This study of mathematical instrumentation in the Mamluk world contains the edition and translation of a unique, richly-illustrated treatise, and provides a fascinating historical account of several instrument models that were thus far unknown or inadequately documented.

In considering the appropriate use of the terms “science” and “scientific instrument,” tracing the history of “mathematical instruments” in the early modern period is offered as an illuminating alternative to the historian's natural instinct to follow the guiding lights of originality and innovation, even if the trail transgresses contemporary boundaries. The mathematical instrument was a well-defined category, shared across the academic, artisanal, and commercial aspects of instrumentation, and its narrative from the sixteenth to the eighteenth century was (...) largely independent from other classes of device, in a period when a “scientific” instrument was unheard of. (shrink)

The paper examines the structure of the mathematical instrument making trade in London from the mid-sixteenth century to the opening of the Hanoverian era. This analysis of the trade is primarily based on evidence drawn from contemporary advertising. A distinction between informal editorial recommendations and advertising per se is made. It is concluded that up to the mid-seventeenth century mathematical instrument makers worked in either wood or metal. After that date a growing number of workshops advertised that they (...) manufactured in all media. Advertising was aimed at informing professional users from whom particular instruments could be purchased, but not on informing customers in specific terms of the range of instruments manufactured. It is concluded that until the early eighteenth century most mathematical instruments were commissioned. Only towards the end of the period is there evidence of over-the-counter sales, and advertising aimed at encouraging the growing consumer market to buy mathematical instruments for the practice of science as a social or recreational activity. (shrink)

Summary A new culture of mathematics was developed in sixteenth-century England, the culture of ?the mathematicalls?. Its representatives were the self-styled mathematical practitioners who presented their art as a practical and worldly activity. The careers of two practitioners, Thomas Bedwell and Thomas Hood, are used as case studies to examine the establishment of this culture of the mathematicalls. Both practitioners self-consciously used mathematical instruments as key resources in negotiating their own roles. Bedwell defined his role in contrast (...) to mechanicians and he secured patronage in military engineering and the service of the commonwealth; Hood worked in the commercial setting of London as a teacher, author, chartmaker, and retailer. Working in new contexts and dealing with new audiences of gentlemen and mechanicians, Bedwell and Hood used instruments to construct a public consensus on the status and aims of mathematics. (shrink)

Scientific explanations are widely recognized to have instrumental value by helping scientists make predictions and control their environment. In this paper I raise, and provide a first analysis of, the question whether explanatory proofs in mathematics have analogous instrumental value. I first identify an important goal in mathematical practice: reusing resources from existing proofs to solve new problems. I then consider the more specific question: do explanatory proofs have instrumental value by promoting reuse of the resources they contain? In (...) general, I argue that the answer to this question is “no” and demonstrate this in detail for the theory of mathematical explanation developed by Marc Lange. (shrink)

ABSTRACTThis paper offers a re-interpretation of the development of practical mathematics in Elizabethan England, placing artisanal know-how and the materials of the discipline at the heart of analysis, and bringing attention to Tudor economic policy by way of historical context. A major new source for the early instrument trade is presented: a manuscript volume of Chancery Court documents c.1565–c.1603, containing details of a patent granting a monopoly on making and selling mathematical instruments, circa 1575, to an unnamed individual, (...) identified here as the instrument maker Humphrey Cole. Drawing on economic and legal history, the paper argues that practical mathematics needs to be understood as one ‘project’ among many, at a time when monopoly patents were used to advance industry, lower unemployment, secure the realm and reward invention. Drawing on the history and sociology of technology, it argues that the management and control of materials – mathematical instruments themselves, and the local socio-legal context within which they could be made – needs to be understood as prior to and separate from the rhetoric of mathematical authors, which is of interest in its own right but which may not have a direct relationship to mathematical practice. (shrink)

Mathematical instruments in the early-modern period lay at the intersection of various knowledge traditions, both practical and scholarly. Scholars treated instrument-related questions in their works, while instrument makers and mathematical practitioners also put much energy into producing instrument books. Assessing the role of that literature in the exchange of knowledge between the different traditions is a complex task. Did it directly influence workshop practice? Here, I will examine instruments from a famous Louvain workshop ca. 1570, focussing (...) on the role of printed images. I will suggest that woodcuts did indeed inspire instrument makers; that images were sometimes more important than the text; and that the viewer’s appreciation of the images depended upon his familiarity with an instrument’s mathematical structure. -/- . (shrink)

Open peer commentary on the target article “Who Conceives of Society?” by Ernst von Glasersfeld. Excerpt: My goal in this commentary is to say enough to suggest that the meanings children impute to the language and actions of other children are based on their current conceptual schemes and that, if the schemes are at different levels of the constructive process, it is no easy feat for children to use their schemes in interactive mathematical communication.

