In [U. Kohlenbach, Some logical metatheorems with applications in functional analysis, Trans. Amer. Math. Soc. 357 89–128], the second author obtained metatheorems for the extraction of effective bounds from classical, prima facie non-constructive proofs in functional analysis. These metatheorems for the first time cover general classes of structures like arbitrary metric, hyperbolic, CAT and normed linear spaces and guarantee the independence of the bounds from parameters ranging over metrically bounded spaces. Recently ]), the authors obtained generalizations of these metatheorems (...) which allow one to prove similar uniformities even for unbounded spaces as long as certain local boundedness conditions are satisfied. The use of classical logic imposes some severe restrictions on the formulas and proofs for which the extraction can be carried out. In this paper we consider similar metatheorems for semi-intuitionistic proofs, i.e. proofs in an intuitionistic setting enriched with certain non-constructive principles. Contrary to the classical case, there are practically no restrictions on the logical complexity of theorems for which bounds can be extracted. Again, our metatheorems guarantee very general uniformities, even in cases where the existence of uniform bounds is not obtainable by straightforward functional analytic means. Already in the purely intuitionistic case, where the existence of effective bounds is implicit, the metatheorems allow one to derive uniformities that may not be obvious at all from a given constructive proof. Finally, we illustrate our main metatheorem by an example from metric fixed point theory. (shrink)

We develop the general theory of topometric spaces, i.e., topological spaces equipped with a well-behaved lower semi-continuous metric. Spaces of global and local types in continuous logic are the motivating examples for the study of such spaces. In particular, we develop Cantor-Bendixson analysis of topometric spaces, which can serve as a basis for the study of local stability (extending the ad hoc development in Ben Yaacov I and Usvyatsov A, Continuous first order logic and local stability. Trans Am (...) Math Soc, in press), as well as of global ${\aleph_0}$ -stability. We conclude with a study of perturbation systems (see Ben Yaacov I, On perturbations of continuous structures, submitted) in the formalism of topometric spaces. In particular, we show how the abstract development applies to ${\aleph_0}$ -stability up to perturbation. (shrink)

This paper aims to investigate the current state of play on Environmental Social and Governance (ESG) integration and check the validity of the current metrics system by assessing if it will survive the COVID-19 crisis. By adopting a qualitative research approach through semi-structured anonymous interviews with 14 senior managers of six European listed companies we use a framework by assessing the mechanisms of reactivity on the effectiveness of ESG measures in times of COVID-19. By interpreting the practitioners’ points of (...) view through the lens of the sociological framework by Espeland and Sauder (Am J Sociol 113:1–40, 2007) our findings show different mechanisms of reactivity by companies on the effectiveness of ESG measures in times of COVID-19, i.e., active and passive conformity and active resistance. We also identified the main Corporate Social Responsibility (CSR) institutional factors that affect managers’ reactivity. An extensive re-formulation of the ESG metrics is required in the light of times of crisis, given that accountability and transparency are strongly linked to quantitative measures which can play a critical role in the financial system and investors’ engagement. Particularly, the strict distinction between “E”, “S” and “G” issues should be abandoned claiming a different holistic re-design of sustainability measures by considering the increasing relevance of the Social dimension in time of COVID-19. This study provides a valuable contribution to the existing literature on the measurement of sustainability within the link of accountability and crisis by highlighting new corporate needs to re-design the ESG metrics system. (shrink)

§1. Introduction. Asymptotic cones of metric spaces were first invented by Gromov. They are metric spaces which capture the ‘large-scale structure’ of the underlying metric space. Later, van den Dries and Wilkie gave a more general construction of asymptotic cones using ultrapowers. Certain facts about asymptotic cones, like the completeness of the metric space, now follow rather easily from saturation properties of ultrapowers, and in this survey, we want to present two applications of the van den (...) Dries-Wilkie approach. Using ultrapowers we obtain an explicit description of the asymptotic cone of a semisimple Lie group. From this description, using semi-algebraic groups and non-standard methods, we can give a short proof of the Margulis Conjecture. In a second application, we use set theory to answer a question of Gromov.§2. Definitions. The intuitive idea behind Gromov's concept of an asymptotic cone was to look at a given metric space from an ‘infinite distance’, so that large-scale patterns should become visible. In his original definition this was done by gradually scaling down the metric by factors 1/nfornϵ ℕ. In the approach by van den Dries and Wilkie, this idea was captured by ultrapowers. Their construction is more general in the sense that the asymptotic cone exists for any metric space, whereas in Gromov's original definition, the asymptotic cone existed only for a rather restricted class of spaces. (shrink)

We present a formal derivation of the Mino–Sasaki–Tanaka–Quinn–Wald (MSTQW) equation describing the self-force on a (semi-) classical relativistic point mass moving under the influence of quantized linear metric perturbations on a curved background space–time. The curvature of the space–time implies that the dynamics of the particle and the field is history-dependent and as such requires a non-equilibrium formalism to ensure the consistent evolution of both particle and field, viz., the worldline influence functional and the closed- time-path (CTP) coarse-grained (...) effective action. In the spirit of effective field theory, we regularize the formally divergent self-force by smearing the local part of the retarded Green’s function and employing a quasi-local expansion. We derive the MSTQW–Langevin equations describing the perturbations of the particle’s worldline about its semi-classical trajectory resulting from interactions with the quantum fluctuations of the linear metric perturbations. Finally, we demonstrate that the quantum fluctuations of the field could, in principle, leave imprints on gravitational waveforms expected to be observed by gravitational interferometers, thereby encoding information about tree-level perturbative quantum gravity. (shrink)

