Diodorean modality in Minkowski spacetime

The Diodorean interpretation of modality reads the operator as it is now and always will be the case that. In this paper time is modelled by the four-dimensional Minkowskian geometry that forms the basis of Einstein's special theory of relativity, with event y coming after event x just in case a signal can be sent from x to y at a speed at most that of the speed of light (so that y is in the causal future of x).It is shown that the modal sentences valid in this structure are precisely the theorems of the well-known logic S4.2, and that this system axiomatises the logics of two and three dimensional spacetimes as well.Requiring signals to travel slower than light makes no difference to what is valid under the Diodorean interpretation. However if the is now part is deleted, so that the temporal ordering becomes irreflexive, then there are sentences that distinguish two and three dimensions, and sentences that can be falsified by approaching the future at the speed of light, but not otherwise.     

Interpolation and definability in abstract logics

A semantical definition of abstract logics is given. It is shown that the Craig interpolation property implies the Beth definability property, and that the Souslin-Kleene interpolation property implies the weak Beth definability property. An example is given, showing that Beth does not imply Souslin-Kleene.     

The curious case of spacetime emergence

Philosophical Studies - Work in quantum gravity suggests that spacetime is not fundamental. Rather, spacetime emerges from an underlying, non-spatiotemporal reality. After clarifying the type of...     

Deduction and definability in infinite statistical systems

Synthese - Classical accounts of intertheoretic reduction involve two pieces: first, the new terms of the higher-level theory must be definable from the terms of the lower-level theory, and second,...     

Correction to: Deduction and definability in infinite statistical systems

Synthese - Prop. 1 on p. 10 is false as stated. The proof implicitly assumes that all Cauchy sequences.     

The challenge of becoming an integrative counsellor: The trainee's perspective

Aim: Integrative therapeutic practice is commonplace within the UK. Counsellors and psychotherapists increasingly report working in this way and numerous training courses have developed which advocate such practice. Despite its popularity, researchers have paid little attention to the impact that such training has upon students. This study therefore explores newly qualified counsellors' reflections of undertaking professional training in integrative counselling. Design: Newly qualified counsellors were invited to take part in a focus group to discuss their training experiences. Two groups were held involving a total of seven people. The data generated was analysed using Grounded Theory. Findings: The core-category ‘The challenge of becoming an integrative counsellor’ was identified. Embedded within this were four sub-categories: (1) ‘training issues’, (2) ‘applied issues’, (3) ‘the development of an integrative theory and identity’, and (4) ‘the impact of integrative training post qualification’. Key findings include the willingness of trainees to tolerate theoretical ambiguity and the discomfort that surrounded not belonging to a pure paradigm community. Discussion: Recommendations are made that trainers and practice supervisors are mindful of the distinct struggles that integrative trainees encounter. Additionally, in response to the isolation that some trainees report, greater use of peer support networks is encouraged.     

The psychoanalyst: On becoming more human than otherwise

Classical psychoanalytic technique, which called for the role of the analyst to be a scientific observer, removed from interaction with the patient, imposed such restrictions on the analyst that often his or her simple human responsiveness to the patient was curtailed. Harry Stack Sullivan revolutionized the field by introducing the concept of “participant observation,” and others of his time made similar observations. Gradually, over the years, analysts have become more real, more human, and more interactive with their patients. Contrary to classical opinion, this departure from the original technique does not interfere with analytic work, and, in fact, enhances it, if the analyst monitors and analyzes the reactions of patients to this more human engagement. Examples are provided to support this conclusion. Murray Krim is a supervising analyst at the William Alanson White Institute, Adjunct Associate Clinical Professor of Psychology in the Postdoctoral Program at Adelphi University, and supervisor at the Institute for Contemporary Psychotherapy.     

Enduring and Perduring Objects in Minkowski Space-Time

I examine the issue of persistence over time in thecontext of the special theory of relativity (SR). Thefour-dimensional ontology of perduring objects isclearly favored by SR. But it is a different questionif and to what extent this ontology is required, andthe rival endurantist ontology ruled out, by thistheory. In addressing this question, I take theessential idea of endurantism, that objects are whollypresent at single moments of time, and argue that itcommits one to unacceptable conclusions regardingcoexistence, in the context of SR. I then propose anddiscuss a plausible account of coexistence forperduring objects, which is free of these defects. This leaves the endurantist room for some maneuvers. I consider them and show that they do not really helpthe endurantist out. She can accommodate the notionof coexistence in the relativistic framework only atthe cost of renouncing central endurantist intuitions.