In his Paralipomena Johannes Kepler reported an experimentum that he had seen in the Dresden Kunstkammer. In one of the rooms there, which had been turned in its entirety into a camera obscura, he had witnessed the images formed by a lens. I discuss the role of this experiment in the development and foundation of his new theory of optical imagery, which made a distinction between two concepts of image, pictura and imago. My focus is on how Kepler used his (...) report of the experiment inside the camera obscura to criticize the account of image formation given in Giovanbattista Della Porta's Magia naturalis. I argue that this experiment allowed Kepler to sort out the confusion between images 'in the air'—referring to the geometrical locus of images in the perspectivist tradition of optics—and the experimentally produced 'projected images', which were empirically familiar but conceptually alien to perspectivist optics. (shrink)

Despite recent work on scientific instruments by historians of science, the meeting ground between historians and curators of collections has been disappointingly narrow. This study offers, first, a characterization of sixteenth-century mathematical instruments, drawing on the work of curators, as represented by the online database Epact. An examination of the relationship between these instruments and the natural world suggests that the ‘theoric’, familiar from studies of the history of astronomy, has a wider relevance to the domain of practical mathematics. This (...) outcome from a study of collections is then used in re-examining an established question in the history of science, the position of William Gilbert on the motion of the Earth. (shrink)

Here, Rhonda Martens offers the first extended study of Kepler's philosophical views and shows how those views helped him construct and justify the new astronomy.

: Although Galileo's struggle to mathematize the study of nature is well known and oft discussed, less discussed is the form this struggle takes in relation to Galileo's first new science, the science of the second day of the Discorsi. This essay argues that Galileo's first science ought to be understood as the science of matter—not, as it is usually understood, the science of the strength of materials. This understanding sheds light on the convoluted structure of the Discorsi's first day. (...) It suggests that the day's meandering discussions of the continuum, infinity, the vacuum, and condensation and rarefaction establish that a formal treatment of the "eternal and necessary" properties of matter is possible; i.e., that matter as such can be considered mathematically. This would have been a necessary, and indeed revolutionary, preliminary to the mathematical science of the second day because matter itself was thought in the Aristotelian tradition to be responsible for the departure of natural bodies from the unchanging and thus mathematizable character of abstract objects. In addition, the first day establishes that when considered physically, these properties account for matter's force of cohesion and resistance to fracture. This essay closes by showing that this dual style of reasoning accords with the conceptual structure of mixed mathematics. (shrink)

Seventeenth-century optics naturalizes the eye while estranging the mind from objects. A mere screen, on which rests a blurry array of light stains, the eye no longer furnishes the observer with genuine re-presentations of visible objects. The intellect is thus compelled to decipher flat images of no inherent epistemic value, accidental effects of a purely causal process, as vague, reversed reflections of wholly independent objects. Reflecting on and trespassing the boundaries between natural and artificial, orderly and disorderly, this optical paradox (...) is a Baroque phenomenon; and it is the origin of Descartes’ celebrated doubt---whether we know anything at all. (shrink)

“Although up to now the [visual] image has been [understood as] a construct of reason,” Kepler observes in the fifth chapter of his Ad Vitellionem Paralipomena, “henceforth the [visible] representations of objects should be considered as paintings [ picturae ] that are actual[ly projected] on paper or some other screen.” While not intended as a historical generalization, this claim nonetheless reflects historical reality. Virtually all visual theorists before Kepler did, in fact, conceive of optical images as subjective, not objective constructs (...) – or, to put it in modern terms, as virtual rather than real entities. By current lights, of course, the distinction between virtual and real images is both obvious and common-place: whereas the latter can be physically projected upon a screen, the former cannot. (shrink)

In his Paralipomena Johannes Kepler reported an experimentum that he had seen in the Dresden Kunstkammer. In one of the rooms there, which had been turned in its entirety into a camera obscura, he had witnessed the images formed by a lens. I discuss the role of this experiment in the development and foundation of his new theory of optical imagery, which made a distinction between two concepts of image, pictura and imago. My focus is on how Kepler used his (...) report of the experiment inside the camera obscura to criticize the account of image formation given in Giovanbattista Della Porta's Magia naturalis . I argue that this experiment allowed Kepler to sort out the confusion between images 'in the air'—referring to the geometrical locus of images in the perspectivist tradition of optics—and the experimentally produced 'projected images', which were empirically familiar but conceptually alien to perspectivist optics. (shrink)

