive analysis of dysfunctional beliefs are needed. Often, in more serious cases, the role of nonqualified object must be accepted at the beginning, due to the patient's need to be in control of the situation. Only then can a therapeutic phase begin, in most cases, through an integrated approach that includes pharmacological, psychodynamic, and cognitive modalities.     

The Prediction of Negative Events Associated with Anxiety and Dietary Restraint: A Test of the Content Specificity Hypothesis

The prediction of future negative events was studied in a sample of undergraduate students varying on measures of anxiety and dietary restraint. Cognitive theories of psychopathology hypothesize that the emotional concerns of an individual determine which types of information are most often cognitively processed with a biased interpretation. This prediction has generally been called the content specificity hypothesis. Based upon this aspect of cognitive theory, we hypothesized that a high level of trait anxiety would be associated with higher ratings of the probability of future physically threatening events. In addition, it was hypothesized that a high level of dietary restraint would be associated with lower ratings of the probability of future occurrences of overeating. The results of the study supported these hypotheses. These prediction biases were found to be more pronounced in women, as compared to men. The findings were interpreted as supportive of the content specificity hypothesis.