ArgumentMetrological techniques to establish shared quantitative measures have often been seen as signs of rational modernization. The cases considered here show instead the close relation of such techniques with antiquarian and revivalist programs under imperial regimes. Enterprises in survey sciences in Egypt in the wake of the French invasion of 1798 and in India during the East India Company's revenue surveys involved the promotion of a new kind oforiental metrologydesigned to represent colonizers’ measures as restorations of ancient values to be (...) applied to current systems of survey and measurement. Surveyors’ practice and hardware help clarify the significance of the complex historical and political functions of scientific standards. The balance of the paper discusses the survey work of later nineteenth-century indigenous Egyptian astronomers at a conjuncture of major economic and political dislocation to explore the various versions of antiquity at stake in these metrological programs. (shrink)

The stadion is the unit of length by which distances are reported in ancient Greek geographical sources. The itinerary indications in stadia can be found in several texts, but no specific unit values are given in the ancient geographers’ surviving works. However, the notion of a vaguely quantified, non-metrological itinerary unit is contradicted by the presence, since Hellenistic times, of road marker stones bearing distance indications along major ancient roads. The key assumption in this study is that, whatever the unit (...) involved, main roads were actually measured to the best of capabilities, and distance measurements in ancient works did refer to some specific metrological system. Some well-known Greek languagecxesst sources are analyzed with the support of archeologic information obtained from a small number of pre-Roman road markers, and from modern reports of investigations about ancient roads and sites. Based on the evidence, it is shown that two different stadion values were most often used as itinerary units in the Greek and Hellenistic world, namely 177 m and 210 m, that can be traced respectively to the so-called Attic foot and Philetaeric (Ionic/Samian) foot. Conversion among units did also occur, and this may offer explanations for supposed textual inconsistencies that have so far proved hard to understand. (shrink)

The representational theory of measurement has long been the central paradigm in the philosophy of measurement. Such is not the case anymore, partly under the influence of the critique according to which RTM offers too poor descriptions of the measurement procedures actually followed in science. This can be called the metrological critique of RTM. I claim that the critique is partly irrelevant. This is because, in general, RTM is not in the business of describing measurement procedures, be it in idealized (...) form. To support this claim, I present various cases where RTM can be said to investigate measurement without providing any measurement procedure. Such limit cases lead to a better understanding of the RTM project. They also illustrate some of the questions which the philosophy of measurement can explore, when it is ready to go beyond the metrological viewpoint. (shrink)

Astronomer Charles Piazzi Smyth’s 1864–65 expedition to measure the Great Pyramid of Giza was planned around a system of linear measures designed to guarantee the validity of his measurements and settle ongoing uncertainties as to the Pyramid’s true size. When the intended system failed to come together, Piazzi Smyth was forced to improvise a replacement that presented a fundamental challenge to the metrological enterprise upon which his system had been based. The astronomer’s new system centered around a small lump of (...) basalt, now held at Cambridge’s Whipple Museum of the History of Science, which nucleated a wide array of material and scientific considerations. Through a bipartite analysis of the physical and narrative dimensions of Piazzi Smyth’s basalt Standard, I develop the implications of its use and construction for understanding the material constitution of scientific instruments. In particular, I illustrate how instruments are locally constituted through co-accountable systems and how their material features become integrally implicated in both their uses and meanings. (shrink)

