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 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)

We classify countable metrically homogeneous graphs of diameter 3.

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)

The idea that sentences can be closer or further apart in meaning is highly intuitive. Not only that, it is also a pillar of logic, semantic theory and the philosophy of science, and follows from other commitments about similarity. The present paper proposes a novel way of comparing the ‘distance’ between two pairs of propositions. We define ‘\ is closer in meaning to \ than \ is to \’ and thereby give a precise account of comparative propositional similarity facts. Notably, (...) our definition eschews metric assumptions, which are unrealistic in most applications of interest. (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.

£ The existence of a model for a logic program is generally established by lattice-theoretic arguments. We present three examples to show that metric methods can often be used instead, generally in a direct, straightforward way. One example is a game program, which is not stratified or locally stratified, but which has a unique supported model whose existence is easily established using metric methods. The second example is a program without a unique supported model, but having a part (...) that is ‘well-behaved.’ The third example is a program in which one part depends on another, illustrating how modularity might be treated metrically. Finally we use ideas from this third example to prove a general result from [3]. The intention in presenting these examples and the theorem is to stimulate interest in.. (shrink)

It is shown that for compact metric spaces the following statements are pairwise equivalent: “X is Loeb”, “X is separable”, “X has a we ordered dense subset”, “X is second countable”, and “X has a dense set G = ∪{Gn : n ∈ ω}, ∣Gn∣ < ω, with limn→∞ diam = 0”. Further, it is shown that the statement: “Compact metric spaces are weakly Loeb” is not provable in ZF0 , the Zermelo-Fraenkel set theory without the axiom of (...) regularity, and that the countable axiom of choice for families of finite sets CACfin does not imply the statement “Compact metric spaces are separable”. (shrink)

Citation metrics are statistical measures of scientific output that draw on citation indexes. They purport to capture the impact of scientific articles and the journals in which they appear. As evaluative tools they are mostly used in the natural sciences, but they are also acquiring an important role in the humanities. While the strengths and weaknesses of citation metrics are extensively debated in a variety of fields, they have only recently started attracting attention in the philosophy of science. This paper (...) takes a further step in this direction and presents an analysis of citation metrics from the perspective of a Kuhnian model for the development of science. To do so, it assesses the argument made against the use of citation metrics for scientific research by Gillies (2008). According to Gillies, citations metrics tend to over-protect normal science at the expenses of revolutionary science–in other words, reinforce the status quo rather than supporting innovations and breakthroughs. Unlike Gillies, this paper focuses on the context of normal science and shows that citation metrics can in fact arbitrarily hinder its development when they do not take field-specific differences into account. In light of this, the paper cautions against their use for evaluative purposes. To argue for this conclusion, the paper shows that citation metrics fail to “carve science at its joints” and thus cannot be relied upon as indicators of scientific quality that can support the development of normal science. (shrink)

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)

General relativity poses serious problems for counterfactual propositions peculiar to it as a physical theory. Because these problems arise solely from the dynamical nature of spacetime geometry, they are shared by all schools of thought on how counterfactuals should be interpreted and understood. Given the role of counterfactuals in the characterization of, inter alia, many accounts of scientific laws, theory confirmation and causation, general relativity once again presents us with idiosyncratic puzzles any attempt to analyze and understand the nature of (...) scientific knowledge must face. (shrink)

The paper introduces a broad family of metrics applicable to finite and countably infinite strings, or, by extension, to formal structures serving as semantics for countable languages. The main focus is on applications to sets of pointed Kripke models, a semantics for modal logics. For the resulting metric spaces, the paper classifies topological properties including which metrics are topologically equivalent, providing sufficient conditions for compactness, characterizing clopen sets and isolated points, and characterizing the metrical topologies by a concept of (...) logical convergence. We then apply the approach to maps from dynamic epistemic logic, showing that product updates with action models yield continuous maps, hence allowing for an interpretation of the iterated updates as discrete time dynamical systems. (shrink)

Text, interpretation and metre present a tangled problem in this threnody, and the solutions of editors differ widely. The chief function of detailed metrical study in such corrupt passages of lyric is to weight the scales in favour of—or more often against—certain methods of handling the text. The positive results of this present attempt to apply metrical criteria are necessarily modest and tentative; negatively they are, I think, sometimes decisive.

