Purpose – The purpose of this study is to improve our understanding of bracketing, one of the most central philosophical and theoretical constructs of phenomenology, as a theory of mind. Furthermore, we wanted to showcase how this theoretical construct can be implemented as a methodological tool. -/- Design/methodology/approach – In this study we have adopted an approach similar to a qualitative metasynthesis, comparing the emergent patterns of two empirical projects, seeking synergies and contradictions and looking for additional insights from (...) new emerging patterns. -/- Findings – On a philosophical level, we have found that bracketing, as a theoretical construct, is not about the achievement of objectivity; quite to the contrary, it embraces subjectivity and puts it centre-stage. On a theoretical level, we have achieved a better understanding of Husserl’s phenomenology, as a theory of mind. On a methodological level, we have achieved a powerful way of supplementing and/or clarifying research findings, by using a theoretical construct as a methodological tool. -/- Originality/value – Our paper contributes to the phenomenology literature at a philosophical, theoretical and methodological level, by offering a better understanding and a novel implementation of one of the central theoretical constructs of phenomenology. (shrink)

In this paper we describe a framework for the construction of entities that can serve as interpretations of arbitrary contiguous chunks of text. An important part of the paper is devoted to describing stacking cells, or the proposed meanings for bracket-structures.

Translations from Lambda calculi into combinatory logics can be used to avoid some implementational problems of the former systems. However, this scheme can only be efficient if the translation produces short output with a small number of combinators, in order to reduce the time and transient storage space spent during reduction of combinatory terms. In this paper we present a combinatory system and an abstraction algorithm, based on the original bracket abstraction operator of Schonfinkel [9]. The algorithm introduces at most (...) one combinator for each abstraction in the initial Lambda term. This avoids explosive term growth during successive abstractions and makes the system suitable for practical applications. We prove the correctness of the algorithm and establish some relations between the combinatory system and the Lambda calculus. (shrink)

In this article, following on from earlier debates in the journal regarding the ‘thorny issue’ of epochē and bracketing in sociological phenomenological research, we consider more generally the challenges of engaging in reflexivity and bracketing when undertaking ethnographic ‘insider’ research, or research in familiar settings. We ground our discussion and illustrate some of the key challenges by drawing on the experience of undertaking this research approach with a group of competitive swimmers, who were participating in a British university (...) performance swimming programme at the time of the doctoral study. The primary researcher was highly familiar with the phenomenon of competitive swimming, having been both a competitive swimmer and swimming coach. Some of the key elements of a sociological phenomenological approach to studying physical-cultural embodiment are first delineated, before addressing the considerable challenges of engaging in sustained reflexivity and bracketing, using the swimming research for illustrative purposes. We suggest some practical ways in which researchers in sport and physical cultures might approach epochē and bracketing in ethnographic ‘insider’ research. -/- KEYWORDS: Sociological phenomenology, competitive swimming, insider research, epochē/bracketing. (shrink)

The Hamiltonian for the Einstein equations is constructed on a outgoing null cone with the help of the usual null tetrad. The resulting null surface constraints are shown to be second class in the terminology of Dirac. These second class constraints are eliminated by use of the “starring” procedure of Bergmann and Komar.

Michel Bitbol offers a well-thought-out system of metaphysical coordinates. Despite the elegance and soundness of the proposed system, I nevertheless have concerns about the very need for a tailor-….

Paradox is a complex notion that has assumed a diverse range of forms within philosophy, and Søren Kierkegaard contributes one of the more interesting variations by employing a fairy tale to introduce what he identifies as the absolute paradox of the Incarnation. Despite this, more recent discussion on paradox has given little attention to Kierkegaard and has largely bracketed out any interaction with paradox that does not fit within the general analytic framework. In this paper, I evaluate the different characterizations (...) of paradox offered by Kierkegaard and representative thinkers in the analytic tradition. I argue that the non-bracketing of Kierkegaard’s fairy tale as a valid form of paradox discourse not only provides a fuller account of paradox but also offers a critique of the attempt to exclude any form of paradox from philosophical discussion that does not already conform to the restrictions of the analytic approach. (shrink)

The symplectic structures (brackets, Hamilton's equations, and Lagrange's equations) for the Dirac electron and its classical model have exactly the same form. We give explicitly the Poisson brackets in the dynamical variables (x μ,p μ,v μ,S μv). The only difference is in the normalization of the Dirac velocities γμγμ=4 which has significant consequences.