Summary The growing need for standardized units of measure led to major metrological reforms in the mid-nineteenth century. This paper focusses on their implementation in the Kingdom of Hanover and the involvement of C.F. Gauss. His papers reveal how much the success of his precision measurements hinged on the skill of his mechanic M. Meyerstein. A discussion of the regional weights and measures and the standardization procedure is followed by a description of various precision balances and the weighing methods employed (...) as well as a review of the problems posed by reliable length calibration. The success of the enterprise rested not only on intellectual prestige and ministerial clout but also on the hands-on skill of the mechanical practitioner. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 63.4 (2002) 555-575 [Access article in PDF] Measurer of All Things:John Greaves (1602-1652), the Great Pyramid, and Early Modern Metrology Zur Shalev [Figures]Writing from Istanbul to Peter Turner, one of his colleagues at Merton College, Oxford, John Greaves was deeply worried: Onley I wonder that in so long time since I left England I should neither have received my brasse quadrant which I (...) left to be finished for my journey thither, nor any notice of it [...]. I agreed with mr. Allen upon price and the time that he should finish it, if he hath failed me he hath done me the greatest injury that can be. 1A great injury indeed, because Greaves's journey to Italy and the Levant was all about measuring—luckily the instrument did reach him at some later stage. The thirty-six-year-old Professor of Geometry at Gresham College was taking the measurements of countless monuments and objects in the locations he visited. In Rome he measured, among many other ancient structures, Cestius' Pyramid and St. Peter's basilica. In Lucca, deeply impressed, he counted his paces around the beautiful city walls. In Siena he observed together with a "Mathematical Professor" one of the Sidera Medicea using "a glass." In Egypt he even hurt his eyes gazing at the sun, looking for sunspots and measuring its diameter. 2 His measuring mission, however, culminated in the fixing of the [End Page 555] latitudes of Istanbul, Rhodes, and Alexandria. As Bishop Juxton wrote before the trip to Greaves's employers at Gresham College (apparently using Greaves's own promotional language): This worke I find by the best astronomers, especially by Ticho Brache [ sic ] and Kepler, hath beene much desired as tending to the advancement of that science, and I hope it wil be an honour to that nation and prove ours if we first observe it. 3A mathematician-Orientalist, commanding the ancient and modern astronomical and geographical literature of Latin, Greek, Hebrew, Arabic, and Persian authors, Greaves was arguably the best qualified European at the period to perform the task. That he miscalculated the latitude of Rhodes is of less consequence for his present-day readers. 4 However, one of the most obscure and therefore telling of his measurement activities was the survey of the Pyramids of Giza, which resulted in the Pyramidographia (1646). 5 This remarkable learned treatise and travel account hybrid, which is at the focus of the present study, gives us a glimpse into the rich and complex world of scientific antiquarians.Greaves is most conveniently remembered today as an Orientalist. While we must be thankful to Edward Said for broadening the meaning of Orient-alism—from an academic discipline, accumulating objective knowledge of the East, into a much wider cultural discourse, his emphasis on the nineteenth and twentieth centuries and on the European colonial mindset is less useful for making historical sense of what early modern Orientalists were doing—physically and culturally. We can understand Greaves's "Oriental" enterprise in its [End Page 556] depth and variety only within long established European traditions of scholarship and keeping the intellectual concerns of his time in mind. 6But beyond articulating for us the nature of early Orientalism, the Pyramidographia, as well as Greaves's entire scientific career, situated in their wider European context, provide a fine entry point into a foreign world of learned practices and methods. It teaches us how well into the seventeenth century astronomy and philology, observation and bookishness, could coalesce in one figure, in one enterprise. 7 We still lack a modern biography of Greaves, a complex protagonist of a complex period, and even a full evaluation of his intellectual work. While this paper surely cannot compensate for that, I do attempt here a brief exposition of Greaves's Pyramidographia. 8Modern historians of archaeology and Egyptology, preoccupied mostly with the disciplines' progress and development of scientific standards, have noted the Pyramidographia in passing and praised its precise language and rigorous research... (shrink)

Metrology is a discipline of expunging impurities. The mid-nineteenth century French physicist Henri-Victor Regnault created a whole new way of doing experiments, attempting to produce standards physically by the "direct method." His immodest ambition to control all disturbing parameters represents a relict in the physical sciences of Romantic hopes for an all-embracing, artistic and aesthetic approach to nature, expressed in the absolute, eternal determination of nature's constants and their numerical relationships. The novelist Gustave Flaubert, whose rejection of metaphysics, love for (...) finest detail, concern for impartial treatment of the human psyche, and perfectionism, made him Regnault's literary complement, likewise hoped for this utopian union of science and art. There is a romantic and a modern ring to their ideals which were not to be achieved by optimism, but by introducing systematic doubt, by thoroughly studying impurities and expunging them. Nature did not speak clearly, but hid behind a multitude of disturbing effects—revealed only by the experimenter's or writer's voluntary restraint and self-denial, a disinterestedness Regnault and Flaubert celebrated as the highest and holiest morality. For them, attention to secondary matters became primary, because they expected them to lead the way to the grail. (shrink)