A serious flaw in Hartry Field’s instrumental account of applied mathematics, namely that Field must overestimate the extent to which many of the structures of our mathematical theories are reflected in the physical world, underlies much of the criticism of this account. After reviewing some of this criticism, I illustrate through an examination of the prospects for extending Field’s account to classical equilibrium statistical mechanics how this flaw will prevent any significant extension of this account beyond field theories. I (...) note in the conclusion that this diagnosis of Field’s program also points the way to modifications that may work. (shrink)

ObjectiveTo investigate the reciprocal relationship between high school students’ academic self-efficacy and achievement in mathematics using US data from the HSLS:2009 and first follow-up longitudinal surveys, while accounting for biases in effect estimates due to unobserved heterogeneity.MethodsInstrumental Variables regressions were estimated, to derive causal effect estimates of earlier math self-efficacy on later math achievement and vice versa. Particular attention was paid to testing the validity of instruments used. Models were estimated separately by gender, to uncover gender differences in effects.ResultsEvidence (...) of robust reciprocal effects between self-efficacy and achievement for male students is presented, with the dominant effect from earlier achievement to later self-efficacy. For girls, evidence of such effects is weak. Generally, IV estimates are higher than OLS estimates for males, but not for females. As opposed to earlier correlational studies which did not find significant gender differences despite theoretical expectations for their existence, the findings support higher effects for male students. (shrink)

Creativity is an essential factor in ensuring the sustainable development of a society. Improving students’ creativity has gained much attention in education, especially in Science, Technology, Engineering, Arts, and Mathematics education. In a quasi-experimental design, this study examines the effectiveness of a project-based STEAM program on the development of creativity in Chinese elementary school science education. We selected two fourth-graders classes. One received a project-based STEAM program, and the other received a conventional science teaching over 6 weeks. Students’ creativity was (...) assessed before and after the intervention using a multi-method approach, including a test of divergent thinking, a story completion through the Consensus Assessment Technique, a creative self-efficacy measure, and a group-based creative project. Moreover, all students received a test of their science knowledge after the intervention. The results showed that compared with the control group, the creativity of the experimental group students improved significantly for 6 weeks at both individual and group level, even though their knowledge in science were comparable. This result confirmed the effectiveness of a project-based STEAM educational program improving elementary school students’ creativity. Implications are discussed. (shrink)

SummaryWhen mathematical instrument-makers brought the craft to London from the continent in the mid-sixteenth century, the severity of the legislation obliged them to join a guild company. As there was no company specialising in their craft, they joined the company of their choice, a practice allowed by the so-called ‘custom of London’. Research has revealed many in the Grocers' Company, and their position there is compared with that of instrument-makers who joined the Clockmakers' Company after its incorporation in 1631. (...) While the Grocers' Company steadily declined from this date in its industrial function, the Clock-makers' Company strove to exert a tight trade control over its members, and this continued until the end of the eighteenth century. Numbers of apprentices bound in each company are compared, and instrument-makers in the Clockmakers' Company listed. Much of interest to our understanding of the origins and organisation of the instrument-making trade can be discovered through the examination of guild company records. (shrink)