A bracket abstraction algorithm is a means of translating $\lambda$-terms into combinators. Broda and Damas, in [1], introduce a new, rather natural set of combinators and a new form of bracket abstraction which introduces at most one combinator for each $\lambda$-abstraction. This leads to particularly compact combinatory terms. A disadvantage of their abstraction process is that it includes the whole Schonfinkel [4] algorithm plus two mappings which convert the Schonfinkel abstract into the new abstract. This paper shows how the new (...) abstraction can be done more directly, in fact, using only 2n - 1 algorithm steps if there are n occurrences of the variable to be abstracted in the term. Some properties of the Broda-Damas combinators are also considered. (shrink)

The purpose of this paper is to shed some fresh light on the long-standing conceptual question of the origin of the well-known Poisson bracket structure of the constraints that govern the canonical dynamics of generally relativistic field theories, i.e. geometrodynamics. This structure has long been known to be the same for a wide class of fields that inhabit the space-time, namely those with non-differential coupling to gravity. It has also been noticed that an identical bracket structure can be derived independently (...) of any dynamical theory, by purely geometrical considerations in Lorentzian geometry. Here we attempt to provide the missing link between the dynamics and geometry, which we understand to be the reason for this structure to be of the specific kind. We achieve this by a careful analysis of the geometrodynamical approach, which allows us to derive the structure in question and understand it as a consistency requirement for any such theory. In order to stay close to the classical literature on the subject we stick to the metric formulation of general relativity, but the reasoning should carry over to any other formulation as long as the non-metricity tensor vanishes. The discussion section is devoted to derive some interesting consequences of the presented result in the context of reconstructing the Arnowitt–Deser–Misner framework, thus providing a precise sense to the inevitability of the Einstein’s theory under minimal assumptions. (shrink)

Although Montague claims that the system of The proper treatment of quantification in ordinary English includes some conjunction and disjunction, the rules for other grammatical constructions do not take conjunction or disjunction into account, and in general fail either syntactically or semantically when one of their arguments is so formed. Using an unlabeled bracketing of syntactic structure and recursive definitions, we have been able to rewrite the rules so that correct results are obtained.These results should provide a firmer basis (...) for extension of PTQ. (shrink)

We study the partition relation $X@>{\rm w}>>[Y]_{p}^{2}$ that is a weakening of the usual partition relation $X\rightarrow [Y]_{p}^{2}$ . Our main result asserts that if κ is an uncountable strongly compact cardinal and $\germ{d}_{\kappa}\leq \lambda ^{<\kappa}$ , then $I_{\kappa,\lambda}^{+}@>{\rm w}>>[I_{\kappa,\lambda}^{+}]_{\lambda <\kappa}^{2}$ does not hold.

This paper attempts to give an account of bracketing paradoxes by developing the theory of alignment (McCarthy and Prince 1993b). The rubric ‘bracketing paradox’ (BP) has been used to cover a number of disparate phenomena, though it is not obvious that these phenomena should be given a unitary analysis. I will confine my attention here to the kind of BP illustrated in (1).

From the viral social media feeds showing Chief Justice Mogoeng Mogoeng in fervent prayer for the nation, to professed Christian Thuli Madonsela’s careful expression of the separation between religion and state, faith identity in the public sphere emerges as anything but a straightforward matter. By placing ‘Christian’ in parenthesis, the 2019 theme of the Theological Society of South Africa conference acknowledged that leaders operate in negotiated spaces and confirmed the complexity of the context in which we attempt to conceptualise leadership (...) from a theological perspective. This raises the question of the role that personal faith convictions play and may be allowed to play in public life. While conceptualising leadership from a faith perspective in a context that is at once secular and post-secular may be complex, evidence emerging from leadership studies of the importance of spirituality in leadership necessitates such a reflection. This article considers the problem from a theological point of view, drawing on Schleiermacher and Bonhoeffer’s later letters from prison to provide a theological foundation for a public spirituality of leadership. (shrink)