The main aim of this research is to analyse the peculiarities of legal regulation of metrology and the problems arising in this area. The content of the article is divided into two parts. The first part of the article analyses the concept of metrology, reveals the relation between fundamental and legal metrology and accentuates problems of metrology as well as repressive means applied in the metrological procedure. The second part analyses the European Union as well as national legislation regulating the (...) implementation of metrology in Lithuania and peculiarities of harmonisation of national law with the European Union legislation. (shrink)

In this paper I propose to read the history of systems of units, and in particular the current reform of the International System of Units (SI), understood as a set of measuring norms, in the light of reflective equilibria. The idea is that the model of reflective equilibria actually applies to processes which can be empirically observed or studied. This can help us to understand the nature of normativity and to shed light on its relativity to, and dependence on, practice.

I argue that dimensional analysis provides an answer to a skeptical challenge to the theory of model mediated measurement. The problem arises when considering the task of calibrating a novel measurement procedure, with greater range, to the results of a prior measurement procedure. The skeptical worry is that the agreement of the novel and prior measurement procedures in their shared range may only be apparent due to the emergence of systematic error in the exclusive range of the novel measurement procedure. (...) Alternatively: what if the two measurement procedures are not in fact measuring the same quantity? The theory of model mediated measurement can only say that we _assume_ that there is a common quantity. In contrast, I show that the satisfaction of dimensional homogeneity across the metrological extension is independent evidence for the so-called assumption. This is illustrated by the use of dimensional analysis in high pressure experiments. This results in an extension of the theory of model mediated measurement, in which a common quantity in metrological extension is no longer assumed, but hypothesized. (shrink)

In 2012, the Geological Time Scale, which sets the temporal framework for studying the timing and tempo of all major geological, biological, and climatic events in Earth’s history, had one-quarter of its boundaries moved in a widespread revision of radiometric dates. The philosophy of metrology helps us understand this episode, and it, in turn, elucidates the notions of calibration, coherence, and consilience. I argue that coherence testing is a distinct activity preceding calibration and consilience, and I highlight the value of (...) discordant evidence and trade-offs scientists face in calibration. The iterative nature of calibration, moreover, raises the problem of legacy data. (shrink)

Exactitude. The Genesis of an Epistemic Virtue in the ‘Long Nineteenth Century’. The article examines the genesis of exactitude as an epistemic virtue in both scholarly and scientific contexts in the 19th century, mainly in Prussia. Starting with an influential historiographic work on ancient metrology three semantic fields of accuracy, exactitude and precision are differentiated and pursued in their etymologies as well as applications. The historic situation between 1790 and 1860 is identified as the crucial period when the exactness of (...) the exact sciences as well as the notion of accuracy in the humanities start to diverge from one another in order to develop an epistemic virtue each on its own. (shrink)

At the intersection of taxonomy and nomenclature lies the scientific practice of typification. This practice occurs in biology with the use of holotypes (type specimens), in geology with the use of stratotypes, and in metrology with the use of measurement prototypes. In this paper I develop the first general definition of a scientific type and outline a new philosophical theory of types inspired by Pierre Duhem. I use this general framework to resolve the necessity-contingency debate about type specimens in philosophy (...) of biology, to advance the debate over the myth of the absolute accuracy of standards in metrology, and to address the definition-correlation debate in geology. I conclude that just as there has been a productive synergy between philosophical accounts of natural kinds and scientific taxonomic practices, so too there is much to be gained from developing a deeper understanding of the practices and philosophy of scientific types. (shrink)

Academia’s mathematical metaphysics are briefly explored en route to an elaboration of the qualitatively rigorous requirements underpinning the calibration and unambiguous interpretation of quantitative instrumentation in any science. Of particular interest are Gadamer’s emphases on number as the paradigm of the noetic, on the role of play in interpretation, and on Hegel’s sense of method as the activity of the thing itself that thought experiences. These point toward and overlap with (1) Latour’s study of the metrological social networks through which (...) technological phenomena are brought into language as modes of being that can be understood, and (2) the way that Rasch’s models for measurement comprise a potential beginning for metaphysically astute, qualitatively and quantitatively integrated, mathematical methods in the social sciences. The paper closes with observations on the general problem that is philosophy, the need to remain open to multiplicities of meaning even as clear understandings are sought and obtained. (shrink)