This paper intends to reveal the essential value of interactive media by fully understanding the complex interactive mechanism of human experience. Following Cartesian dualistic thought, interactive technology has primarily been utilized as a physical control device. It hasn’t sufficiently explored its gigantic potential as a true interactive medium. Interactive technology reflects our desire to interact with someone or something. Historically, human desire for interaction has been continuously manifested from the day of primitive ritual to contemporary cyberspace. Our interactive routines have (...) continued, from micro to macro scale, in order to confirm our existence in every day life. This universal repetitive pattern of human activity is ‘the ritual’. It is ritual because it is the archetypes of cycles driven by human instinct, regardless of their cultural and historical period. In this paper, I am defining ‘the form of ritual’, to explain the fundamental human process of interaction and becoming, and furthermore, to find the imperative potential of interactive media. The form of ritual will be explained in detail, with agent, driving force, process and by-product, taking reference from Korean shaman ritual, Yin/Yang process and Alfred North Whitehead’s process philosophy. My virtual puppetry with spiralling interaction, ‘Yong-Shin-Gud’ (calling-dragon-spirit), will be introduced as an art example to carry out the ritual. Interactive technology is an ongoing expression of human desire. Its essential value would be found in understanding human beings, nature and cosmos. Revealing its hidden essence, historical presence and spiritual value will be the next paradigm of interactive art practice. (shrink)

We live in layers of mixed realities with continuous conflicts, negotiation and becoming. I find it interesting to look at our situation as a continuous struggle in the fusion of virtual/actual presences, and machine/human. However, we seem to be far from understanding these relationships. Maybe the problem lies in the questions themselves, promoting unidirectional preconceptions. By reversing the questions, we might be able to identify something that has been missing in previous discussions: Can we talk about disconnection to further discuss (...) connection? Can we talk about distancing to further discuss the process of becoming? Can we talk about love impossible, to further discuss love? This paradoxical journey would maintain us in the continuum of struggle and massive doubts, and encounter deep aspects of human being. In this article, I examine the Korean cultural psyche called han in the context of a paradoxical state of consciousness and the story of love impossible, and argue that han is a driving force of transformative ritual in human consciousness. Beyond cultural boundaries, this article also positions han in a microscopic view of contemporary life. han underlies paradoxical human relationships with objects, and with my virtual puppets, in the context of distance, disconnection and love impossible. (shrink)

A summary of recent experimental results shows that entanglement can be generated more easily than before, and that there are improved chances for its persistence. An eminent finding of Generalised Quantum Theory is the insight that the notion of entanglement can be extended, such that, e.g., psychological or psychophysical problem areas can be included, too. First, a general condition for entanglement to occur is given by the term ‘common prearranged context’. A formalised treatment requires a quantitative definition of the similarity (...) or dissimilarity between two complex structures which takes their internal structures into account. After some specific remarks on distance, metrics, and semi-metrics in mathematics, a procedure is described for setting up a similarity function with the required properties. This procedure is in analogy with the two-step character of measurement and with the well-known properties of perspective notions. A general methodology can be derived for handling perspective notions. Finally, these concepts supply heuristic clues towards a formalised treatment of the notions of ‘meaning’ and ‘interpretation’. (shrink)

A beautiful and thoughtful collection of essays on reading, writing and learning, _Writing and Psychoanalysis_ grows out of a colloquium. The results are wondrous and impact on the reader at many different levels. In the act of writing, we all discover something about what we know previously unknown to us, and we learn more about our inner world that we knew before we set pen to paper. Patrick Mahony goes so far as to argue that Freud's self-analysis was essentially a (...) "writing cure." _Writing in Psychoanalysis_ is the first volume in the projected Monograph Series, Psychoanalytic Issues, the _Rivista di Psicoanalisi_ is undertaking in conjunction with Karnac Books. This series constitutes a major effort to bring about a dialogue among psychoanalysts who while ultimately bound together by a common psychoanalytic heritage nonetheless are separated in their thinking by different idioms, whether linguistic or theoretical. While featuring writers of very different idioms, this series will also present a venue to make some important Italian voices known to English speaking analysts. (shrink)

It is shown that, relative to Bishop-style constructive mathematics, the boundedness principle BD-N is equivalent both to a general result about the convergence of double sequences and to a particular one about Cauchyness in a semi-metric space.

Metrics and their weaker forms are used to measure the difference between two data. There are many metrics that are available but not desired by a practitioner. This paper recommends in a plausible reasoning manner an easy-to-understand method to construct desired distance-like measures: to fuse easy-to-obtain pseudo-semi-metrics, pseudo-metrics, or metrics by making full use of well-known t-norms, t-conorms, aggregation operators, and similar operators. The simple reason to do this is that data for a real world problem are sometimes from (...) multiagents. A distance-like notion, called weak interval-valued pseudo-metrics, is defined by using known notions of pseudo-semi-metrics, pseudo-metrics, and metrics; this notion is topologically good and shows precision, flexibility, and compatibility than single pseudo-semi-metrics, pseudo-metrics, or metrics. Propositions and detailed examples are given to illustrate how to fabricate an expected or demanded WIVP-metric in practical problems, and WIVP-metric and its special cases are characterized by using axioms. Moreover, some WIVP-metrics pertinent to quantitative logic theory or interval-valued fuzzy graphs are constructed, and fixed point theorems and common fixed point theorems in weak interval-valued metric spaces are also presented. Topics and strategies for further study are also put forward concretely and clearly. (shrink)

