The purpose of this paper is first to show that if X is any locally compact but not compact perfect Polish space and stands for the one-point compactification of X, while E X is the equivalence relation which is defined on the Polish group C(X,R +*) by where f, g are in C(X,R +*), then E X is induced by a turbulent Polish group action. Second we show that given any if we identify the n-dimensional unit sphere S n with (...) the one-point compactification of R n via the stereographic projection, while E n , r is the equivalence relation which is defined on the Polish group C r (R n ,R +*) by where f, g are in C r (R n ,R +*), then E n , r is also induced by a turbulent Polish group action. (shrink)

If X is a locally compact Polish space, then LSC denotes the compact Polish space of lower semi-continuous real-valued functions on X equipped with the topology of epi-convergence.Our purpose in this article is to prove the following: if –∞ < α < β < ∞ and –∞ < a < b < ∞, while r ∈ ℕ \ {0}, then the set CV of all f ∈ LSC for which there is u ∈ Cr such that for any v ∈ (...) Cr we have that ∫αβf , v ′)dx ≥ ∫αβf , v )dx is not Borel. (shrink)

Background:Withdrawal of treatment is a common practice in intensive care units when treatment is considered futile. Compassion is an important aspect of care; however, it has not been explored much within the context of treatment withdrawal in intensive care units.Objectives:The aim was to examine how concepts of compassion are framed, utilised and communicated by intensive care nurses in the context of treatment withdrawal.Design:The study employed a qualitative approach conducting secondary analysis of an original data set. In the primary study, 13 (...) nurses were recruited from three intensive care units within a large hospital in United Kingdom. Deductive framework analysis was used to analyse the data in relation to compassionate care.Ethical considerations:The primary study was approved by the local Research Ethics Committee and the hospital’s Research and Development services.Findings:Compassionate care was mostly directed to the patient’s family and was demonstrated through care and emotional support to the family. It was predominantly expressed through attempts to maintain the patient’s dignity by controlling symptoms, maintaining patient cleanliness and removing technical apparatus.Conclusion:This study’s findings provide insight about compassionate care during treatment withdrawal which could help to understand and develop further clinicians’ roles. Prioritising the family over the patient raised concerns among nurses, who motivated by compassion, may feel justified in taking measures that are in the interests of the family rather than the patient. Further work is needed to explore the ethics of this. (shrink)

Equivalences and translations between consequence relations abound in logic. The notion of equivalence can be defined syntactically, in terms of translations of formulas, and order-theoretically, in terms of the associated lattices of theories. W. Blok and D. Pigozzi proved in [4] that the two definitions coincide in the case of an algebraizable sentential deductive system. A refined treatment of this equivalence was provided by W. Blok and B. Jónsson in [3]. Other authors have extended this result to the cases of (...) k-deductive systems and of consequence relations on associative, commutative, multiple conclusion sequents. Our main result subsumes all existing results in the literature and reveals their common character. The proofs are of order-theoretic and categorical nature. (shrink)

It is well known that classical propositional logic can be interpreted in intuitionistic propositional logic. In particular Glivenko's theorem states that a formula is provable in the former iff its double negation is provable in the latter. We extend Glivenko's theorem and show that for every involutive substructural logic there exists a minimum substructural logic that contains the first via a double negation interpretation. Our presentation is algebraic and is formulated in the context of residuated lattices. In the last part (...) of the paper, we also discuss some extended forms of the Kolmogorov translation and we compare it to the Glivenko translation. (shrink)

This is also where we begin investigating lattices of logics and varieties, rather than particular examples.

Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain interpolation properties and explain how they imply the amalgamation property for certain varieties of residuated lattices.