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)

This work copiles key metrics to measure and evalute the impact of science and technology on academia, industry and government. it covers such topics as ...

In his Works of Pindar, Vol. II, p. xxiii, Dr. L. R. Farnell discusses the admission of metrical licences into Pindar's text, and pronounces that ‘the “Responsion-law” should not be pressed with over-strained severity.’ In general he agrees with Wilamowitz and Schroeder and disagrees with the stricter school of P. Maas. But none of these scholars have formulated the principles by which long syllables may be equated with short in Pindar's text, or even those by which two short syllables may (...) take the place of one long and vice versa. Such attempts were made by great scholars of the past, notably by Erasmus Schmid, Hermann and Boeckh, but recent developments in metric and textual criticism have created a new attitude towards metrical problems and provided a new vocabulary. It is time that Pindar's practice was re-examined. Only from it can we deduce what his rules of composition were and find out what licences he allowed and what not. The question is important both for the textual critic and for the student of Greek metric. If we can discover the principles on which Pindar used such metrical licences, we shall be more qualified to consider emendations which involve them and to understand the rules which he set before himself when composing an ode. (shrink)

We study Polish spaces for which a set of possible distances $A \subseteq R^+$ is fixed in advance. We determine, depending on the properties of A, the complexity of the collection of all Polish metric spaces with distances in A, obtaining also example of sets in some Wadge classes where not many natural examples are known. Moreover we describe the properties that A must have in order that all Polish spaces with distances in that set belong to a given (...) class, such as zero-dimensional, locally compact, etc. These results lead us to give a fairly complete description of the complexity, with respect to Borel reducibility and again depending on the properties of A, of the relations of isometry and isometric embeddability between these Polish spaces. (shrink)

The core aims of the Global Health Impact Project include incentivizing pharmaceutical companies for socially conscious production and promoting socially conscious consumption among consumers. Its backbone is a metric that computes the amount of illness burden alleviated by a pharmaceutical drug. This essay aims to assess the connection between values and numbers in the Global Health Impact Project. Specifically, I concentrate on two issues, the anonymity of illness burden and the distribution of health benefits. The former issue asks whether (...) we should treat the illness burden of every person the same. The latter issue asks among whom health benefits should be fairly distributed. Examination of these issues begs for clarification of some of the key concepts of the Global Health Impact Project, such as the definition of essential medicines and the significance of national borders. Although this essay focuses on the two particular metric issues in the Global Health Impact Project, its core argument is applicable to other metrics for ethically motivated initiatives—to construct a metric for an ethically motivated initiative, it is not only important to articulate underlying concepts and values, but it is also important to operationalize them, so they are consistently reflected in the metric. (shrink)

We classify countable metrically homogeneous graphs of diameter 3.

The size of animal exhibits has important effects on their lives and welfare. However, most references to exhibit size only consider floor space and height dimensions, without considering the space afforded by usable features within the exhibit. In this paper, we develop two possible methods for measuring the usable space of zoo exhibits and apply these to a sample exhibit. Having a metric for usable space in place will provide a better reflection of the quality of different exhibits, and (...) enhance comparisons between exhibits. (shrink)

In the mid twenty-tens, many major food companies committed to sustainably source their priority ingredients, including North American commodity crops. With deadlines set for the decade’s end, companies joined multi-stakeholder initiatives and developed standards, metrics, and other assessment tools to help them track and drive progress. In short, they embarked on the sort of corporate supply chain governance that agri-food scholars have long studied. But how would this governance happen, especially in the commodity supply chains where companies knew and controlled (...) little about upstream production? Treating supply chain governance as not just a corporate undertaking but also the work of mid-level sustainability managers, this paper examines the practical skills and knowledge, or mētis, employed by managers in their efforts to win the support of colleagues, farmers, and other supply chain actors. This analysis provides insight into how and why food companies’ approaches to governing agricultural sustainability have changed since they set their 2020 sourcing goals. More broadly, it highlights the contingent nature of their governance. (shrink)