Autism has been defined as a disorder of social cognition, interaction and communication where ritualistic, repetitive behaviors are commonly observed. But how should we understand the behavioral and cognitive differences that have been the main focus of so much autism research? Can high-level cognitive processes and behaviors be identified as the core issues people with autism face, or do these characteristics perhaps often rather reflect individual attempts to cope with underlying physiological issues? Much research presented in this volume will point (...) to the latter possibility, i.e. that people on the autism spectrum cope with issues at much lower physiological levels pertaining not only to Central Nervous Systems (CNS) function, but also to peripheral and autonomic systems (PNS, ANS) (Torres, Brincker, et al. 2013). The question that we pursue in this chapter is what might be fruitful ways of gaining objective measures of the large-scale systemic and heterogeneous effects of early atypical neurodevelopment; how to track their evolution over time and how to identify critical changes along the continuum of human development and aging. We suggest that the study of movement variability—very broadly conceived as including all minute fluctuations in bodily rhythms and their rates of change over time (coined micro-movements (Figure 1A-B) (Torres, Brincker, et al. 2013))—offers a uniquely valuable and entirely objectively quantifiable lens to better assess, understand and track not only autism but cognitive development and degeneration in general. This chapter presents the rationale firstly behind this focus on micro-movements and secondly behind the choice of specific kinds of data collection and statistical metrics as tools of analysis (Figure 1C). In brief the proposal is that the micro-movements (defined in Part I – Chapter 1), obtained using various time scales applied to different physiological data-types (Figure 1), contain information about layered influences and temporal adaptations, transformations and integrations across anatomically semi-independent subsystems that crosstalk and interact. Further, the notion of sensorimotor re-afference is used to highlight the fact that these layered micro-motions are sensed and that this sensory feedback plays a crucial role in the generation and control of movements in the first place. In other words, the measurements of various motoric and rhythmic variations provide an access point not only to the “motor systems”, but also access to much broader central and peripheral sensorimotor and regulatory systems. Lastly, we posit that this new lens can also be used to capture influences from systems of multiple entry points or collaborative control and regulation, such as those that emerge during dyadic social interactions. (shrink)

The feminization of agriculture narrative has been reproduced in development literature as an oversimplified metric of empowerment through changes in women’s labor and managerial roles with little attention to individuals’ heterogeneous livelihoods. Grounded in feminist political ecology, we sought to critically understand how labor and managerial feminization interact with changing agricultural practices. Working with a local NGO as part of an international, donor-funded research-for-development project, we conducted semi-structured interviews, focus group discussions, and participant observation with over 100 farmers (...) in Mid-Western Nepal in 2017. Household structure and headship are dynamic in the context of male out-migration, pushing women to take on new agricultural duties and increasing household labor responsibilities. In this context, decision-making processes related to agricultural management and new cultivation practices illustrate ongoing renegotiations of gender and cultivation practices within and beyond the household. We contend that the heterogeneity of household power dynamics muddies the empowering impacts of migration and emphasize the importance of community spaces as a locus of subjectivity formation and social value. We conclude that FPE can illuminate complexities of power, space, and individual responses to socio-ecological conditions that challenge the current feminization of agriculture framework. (shrink)

A possible way out of the conundrum of quantum gravity is the proposal that general relativity (GR) emerges from an underlying microscopic description. Despite recent interest in the emergent gravity program within the physics as well as the philosophy community, an assessment of the general motivation for this idea is lacking at the moment. We intend to fill this gap in the literature by discussing the main arguments in favour of the hypothesis that the metric field and its dynamics (...) are emergent. First, we distinguish between microstructure inspired from GR, such as through quantization or discretization, and microstructure that is not directly motivated from GR, such as strings, quantum bits or condensed matter fields. The emergent gravity approach can then be defined as the view that the metric field and its dynamics are derivable from the latter type of microstructure. Subsequently, we assess in how far the following properties of (semi-classical) GR are suggestive of underlying microstructure: (1) the metric's universal coupling to matter fields, (2) perturbative non-renormalizability, (3) black hole thermodynamics, and (4) the holographic principle. In the conclusion we formalize the general structure of the plausibility arguments put forward. (shrink)

In this paper we study a reducibility that has been introduced by Klaus Weihrauch or, more precisely, a natural extension for multi-valued functions on represented spaces. We call the corresponding equivalence classes Weihrauch degrees and we show that the corresponding partial order induces a lower semi-lattice. It turns out that parallelization is a closure operator for this semi-lattice and that the parallelized Weihrauch degrees even form a lattice into which the Medvedev lattice and the Turing degrees can be (...) embedded. The importance of Weihrauch degrees is based on the fact that multi-valued functions on represented spaces can be considered as realizers of mathematical theorems in a very natural way and studying the Weihrauch reductions between theorems in this sense means to ask which theorems can be transformed continuously or computably into each other. As crucial corner points of this classification scheme the limited principle of omniscience LPO, the lesser limited principle of omniscience LLPO and their parallelizations are studied. It is proved that parallelized LLPO is equivalent to Weak Kőnig's Lemma and hence to the Hahn—Banach Theorem in this new and very strong sense. We call a multi-valued function weakly computable if it is reducible to the Weihrauch degree of parallelized LLPO and we present a new proof, based on a computational version of Kleene's ternary logic, that the class of weakly computable operations is closed under composition. Moreover, weakly computable operations on computable metric spaces are characterized as operations that admit upper semi-computable compact-valued selectors and it is proved that any single-valued weakly computable operation is already computable in the ordinary sense. (shrink)