PurposeSelf-efficacy has been argued theoretically and shown empirically to be an essential construct for students’ improved learning outcomes. However, there is a dearth of studies on its causal effects on performance in mathematics among university students. Meanwhile, it will be erroneous to assume that results from other fields of studies generalize to mathematics learning due to the task-specificity of the construct. As such, attempts are made in the present study to provide evidence for a causal relationship between self-efficacy and performance (...) with a focus on engineering students following a mathematics course at a Norwegian university.MethodThe adopted research design in the present study is a survey type in which collected data from first-year university students are analyzed using structural equation modeling with weighted least square mean and variance adjusted estimator. Data were generated using mainly questionnaires, a test of prior mathematics knowledge, and the students’ final examination scores in the course. The causal effect of self-efficacy was discerned from disturbance effects on performance by using an innovative instrumental variable approach to structural equation modeling.ResultsThe findings confirmed a significant direct effect of the prior mathematics knowledge test on self-efficacy, a significant direct effect of self-efficacy on performance, and a substantial mediating effect of self-efficacy between a prior mathematics knowledge test and performance. Prior mathematics knowledge and self-efficacy explained 30% variance of the performance. These findings are interpreted to be substantial evidence for the causal effect of self-efficacy on students’ performance in an introductory mathematics course.ConclusionThe findings of the present study provide empirically supports for designing self-efficacy interventions as proxies to improve students’ performance in university mathematics. Further, the findings of the present study confirm some postulates of Bandura’s agentic social cognitive theory. (shrink)

Mathematical instrumentalism construes some parts of mathematics, typically the abstract ones, as an instrument for establishing statements in other parts of mathematics, typically the elementary ones. Gödel’s second incompleteness theorem seems to show that one cannot prove the consistency of all of mathematics from within elementary mathematics. It is therefore generally thought to defeat instrumentalisms that insist on a proof of the consistency of abstract mathematics from within the elementary portion. This article argues that though some versions of (...) class='Hi'>mathematical instrumentalism are defeated by Gödel’s theorem, not all are. By considering inductive reasons in mathematics, we show that some mathematical instrumentalisms survive the theorem. (shrink)

This paper examines the role of mathematical instrument makers in establishing a public culture of precision measurement in early-modern England. I argue that this culture was promoted through trials and demonstrations, in the context of which artisans held a privileged position. The trials described here cover land surveying, the measurement of magnetic variation, and standards of measurement for customs and excise. These trials were decisive moments in the ‘cultural biographies’ of precision instruments. I ask how it was that (...) instrument makers were able to assume positions of authority, and what this means for our understanding of the socio-material system of precision measurement in the early-modern period, and the contemporary rise of ‘experimental’ and ‘philosophical’ trials. Because practical mathematics was a self-consciously economic activity – motivated by trade, commerce, exploration and colonization – direct connections to natural philosophy are significant, a point explored in my conclusion. (shrink)

This paper surveys the evidence for the use of scientific and mathematical instruments from tenth-century Kiev Rus' to the death of Peter the Great in 1725 and the literature devoted to the subject. The evidence is extremely sparse before the sixteenth century; in the seventeenth century there is more, both in the form of artefacts, either local or imported, and texts; at the end of the seventeenth century and in the first quarter of the eighteenth century, Peter the (...) Great opted for complete Westernization, and both by edict and by creating a need for their products in effect established the instrument making and scientific book publishing trades in Russia. (shrink)

The mathematical or theoretical approach to the theory of measurement (opposed to the operational approach) is usually accepted by philosophers, at least in its general lines. Some recent criticimsms against this theory can be answered by qualifying the requirements of the theoretical approach as "desiderata", not as strict impositions or prohibitions. Besides, it is shown that the use of this approach is instrumental in creating mathematically simple quantitative laws and in allowing the development of a "scientific intuition" concerning the (...) relevant phenomena. RESUMO: Os filósofos geralmente aceitam pelo menos as idéias gerais da abordagem matemática ou teórica da teoria da mensuração. Essa abordagem opõe-se ao operacionalismo. Algumas críticas recentes contra a abordagem teórica podem ser respondidas qualificando-se as normas que ela propõe como "desiderata", e não como imposições ou proibições estritas. Além disso, mostra-se que o uso dessa abordagem ajuda a criar leis quantitativas matematicamente simples, e permite o desenvolvimento de um tipo de "intuição científica" sobre os fenômenos relevantes. (shrink)

Mathematics plays a central role in modern science. However, it is very common an instrumental and utilitarian view of math leading to the underestimation of its scientific nature. We propose some consideration to emphasize a different idea on the fundamental role of math in modern science.