This article considers a novel approach to researching sporting embodiment via what has been termed ‘autophenomenography’. Whilst having some similarities with autoethnography, autophenomenography provides a distinctive research form, located within phenomenology as theoretical and methodological tradition. Its focus is upon the researcher’s own lived experience of a phenomenon or phenomena. This article examines some of the key elements of a sociological phenomenological approach to studying sporting embodiment in general before portraying how autophenomenography was utilised specifically within two recent research projects (...) on distance running. The thorny issues of epoche and bracketing within phenomenological and autophenomenographical research are addressed and some practical suggestions tentatively posited. (shrink)

La centralidad que tiene la dimensión erótica en nuestras sociedades occidentales se refleja, entre otros múltiples fenómenos, en amplios y diversos nichos de mercado tendientes a generar ganancias por medio de la oferta de cuerpos, bienes y servicios que promueven la maximización de las experiencias sensorio-sexuales y la optimización del cuerpo en términos estéticos y eróticos. La producción de subjetividades se juega en el marco de un mercado que ofrece experiencias que combinan diversión, esfuerzo y autopromoción bajo las lógicas de (...) los insoslayables marcadores sociales de la diferencia.Al calor de estos fenómenos contemporáneos, tejidos por las tramas del erotismo, el género y el mercado, el presente artículo se propone realizar un análisis performático y performativo de una experiencia de participación observante en un taller de seducción femenina realizado en la ciudad de Córdoba. Se abordarán las técnicas corporales que fueron enseñadas, aprendidas y ensayadas en el taller y, en un segundo momento, el tipo específico de ideal regulatorio de la feminidad que estaba siendo propuesto tanto por medio de las particulares citaciones erótico-corporales que fuimos instadas a reiterar como por el discurso experto del profesor del taller. Con ello, se busca construir una descripción densa de esta instancia apostando a que amplíe los modos de abordar y conocer cómo estos paradójicos espacios reúnen experiencias y discursos de normalización y reactivación de viejos mandatos femeninos, a la par que transforman convenciones ligadas al género y la sexualidad. (shrink)

Problem: Starting with his personal experience the author pursues the question: How can we alter our way of living, sensoriality and reflective skills so that we can handle today’s information flows, which nowadays are so large that they create confusion and ineffective educational actions? Method: The approach to follow is called “parenthesism,” a practice based on Maturana’s theoretical frameworks of the “biology of cognition” and the “biology of love.” Results: One of the findings when a person lives in parenthesism is (...) the ability to see their own dogmatism and stubbornness when that person would otherwise be blind to his/her own convictions. Implications: Many aspects of this essay, and this manner of thinking, are circular and tautological, and hence may appear illogical to the reader. However, the author claims that existence is not solely logical, and that in a complex matrix circular and recursive relationships are common, and that these can best be understood through circular and recursive logics. Furthermore the relevance of parenthesism for UNESCO’s view on learning paradigms is reviewed in this light. (shrink)

In a loose analogy to the history of the autonomous movement, the article pleads for the elaboration of a post-autonomous concept of literature in literary studies – which must also include a revision of the scholars’ criteria of aesthetic evaluation. »Post-autonomous« should be understood here as the reflected expression of some of the paradoxes of the autonomous itself.

What can writing, the literary perspective, contribute towards the academic discourse? How can literature describe or explore the world we experience? In this article I argue that the essential porousness, the cuts and in-betweens of the world that are embodied in the poetic writing (and reading as writing) process not only embrace the absence of an objective reality or truth but also the subjectivity, the ephemeral and the ineffable as a general (postmodern) condition.