This book intends to show that radical naturalism, nominalism and strict finitism account for the applications of classical mathematics in current scientific theories. The applied mathematical theories developed in the book include the basics of calculus, metric space theory, complex analysis, Lebesgue integration, Hilbert spaces, and semi-Riemann geometry. The fact that so much applied mathematics can be developed within such a weak, strictly finitistic system, is surprising in itself. It also shows that the applications of those classical theories (...) to the finite physical world can be translated into the applications of strict finitism, which demonstrates the applicability of those classical theories without assuming the literal truth of those theories or the reality of infinity. Both professional researchers and students of philosophy of mathematics will benefit greatly from reading this book. (shrink)

The conceptual incompatibility between General Relativity and Quantum Mechanics is generally seen as a sufficient motivation for the development of a theory of Quantum Gravity. If - so a typical argumentation - Quantum Mechanics gives a universally valid basis for the description of the dynamical behavior of all natural systems, then the gravitational field should have quantum properties, like all other fundamental interaction fields. And, if General Relativity can be seen as an adequate description of the classical aspects of gravity (...) and spacetime - and their mutual relation -, this leads, together with the rather convincing arguments against semi-classical theories of gravity, to a strategy which takes a quantization of General Relativity as the natural avenue to a theory of Quantum Gravity. And, because in General Relativity the gravitational field is represented by the spacetime metric, a quantization of the gravitational field would in some sense correspond to a quantization of geometry. Spacetime would have quantum properties. But, this direct quantization strategy to Quantum Gravity will only be successful, if gravity is indeed a fundamental interaction. Only if it is a fundamental interaction, the given argumentation is valid, and the gravitational field, as well as spacetime, should have quantum properties. - What, if gravity is instead an intrinsically classical phenomenon? Then, if Quantum Mechanics is nevertheless fundamentally valid, gravity can not be a fundamental interaction; a classical and at the same time fundamental gravity is excluded by the arguments against semi-classical theories of gravity. An intrinsically classical gravity in a quantum world would have to be an emergent, induced or residual, macroscopic effect, caused by a quantum substrate dominated by other interactions, not by gravity. Then, the gravitational field (as well as spacetime) would not have any quantum properties. And then, a quantization of gravity (i.e. of General Relativity) would lead to artifacts without any relation to nature. The serious problems of all approaches to Quantum Gravity that start from a direct quantization of General Relativity (e.g. non-perturbative canonical quantization approaches like Loop Quantum Gravity) or try to capture the quantum properties of gravity in form of a 'graviton' dynamics (e.g. Covariant Quantization, String Theory) - together with the, meanwhile, rich spectrum of (more or less advanced) theoretical approaches to an emergent gravity and/or spacetime - make this latter option more and more interesting for the development of a theory of Quantum Gravity. The most advanced emergent gravity (and spacetime) scenarios are of an information-theoretical, quantum-computational type. A paradigmatic model for the emergence of gravity and spacetime comes from the Pregeometric Quantum Causal Histories approach. (shrink)

The classical Hahn–Banach Theorem states that any linear bounded functional defined on a linear subspace of a normed space admits a norm-preserving linear bounded extension to the whole space. The constructive and computational content of this theorem has been studied by Bishop, Bridges, Metakides, Nerode, Shore, Kalantari Downey, Ishihara and others and it is known that the theorem does not admit a general computable version. We prove a new computable version of this theorem without unrolling the classical proof of the (...) theorem itself. More precisely, we study computability properties of the uniform extension operator which maps each functional and subspace to the set of corresponding extensions. It turns out that this operator is upper semi-computable in a well-defined sense. By applying a computable version of the Banach–Alaoglu Theorem we can show that computing a Hahn–Banach extension cannot be harder than finding a zero in a compact metric space. This allows us to conclude that the Hahn–Banach extension operator is ${\bf {\Sigma^{0}_{2}}}$ -computable while it is easy to see that it is not lower semi-computable in general. Moreover, we can derive computable versions of the Hahn–Banach Theorem for those functionals and subspaces which admit unique extensions. (shrink)

