: Scientific observation is determined by the human sensory system, which generally relies on instruments that serve as mediators between the world and the senses. Instruments came in the shape of Heron's Dioptra, Levi Ben Gerson's Cross-staff, Egnatio Danti's Torqvetto Astronomico, Tycho's Quadrant, Galileo's Geometric Military Compass, or Kepler's Ecliptic Instrument. At the beginning of the seventeenth century, however, it was unclear how an instrument such as the telescope could be employed to acquire new information and expand knowledge about the (...) world. To exploit the telescope as a device for astronomical observations Galileo had to: 1. establish that telescopic images are not optical defects, imperfections in the eye of the observer, or illusions caused by lenses; 2. develop procedures for systematically handling errors that may occur during observation and measurement and methods of processing data. Galileo made it clear that in order to measure and interpret natural phenomena accurately, a suitable method and instrument would need to be developed. It is intriguing, therefore, to regard the Galilean telescope in this light and to discover the linkage established by Galileo among theory, method, and instrument—the telescope. Although the telescope was not invented through science, it is instructive to see how Galileo used optics to employ a theory-laden instrument for bridging the gulf between picture and scientific language, between drawing and reporting physical facts, and between merely sketching the world and actually describing it. (shrink)

ArgumentJohannes Kepler published hisAstronomia novain 1609, based upon a huge amount of computations. The aim of this paper is to show that Kepler's new astronomy was grounded on methods from numerical analysis. In his research he applied and improved methods that required iterative calculations, and he developed precompiled mathematical tables to solve the problems, including a transcendental equation. Kepler was aware of the shortcomings of his novel methods, and called for a new Apollonius to offer a formal mathematical deduction. He (...) was also in great need of computational power, and his friend and colleague, Wilhelm Schickard, constructed the first prototype of a true mechanical calculator, although it never came into regular use. The article concludes that Kepler's new astronomy was clearly backed up by numerical methods and embedded concepts and challenges of great importance for the future development of numerical analysis. (shrink)

Thomas Kuhn has argued that scientists never reject a paradigm without simultaneously accepting a new paradigm. Coupled with Kuhn's claim that it is paradigms as a whole, and not individual theories, that are accepted or rejected, this thesis is seen as one of Kuhn's main challenges to the rationality of science. I argue that Kuhn is mistaken in this claim; at least in some instances, science rejects a paradigm despite the absence of a successor. In particular, such a description best (...) fits Kuhn's most discussed example, the Copernican Revolution. By differentiating scientific discoveries into three types, spontaneous, implicit, and directed, we see that Kuhn's thesis holds for spontaneous and implicit discoveries, but not directed discoveries. Directed discoveries must be understood by an alternative account of falsifiability, based on argument by reductio ad absurdum rather than argument by modus tollens as traditional accounts of falsifiability would have it. (shrink)

This essay is concerned with the epistemic roles of error in scientific practice. Usually, error is regarded as something negative, as an impediment or obstacle for the advancement of science. However, we also frequently say that we are learning from error. This common expression suggests that the role of error is not—at least not always—negative but that errors can make a fruitful contribution to the scientific enterprise. My paper explores the latter possibility. Can errors play an epistemically productive role in (...) scientific research? The paper begins with a review of several twentieth-century approaches to error and the various agendas behind them. It is shown that only very few scholars have considered whether errors can be productive. The main part of the paper examines a concrete debate in early nineteenth-century microscopy and analyses how the microscopists coped with the problem of error. Drawing on this material, the article offers some terminological clarifications of the common notion ‘learning from error’. The conclusion argues that error can indeed play epistemically productive roles in scientific practice.Keywords: Error; Nineteenth-century microscopic anatomy. (shrink)

This paper is concerned with the problem of experimental error. The prevalent view that experimental errors can be dismissed as a tiresome but trivial blemish on the method of experimentation is criticized. It is stressed that the occurrence of errors in experiments constitutes a permanent feature of the attempt to test theories in the physical world, and this feature deserves proper attention. It is suggested that a classification of types of experimental error may be useful as a heuristic device in (...) studying the nature of these errors. However, the standard classification of systematic and random errors is mathematically based does not focus on the causes of the errors, their origins, or the contexts in which they arise. A new typology of experimental errors is therefore proposed whose criterion is epistemological. This typology reflects the various stages that can be discerned in the execution of an experiment, each stage constituting a category of a certain type of experimental error. The proposed classification consists of four categories which are illustrated by historical cases. (shrink)

The attempt to narrow the general discourse of the problem of error and to focus it on the specific problem of experimental error may be approached from different directions. One possibility is to establish a focusing process from the standpoint of history; such an approach requires a careful scrutiny of the history of science with a view to identifying the juncture when the problem of experimental error was properly understood and accounted for. In a study of this kind one would (...) have to examine the evolution of the method of experimentation and related topics so that clear criteria would underlie the analysis. (shrink)