The Peanese convention for the use of dots as brackets has the disadvantage that it gives only an awkward method for representing chains of indefinite length, such as the compound implicationSuch chains occur frequently in logical investigations of a metatheoretic nature, and it is convenient to have a systematic method of abbreviating them. The most obvious method of doing this would be to leave the parentheses out entirely, and to understand that in such cases the implication sign or other operation (...) appearing on the extreme left is the most inclusive; but this method, which has been followed by Quine, is at variance with our ordinary algebraic usage, in which we write a − b + c − d for ((a − b) + c) − d, and consequently leads to confusion. It is desirable to have a modification of the Peanese convention which gives a simple method of representing such chain implications, and at the same time avoids this difficulty.Such a modification is easily obtained by generalizing somewhat a procedure of Church. The latter author uses only a single dot, which he writes on the right of an operator to signify a bracket extending from that point to the end of the formula (or parenthesized expression). If dots are used only on the right of operations this is all that can be desired. But the essential idea of this device can be extended to the case where dots are used also on the left, as follows: let us suppose that a group of dots on the right of an operation or prefix denotes the beginning of a bracket which extends to the right until it meets a group with an equal or larger number of dots on the left of an operation; and that the scope of a group of dots on the left of an operation shall extend to the left until it reaches a larger group of dots on the right of some operation. (shrink)

The present study examined differences in moral behavior and judgment in sport and student life. Participants were students at a British university who responded to moral dilemmas pertaining to sport and student life. They indicated the likelihood that they would act antisocially or prosocially and provided judgment ratings of the behaviors described in the dilemmas. Likelihood to act antisocially was higher toward opponents in sport than other students at university, whereas likelihood to behave prosocially was lower toward opponents in sport (...) than other students at university. Finally, antisocial behavior was less likely toward teammates than other students. The sport–university difference in antisocial opponent/student behavior was fully mediated by moral judgment, whereas the difference in prosocial behavior was partially mediated by moral judgment. These findings reveal a more nuanced aspect to bracketed morality that considers in-group loyalty when understanding moral judgment and behavior in and outside of the sport context. (shrink)

Every language recognized by the Lambek calculus with brackets is context-free. This is shown by combining an observation by Jäger with an entirely straightforward adaptation of the method Pentus used for the original Lambek calculus. The case of the variant of the calculus allowing sequents with empty antecedents is slightly more complicated, requiring a restricted use of the multiplicative unit.

We propose a Lorentz-covariant deformed algebra describing a -dimensional quantized spacetime, which in the nonrelativistic limit leads to undeformed one. The deformed Poincaré transformations leaving the algebra invariant are identified. In the classical limit the Lorentz-covariant deformed algebra yields the deformed Lorentz-covariant Poisson brackets. Kepler problem with the deformed Lorentz-covariant Poisson brackets is studied. We obtain that the precession angle of an orbit of the relativistic particle in the gravitational field depends on the mass of the particle, i.e. equivalence principle (...) is violated. We propose a condition for the recovery of the equivalence principle in the space with the deformed Poisson brackets. Comparing our analytical result with the experimental data for the precession angle of Mercury’s orbit we provide an estimation of minimal length. (shrink)

We give a proof-theoretic and algorithmic complexity analysis for systems introduced by Morrill to serve as the core of the CatLog categorial grammar parser. We consider two recent versions of Morrill’s calculi, and focus on their fragments including multiplicative connectives, additive conjunction and disjunction, brackets and bracket modalities, and the! subexponential modality. For both systems, we resolve issues connected with the cut rule and provide necessary modifications, after which we prove admissibility of cut. We also prove algorithmic undecidability for both (...) calculi, and show that categorial grammars based on them can generate arbitrary recursively enumerable languages. (shrink)

According to ‘purification interpretations’, the point of the epoché is to purify our ordinary experience of certain assumptions inherent in it. In this paper, I argue that purification interpretations are wrong. Ordinary experience is just fine as it is, and phenomenology has no intention of correcting or purifying it. To understand the epoché, we must keep the reflective nature of phenomenology firmly in mind. When we do phenomenology, we occupy two distinct roles, which come with very different responsibilities. As reflecting (...) phenomenologists, we must deactivate all our beliefs about the world. But the only point of this is to be able to describe the experiences we have as experiencing subjects, including all those beliefs about the world that may be part and parcel of those experiences. I end by suggesting that there is a useful analogy between phenomenological reflection and the familiar practice of quoting. (shrink)