This book is a collection of three papers authored by Dr. Raman K Attri between 1999 to 2005. The book provides a theoretical and conceptual understanding of concepts and principles of detection and measurements of the seismic signal. The papers provide fundamental concepts in seismic instrumentation design. The first paper presents a simplified mathematical framework of the seismic events and backend computational software logic that will enable software engineers to develop a customized seismic analysis and computation software. The second (...) paper presents a simplified description of various earthquake parameters of interest to a seismologist and how these complex parameters are computed using equations. In the third paper, a visionary concept is presented to integrate geo-scientific instrumentation equipment such as seismic measurement systems to information technology network that would create a centralized web-enabled database that would allow to transmit the data acquired by geographically distributed but networked observatories to better predict or alert about the phenomena like earthquakes. (shrink)

ZusammenfassungTrotz seiner großen Verbreitung in den Lebenswissenschaften wurde dem Aquarium bisher wenig wissenschafts- und technikhistorische Aufmerksamkeit zuteil. Dies ist nicht zuletzt durch den Umstand begründet, dass das Aquarium und seine Geschichte bisher größtenteils als außerwissenschaftlich aufgefasst wurden. Dabei spielen so unterschiedliche Kontexte wie Akklimatisierung, Amateurnaturkunde und bürgerliche Populärkultur eine wichtige Rolle. Gleichzeitig ist die Entwicklung des Aquariums aber auch eng mit der Geschichte der Lebenswissenschaften verbunden. Mit Blick auf die zweite Hälfte des 19. Jahrhunderts verstehe ich das Aquarium als techno-natural (...) assemblage, in der Technologie, Kultur und Natur zu einem künstlichen Naturraum verbunden sind. Seine Geschichte beginnt in der britischen Amateurnaturkunde und der französischen Akklimatisierungsbewegung. Im Deutschland des späten 19. Jahrhunderts entwickelte sich das Aquarium zu einem Massenphänomen. Gleichzeitig hielt es Einzug in die Lebenswissenschaften, wo es als Einfallstor, Instrument und Umwelt Verwendung fand. Wie sich zeigt, ist das Aquarium eine hochgradig konstruierte Technologie, die sich aus einer Verbindung unterschiedlicher Traditionen herausgebildet und das Leben in die Lebenswissenschaften gebracht hat. (shrink)

This paper details efforts by the Purdue School of Engineering and Technology at Indiana University Purdue University Indianapolis to create a single instrument for honors science, technology, engineering and mathematics students wishing to demonstrate competence in the IUPUI Principles of Undergraduate Learning and Accreditation Board for Engineering and Technology Engineering Accreditation Criterion and Technology Accreditation Criterion 2, a through k. Honors courses in Human Behavior, Ethical Decision-Making, Applied Leadership, International Issues and Leadership Theories and Processes were created along with a (...) specific menu of activities and an assessment rubric based on PUL’s and ABET criteria to evaluate student performance in the aforementioned courses. Students who complete the series of 18 Honors Credit hours are eligible for an Honors Certificate in Leadership Studies from the Department of Organizational Leadership and Supervision. Finally, an accounting of how various university assessment criteria, in this case the IUPUI Principles of Undergraduate Learning, can be linked to ABET outcomes and prove student competence in both, using the aforementioned courses, menu of items, and assessment rubrics; these will be analyzed and discussed. (shrink)

One of the chief concerns of the young Descartes was with what he, and others, termed “physico-mathematics”. This signalled a questioning of the Scholastic Aristotelian view of the mixed mathematical sciences as subordinate to natural philosophy, non explanatory, and merely instrumental. Somehow, the mixed mathematical disciplines were now to become intimately related to natural philosophical issues of matter and cause. That is, they were to become more ’physicalised’, more closely intertwined with natural philosophising, regardless of which species of (...) natural philosophy one advocated. A curious, short-lived yet portentous epistemological conceit lay at the core of Descartes’ physico-mathematics—the belief that solid geometrical results in the mixed mathematical sciences literally offered windows into the realm of natural philosophical causation—that in such cases one could literally “see the causes”. Optics took pride of place within Descartes’ physico-mathematics project, because he believed it offered unique possibilities for the successful vision of causes. This paper traces Descartes’ early physico-mathematical program in optics, its origins, pitfalls and its successes, which were crucial in providing Descartes resources for his later work in systematic natural philosophy. It explores how Descartes exploited his discovery of the law of refraction of light—an achievement well within the bounds of traditional mixed mathematical optics—in order to derive—in the manner of physico-mathematics—causal knowledge about light, and indeed insight about the principles of a “dynamics” that would provide the laws of corpuscular motion and tendency to motion in his natural philosophical system. (shrink)

