I take another look at the history of science and offer some fresh insights into why the history of science is filled with discarded theories. I argue that the history of science is just as we should expect it to be, given the following two facts about science: theories are always only partial representations of the world, and almost inevitably scientists will be led to investigate phenomena that the accepted theory is not fit to account for. Together these facts suggest (...) that most scientific theories are apt to be discarded sometime, superseded by new theories that better serve scientists’ new research interests. Consequently, it is reasonable to expect that many of the theories we currently accept, despite their many impressive successes, will be discarded sometime in the future. But I also argue that discarded theories are not always aptly characterized as a sign of failure or as a sign of some sort of shortcoming with science. Theories are discarded because scientists are making advances in their pursuit of knowledge. Thus, discarded theories are often a sign of the good health of science. Scientists are responding to their changing research interests. (shrink)

This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the (...) field, it lays down a much-needed marker of progress to date and provides a platform for informed and coherent future analysis and research of the subject. -/- The publication comes at a time of heightened worldwide concern over the standard of science and mathematics education, attended by fierce debate over how best to reform curricula and enliven student engagement in the subjects There is a growing recognition among educators and policy makers that the learning of science must dovetail with learning about science; this handbook is uniquely positioned as a locus for the discussion. -/- The handbook features sections on pedagogical, theoretical, national, and biographical research, setting the literature of each tradition in its historical context. Each chapter engages in an assessment of the strengths and weakness of the research addressed, and suggests potentially fruitful avenues of future research. A key element of the handbook’s broader analytical framework is its identification and examination of unnoticed philosophical assumptions in science and mathematics research. It reminds readers at a crucial juncture that there has been a long and rich tradition of historical and philosophical engagements with science and mathematics teaching, and that lessons can be learnt from these engagements for the resolution of current theoretical, curricular and pedagogical questions that face teachers and administrators. (shrink)

: We question the claim, common since Duhem, that sixteenth century astronomy, and especially the Wittenberg interpretation of Copernicus, was instrumentalistic rather than realistic. We identify a previously unrecognized Wittenberg astronomer, Edo Hildericus (Hilderich von Varel), who presents a detailed exposition of Copernicus's cosmology that is incompatible with instrumentalism. Quotations from other sixteenth century astronomers show that knowledge of the real configuration of the heavens was unattainable practically, rather than in principle. Astronomy was limited to quia demonstrations, although demonstration propter (...) quid remained the ideal. We suggest that Osiander's notorious preface to Copernicus expresses these sixteenth century commonplaces rather than twentieth century instrumentalism, and that neither `realism', nor `instrumentalism', in their modern meanings, apply to sixteenth century astronomy. (shrink)

The paper considers the development of physics‐teaching at the universities of Königsberg (founded 1544) and Helmstedt (founded 1576). The question is: How many teachers of physics professed Aristotelianism and how long? and why did most of them reject Copernicanismus? The paper suggests that Melanchthon, not only the founder of early German philosophy ‘was also the propounder of a form of, modern Aristotelianism’ which proved very valuable in mediating between theologians and philosophers on the one side and between philosophers and experimentalists (...) on the other side. (shrink)

A corpus of 360 distinct early modern printed editions containing Johannes de Sacrobosco’s Tractatus de sphaera is “dissected” into a corpus of 540 text-parts, 241 of them re-occurring at least once. Through the exploration of the data, we recognized a relevant position for four anonymous authors in their social network. We demonstrate that the text-parts originally assigned to the anonymous authors were authored or edited by Georg Rheticus. By means of data analysis, we conclusively establish that Rheticus profoundly impacted the (...) content of such textbooks for the introductory class in geocentric astronomy all over Europe between 1538 and 1629. (shrink)

I revisit an older defense of scientific realism, the methodological defense, a defense developed by both Popper and Feyerabend. The methodological defense of realism concerns the attitude of scientists, not philosophers of science. The methodological defense is as follows: a commitment to realism leads scientists to pursue the truth, which in turn is apt to put them in a better position to get at the truth. In contrast, anti-realists lack the tenacity required to develop a theory to its fullest. As (...) a consequence, they are less likely to get at the truth. -/- My aim is to show that the methodological defense is flawed. I argue that a commitment to realism does not always benefit science, and that there is reason to believe that a research community with both realists and anti-realists in it may be better suited to advancing science. A case study of the Copernican Revolution in astronomy supports this claim. (shrink)