[ENGLISH] The present article is a contribution to the development of metrological structural realism. This position of philosophy of science goes back to Matthias Neuber, who introduces it as a third variation of the main structural realisms: epistemic structural realism and ontic structural realism. Here, Neuber attempts to tackle the problems of OSR and ESR while preserving their respective strengths. Of central importance to his approach, are the concepts of invariance, structure and, especially, measurement. Starting from Eino Kaila’s „non-linguistic, realist (...) account of logical empricism“, the present article investigates the necessity of yet another position of structural realism. The established structural realisms are examined for their strengths and weaknesses. Afterwards, the requirements on MSR are formulated in a way that extends beyond Neuber’s account. These requirements are of ontological, epistemological and metrological nature. -/- [DEUTSCH] Der vorliegende Aufsatz ist ein Beitrag zur Entwicklung des Metrologischen Strukturenrealismus. Diese Wissenschaftstheoretische Position geht auf Matthias Neuber zurück, der sie als dritte Spielart zwischen den großen Strukturenrealismen – dem Epistemischen Strukturenrealismus und dem Ontischen Strukturenrealismus – ansiedelt. Neuber versucht, die wissenschaftstheoretischen Probleme von ESR und OSR anzugehen, gleichzeitig aber ihre jeweiligen Stärken beizubehalten. Dabei sind die Konzepte der Invarianz, der Struktur und besonders der Messung von zentraler Bedeutung. Ausgehend von Eino Kailas „non-linguistic, realist account of logical empiricism“ untersucht der vorliegende Aufsatz die Notwendigkeit einer weiteren strukturenrealistischen Position. Dazu werden die etablierten Strukturenrealismen auf ihre Stärken und Schwächen hin untersucht. Es folgt eine Ausformulierung der Forderungen an den MSR, die über die Darstellung bei Neuber hinaus geht. Diese Forderungen sind ontologischer, epistemischer und metrologischer Natur. (shrink)

This article discusses the definitions of ‘‘measurement uncertainty” given in the three editions of the International Vocabulary of Metrology (VIM) and a fourth definition which was suggested for the next edition of this document. It is argued that none of the definitions is satisfying. First, a thorough definition of measurement uncertainty should supply an explanation about the meaning of the concept, which is missing from the VIM2&3. Secondly, when provided, the meanings are not accurate enough: the VIM1 version is flawed (...) and the possible future definition appeals to an overly restrictive notion of ‘‘belief”. Alternative options are then proposed, based on the conclusions that (i) measurement uncertainty is a statement – an inference – made by the experimenter about the measurand; (ii) it is only based on what is accessible to one’s knowledge, and therefore rests on the hypothesis that no unknown systematic error affects the measurement. (shrink)

The metrology literature neglects a strong empirical measurement tradition in economics, which is different from the traditions as accounted for by the formalist representational theory of measurement. This empirical tradition comes closest to Mari's characterization of measurement in which he describes measurement results as informationally adequate to given goals. In economics, one has to deal with soft systems, which induces problems of invariance and of self-awareness. It will be shown that in the empirical economic measurement tradition both problems have been (...) on the agenda for a long while, and that the proposed solutions to these problems provide clues for the directions in which one could develop a measurement theory that takes account of soft systems. (shrink)

The science of metrology characterizes the concept of precision in exceptionally loose and open terms. That is because the details of the concept must be filled in—what I call narrowing of the concept—in ways that are sensitive to the details of a particular measurement or measurement system and its use. Since these details can never be filled in completely, the concept of the actual precision of an instrument system must always retain some of the openness of its general characterization. The (...) idea that there is something that counts as the actual precision of a measurement system must therefore always remain an idealization, a conclusion that would appear to hold very broadly for terms and the concepts they express. (shrink)

