Theorema: Towards computer-aided mathematical theory exploration

Theorema is a project that aims at supporting the entire process of mathematical theory exploration within one coherent logic and software system. This survey paper illustrates the style of Theorema-supported mathematical theory exploration by a case study (the automated synthesis of an algorithm for the construction of Gröbner Bases) and gives an overview on some reasoners and organizational tools for theory exploration developed in the Theorema project.     

What do we want? Critical psychotherapy and counselling! When do we want it? Now,now, now! A critical review of a critical issue

This review offers a critical commentary on the contributions to this issue. It outlines four aspects to a critical approach and uses them to read horizontally across all five papers.     

Isolating the effects of active responding in computer-based instruction

This experiment evaluated the effects of requiring overt answer construction in computer-based programmed instruction using an alternating treatments design. Four college students worked through an instructional program that alternated between presenting frames with blanks requiring overt responses and complete frames without blanks. All students produced a higher percentage of correct posttest answers corresponding to program segments that required overt answer construction.     

Value for money?: Issues of fees in counselling and psychotherapy

Drawing on literature from different psychotherapeutic traditions, the meaning of money is reviewed, and the psychological and practical issues which arise from the setting, changing and payment of fees in counselling and psychotherapy are discussed. A person-centred approach is offered as a framework for the counsellor's understanding of fees in the therapeutic relationship.     

Stress, Glucocorticoids, and Damage to the Nervous System: The Current State of Confusion

An extensive literature demonstrates that glucocorticoids (GCs), the adrenal steroids secreted during stress, can have a broad range of deleterious effects in the brain. The actions occur predominately, but not exclusively, in the hippocampus, a structure rich in corticosteroid receptors and particularly sensitive to GCs. The first half of this review considers three types of GC effects: a) GC-induced atrophy, in which a few weeks' exposure to high GC concentrations or to stress causes reversible atrophy of dendritic processes in the hippocampus; b) GC neurotoxicity where, over the course of months, GC exposure kills hippocampal neurons; c) GC neuroendangerment, in which elevated GC concentrations at the time of a neurological insult such as a stroke or seizure impairs the ability of neurons to survive the insult. The second half considers the rather confusing literature as to the possible mechanisms underlying these deleterious GC actions. Five broad themes are discerned: a) that GCs induce a metabolic vulnerability in neurons due to inhibition of glucose uptake; b) that GCs exacerbate various steps in a damaging cascade of glutamate excess, calcium mobilization and oxygen radical generation. In a review a number of years ago, I concluded that these two components accounted for the deleterious GC effects. Specifically, the energetic vulnerability induced by GCs left neurons metabolically compromised, and less able to carry out the costly task of containing glutamate, calcium and oxygen radicals. More recent work has shown this conclusion to be simplistic, and GC actions are shown to probably involve at least three additional components: c) that GCs impair a variety of neuronal defenses against neurologic insults; d) that GCs disrupt the mobilization of neurotrophins; e) that GCs have a variety of electrophysiological effects which can damage neurons. The relevance of each of those mechanisms to GC-induced atrophy, neurotoxicity and neuroendangerment is considered, as are the likely interactions among them.     

Computer-programmed instruction: The relation of required interaction to practical application

Computers were used to evaluate the effects of supplying answers to programmed instruction frames. A group experimental design compared passive reading, covert responding to frame blanks, and actively typing answers to blanks with and without immediate confirmation of correctness. Effects of a 315-frame program, teaching elements of programmed instruction design, were evaluated by analyzing answers to posttest generalization questions and an application test. Results strongly supported the effectiveness of requiring the student to supply fragments of a terminal repertoire while working through a program. Students who could either covertly respond to frame blanks or who were required to type frame answers performed significantly better on the frame generalization posttest and, more importantly, carefully followed program rules when preparing elements of a new instructional program.     

Psychological Factors Associated with Emotional Responses to Receiving Genetic Risk Information

This study identified levels of distress, and predictors of levels of distress, in women undergoing assessment for genetic risk of breast/ovarian cancer based on their family history. It comprised a cohort study following 154 women who completed questionnaires at entry into a cancer genetic assessment programme and following risk provision. Independent significant associates of anxiety following risk provision were age, neuroticism, feeling hopeless about developing cancer, a perceived lack of control over developing cancer, lack of a social confidant, and a coping response involving acceptance/resignation. Depression was associated with age, neuroticism, feeling hopeless about developing cancer, lack of social confidant, and a coping response involving acceptance/resignation. To avoid high levels of psychological morbidity in future cohorts undergoing cancer genetic risk assessment, information should be given that emphasises that some degree of control over health outcomes through behaviour change or increased surveillance is possible.     

Discovering knowability: a semantic analysis

In this paper, we provide a semantic analysis of the well-known knowability paradox stemming from the Church–Fitch observation that the meaningful knowability principle all truths are knowable, when expressed as a bi-modal principle ${\diamondsuit}$ , yields an unacceptable omniscience property all truths are known. We offer an alternative semantic proof of this fact independent of the Church–Fitch argument. This shows that the knowability paradox is not intrinsically related to the Church–Fitch proof, nor to the Moore sentence upon which it relies, but rather to the knowability principle itself. Further, we show that, from a verifiability perspective, the knowability principle fails in the classical logic setting because it is missing the explicit incorporation of a hidden assumption of stability: ‘the proposition in question does not change from true to false in the process of discovery.’ Once stability is taken into account, the resulting stable knowability principle and its nuanced versions more accurately represent verification-based knowability and do not yield omniscience.