There are two axes of Leibniz’s philosophy about bodies that are deeply inter- twined, as this paper shows: the scientific investigation of bodies due to the application of mathematics to nature – Leibniz’s mixed mathematics – and the issue of matter/bodies ide- alism. This intertwinement raises an issue: How did Leibniz frame the relationship between mathematics, natural sciences, and metaphysics? Due to the increasing application of mathe- matics to natural sciences, especially physics, philosophers of the early modern period used the (...) reliability of mathematics to predict phenomena as the basis to infer the metaphysical outlook of nature. I argue that although Leibniz thought metaphysics must be scientifically informed and that mathematics is a valuable instrument to understand nature, metaphysics is more fun- damental than mathematics and natural sciences. By highlighting the foundational relation be- tween metaphysics and the sciences, this paper showcases an argument for the reality of bodies: the ideality of bodies, necessary for epistemic purposes, is not proof that they are not real. Keywords: Metaphysics, Application of Mathematics, Body, Idealism, Fundamentality. (shrink)

The goal of this paper is to answer the following question: Does it make sense to speak of thought experiments not only in physics, but also in mathematics, to refer to an authentic type of activity? One may hesitate because mathematics as such is the exercise of reasoning par excellence, an activity where experience does not seem to play an important role. After reviewing some results of the research on thought experiments in the natural sciences, we turn our attention to (...) experiments and thought experiments in mathematics, especially in fundamental mathematics, and investigate what thought experiments can teach us there. If we accept the principle that mathematical practice can sometimes be best described by a pragmatist approach where the concept of experience in mathematics is considered from a new perspective, thought experiments can in some cases be a useful instrument different from both ‘mathematical experiments’ and ‘formal’ proofs: they are mathematical experiments using deviant methods. (shrink)