Given a positive universal formula in the language of residuated lattices, we construct a recursive basis of equations for a variety, such that a subdirectly irreducible residuated lattice is in the variety exactly when it satisfies the positive universal formula. We use this correspondence to prove, among other things, that the join of two finitely based varieties of commutative residuated lattices is also finitely based. This implies that the intersection of two finitely axiomatized substructural logics over FL + is also (...) finitely axiomatized. Finally, we give examples of cases where the join of two varieties is their Cartesian product. (shrink)

This paper argues that challenges that are grand in scope such as "lifelong health and wellbeing", "climate action", or "food security" cannot be addressed through scientific research only. Indeed scientific research could inhibit addressing such challenges if scientific analysis constrains the multiple possible understandings of these challenges into already available scientific categories and concepts without translating between these and everyday concerns. This argument builds on work in philosophy of science and race to postulate a process through which non-scientific notions become (...) part of science. My aim is to make this process available to scrutiny: what I call founding everyday ideas in science is both culturally and epistemologically conditioned. Founding transforms a common idea into one or more scientifically relevant ones, which can be articulated into descriptively thicker and evaluatively deflated terms and enable operationalisation and measurement. The risk of founding however is that it can invisibilise or exclude from realms of scientific scrutiny interpretations that are deemed irrelevant, uninteresting or nonsensical in the domain in question-but which may remain salient for addressing grand-in-scope challenges. The paper considers concepts of "wellbeing" in development economics versus in gerontology to illustrate this process. (shrink)

Two constructions for adding an involution operator to residuated ordered monoids are investigated. One preserves integrality and the mingle axiom x 2x but fails to preserve the contraction property xx 2. The other has the opposite preservation properties. Both constructions preserve commutativity as well as existent nonempty meets and joins and self-dual order properties. Used in conjunction with either construction, a result of R.T. Brady can be seen to show that the equational theory of commutative distributive residuated lattices (without involution) (...) is decidable, settling a question implicitly posed by P. Jipsen and C. Tsinakis. The corresponding logical result is the (theorem-) decidability of the negation-free axioms and rules of the logic RW, formulated with fusion and the Ackermann constant t. This completes a result of S. Giambrone whose proof relied on the absence of t. (shrink)

We develop a general algebraic and proof-theoretic study of substructural logics that may lack associativity, along with other structural rules. Our study extends existing work on substructural logics over the full Lambek Calculus [34], Galatos and Ono [18], Galatos et al. [17]). We present a Gentzen-style sequent system that lacks the structural rules of contraction, weakening, exchange and associativity, and can be considered a non-associative formulation of . Moreover, we introduce an equivalent Hilbert-style system and show that the logic associated (...) with and is algebraizable, with the variety of residuated lattice-ordered groupoids with unit serving as its equivalent algebraic semantics. Overcoming technical complications arising from the lack of associativity, we introduce a generalized version of a logical matrix and apply the method of quasicompletions to obtain an algebra and a quasiembedding from the matrix to the algebra. By applying the general result to specific cases, we obtain important logical and algebraic properties, including the cut elimination of and various extensions, the strong separation of , and the finite generation of the variety of residuated lattice-ordered groupoids with unit. (shrink)

I propose that the intensification of meat production ironically makes meat concepts available to be populated by plants. I argue that what I call “technologies of effacement” facilitate the intensification of animal farming and slaughter by blocking face-to-face encounters between animals and people (Levinas 1969; Efstathiou 2018, 2019). My previous ethnographic work on animal research identifies technologies of effacement as including (a) architectures and the built environment, (b) entry and exit rules, (c) special garments, (d) naming and labeling procedures, (...) and (e) protocols for handling animals (Efstathiou 2018, 2019). Building on ethnographic research by Dawn Coppin (2003) and Nöellie Vialles (1994), in the United States and France respectively, I propose that (a) Concentrated Animal Feeding Operation (CAFO) buildings, gestation, and farrowing crates; (b) rules for entering and exiting the slaughterhouse; (c) white slaughterhouse garments; (d) unique identification systems; and (e) “trapping” animals before stunning can all operate as technologies of effacement. Though developed to serve other manifest aims, like hygiene, expediency, or safety, these technologies operate to sustain routine, inviting one to look at animals as tokens of a known type while blocking encounters between humans and animals (and also among animals) as radically different, morally significant Others (Efstathiou 2018, 2019). (shrink)

We provide an alternative proof of the decidability of the equational theory of lattices. The proof presented here is quite short and elementary.