The mutual conceptual incompatibility between General Relativity and Quantum Mechanics / Quantum Field Theory is generally seen as the most essential motivation for the development of a theory of Quantum Gravity. It leads to the insight that, if gravity is a fundamental interaction and Quantum Mechanics is universally valid, the gravitational field will have to be quantized, not at least because of the inconsistency of semi-classical theories of gravity. The objective of a theory of Quantum Gravity would then be (...) to identify the quantum properties and the quantum dynamics of the gravitational field. If this means to quantize General Relativity, the general-relativistic identification of the gravitational field with the spacetime metric has to be taken into account. The quantization has to be conceptually adequate, which means in particular that the resulting quantum theory has to be background-independent. This can not be achieved by means of quantum field theoretical procedures. More sophisticated strategies, like those of Loop Quantum Gravity, have to be applied. One of the basic requirements for such a quantization strategy is that the resulting quantum theory has a classical limit that is (at least approximately, and up to the known phenomenology) identical to General Relativity. However, should gravity not be a fundamental, but an induced, residual, emergent interaction, it could very well be an intrinsically classical phenomenon. Should Quantum Mechanics be nonetheless universally valid, we had to assume a quantum substrate from which gravity would result as an emergent classical phenomenon. And there would be no conflict with the arguments against semi-classical theories, because there would be no gravity at all on the substrate level. The gravitational field would not have any quantum properties to be captured by a theory of Quantum Gravity, and a quantization of General Relativity would not lead to any fundamental theory. The objective of a theory of 'Quantum Gravity' would instead be the identification of the quantum substrate from which gravity results. The requirement that the substrate theory has General Relativity as a classical limit – that it reproduces at least the known phenomenology – would remain. The paper tries to give an overview over the main options for theory construction in the field of Quantum Gravity. Because of the still unclear status of gravity and spacetime, it pleads for the necessity of a plurality of conceptually different approaches to Quantum Gravity. (shrink)

Exception from Informed Consent (EFIC) regulations detail specific circumstances in which Institutional Review Boards (IRB) can approve studies where obtaining informed consent is not possible prior to subject enrollment.To better understand how IRB members evaluate community consultation (CC) and public disclosure (PD) processes and results, semi-structured interviews of EFIC-experienced IRB members were conducted and analyzed using thematic analysis.Interviews with 11 IRB members revealed similar approaches to reviewing EFIC studies. Most use summaries of CC activities to determine community members’ attitudes; (...) none reported using specific criteria nor recalled any CC reviews that resulted in modifications to or denials of EFIC studies. Most interviewees thought metrics based on Community VOICES’s domains (feasibility, participant selection, quality of communication, community perceptions, investigator/IRB perceptions) would be helpful.IRB members had similar experiences and concerns about reviewing EFIC studies. Development of metrics to assess CC processes may be useful to IRBs reviewing EFIC studies. (shrink)

Speakers routinely rely on a vast store of fixed and semi-fixed institutionalized utterances. In our mother tongue, we know how to combine pre-patterned phrases, complete semi-fixed expressions, and produce deviant versions for humorous effect. There are analogies with the way traditional folk musicians embellish tunes with a largely fixed structure, and the way jazz musicians improvise, and also with oral traditions in which poets composed or improvised tales during performance by using fixed formulas and formulaic phrases (though without (...) the metrical requirements of Homeric poetry). In written literature, the use of ready-made language was long disparaged as the opposite of creativity, but Barthes describes both speech and literature in general as consisting entirely of transformations of words that have already been set in order, and describes individual style as essentially a citational process, and the transformation of earlier formulae. Formulaic language can be shown to underlie much linguistic creativity. (shrink)

Scale invariance provides a principled reason for the physical importance of Hilbert space, the Virasoro algebra, the string mode expansion, canonical commutators and Schrödinger evolution of states, independent of the assumptions of string theory and quantum theory. The usual properties of dimensionful fields imply an infinite, projective tower of conformal weights associated with the tangent space to scale-invariant spacetimes. Convergence and measurability on this tangent tower are guaranteed using a scale-invariant norm, restricted to conformally self-dual vectors. Maps on the resulting (...) Hilbert space are correspondingly restricted to semi-definite conformal weight. We find the maximally- and minimally-commuting, complete Lie algebras of definite-weight operators. The projective symmetry of the tower gives these algebras central charges, giving the canonical commutator and quantum Virasoro algebras, respectively. Using a continuous, m-parameter representation for rank-m tower tensors, we show that the parallel transport equation for the momentum-vector of a particle is the Schrödinger equation, while the associated definite-weight operators obey canonical commutation relations. Generalizing to the set of integral curves of general timelike, self-dual vector-valued weight maps gives a lifting such that the action of the curves parallel transports arbitrary tower vectors. We prove that the full set of Schrödinger-lifted integral curves of a general self-dual map gives an immersion of its 2-dim parameter space into spacetime, inducing a Lorentzian metric on the parameter space. This immersion is shown to satisfy the full variational equations of open string. (shrink)

Euler’s interpretation of Newton’s gravity (NG) as Archimedes’ thrust in a fluid ether is presented in some detail. Then a semi-heuristic mechanism for gravity, close to Euler’s, is recalled and compared with the latter. None of these two ‘‘gravitational ethers’’ can obey classical mechanics. This is logical since the ether defines the very reference frame, in which mechanics is defined. This concept is used to build a scalar theory of gravity: NG corresponds to an incompressible ether, a compressible ether (...) leads to gravitational waves. In the Lorentz–Poincaré version, special relativity is compatible with the ether, but, with the heterogeneous ether of gravity, it applies only locally. A correspondence between metrical effects of uniform motion and gravitation is assumed, yet in two possible versions (one is new). Dynamics is based on a (non-trivial) extension of Newton’s second law. The observational status for the theory with the older version of the correspondence is summarized. (shrink)