The year 2009 marks the 400th anniversary of the publication of one of the most revolutionary scientific texts ever written. In this book, appropriately entitled, Astronomia nova, Johannes Kepler developed an astronomical theory which departs fundamentally from the systems of Ptolemy and Copernicus. One of the great innovations of this theory is its dependence on the science of optics. The declared goal of Kepler in his earlier publication, Paralipomena to Witelo whereby The Optical Part of Astronomy is Treated , was (...) to solve difficulties and expose illusions astronomers face when conducting astronomical observations with optical instruments. To avoid observational errors that had plagued the antiquated measuring techniques for calculating the apparent diameter and angular position of the luminaries, Kepler designed a novel device: the ecliptic instrument. In this paper we seek to shed light on the role optical instruments play in Kepler's scheme: they impose constraints on theory, but at the same time render astronomical knowledge secure. To get a comprehensive grasp of Kepler's astonishing achievements it is required to widen the approach to his writings and study Kepler not only as a mathematico-physical astronomer, but also as a designer of instruments and a practicing observer. (shrink)

Can a theory turn back, as it were, upon itselfand vouch for its own features? That is, canthe derived elements of a theory be the veryprimitive terms that provide thepresuppositions of the theory? This form of anall-embracing feature assumes a totality inwhich there occurs quantification over thattotality, quantification that is defined bythis very totality. I argue that the Machprinciple exhibits such a feature ofall-embracing nature. To clarify the argument,I distinguish between on the one handcompleteness and on the other wholeness andtotality, (...) as different all-embracing features:the former being epistemic while the latter –ontological.I propose an analogy between the Mach principleas a possible selection principle in generalrelativity, and the vicious-circle principle infoundations of mathematics. I finally concludewith a consequence of this analogyvis-à-vis completeness and totality,viz., both should be constrained if they wereto be valid concepts for a physical theory. (shrink)

The question is raised as to the kind of methodology required to deal with foundational issues. A comparative study of the methodologies of Gödel and Einstein reveals some similar traits which reflect a concern with foundational problems. It is claimed that the interest in foundational problems stipulates a certain methodology, namely, the methodology of limiting cases.

: This study of the concept of orbit is intended to throw light on the nature of revolutionary concepts in science. We observe that Kepler transformed theoretical astronomy that was understood in terms of orbs [Latin: orbes] (spherical shells to which the planets were attached) and models (called hypotheses at the time), by introducing a single term, orbit [Latin: orbita], that is, the path of a planet in space resulting from the action of physical causes expressed in laws of nature. (...) To demonstrate the claim that orbit is a revolutionary concept we pursue three lines of argument. First we trace the origin of the term; second, we document its development and specify the meaning of the novel term as it was introduced into astronomy by Kepler in his Astronomia nova (1609). Finally, in order to establish in what sense the concept is revolutionary, we pay attention to the enduring impact that the concept has had on the relevant sciences, in this case astronomy and indeed physics. We claim that orbit is an instance of a revolutionary concept whose provenance and use can provide the insights we are seeking. (shrink)

This study of the concept of orbit is intended to throw light on the nature of revolutionary concepts in science. We observe that Kepler transformed theoretical astronomy that was understood in terms of orbs [Latin: orbes] and models , by introducing a single term, orbit [Latin: orbita], that is, the path of a planet in space resulting from the action of physical causes expressed in laws of nature. To demonstrate the claim that orbit is a revolutionary concept we pursue three (...) lines of argument. First we trace the origin of the term; second, we document its development and specify the meaning of the novel term as it was introduced into astronomy by Kepler in his Astronomia nova . Finally, in order to establish in what sense the concept is revolutionary, we pay attention to the enduring impact that the concept has had on the relevant sciences, in this case astronomy and indeed physics. We claim that orbit is an instance of a revolutionary concept whose provenance and use can provide the insights we are seeking. (shrink)

Abstract : A measurement result is never absolutely accurate: it is affected by an unknown “measurement error” which characterizes the discrepancy between the obtained value and the “true value” of the quantity intended to be measured. As a consequence, to be acceptable a measurement result cannot take the form of a unique numerical value, but has to be accompanied by an indication of its “measurement uncertainty”, which enunciates a state of doubt. What, though, is the value of measurement uncertainty? What (...) is its numerical value: how does one calculate it? What is its epistemic value: how one should interpret a measurement result? Firstly, we describe the statistical models that scientists make use of in contemporary metrology to perform an uncertainty analysis, and we show that the issue of the interpretation of probabilities is vigorously debated. This debate brings out epistemological issues about the nature and function of physical measurements, metrologists insisting in particular on the subjective aspect of measurement. Secondly, we examine the philosophical elaboration of metrologists in their technical works, where they criticize the use of the notion of “true value” of a physical quantity. We then challenge this elaboration and defend such a notion. The third part turns to a specific use of measurement uncertainty in order to address our thematic from the perspective of precision physics, considering the activity of the adjustments of physical constants. In the course of this activity, physicists have developed a dynamic conception of the accuracy of their measurement results, oriented towards a future progress of knowledge, and underlining the epistemic virtues of a never-ending process of identification and correction of measurement errors. (shrink)