ArgumentWhat kind of mathematical research activities took place in prisoner of war camps in Germany during the Second World War? And can one inspect such activities in order to re-examine, on the one hand, Herbert Mehrtens’ analysis of the modernism/counter-modernism divide of early twentieth-century mathematics, and on the other, his research on the instrumentalization of mathematics during the war? Closely examining the work carried out in the field of algebraic geometry by the French mathematician Bernard d’Orgeval, who was held (...) in three of such camps between 1940 and 1945, the paper aims not only to unfold this unique episode in the history of mathematics, presenting it as an ephemeral configuration, but also to show the limitations of Mehrtens’ approach and the narrative of modern and counter-modern mathematics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Abraham, Planter of Mathematics":Histories of Mathematics and Astrology in Early Modern EuropeNicholas PopperFrancis Bacon's 1605 Advancement of Learning proposed to dedicatee James I a massive reorganization of the institutions, goals, and methods of generating and transmitting knowledge. The numerous defects crippling the contemporary educational regime, Bacon claimed, should be addressed by strengthening emphasis on philosophy and natural knowledge. To that end, university positions were to be created devoted to (...) "Artes and Sciences at large," rather than to the professions. High salaries would render lecturers "able and sufficient," undistracted from their task. Most famously, he argued that teaching of the "operatiue studie of many Scyences" should involve sophisticated technical education. The study of natural philosophy demanded not only books, but globes, astrolabes, and other "instrumentals." Most significantly, yielding reliable and meaningful knowledge from experiential gleanings required a rigorous system of deductive reasoning.The legacy of this colossal proposal has earned Bacon honored status as devisor of the scientific method.1 But Bacon's educational reform extended [End Page 87] beyond the methods of producing and transmitting knowledge. To facilitate more efficient "vse and administration" of the knowledge produced by his system, he also demanded a searching examination of the history of learning. This history would provide a mirror enabling his contemporaries to deploy the fruits of his method, by considering how learning in the past had been used successfully or ill-advisedly. Producing this history was the ambition of the Advancement, for he explained: "no man hath propounded to himselfe the generall state of learning to bee described and represented from age to age, as many have done the works of Nature, & the State civile and Ecclesiastical." He continued:And yet I am not ignorant that in divers particular sciences, as of the Iurisconsults, the Mathematicians, the Rhetoricians, the Philosophers, there are set down some smal memorials of the Schooles, Authors, and Bookes: and so likewise some barren relations touching the Invention of Arts, or usages. But a iust story of learning, containing the Antiquities and Originalls of Knowledges, & their Sects; their Inventions, their Traditions; their diverse Administrations and Managings; their Flourishings, their Oppositions, Decayes, Depressions, Oblivions, Removes, with the causes, and occasions of them, and all other events concerning learning, throughout the ages of the world; I may truly affirme to be wanting.2Bacon thus positioned himself not only as a Father of Modern Science, but also a Father of the History of Science.Following Bacon's suggestion, I will examine the "small memorials" of the history of mathematics—and particularly the mathematical art of astrology—in the sixteenth and seventeenth centuries. My conclusion, however, will not bear out Bacon's claims. Despite his frustration, Bacon was only one of many early modern scholars appraising the role of mathematics within history. And he devoted less energy than others to mapping its origins and tracing its transmissions between communities. In fact, Bacon's 1605 proposal for a history of mathematics was already out-of-date. Discussions [End Page 88] of the history of mathematics had been rife on the continent and in England throughout the previous century.3The evidence that Renaissance scholars inherited was sprawling and inconclusive. Several genealogies for mathematics could be found within classical Greek, Latin, and patristic references. One lineage claimed mathematics began in ancient Assyria, where the priestly caste, the Chaldeans, practiced a form of mathematics that seemed a corrupt admixture of philosophy, medicine, and religion, and relied heavily on observation of the heavens. Other scholars traced the origins to Egypt, claiming that the field developed to survey lands frequently flooded by the Nile. The real problem for ancient, late antique, and medieval scholars had not been the origins of mathematics, but what exactly mathematics were. For some, the term strictly referred to the quadrivium: geometry, arithmetic, astronomy, and music. But for others, mathematics' origins amongst the Egyptians or Chaldeans inextricably linked it to forms of astrological divination, augury, and necromancy that were unsavory to both Latin and Christian traditions. Mathematici were included alongside ghastly lists of Magi, Brahmins, Aruspices, Genethliaci, and other diabolic practitioners of idolatrous magic. These might or might not be distinguished from mathematici such as Pythagoras... (shrink)

We mathematical animals should be grateful that mathematics is instrumentally useful. We should not, however, forget its other contributions to human happiness. Bertrand Russell and John Dewey offer timely reminders that provide insight into the role of non-mathematicians in the evaluation of mathematics.

This paper explores the interactions between scientific travel, politics, instrument making and the epistemology of scientific instruments in Napoleon's Europe. In the early 1800s, the German astronomer Franz Xaver von Zach toured Italy and Southern France with instruments made by G. Reichenbach in his newly-established Bavarian workshop. I argue that von Zach acted as a broker for German technology and science and that travel, personal contacts and direct demonstrations were crucial in establishing Reichenbach's reputation and in conquering new (...) markets. The rise of German instrument making highlights the complexity of the scientific relationship between the centre and the peripheries in Napoleon's empire, and reveals the existence of diverging views on the role of instruments and of their makers. In von Zach's view, Reichenbach's instruments could not penetrate the French market because Parisian astronomers focused on mathematical astronomy and, for both political and epistemological reasons, dismissed instruments and material innovations from the peripheries. The German astronomer and his Italian colleagues, on the contrary, regarded Reichenbach's technical achievements as outstanding contributions to astronomy, and considered the political and cultural hegemony of the capital as a hindrance to the advancement of science. (shrink)

Computer simulations have conventionally been understood to be either extensions of formal methods such as mathematical models or as special cases of empirical practices such as experiments. Here, I argue that computer simulations are best understood as instruments. Understanding them as such can better elucidate their actual role as well as their potential epistemic standing in relation to science and other scientific methods, practices and devices.