We will examine Kepler's use of a relation between velocity and distance from a centre of circular motion. This relation plays an essential role, through a derivation in chapter 40 of the Astronomia Nova, in the presentation of the Area Law of planetary motion. Kepler transcends ancient and contemporary applications of the distance-velocity relation by connecting it with his metaphysical commitment to the causal role of the Sun. His second main innovation is to replace the astronomical models of his predecessors (...) with an account that derives trajectories from physical principles. In this paper we restrict our attention primarily to the first 40 chapters of Kepler's Astronomia Nova. Hence, we do not discuss Kepler's discovery of elliptical planetary orbits. (shrink)

General discussions of the appropriate relations between history and philosophy of science must be complemented by examinations of particular studies involving both fields. Martin Curd's attempt to illuminate the rationality of theory change through analysis of the Copernican Revolution is such a study; his work is undercut by serious flaws and actually displays an ahistorical approach. The result misleads both about the Copernican Revolution and the general problem of theory change in science. The study does illustrate several types of failing (...) that can vitiate efforts to bring historical considerations into philosophical discussion, namely, pitfalls in the characterization of theories, arguments, range of choices, and criteria. (shrink)

The history of the continuous inclusion of mathematics in liberal education in the West, from ancient times through the modern period, is sketched in the first two sections of this chapter. Next, the heart of this essay (Sects. 3, 4, 5, 6, and 7) delineates the central role mathematics has played throughout the history of Western civilization: not just a tool for science and technology, mathematics continually illuminates, interacts with, and sometimes challenges fields like art, music, literature, and philosophy – (...) subjects now universally considered to be liberal arts. Section 8 adds an international perspective to the contemporary liberal arts story by describing some instructive mathematical achievements from many cultures and societies. Finally, Sect. 9 addresses how contemporary mathematics teaching can use the history of mathematics viewed as a liberal art to enhance the appreciation and understanding of mathematics for all students. (shrink)

Some of Kepler's works seem very different in character. His youthful Mysterium cosmographicum (1596) argues for heliocentrism on the basis of metaphysical, astronomical, astrological, numerological and architectonic principles. By contrast, Astronomia nova (1609) is far more tightly argued on the basis of only a few dynamical principles. In the eyes of many, such a contrast embodies a transition from Renaissance to early modern science. I suggest that Karl Popper's fallibilist and piecemeal approach, and especially his theory of errors, might prove (...) extremely helpful in resolving such alleged tension. By abandoning the perspective of the inductivist philosophy of science, which is forced by its own standards to portray Kepler as a "sleepwalker", I focus on the method he followed: he never hesitated to discuss his own intellectual journey, offering a rational reconstruction of the series of false starts, blind alleys and failures he encountered. The critical dialogue he managed to establish in private correspondence with fellow astronomers he later transplanted into his printed works, whose structure closely resembles that of a dialogue, however implicit. (shrink)

In the present paper, I present and discuss some new information about the life of Paul Wittich from Wrocław, Poland (formerly Breslau, Germany), an elusive mathematician and astronomer of the late 16th century. Wittich seems to have played a significant role in the emergence of two important, though short-lived, developments of late 16th-century science: the so-called prosthaphaeresis calculating method, and the geoheliocentric model of the universe usually attributed to Tycho Brahe. His role in both achievements, however, has not been sufficiently (...) explained so far, and it is my belief that one of the main obstacles to that endeavor has been our scarce knowledge about the details of Wittich's life. Thus, I attempt to reconstruct his life with aim of being able to evaluate, eventually, his involvement in the development of mathematics and astronomy towards the end of the 16th century, primarily with the use of whatever scant sources can be found concerning Wittich. The source that I present here—a notebook of Bartholomäus Scultetus, an astronomer from Görlitz—is known and has already been used, but only to a limited extent by the community of historians of science, or by those of astronomy and mathematics. By presenting the information about Wittich from Scultetus's notebook, I aim to bring this source to the attention of those communities, clarify some hitherto unclear details from Wittich's life, and set out new paths for further investigation into his biography. (shrink)

In this paper, we demonstrate how a systematic taxonomy of stances can help elucidate two classic debates of the historical turn—the Lakatos–Feyerabend debate concerning theory rejection and the Feyerabend–Kuhn debate about pluralism during normal science. We contend that Kuhn, Feyerabend, and Lakatos were often talking at cross-purposes due to the lack of an agreed upon taxonomy of stances. Specifically, we provide three distinct stances that scientists take towards theories: acceptance of a theory as the best available description of its domain, (...) use of a theory in practical applications, and pursuit (elaboration) of a theory. We argue that in the Lakatos–Feyerabend debate, Lakatos was concerned with acceptance whereas Feyerabend was mainly concerned with pursuit. Additionally, we show how Feyerabend and Kuhn’s debate on the role of pluralism/monism in normal science involved a crucial conflation of all three stances. Finally, we outline a few general lessons concerning the process of scientific change. (shrink)