§1. Introduction. Asymptotic cones of metric spaces were first invented by Gromov. They are metric spaces which capture the ‘large-scale structure’ of the underlying metric space. Later, van den Dries and Wilkie gave a more general construction of asymptotic cones using ultrapowers. Certain facts about asymptotic cones, like the completeness of the metric space, now follow rather easily from saturation properties of ultrapowers, and in this survey, we want to present two applications of the van den (...) Dries-Wilkie approach. Using ultrapowers we obtain an explicit description of the asymptotic cone of a semisimple Lie group. From this description, using semi-algebraic groups and non-standard methods, we can give a short proof of the Margulis Conjecture. In a second application, we use set theory to answer a question of Gromov.§2. Definitions. The intuitive idea behind Gromov's concept of an asymptotic cone was to look at a given metric space from an ‘infinite distance’, so that large-scale patterns should become visible. In his original definition this was done by gradually scaling down the metric by factors 1/nfornϵ ℕ. In the approach by van den Dries and Wilkie, this idea was captured by ultrapowers. Their construction is more general in the sense that the asymptotic cone exists for any metric space, whereas in Gromov's original definition, the asymptotic cone existed only for a rather restricted class of spaces. (shrink)

This book intends to show that, in philosophy of mathematics, radical naturalism (or physicalism), nominalism and strict finitism (which does not assume the reality of infinity in any format, not even potential infinity) can account for the applications of classical mathematics in current scientific theories about the finite physical world above the Planck scale. For that purpose, the book develops some significant applied mathematics in strict finitism, which is essentially quantifier-free elementary recursive arithmetic (with real numbers encoded as elementary recursive (...) Cauchy sequences of rational numbers). Applied mathematical theories developed in the book include the basics of calculus, metric space theory, complex analysis, Lebesgue integration, Hilbert spaces, and semi-Riemann geometry (sufficient for the basic applications in classical quantum mechanics and general relativity). The fact that so much applied mathematics can be developed within such a weak, strictly finitisitc system is perhaps surprising in itself. It also shows that the applications of those classical theories to the finite physical world can be translated into the applications of strict finitism, which demonstrates the applicability of those classical theories without assuming the literal truth of those theories or the reality of infinity. The first chapter of the book contains an informal introduction to its philosophical motivation and technical strategy. The book is intended for students and researchers in philosophy of mathematics. -/- Contents -/- Preface 1 Introduction 2 Strict Finitism 3 Calculus 4 Metric Space 5 Complex Analysis 6 Integration 7 Hilbert Space 8 Semi-Riemann Geometry References Index. (shrink)

The main features of how to build a Born’s Reciprocal Gravitational theory in curved phase-spaces are developed. By recurring to the nonlinear connection formalism of Finsler geometry a generalized gravitational action in the 8D cotangent space (curved phase space) can be constructed involving sums of 5 distinct types of torsion squared terms and 2 distinct curvature scalars ${\mathcal{R}}, {\mathcal{S}}$ which are associated with the curvature in the horizontal and vertical spaces, respectively. A Kaluza-Klein-like approach to the construction of the curvature (...) of the 8D cotangent space and based on the (torsionless) Levi-Civita connection is provided that yields the observed value of the cosmological constant and the Brans-Dicke-Jordan Gravity action in 4D as two special cases. It is found that the geometry of the momentum space can be linked to the observed value of the cosmological constant when the curvature in $\mathit{momentum}$ space is very large, namely the small size of P is of the order of $( 1/R_{\mathit{Hubble}})$ . Finally we develop a Born’s reciprocal complex gravitational theory as a local gauge theory in 8D of the $\mathit{deformed}$ Quaplectic group that is given by the semi-direct product of U(1,3) with the $\mathit{deformed}$ (noncommutative) Weyl-Heisenberg group involving four $\mathit{noncommutative}$ coordinates and momenta. The metric is complex with symmetric real components and antisymmetric imaginary ones. An action in 8D involving 2 curvature scalars and torsion squared terms is presented. (shrink)

Mathematically, the fusion of space and time may be explained as follows. In pre-relativity physics, space was envisaged as a three-dimensional Euclidean continuum. Such a continuum is homogeneous and isotropic, and its metrical character can be specified by the definition of the distance between any two points in the continuum: s2 = 2 + 2 + 2. Now, while it is possible to speak of a four-dimensional continuum in pre-relativity physics by adding the time-coordinate to the three space-coordinates, there is (...) no way, corresponding to the definition of s, to define the spatio-temporal "separation" or "interval" between any two points in this new four-dimensional continuum. Thus, while it makes sense from the classical point of view to ask for the distance between two points in space, it does not make sense to ask for the spatio-temporal interval between two events occurring in different places at different times. The spatio-temporal interval between non-simultaneous, spatially separated events is simply not defined in pre-relativity physics. Another way of putting it is that in classical physics space and time are measured in entirely disparate units and no method is provided for making these units comparable with one another. In relativity physics, on the other hand, light--or rather the velocity of light--provides the means for making the results of spatial and temporal measurement comparable quantities: one simply multiplies the time-like intervals by c, the fixed velocity of light, in order to obtain space-like intervals. The interval between any two events is defined as: s2 = 2 + 2 + 2 - c22. Interval, so defined, is an invariant, whereas spatial and temporal "separation" are now relative to the state of motion of the observer. The geometry of the four-dimensional continuum characterized by this formula is called "semi-Euclidean". (shrink)