In the philosophy of mathematics, indispensability arguments aim to show that we are justified in believing that abstract mathematical objects exist. I wish to defend a particular objection to such arguments that has become increasingly popular recently. It is called instrumental nominalism. I consider the recent versions of this view and conclude that it has yet to be given an adequate formulation. I provide such a formulation and show that it can be used to answer the indispensability arguments. -/- (...) There are two main indispensability arguments in the literature, though one has received nearly all of the attention. They correspond to two ways in which we use mathematics in science and in everyday life. We use mathematical language to help us describe non-mathematical reality; and we use mathematical reasoning to help us perform inferences concerning non-mathematical reality using only a feasible amount of cognitive power. The former use is the starting point of the Quine-Putnam indispensability argument ([Quine, 1980a], [Quine, 1980b], [Quine, 1981a], [Quine, 1981b], [Putnam, 1979a], [Putnam, 1979b]); the latter provides the basis for Ketland’s more recent argument ([Ketland, 2005]). I begin by considering the Quine-Putnam argument and introduce instrumental nominalism to defuse it. Then I show that Ketland’s argument can be defused in a similar way. (shrink)

Records of certain Government Departments known to have purchased scientific instruments from designated suppliers over long periods are potentially important sources of information on both instruments and their makers. The Office of Ordnance was one such Department. Investigation of its financial and administrative records has shown that the appointment ‘Mathematical Instrument Maker to his Majesty's Office of Ordnance’ brought the holder a substantial trade in instruments for drawing, surveying, and military purposes. Detailed entries in the Bill (...) Books enable not only types, quantities, and prices of instruments supplied to be determined, but also the purposes for which they were required. In many cases the actual users of the instruments are named, with their locations in Great Britain and overseas.The records of the Office of Ordnance are extensive, covering the mid-seventeenth to the mid-nineteenth century in over ten thousand volumes or bundles. This paper provides an introduction to what is available, and examines in particular the period 1748–1772 when George Adams senior was Mathematical Instrument Maker to this Office. It is shown that during this period Adams supplied over 1500 instruments, ranging from drawing pens to theodolites, detailed in 148 bills amounting to a total value of £2425. Some other well-known instrument makers, such as Thomas Wright, Benjamin Cole & Son, and Jesse Ramsden, were also occasional suppliers of instruments in the same period, while from 1765 onwards the records include bills for instruments purchased by the Office of Ordnance for the Royal Observatory from makers such as Dollond and Bird. The total number of instrument makers' bills located and examined in the period searched, including the 148 by Adams, was 166. In addition, though not within the scope of this paper it was observed that the records contain numerous bills by William Deane before, and by Jeremiah Sisson after, the period of Adams' appointment respectively. (shrink)

In the present paper, I go beyond these examples by bringing into play an example that I nd more experimental in nature, namely that of the use of the so-called PSLQ algorithm in researching integer relations between numerical constants. It is the purpose of this paper to combine a historical presentation with a preliminary exploration of some philosophical aspects of the notion of experiment in experimental mathematics. This dual goal will be sought by analysing these aspects as they are presented (...) by some of the protagonists of the eld and discussing them using notions from contemporary philosophy of science. (shrink)

According to formalism, a mathematician is not concerned with mysterious metaphysical entities but with mathematical symbols. As a result, mathematical entities become simply sensible signs. However, the price that has to be paid for this move seems to be too high, for mathematics, at present considered to be the queen of sciences, turns out to be a to a contentless game. That is why it seems absurd to regard numbers and all mathematical entities as mere symbols. The (...) aim of our paper is to show the reasons that have led some philosophers and mathematicians to adopt the view that mathematical terms in the proper sense refer to nothing and mathematical propositions have no real content. At the same time we want to explain how formalism helped to overcome the traditional concept of science. (shrink)

This paper explores the various meanings of precision during the early modern period in Europe. In contrast with existing literature focused on assessing the precision of early instruments, this study delves into the intended significance of the term ‘precision’ as understood by historical figures such as J. Stöffler, P. Nunes or F. Mordente. By analysing a selection of instruments equipped with scales, both in their physical form and as they are described in instrument texts, several facets of precision (...) emerge. Some findings demonstrate that the precision of scales can be enhanced through corrections obtained from tables. In other cases, visual estimation is substituted with a method for obtaining values of multiple sexagesimal places. Furthermore, certain instruments designed to represent theoretical concepts achieve greater precision by incorporating the most intricate details of these notions. This investigation into lesser-known meanings of precision underscores the need of comprehensively exploring the concepts, the practices and the terminology surrounding precision that were in use over the fifteenth and sixteenth centuries. (shrink)