Students of ancient metrology have long since been acquainted with a short tract, though so far none seems to have been aware of the fact that it has been published in four different versions: Themanuale legum, orHexabiblos, of Constantine Harmenopulos, a Byzantine compilation dating from 1345 and transmitted in a great number of manuscripts, has been published a number of times since theeditio princepsof 1540; the most accessible edition, with Latin translation and some notes, is that of Heimbach. In book (...) 2 ch. 4, there appears a page-long metrological table, purporting to derive from an architect Julian of Ascalon, according to the editors not attested elsewhere. The text in the still basic collection of F. Hultsch,Metrologici scriptores i. 54 ff.; 200 f., on which all students of ancient metrology depend, derives from this authority. Though there is nothing in the text of Harmenopulos that indicates the end of his excerpt of Julian, it is implicit in the discussions of modern scholars that only the metrological table is Julian's work and that the paragraphs devoted to building laws which follow it derive from a different source. (shrink)

Measurement is a process aimed at acquiring and codifying information about properties of empirical entities. In this paper we provide an interpretation of such a process comparing it with what is nowadays considered the standard measurement theory, i.e., representational theory of measurement. It is maintained here that this theory has its own merits but it is incomplete and too abstract, its main weakness being the scant attention reserved to the empirical side of measurement, i.e., to measurement systems and to the (...) ways in which the interactions of such systems with the entities under measurement provide a structure to an empirical domain. In particular it is claimed that (1) it is on the ground of the interaction with a measurement system that a partition can be induced on the domain of entities under measurement and that relations among such entities can be established, and that (2) it is the usage of measurement systems that guarantees a degree of objectivity and intersubjectivity to measurement results. As modeled in this paper, measurement systems link the abstract theory of measuring, as developed in representational terms, and the practice of measuring, as coded in standard documents such as the International Vocabulary of Metrology. (shrink)

This volume connects chemistry and philosophy in order to face questions raised by chemistry in our present world. The idea is first to develop a kind of philosophy of chemistry which is deeply rooted in the exploration of chemical activities. We thus work in close contact with chemists. Following this line of reasoning, the first part of the book encourages current chemists to describe their workaday practices while insisting on the importance of attending to methodological, metrological, philosophical, and epistemological questions (...) related to their activities. It deals with sustainable chemistry, chemical metrology, nanochemistry, and biochemistry, among other crucial topics. In doing so, those chemists invite historians and philosophers to provide ideas for future developments. In a nutshell, this part is a call for forthcoming collaborations focused on instruments and methods, that is on ways of doing chemistry. The second part of the book illustrates the multifarious ways to study chemistry and even proposes new approaches to doing so. Each approach is interesting and incomplete but the emergent whole is richer than any of its components. Analytical work needs socio-historical expertise as well as many other approaches in order to keep on investigating chemistry to greater and greater depth. This heterogeneity provides a wide set of methodological perspectives not only about current chemical practices but also about the ways to explore them philosophically. Each approach is a resource to study chemistry and to reflect upon what doing philosophy of science can mean. In the last part of the volume, philosophers and chemists propose new concepts or reshape older ones in order to think about chemistry. The act of conceptualization itself is queried as well as the relationships between concepts and chemical activities. Prefaced by Nobel Laureate in Chemistry, Roald Hoffmann, and by the President of the International Society for the Philosophy of Chemistry, Rom Harrè, this volume is a plea for the emergence of a collective cleverness and aims to foster inventiveness. (shrink)

In the last few decades the role played by models and modeling activities has become a central topic in the scientific enterprise. In particular, it has been highlighted both that the development of models constitutes a crucial step for understanding the world and that the developed models operate as mediators between theories and the world. Such perspective is exploited here to cope with the issue as to whether error-based and uncertainty-based modeling of measurement are incompatible, and thus alternative with one (...) another, as sometimes claimed nowadays. The crucial problem is whether assuming this standpoint implies definitely renouncing to maintain a role for truth and the related concepts, particularly accuracy, in measurement. It is argued here that the well known objections against true values in measurement, which would lead to refuse the concept of accuracy as non-operational, or to maintain it as only qualitative, derive from a not clear distinction between three distinct processes: the metrological characterization of measuring systems, their calibration, and finally measurement. Under the hypotheses that (1) the concept of true value is related to the model of a measurement process, (2) the concept of uncertainty is related to the connection between such model and the world, and (3) accuracy is a property of measuring systems (and not of measurement results) and uncertainty is a property of measurement results (and not of measuring systems), not only the compatibility but actually the conjoint need of error-based and uncertainty-based modeling emerges. (shrink)