In the first section I outline the theory of abstraction, discussing first its con- ceptual basis, then its psychological-epistemological basis, and last its causal basis. My purpose throughout is to show how these bases, and thus the theory itself, were not only paramountly Aristotelian, but also eminently sensible. In the second section I draw the perspectivist account of vision within the bounds of the theory of abstraction and show stage by stage how that account unfolds coherently within those bounds. This (...) procedure should make clear that what the perspecti- vists actually offered was less a scientific theory of light or vision than a scientifi- cally justified world view. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Method and Mathematics:Peter Ramus's Histories of the SciencesRobert GouldingPeter Ramus (1515–72) was, at first sight, the least likely person to write an influential history of mathematics. For one thing, he was clearly no great mathematician himself. His sympathetic biographer Nicholas Nancel related that Ramus would spend the mornings being coached in mathematics by a team of experts he had assembled, and in the afternoon would lecture on the very (...) same subjects.1 But there can be no doubt that Ramus held mathematics in particular esteem and even played a crucial role in linking philosophical discourse to mathematics and in promoting the use of quadrivial reasoning in the study of the natural world.2The origins for his enthusiasm for mathematics are to be found in his account of the nature of the arts and critique of the curriculum of the universities. From his earliest career, Ramus was a logician and remained one in all his works, whether writing on mathematics or Virgil, and he conceived [End Page 63] of all the arts, especially mathematics, as unchanging structures of necessarily true propositions—not prima facie a position which lends itself to notions of historical change and development.3 His career as a historian of mathematics, I will argue, was directed by problems that arose in his theoretical understanding of mathematics as he began to immerse himself in the sciences of the ancient world.Ramus and the Reform of DialecticRamus set out his fundamental logical positions in his very first printed work, the Dialecticae institutiones (Education in Dialectic) of 1543, a contribution to the ongoing humanist attack on scholastic logic, in which Ramus rehearsed many of the commonplace criticisms of the university dialectic. Humanists complained that logic no longer concerned itself with real human reasoning; instead, it had become a discipline studied for its own sake, using its own incomprehensible jargon, and was of no practical interest. The new humanist dialectics of Lorenzo Valla and Rudolph Agricola attempted to teach the kind of practical reasoning useful for composing a speech or letter, and they borrowed extensively from rhetorical works of Cicero and Quintilian to develop a highly rhetoricized logic. Questions about the formal validity of arguments were of little interest; what mattered was whether the arguments were persuasive.4In his Dialecticae institutiones, Ramus took this humanist reformulation of dialectic a step further. Dialectic—or, in fact, any art or science—consisted of nature, doctrine, and exercise. The natural workings of the mind formed the most significant element. Doctrine was nothing more than a record of natural reasoning; in importance it paled next to nature and practice.5 The logic of the universities bore no resemblance to the true, natural dialectic, as he argued at length in the companion volume to the Institutiones, the innocuously titled but exuberantly offensive Aristotelicae animadversiones [End Page 64] (Observations on Aristotle).6 The question, then, remained: how can we gain access to this "natural reasoning"?Ramus's answer was surprising. He asks us to find a group of men—not scholars, but completely uneducated vineyard workers. Question them about the coming year: the fertility of the soil, the quality and quantity of the crop. "And then," he writes "from their minds as from a mirror an image of nature will be reflected."7 In the reasoned replies of these uneducated men, says Ramus, we discover every part of logic needed for any purpose, whether everyday discourse or composition of poetry: the invention of arguments, the assessment of their truth and their proper and orderly presentation. Other humanists had praised man's natural logical faculties, elevating them over artificial technique, but Ramus was the first to look beyond the walls of the university and the writings of the ancients to find natural dialectic at work.If even the uneducated have some possession of the arts, then the arts taught at the university should do no more than clear away the misleading junk in the mind, and allow its natural clarity to shine through.8 Logic should be easy to learn—not because this is a pedagogic ideal, but from the very nature of the art. And if logic as it is... (shrink)

In developing a new theory of vision in Ad Vitellionem paralipomena Kepler introduced a new optical concept, pictura, which is an image projected on to a screen by a camera obscura. He distinguished this pictura from an imago, the traditional image of medieval optics that existed only in the imagination. By the 1670s a new theory of optical imagery had been developed, and Kepler's pictura and imago became real and virtual images, two aspects of a unified concept of image. The (...) new concept of image developed out of a synthesis of Kepler's determination of the geometrical location of a pictura as the limit, or focus, of refracted pencils of rays and the triangulation used by a single eye to determine the perceived location of an imago. The distinction between real and imaginary images was largely developed by Gilles Personne de Roberval and the Jesuits Francesco Eschinardi and Claude François Milliet Dechales. (shrink)