This paper examines how aesthetic ideals shaped the practice of Nazi medicine. It proposes that Nazi eugenics relied on the conflation of norms of health with norms of beauty determined and performed by Nazi cultures of action. Though theories of biological holism served as vehicles of Nazi ideology, they did so contingently. The anti-totalitarian thinking of biological holist Kurt Goldstein shows that the use of biological holism to promote Nazi ideology was not inevitable. This examination of aesthetic influences on Nazi (...) medicine shows that traditionally speaking ‘non-rational’ factors shaped the Nazi biomedical program’s aims and methods. (shrink)

With increasing publication and data production, scientific knowledge presents not simply an achievement but also a challenge. Scientific publications and data are increasingly treated as resources that need to be digitally ‘managed.’ This gives rise to scientific Knowledge Management : second-order scientific work aiming to systematically collect, take care of and mobilise first-hand disciplinary knowledge and data in order to provide new first-order scientific knowledge. We follow the work of Leonelli, Efstathiou and Hislop in our analysis of the use (...) of KM in semantic systems biology. Through an empirical philosophical account of KM-enabled biological research, we argue that KM helps produce new first-order biological knowledge that did not exist before, and which could not have been produced by traditional means. KM work is enabled by conceiving of ‘knowledge’ as an object for computational science: as explicated in the text of biological articles and computable via appropriate data and metadata. However, these founded knowledge concepts enabling computational KM risk focusing on only computationally tractable data as knowledge, underestimating practice-based knowing and its significance in ensuring the validity of ‘manageable’ knowledge as knowledge. (shrink)

All known structural extensions of the substructural logic $\textbf{FL}_{\textbf{e}}$, the Full Lambek calculus with exchange/commutativity (corresponding to subvarieties of commutative residuated lattices axiomatized by $\{\vee, \cdot, 1\}$ -equations), have decidable theoremhood; in particular all the ones defined by knotted axioms enjoy strong decidability properties (such as the finite embeddability property). We provide infinitely many such extensions that have undecidable theoremhood, by encoding machines with undecidable halting problem. An even bigger class of extensions is shown to have undecidable deducibility problem (the (...) corresponding varieties of residuated lattices have undecidable word problem); actually with very few exceptions, such as the knotted axioms and the other prespinal axioms, we prove that undecidability is ubiquitous. Known undecidability results for non-commutative extensions use an encoding that fails in the presence of commutativity, so and-branching counter machines are employed. Even these machines provide encodings that fail to capture proper extensions of commutativity, therefore we introduce a new variant that works on an exponential scale. The correctness of the encoding is established by employing the theory of residuated frames. (shrink)

This collection addresses two different audiences: 1) historians and philosophers of the life sciences reflecting on collaborations across disciplines, especially as regards defining and addressing Grand Challenges; 2) researchers and other stakeholders involved in cross-disciplinary collaborations aimed at tackling Grand Challenges in the life and medical sciences. The essays collected here offer ideas and resources both for the study and for the practice of goal-driven cross-disciplinary research in the life and medical sciences. We organise this introduction in three sections. The (...) first section provides some background and context. The second motivates our take on this topic and then outlines the central ideas of each paper. The third section highlights the specificity and significance of this approach by considering: a) how this collection departs from existing literature on inter- and trans-disciplinarity, b) what is characteristic about this approach, and c) what role this suggests for the history and philosophy of the life sciences in addressing Grand Challenges. (shrink)

Causation is in trouble—at least as it is pictured in current theories in philosophy and in economics as well, where causation is also once again in fashion. In both disciplines the accounts of causality on offer are either modelled too closely on one or another favoured method for hunting causes or on assumptions about the uses to which causal knowledge can be put—generally for predicting the results of our efforts to change the world. The first kind of account supplies no (...) reason to think that causal knowledge, as it is pictured, is of any use; the second supplies no reason to think our best methods will be reliable for establishing causal knowledge. So, if these accounts are all there is to be had, how do we get from method to use? Of what use is knowledge of causal laws that we work so hard to obtain? (shrink)

This essay unpacks a seeming paradox: a concept used to formulate, promote, and legitimate oppressive ideologies—a concept used to formulate mistaken, because they were typological, biological theories about human diversity—is, it seems, the same concept that now promises to deliver wonderful, socially sensitized, innovative results in social and genetic epidemiology. But how could that be? How could scientists expect a concept as problematic as ordinary race to deliver useful scientific results? I propose that there is a process for retranslating Ballungen (...) race concepts in appropriate ways to make them fit and work within social scientific and bioscientific contexts. (shrink)

Within a geometric and algebraic framework, the structures which are related to the spin-statistics connection are discussed. A comparison with the Berry-Robbins approach is made. The underlying geometric structure constitutes an additional support for this approach. In our work, a geometric approach to quantum indistinguishability is introduced which allows the treatment of singlevaluedness of wave functions in a global, model independent way.