Many perception and processing effects of the lexical status of tone have been found in behavioral, psycholinguistic, and neuroscientific research, often pitting varieties of tonal Chinese against non-tonal Germanic languages. While the linguistic and cognitive evidence for lexical tone is therefore beyond dispute, the word prosodic systems of many languages continue to escape the categorizations of typologists. One controversy concerns the existence of a typological class of “pitch accent languages,” another the underlying phonological nature of surface tone contrasts, which in (...) some cases have been claimed to be metrical rather than tonal. We address the question whether the Sequence Recall Task, which has been shown to discriminate between languages with and without word stress, can distinguish languages with and without lexical tone. Using participants from non-tonal Indonesian, semi-tonal Swedish, and two varieties of tonal Mandarin, we ran SRTs with monosyllabic tonal contrasts to test the hypothesis that high performance in a tonal SRT indicates the lexical status of tone. An additional question concerned the extent to which accuracy scores depended on phonological and phonetic properties of a language’s tone system, like its complexity, the existence of an experimental contrast in a language’s phonology, and the phonetic salience of a contrast. The results suggest that a tonal SRT is not likely to discriminate between tonal and non-tonal languages within a typologically varied group, because of the effects of specific properties of their tone systems. Future research should therefore address the first hypothesis with participants from otherwise similar tonal and non-tonal varieties of the same language, where results from a tonal SRT may make a useful contribution to the typological debate on word prosody. (shrink)

Because ports are considered to be the heart of the maritime transportation system, thereby assessing port performance is necessary for a nation’s development and economic success. This study proposes a novel metric, namely, “_port performance index (PPI)_”, to determine the overall performance and utilization of inland waterway ports based on six criteria,_ port facility, port availability, port economics, port service, port connectivity, and port environment_. Unlike existing literature, which mainly ranks ports based on quantitative factors, this study utilizes a (...) Bayesian Network (BN) model that focuses on both quantitative and qualitative factors to rank a port. The assessment of inland waterway port performance is further analyzed based on different advanced techniques such as sensitivity analysis and belief propagation. Insights drawn from the study show that all the six criteria are necessary to predict PPI. The study also showed that port service has the highest impact while port economics has the lowest impact among the six criteria on PPI for inland waterway ports. (shrink)

Data and metrics play an unmistakably powerful role in today's society. Over the years, their use has expanded to cover almost every sphere of everyday life. This book provides a critical investigation into what we can call a ""metric culture"" in which practices of self-tracking and quantification have become more popular than ever before.

In lieu of an abstract, here is a brief excerpt of the content:A Semi-Personal Story from a Ukrainian NGO Professional (or a Semi-Professional Story from a Ukrainian Person) Living through the WarYuliya NogovitsynaI live in Kyiv with my husband and two daughters. On 24 February 2022, my husband woke me up at 5 am tapping me on the shoulder and saying, “Yulia, wake up. There are bombings outside. The war started”. [End Page 160]That day was our younger daughter’s (...) birthday. She turned six. We had planned a birthday party for her with friends, cake, candles and birthday gifts. Instead, we had to move both daughters to the bathroom where there are no windows so that broken glass did not hurt them if a missile hit.I am the Program Director at Tabletochki Charity Foundation, Ukraine’s largest childhood cancer NGO (https://tabletochki.org/en/). For 11 years before the war, we have been fostering childhood cancer care in Ukraine—through our direct assistance to families, support of pediatric oncology units, professional development of medical personnel, and advocacy.The Russian invasion of Ukraine in February 2022 dramatically changed the healthcare system landscape in Ukraine. The physical threat, treatment disruption, exposure of immunosuppressed patients to improper conditions in bomb shelters and cellars, interruption in supplies, infrastructure damage, logistics failure, and funding constraints have been among the most manifested immediate and deferred implications of the war for the health-care system in Ukraine.That said, the biggest professional challenge was uncertainty and inability to plan. You have nothing to rely on in developing at least a short-term strategy. This may sound speculative and unimportant—who bothers about uncertainty when there is a physical threat to your life? But this is a wrong perception—uncertainty paralyzes and disables long before a bullet or missile reaches you.War also brings the collapse of relationships, partnerships, and coalitions. It depletes and limits resources, whether human, financial, or emotional. Scarce resources make hospitals, healthcare professionals, and NGOs compete for patients, donors, and financing. The war and the external threat unite only for a short period of emergency response. Once the situation transitions to a protracted conflict, people and institutions start fighting for their own survival.My family stayed in Ukraine but moved to Lviv, a city in Western Ukraine, which turned into an evacuation hub for children with cancer. More than 1,000 children with cancer were evacuated and referred for treatment abroad through the SAFER Ukraine collaborative initiative by St. Jude Global, Tabletochki, West-Ukrainian Specialized Children’s Medical Center (WUSCMC), and other international and local partners.During the first months of the war, we worked hand-in-hand day and night to bring critically ill children to safety and treatment. We sent evacuation convoys from Lviv to Poland twice a week, the largest one with 71 families, included four buses and 11 ambulances. We slept 4-5 hours per day. Within two weeks, my hands and legs were trembling from constant tension, concentration, and tiredness.And even this extremely fast-responding and effective evacuation may be questioned. We have been facing an ethical dilemma—whether the safety needs of the existing patients prevail over the needs of future patients in diagnostics and treatment in Ukraine. We discussed more than once whether we should stop evacuation and referral of children to European hospitals to sustain the Ukrainian childhood cancer care system and prevent it from degradation. It is very uncomfortable to confront such questions. Could our heroic efforts to evacuate as many Ukrainian children with cancer as possible turn into an evil for future patients to come? By evacuating patients, we left pediatric oncology units empty, without work for Ukrainian pediatric oncologists, and the usual pathways for diagnostics and treatment were disrupted. A healthcare system without patients is like a cardiovascular system without blood.My family returned to Kyiv in August 2022 for our daughters to continue their schooling. There were (and still are) only five to seven kids in a class; other children left Ukraine or switched to online studies. My husband and I decided that our children will attend school offline—despite the regular missile attacks. This is a private school; we pay for it. In such a way... (shrink)