This article focuses on some theoretical developments prompted by the use and construction of telescopes in the first half of the seventeenth century. It argues that today's notion of "scientific instrument" cannot be used to categorize these optical devices or explain their impact on natural philosophy. The article analyzes in historical terms the construction of conceptual references for the telescope as an instrument of a new kind, which possessed capabilities and working principles unlike those of traditional "mathematical instruments." (...) It shows that through the 1650s, in both rhetorical and explanatory terms, first-rank telescope makers, theoreticians, and astronomers found it useful to equate the telescope with the eye, suggesting that the data the telescope produced was as reliable as that obtained in naked-eye vision. Kepler's and Descartes' theory of the telescope will be shown to dovetail uncannily with this understanding of the telescope. (shrink)

The city of Kruja (Albania)contains three types of dwellings that date back to different periods of time: the historic ones, the socialist ones, the modern ones. This paper has to deal only with the historic building's typology. The questionnaire that is applied will be considered for the development of mathematical regression based on specific data for this category. Variation between the relevant variables of the questionnaire is fairly or inverse-linked with a certain percentage of influence. The aim of this (...) study is to have better insights into the important role of building occupancy, people's lifestyle, economic level, and the quality of life of the residents in the inner medieval citadel, the physics characteristics, and the energy efficiency of the historical dwellings. The variables such as the number of residents, quality of life, the surface of the dwellings, heating instruments and time spent in the dwelling, current living conditions, monthly bills, level of satisfaction, restoration, and building improvements, interact with each other with probabilities with different positive or negative percentages. (shrink)

: This study examines the effectiveness of systematic desensitizationtreatment on mathematics anxiety and performance among year one collegestudents. This study employs a quasi-experimental research design. The samplefor this study is drawn based on convenience sampling. The sample consistsof 65 year one students of which 32 are under the experimental group andanother 33 are under to control group. The instruments used in collectingdata are The Adopt and Adapt Fennama-Sherman Mathematics Attitude Scale, Neo-Five-Factory Personality Inventory, MathematicsPerformance Test, and The Systematic Desensitization (...) Module. The study postulates: mathematics anxious students who receivesystematic desensitization treatment would report a reduction in the level ofmathematics anxiety as compared to those mathematics anxious students whodo not receive any treatment; mathematics anxious students who receivesystematic desensitization treatment would perform better as comparedto those mathematics anxious students who do not receive any treatment.Quantitative data is analysed using ANOVAs. (shrink)

Summary Although by the mid-eighteenth century colonial American makers of mathematical instruments were producing many of the scientific instruments required in the British Colonies of North America for surveying and navigation, it was not until after the first quarter of the nineteenth century that American makers had the capability to produce sophisticated precision optical instruments for astronomy and microscopy. Until then, these had to be imported from overseas, chiefly England, at considerable cost and after long delays. (...) Included among them were historically important instruments required for establishing provincial and territorial boundaries, and for making astronomical observations. Although generally treated with the utmost care while in use, eventually one after another was misplaced, lost, destroyed by fire, or, in one instance, carefully hidden away then forgotten until it was discovered more than a century later. (shrink)

Mathematical practitioners in seventeenth-century London formed a cohesive knowledge community that intersected closely with instrument-makers, printers and booksellers. Many wrote books for an increasingly numerate metropolitan market on topics covering a wide range of mathematical disciplines, ranging from algebra to arithmetic, from merchants’ accounts to the art of surveying. They were also teachers of mathematics like John Kersey or Euclid Speidell who would use their own rooms or the premises of instrument-makers for instruction. There was a high degree (...) of interdependency even beyond their immediate milieu. Authors would cite not only each other, but also practitioners of other professions, especially those artisans with whom they collaborated closely. Practical mathematical books effectively served as an advertising medium for the increasingly self-conscious members of a new emerging professional class. Contemporaries would talk explicitly of ‘the London mathematicians’ in distinction to their academic counterparts at Oxford or Cambridge. The article takes a closer look at this metropolitan knowledge culture during the second half of the century, considering its locations, its meeting places and the mathematical clubs which helped forge the identity of its practitioners. It discusses their backgrounds, teaching practices and relations to the London book trade, which supplied inexpensive practical mathematical books to a seemingly insatiable public. (shrink)