Paragraph 50 of Wittgenstein'sPhilosophical Investigationsfamously says that there is one thing of which one can neither state that it is 1 m long nor that it isn't: the standard metre in Paris. Consensus appears to be that (1) exegetically speaking, Wittgenstein affirms this claim, and (2) systematically, whether or not one agrees with it, the practice of using a material artefact as a measurement standard has important philosophical consequences. In this paper, in contrast, we show that (1') Wittgenstein does not (...) affirm the standard metre claim and (2') historical facts about material length standards do not warrant deeper philosophical conclusions. References to material measurement standards in the literature gravely distort the actual metrological practices of developing and using such standards. (shrink)

The base units of the SI include six units of continuous quantities and the mole, which is defined as proportional to the number of specified elementary entities in a sample. The existence of the mole as a unit has prompted comment in Metrologia that units of all enumerable entities should be defined though not listed as base units. In a similar vein, the BIPM defines numbers of entities as quantities of dimension one, although without admitting these entities as base units. (...) However, there is a basic ontological distinction between continuous quantities and enumerable aggregates. The distinction is the basis of the difference between real and natural numbers. This paper clarifies the nature of the distinction: (i) in terms of a set of measurement axioms stated by Hölder; and (ii) using the formalism known in metrology as quantity calculus. We argue that a clear and unambiguous scientific distinction should be made between measurement and enumeration. We examine confusion in metrological definitions and nomenclature concerning this distinction, and discuss the implications of this distinction for ontology and epistemology in all scientific disciplines. (shrink)

Peirce's Sign Theory, or Semiotic, is an account of signification, representation, reference and meaning. Although sign theories have a long history, Peirce's accounts are distinctive and innovative for their breadth and complexity, and for capturing the importance of interpretation to signification. For Peirce, developing a thoroughgoing theory of signs was a central philosophical and intellectual preoccupation. The importance of semiotic for Peirce is wide ranging. As he himself said, “[…] it has never been in my power to study anything,—mathematics, ethics, (...) metaphysics, gravitation, thermodynamics, optics, chemistry, comparative anatomy, astronomy, psychology, phonetics, economics, the history of science, whist, men and women, wine, metrology, except as a study of semiotic”. (SS 1977, 85–6). Peirce also treated sign theory as central to his work on logic, as the medium for inquiry and the process of scientific discovery, and even as one possible means for 'proving' his pragmatism. Its importance in Peirce's philosophy, then, cannot be underestimated. -/- Across the course of his intellectual life, Peirce continually returned to and developed his ideas about signs and semiotic and there are three broadly delineable accounts: a concise Early Account from the 1860s; a complete and relatively neat Interim Account developed through the 1880s and 1890s and presented in 1903; and his speculative, rambling, and incomplete Final Account developed between 1906 and 1910. The following entry examines these three accounts, and traces the changes that led Peirce to develop earlier accounts and generate new, more complex, sign theories. However, despite these changes, Peirce's ideas on the basic structure of signs and signification remain largely uniform throughout his developments. Consequently, it is useful to begin with an account of the basic structure of signs according to Peirce. (shrink)

This article provides an overview of the analysis of technological zones. A technological zone can be understood as a space within which differences between technical practices, procedures and forms have been reduced, or common standards have been established. Such technological zones take broadly one of three forms: (1) metrological zones associated with the development of common forms of measurement; (2) infrastructural zones associated with the creation of common connection standards; and (3) zones of qualification which come into being when objects (...) and practices are assessed according to common standards and criteria. The article argues that technological zones can have more or less clear borders, but such borders increasingly do not correspond to the borders of nation-states. Through a discussion of the global oil industry, some of the ways in which the formation of technological zones has become critical to contemporary economic and political life are examined. (shrink)