This essay defines Maoism as an experiment in intimate governance and an attempt—albeit a failed one—to dismantle the divide between political leaders and ordinary people. The Communist Party’s claim to intimacy with the people needs to be constantly reenacted in the relationship between party cadres and ordinary citizens––a cadre’s gestures, habits, and attitudes are magnified and scrutinized under the lens of party legitimacy. The special privileges (tequan, 特权) of party leaders are what I call metrics of exceptionality, which separate the (...) party from the people. The promise to govern on the basis of intimacy with the people did not eradicate ruling class entitlements and arrogance but delegitimized them and opened them up to public scrutiny. Although the process of eradicating privileges was always several steps behind their elaboration and intensification, the former was a normative goal that shaped how ordinary citizens perceived and interacted with party cadres. This dual movement in opposing directions still constitutes the fundamental contradiction of China’s political system as seen from within. This essay revisits and examines crucial historical junctures in the People’s Republic of China as framed by popular contestations of special privilege. The fact that in the post-Mao period, party leaders still speak in the language of intimacy, proximity, and distance indicates the aesthetic importance of this relationship in party ideology, despite public complaints regarding its absence. Even when intimacy as a political mode of communication is able to communicate nothing but its own failure, the proximity between the party and the people takes center stage as the aesthetic foundation of party legitimacy. (shrink)

We introduce a new way of defining metric temporal logic on a real-numbers flow of time. The idea is based on having semantics which allow us to refer to a single universal clock of arbitrary precision in order to impose metric constraints. This gives us a new metric temporal logic which is very expressive, is natural to use, can be applied in very general situations, affords a wide range of useful abbreviations and operators, has a PSPACE decision (...) procedure, and has the promise of being amenable to standard reasoning techniques. Thus it has many advantages over the existing metric temporal logics. We provide a decision procedure via conversion to a non-metric temporal logic, hence doing metric reasoning with no clocks. (shrink)

We study conditions for a topological space to be metrizable, properties of metrizable spaces, and the role the axiom of choice plays in these matters.

§ 1. Introduction. In this communication we present some recent results on the classification of Polish metric spaces up to isometry and on the isometry groups of Polish metric spaces. A Polish metric space is a complete separable metric space.Our first goal is to determine the exact complexity of the classification problem of general Polish metric spaces up to isometry. This work was motivated by a paper of Vershik [1998], where he remarks : “The classification (...) of Polish spaces up to isometry is an enormous task. More precisely, this classification is not ‘smooth’ in the modern terminology.” Our Theorem 2.1 below quantifies precisely the enormity of this task.After doing this, we turn to special classes of Polish metric spaces and investigate the classification problems associated with them. Note that these classification problems are in principle no more complicated than the general one above. However, the determination of their exact complexity is not necessarily easier.The investigation of the classification problems naturally leads to some interesting results on the groups of isometries of Polish metric spaces. We shall also present these results below.The rest of this section is devoted to an introduction of some basic ideas of a theory of complexity for classification problems, which will help to put our results in perspective. Detailed expositions of this general theory can be found, e.g., in Hjorth [2000], Kechris [1999], [2001]. (shrink)

If ${\mathfrak {F}}$ is a type-definable family of commensurable subsets, subgroups or subvector spaces in a metric structure, then there is an invariant subset, subgroup or subvector space commensurable with ${\mathfrak {F}}$. This in particular applies to type-definable or hyper-definable objects in a classical first-order structure.