In a number of publications A.N. Prior considered the use of what he called ‘metric tense logic’. This is a tense logic in which the past and future operators P and F have an index representing a temporal distance, so that Pnα means that α was true n -much ago, and Fn α means that α will be true n -much hence. The paper investigates the use of metric predicate tense logic in formalising phenomena ormally treated by such (...) devices as multiple indexing or quantification over times. (shrink)

This paper examines one aspect of the legacy of the Value-Free Ideal in conservation science: the view that measurements and metrics in conservation are value-free epistemic tools detached from ideological, ethical, social, and, generally, non-epistemic considerations. Contrary to this view, I will argue that traditional measurement practices entrenched in conservation are in fact permeated with non-epistemic values. I challenge the received view by revealing three non-epistemic assumptions underlying traditional metrics: 1) a human-environment demarcation, 2) the desirability of a people-free landscape, (...) and 3) the exclusion of cultural diversity from biodiversity. I also draw a connection between arguments for retaining traditional metrics to “scientific colonialism,” exemplified by a fortress conservation model. I conclude by advocating for abandoning the myth of the intrinsic value-freedom of measurement practices and embracing metrics aligned with societal and scientific goals. (shrink)

The purpose of this paper is to define a new logic $${\mathcal {SI}}$$ called semi-intuitionistic logic such that the semi-Heyting algebras introduced in [ 4 ] by Sankappanavar are the semantics for $${\mathcal {SI}}$$ . Besides, the intuitionistic logic will be an axiomatic extension of $${\mathcal {SI}}$$.

What has the dispositional analysis of properties and laws (e.g. Molnar, Powers, Oxford University Press, Oxford, 2003; Mumford, Laws in nature, Routledge London, 2004; Bird, Nature’s metaphysics, Clarendon Press, Oxford, 2007) to offer to the scientific understanding of physical properties?—The article provides an answer to this question for the case of spacetime points and their metrical properties in General Relativity. The analysis shows that metrical properties are not ‘powers’, i.e. they cannot be understood as producing the effects of spacetime on (...) matter with metaphysical necessity. Instead they possess categorical characteristics which, in connection with specific laws, explain those effects. Thus, the properties of spacetime do not favor the metaphysics of powers with respect to properties and laws. (shrink)

We introduce and study (weakly) semi-equational theories, generalizing equationality in stable theories (in the sense of Srour) to the NIP context. In particular, we establish a connection to distality via one-sided strong honest definitions; demonstrate that certain trees are semi-equational, while algebraically closed valued fields are not weakly semi-equational; and obtain a general criterion for weak semi-equationality of an expansion of a distal structure by a new predicate.

In this paper we introduce a logic that we name semi Heyting–Brouwer logic, \, in such a way that the variety of double semi-Heyting algebras is its algebraic counterpart. We prove that, up to equivalences by translations, the Heyting–Brouwer logic \ is an axiomatic extension of \ and that the propositional calculi of intuitionistic logic \ and semi-intuitionistic logic \ turn out to be fragments of \.

ABSTRACT Semi-revision is a mode of belief change that differs from revision in that the input sentence is not always accepted. A constructive approach to semi-revision is proposed. It requires an efficient treatment of local inconsistencies, which is more easily obtainable in belief base models than in belief set models. Axiomatic characterizations of two semi-revision operators are reported.

Metrics shape our social worlds in many and more ways. Everyday quantifications of our preferences, our behaviors and our relationships, alter us and the institutions that we constitute. This essay takes a brief look at the metrics of business ethics through two analytic devices. Representation explains the notion that metrics can capture or demonstrate ethics and performativity explains the notion that metrics can shape or constitute ethics. The analytic distinction between representation and performativity is obscured in practice when metrics become (...) targets, indeed much of the social power of metrics comes from their use as targets. Hence, we should pay attention to the world of practice in which measuring and doing are entangled. However, we should not lose sight of the limitations of measurement and the possibility that there are areas of ethical life best left unmeasured. (shrink)

De Marchi and Lorenzetti :253-261, 2016) have recently argued that in fields where the journal impact factor is not calculated, such as in the humanities, it is key to find other indicators that would allow the relevant community to assess the quality of scholarly journals and the research outputs that are published in them. The authors' suggestion is that information concerning the journal's rejection rate and the number of subscriptions sold is important and should be used for such assessment. The (...) question addressed by the authors is very important, yet their proposed solutions are problematic. Here I point to some of these problems and illustrate them by considering as a case in point the field of philosophy. Specifically, here I argue for four main claims. First, even assuming that IF provides a reliable indicator of the quality of journals for the assessment of research outputs, De Marchi and Lorenzetti have failed to validate their suggested indicators and proxies. Second, it has not been clarified why, in absence of IF, other journal-based metrics that are currently available should not be used. Third, the relationship between IF and rejection rate is more complex than the authors suggest. Fourth, accepting the number of sold subscriptions as a proxy would result in discrimination against open access journals. The upshot of my analysis is that the question of how to assess journals and research outputs in the humanities is still far from resolved. (shrink)