I analyze the two main theses of Helmholtz's "The Applicability of the Axioms to the Physical World," in which he argued that the axioms of Euclidean geometry are not, as his neo-Kantian opponents had argued, binding on any experience of the external world. This required two argumentative steps: 1) a new account of the structure of our representations which was consistent both with the experience of our (for him) Euclidean world and with experience of a non-Euclidean one, and 2) a (...) demonstration of why geometric propositions are essentially connected to material and temporal aspects of experience. The effect of Helmholtz's discussion is to throw into relief an intermediate category of metrological objects--objects which are required for the properly theoretical activity of doing physical science (in this sense, a priori requirements for doing science), all while being recognizably contingent aspects of experience. (shrink)

A case study is presented of a recent proposal by the major metrology institutes to redefine four of the physical base units, namely kilogram, ampere, mole, and kelvin. The episode shows a number of features that are unusual for progress in an objective science: for example, the progress is not triggered by experimental discoveries or theoretical innovations; also, the new definitions are eventually implemented by means of a voting process. In the philosophical analysis, I will first argue that the episode (...) provides considerable evidence for confirmation holism, i.e. the claim that central statements in fundamental science cannot be tested in isolation; second, that the episode satisfies many of the criteria which Kuhn requires for scientific revolutions even though one would naturally classify it as normal science. These two observations are interrelated since holism can provide within normal science a possible source of future revolutionary periods. (shrink)

The Power of Example is an interdisciplinary examination of the integral role that examples and exemplification play in anthropological theory and practice. Explores the evocative and persuasive power, both positive and negative, of ‘exemplary examples’ in social life Includes contributions from established and up-and-coming anthropologists, as well as leading scholars of religious and cultural studies Features an international array of case studies on exemplification from Left radical activists in Denmark to scientific metrological practice in Brazil.

Famously, Galilei made the ontological claim that the book of nature is written in the language of mathematics. Probably, if only implicitly, most contemporary natural scientists share his view. This paper, in contradistinction, argues that nature is only partly written in the language of mathematics; partly, it is written in the language of functions and partly in a very simple purely qualitative language, too. During the argumentation, three more specific but in themselves interesting theses are put forward: first (in Section (...) 3), there are more shapes than real numbers; second (in Section 4), the metrological notion ‘amount of substance’ can profitably be exchanged for ‘number of entities’; third (in Section 5), prototypical concepts will always be scientifically important. (shrink)

This paper discusses a relational modeling of measurement which is complementary to the standard representational point of view: by focusing on the experimental character of the measurand-related comparison between objects, this modeling emphasizes the role of the measuring systems as the devices which operatively perform such a comparison. The non-idealities of the operation are formalized in terms of non-transitivity of the substitutability relation between measured objects, due to the uncertainty on the measurand value remaining after the measurement. The metrological structure (...) of traceability is shown to be an effective solution to cope with the problem of the general non-transitivity of measurement results. A preliminary theory is introduced as a possible formalization for the presented model. (shrink)

Despite their important applications in metrology and in spite of numerous experimental demonstrations, weak measurements are still confusing for part of the community. This sometimes leads to unjustified criticism. Recent papers have experimentally clarified the meaning and practical significance of weak measurements, yet in Kastner, Kastner seems to take us many years backwards in the the debate, casting doubt on the very term “weak value” and the meaning of weak measurements. Kastner appears to ignore both the basics and frontiers of (...) weak measurements and misinterprets the weak measurement process and its outcomes. In addition, she accuses the authors of Aharonov et al. in statements completely opposite to the ones they have actually made. There are many points of disagreement between Kastner and us, but in this short reply I will leave aside the ontology and focus mainly on the injustice in her criticism. I shall add some general comments regarding the broader theory of weak measurements and the two-state-vector formalism, as well as supporting experimental results. Finally, I will point out some recent promising results, which can be proven by projective measurements, without the need of employing weak measurements. (shrink)