Distributive justice deals with allocations of goods and bads within a group. Different principles and results of distributions are seen as possible ideals. Often those normative approaches are solely framed verbally, which complicates the application to different concrete distribution situations that are supposed to be evaluated in regard to justice. One possibility in order to frame this precisely and to allow for a fine-grained evaluation of justice lies in formal modelling of these ideals by metrics. Choosing a metric that (...) is supposed to map a certain ideal has to be justified. Such justification might be given by demanding specific substantiated axioms, which have to be met by a metric. This paper introduces such axioms for metrics of distributive justice shown by the example of needs-based justice. Furthermore, some exemplary metrics of needs-based justice and a three dimensional method for visualisation of non-comparative justice axioms or evaluations are presented. Therewith, a base worth discussing for the evaluation and modelling of metrics of distributive justice is given. (shrink)

We prove that each ∀1 free amalgamation class K over a finite relational language L admits a countable generic structure M isometrically embedding all countable structuresin K relative to a fixed metric. We expand L by infinitely many binary predicates expressingdistance, and prove that the resulting expansion of K has a model companion axiomatizedby the first-order theory of M. The model companion is non-finitely axiomatizable, evenover a strong form of the axiom scheme of infinity.

There is a long tradition in economics of evaluating social arrangements by the extent to which individuals' preferences are satisfied. This is the tradition of welfarism, which has developed from nineteenth-century utilitarianism. Increasingly, however, the presumption that preference-satisfaction is the appropriate standard for evaluating social arrangements is being challenged by an alternative view: that we should focus on the set of opportunities open to each individual.

Using the Weyl-type canonical coordinates, an integration of Einstein's field equations in the cylindrosymmetric case considered by Kurşunoğlu is reexamined. It is made clear that the resulting metric is not describing the spacetime in a rotating frame, but in astatic cylindrical elastic medium. The conclusion of Kurşunoğlu that “for an observer on a rotating disk there is no way of escape from a curved spacetime” is therefore not valid. The metric in an empty rotating frame is found as (...) a solution of Einstein's field equations, and is not orthogonal. It is shown that the corresponding orthogonal solution represents spacetime in an inertial frame expressed in cylindrical coordinates. Introducing a noncoordinate basis, the metric in a rotating frame is given the static form of Kurşunoğlu's solution. The essential role played by the nonvanishing structure coefficients in this case is made clear. (shrink)

We introduce a new Turing machine based concept of time complexity for functions on computable metric spaces. It generalizes the ordinary complexity of word functions and the complexity of real functions studied by Ko [19] et al. Although this definition of TIME as the maximum of a generally infinite family of numbers looks straightforward, at first glance, examples for which this maximum exists seem to be very rare. It is the main purpose of this paper to prove that, nevertheless, (...) the definition has a large number of important applications. Using the framework of TTE [40], we introduce computable metric spaces and computability on the compact subsets. We prove that every computable metric space has a c-proper c-admissible representation. We prove that Turing machine time complexity of a function computable relative to c-admissible c-proper representations has a computable bound on every computable compact subset. We prove that computably compact computable metric spaces have concise c-proper c-admissible representations and show by examples that many canonical representations are of this kind. Finally, we compare our definition with a similar one by Labhalla et al. [22]. Several examples illustrate the concepts. By these results natural and realistic definitions of computational complexity are now available for a variety of numerical problems such as image processing, integration, continuous Fourier transform or wave propagation. (shrink)

We study versions of limit models adapted to the context of metric abstract elementary classes. Under categoricity and superstability-like assumptions, we generalize some theorems from 7, 15-17. We prove criteria for existence and uniqueness of limit models in the metric context.

Info-metrics is a framework for rational inference based on insufficient information. The complete info-metric framework, accompanied with many interdisciplinary examples and case studies, as well as graphical representations of the theory appear in the new book “Foundations of Info-Metrics: Modeling, Inference and Imperfect Information,” Oxford University Press, 2018. In this commentary, I describe that framework in general terms, demonstrate some of the ideas via simple examples, and provide arguments for using it to transform information into useful knowledge.

The issue of plagiarism—claiming credit for work that is not one’s own, rightly, continues to cause concern in the academic community. An analysis is presented that shows the effects that may arise from metrics-based assessments of research, when credit for an author’s outputs (chiefly publications) is given to an institution that did not support the research but which subsequently employs the author. The incentives for what is termed here “institutional plagiarism” are demonstrated with reference to the UK Research Assessment Exercise (...) in which submitting units of assessment are shown in some instances to derive around twice the credit for papers produced elsewhere by new recruits, compared to papers produced ‘in-house’. (shrink)