I propose that meat replacement is to meat, as drag is to gender. Meat replacement has the potential to shake concepts of meat, like drag does for gender. Meat replacements not only mimic meat but disclose how meat itself is performed in carnivorous culture -and show that it may be performed otherwise. My approach is inspired by the show RuPaul’s Drag Race. The argument builds on an imitation of Judith Butler’s work on gender performativity, performed by replacing ‘drag/ gender/ sex/ (...) heterosexism’ terms and relations in Butler’s text with ‘meat replacement/ meat/ species/ carnism’ ones. (shrink)

Our main research question is how pliable Norwegian meat consumption practices are. However it is not any type of elasticity we are interested in. We are specifically interested in the scope for what we dub the “4Rs” of responsible meat consumption within existing food systems: 1. Reducing the amount of animal-based proteins used 2. Replacing animal-based protein with plant-based, or insect-based alternatives 3. Refining processes of utilization of animal-based protein to minimize emissions, loss and waste 4. Recognising animal-based protein as (...) precious –i.e. recognising the people and the animals involved in meat production. -/- These four principles are derived by analogy to ethical principles guiding the use of animals in research, the so-called “3Rs”, namely: the imperatives to reduce the number of animals needed to make a scientific inference, to replace animal experiments with other types of research, and where not possible to replace ‘more’ with ‘less’ sentient creatures, and to refine the experimental setup so it minimises the discomfort and/or distress inflicted upon the animals (Russell and Burch, 1959). There are no such principles guiding the use of animals in farming, given the farming industry intrinsically relies on increasing its resources, of which animals are one. The current profile of climate change however opens up a way to re-appreciate meat –indeed what we articulate as the fourth principle of recognizing the preciousness of meat, above, given planetary boundaries. We proceed to reflect on how these 4Rs can be modulated, from a cultural-social perspective, that is, we look at cultural factors that could stretch current food practices along the 4R aspects. (shrink)

Causation is in trouble—at least as it is pictured in current theories in philosophy and in economics as well, where causation is also once again in fashion. In both disciplines the accounts of causality on offer are either modelled too closely on one or another favoured method for hunting causes or on assumptions about the uses to which causal knowledge can be put—generally for predicting the results of our efforts to change the world. The first kind of account supplies no (...) reason to think that causal knowledge, as it is pictured, is of any use; the second supplies no reason to think our best methods will be reliable for establishing causal knowledge. So, if these accounts are all there is to be had, how do we get from method to use? Of what use is knowledge of causal laws that we work so hard to obtain? (shrink)

This chapter proposes that encountering the Other through the face can be conditioned by social and built technologies. In “The Name of a Dog, or Natural Rights,” Emmanuel Levinas relates his experience as a prisoner of war, held in a forced-labor camp in Nazi Germany. He contrasts being denied his humanity by other humans, “called free” (DF, 152), while being recognized as human—indeed as a friend—by a dog the prisoners named Bobby. The episode suggests that though the concept of the (...) face applies to humans, the face is not enough for facing, at least not in the setting of the camp. By contrast, the prisoners seem able to face and be faced by Bobby, even if Levinas remains inconclusive about whether the face applies to animals elsewhere. It follows that the face is operating less like a property, and more like a capacity, a mode as Levinas calls it. But what conditions encountering an Other in this mode? If the face is neither sufficient for facing, nor prior to it, then what conditions facing (or effacing)? I propose that social structures, techniques, architectures, professional roles, and so on matter in coming to face (or efface) the Other. I conclude this from analyzing human-animal encounters in a scientific space of exception: the animal lab. Building on empirical accounts of animal research, I propose that animal research is populated by what I call “technologies of effacement.” These include: (1) built architectures; (2) entering and exit procedures; (3) protective garments and equipment; (4) identification and labeling techniques; and (5) experimental protocols. These technologies serve other manifest ends, but they operate to condition encounters between humans and animals in the lab: they help block the face of humans and animals. (shrink)