This article develops a historico-critical analysis of uncertainty and accuracy in measurement through a case-study of the adjustment of the fundamental physical constants, in order to investigate the sceptical “problem of unknowability” undermining realist accounts of measurement. Every scientific result must include a “measurement uncertainty”, but uncertainty cannot be be eval- uated against the unknown, and therefore cannot be taken as an assessment of “accuracy”, defined in the metrological vocabulary as the closeness to the truth. The way scientists use and (...) interpret uncertainty in the adjustment activity illustrates how they try to overcome this predicament. I iden- tify two operative roles of measurement uncertainty, in the comparison and in the combination of measurement results. This duality implies a tension between selection and combination when aggregating results, leading to a crucial question: should the evaluation of uncertainties favour safety over precision? I present contrasting answers and identify a specific account of physicists who implicitly try to conciliate realism with the problem of unknowability. I argue that this invites us to reconsider accuracy from a dynamical standpoint, as the gradual achievement of scientific progress through error correction. Finally, I present two interpretations of measurement uncertainty, objective and epistemic, which I criticize and suggest improvements to. (shrink)

Historians of the sciences have paid great attention to the ways that faith in what has been called the quantitative spirit emerged as a dominant feature of the politics of science, a theme of obvious salience in current epidemiological and climate crises. There are instructive connexions between measurement practices and orientation towards other cultures—as though scientific modernity somehow appeared through the primacy of robust quantification over subaltern, past, and exotic worlds, where merely provisional judgment allegedly still operated. This highly simplistic (...) Orientalist distinction accompanied assumptions that the remote was best understood as the ancient, a viewpoint common at the same late Enlightenment moment as the apparent institutionalisation of the regime of the exact sciences within European polities. Under this regime, precision surveys—the way the state saw—have often been understood as integral for European societies and even more so in colonised territories. This version of what might be called metrological Orientalism can be disoriented through excellent recent scholarship that explores complex entanglements of measurement practices circulating across very different scientific cultures, which shows how precision devices that claimed merely to represent phenomena often helped produce them. Studies of select cases of relations between European practitioners and indigenous experts, in fields such as Egyptian hydraulics or South Pacific surveys, can reveal even more: the role that judgment and exactitude played in forging very different, politically significant versions of the past history of the sciences. These disorientations can aid novel forms of historical understanding of the politics of science. (shrink)

The Mesopotamian system of sexagesimal counting numbers was based on the progressive series of units 1, 10, 1·60, 10·60, …. It may have been in use already before the invention of writing, with the mentioned units represented by various kinds of small clay tokens. After the invention of proto-cuneiform writing, c. 3300 BC, it continued to be used, with the successive units of the system represented by distinctive impressed cup- and disk-shaped number signs. Other kinds of “metrological” number systems in (...) the proto-cuneiform script, with similar number signs, were used to denote area numbers, capacity numbers, etc. In a handful of known mathematical cuneiform texts from the latter half of the third millennium BC, the ancient systems of sexagesimal counting numbers and area numbers were still in use, alongside new kinds of systems of capacity numbers and weight numbers. Large area numbers, capacity numbers, and weight numbers were counted sexagesimally, while each metrological number system had its own kind of fractional units. In the system of counting numbers itself, fractions could be expressed as sixtieths, sixtieths of sixtieths, and so on, but also in terms of small units borrowed from the system of weight numbers. Among them were the “basic fractions” which we would understand as 1/3, 1/2, and 2/3. In a very early series of metro-mathematical division exercises and an equally early metro-mathematical table of squares, “quasi-integers” of the form “integer plus basic fraction” play a prominent role. Quasi-integers play an essential role also in a recently found atypical cuneiform table of reciprocals. The invention of sexagesimal numbers in place-value notation, in the Neo-Sumerian period c. 2000 BC, was based on a series of innovations. The range of the system of sexagesimal counting numbers was extended indefinitely both upward and downward, and the use of quasi-integers was abolished. Sexagesimal place-value numbers were used for all kinds of calculations in Old Babylonian mathematical cuneiform texts, c. 1700 BC, while traditional metrological numbers were retained in both questions and answers of the exercises. Examples of impressive computations of reciprocals of many-place regular sexagesimal place-value numbers, with no practical applications whatsoever, are known from the Old Babylonian period. In the Late Babylonian period, such computations were still popular, performed by the same persons who constructed the many-place sexagesimal tables that make up the corpus of Late Babylonian mathematical astronomy. (shrink)