In setting forth a new theory of the growth of scientific knowledge, Larry Laudan shows that any account of scientific change has consequences for the relationship between the history, philosophy and sociology of science. It is a laudable feature of his work that he does not treat any of these disciplines as undifferentiated monoliths. In fact, one of his main goals is to show that his account of progress requires specific ways of doing and relating these three disciplines. As an (...) historian invited to speak at the Philosophy of Science Association, it seemed appropriate for me to appraise the function of history of science in Laudan’s program. Without going into unnecessary detail, let me begin by examining some of his main claims.The focus of Laudan’s argument is on science construed as a form of problem-solving activity and on progress and rationality as appraisals of problem-solving capabilities. (shrink)

ArgumentThe subject of the paper is the shift from an astrology-oriented astronomy towards an allegedly more objective, mathematically grounded approach to astronomy. This shift is illustrated through a close reading of Tycho Brahe's scientific development and the contemporaneous changes in his communicational strategies. Basing the argument on a substantial array of original sources it is claimed that the Danish astronomer developed a new astronomical discourse in pursuit of credibility, giving priority to observational astronomy and natural philosophical questions. The abandonment of (...) astrology in public discourse is primarily explained by Tycho's social position and greater sensibility to controversial issues. Tycho's example suggests that the changes in rhetorical strategies regarding astrology (which happened earlier than changes in astrological belief) should be given more recognition in the history of astronomy. (shrink)

(1993). Balthasar Bekker's Cartesian hermeneutics and the challenge of Spinozism. British Journal for the History of Philosophy: Vol. 1, No. 1, pp. 55-79.

Ever since its foundation in 1540, the Society of Jesus had had one mission—to restore order where Luther, Calvin and the other instigators of the Reformation had brought chaos. To stop the hemorrhage of believers, the Jesuits needed to form a united front. No signs of internal disagreement could to be shown to the outside world, lest the congregation lose its credibility. But in 1570s two prominent Jesuits, Cristophorus Clavius and Benito Perera, had engaged in a bitter controversy. The issue (...) at stake had apparently nothing to do with the values on which Ignazio of Loyola had built the Society of Jesus. And yet the dispute between Clavius and Perera was matter of concern for the entire Jesuit community. They were... (shrink)

ArgumentThe purpose of this paper is to provide an analysis of Giordano Bruno’s conception of mathematics. Specifically, it intends to highlight two aspects of this conception that have been neglected in previous studies. First, Bruno’s conception of mathematics changed over time and in parallel with another concept that was central to his thought: the concept of infinity. Specifically, Bruno undertook a reform of mathematics in order to accommodate the concept of the infinitely small or “minimum,” which was introduced at a (...) later stage. Second, contrary to what Héléne Védrine claimed, Bruno believed that mathematical objects were mind-dependent. To chart the parallel development of the conceptions of mathematics and infinity, a seven-year time span is considered, from the publication of Bruno’s first Italian dialogue (La cena de le ceneri,1584) to the publication of one of his last Latin works (De minimo, 1591). (shrink)

The early dissemination of Copernicus' work and theories is an intricate and multilayered history. The reception of De revolutionibus orbium coelestium, which was the first early modern work in mathematical astronomy introducing a heliocentric planetary theory, was not purely technical. Rather, the cultural debates surrounding it were affected by physical, philosophical, ethical, and theological concerns from its inception. Georg Joachim Rheticus, who authored the first report on Copernicus' achievement, deemed it appropriate to put a call for independence of spirit on (...) the title page of the Narratio... (shrink)

This article situates Edward Gresham'sAstrostereon, or A Discourse of the Falling of the Planet(1603), a little-known English astronomical treatise, in the context of the cosmo-theological debate on the reconciliation of heliocentrism with the Bible, triggered by the publication of Nicholas Copernicus'sDe revolutionibus orbium coelestiumin 1543. Covering the period from the appearance of the ‘First Account’ of Copernican views presented in Georg Joachim Rheticus'sNarratio Prima(1540) to the composition ofAstrostereonin 1603, this paper places Edward Gresham's commentary and exegesis against the background of (...) the views expressed by his countrymen and the thinkers associated with the Wittenberg University – such as Philipp Melanchthon, Caspar Peucer, and Christoph Rothmann. Comparing the ways in which they employed certain biblical passages – either in favour of or against the Earth's mobility – the paper emphasizes Gresham's ingenious reading of the Hebrew version of the problematic excerpts, and his expansion of the accommodation principle. (shrink)

Narratives about the peaceful and fruitful relationship of religion and science in early-modern times have long since replaced the nineteenth-century vision of the ‘warfare of science with theology...