Giora Hon

This study examines Bacon’s critique of the Unity of Matter Thesis (UMT) as articulated in his Opus maius. In this work, he refutes UMT using mathematical reasoning, particularly targeting its implication of material holenmerism. He argues that if prime matter were numerically identical across all things, it would possess infinite potency, which in turn necessitates an infinite essence. The latter would mean equating matter with God, a heretical conclusion. Bacon focuses particularly on the link between infinite potency and essence. He advances three “geometrical” demonstrations that reject the idea of infinite potency of matter. These demonstrations appeal to the paradox of unequal infinities to show that if actual infinities exist, some would be greater than others, violating mathematical principles. Beyond their specific use in discussing UMT, Bacon’s geometrical demonstrations, modelled after the Euclidean proof, not only exemplify his commitment to “mathematical epistemology” in metaphysics, but also prefigure later attempts to replace logic with mathematics.

In 1618 Girolamo Sirtori published his book, Telescopivm: Siue Ars Perficiendi Novvm Illvd Galilaei Visorivm Instrumentum ad Sydera. The Telescopium is a workshop manual, one of the most detailed optical handbooks published at that time. Sirtori constructed several telescopes but acknowledged that they performed poorly. He consulted authors in the field of optics as sources of optical knowledge but maintained a critical stance since he realized that none of the optical authors had contributed anything of substance to the body of optical knowledge. The Telescopium exposes the nature of the tension between theory and practice: how did it happen that authors who wrote on optics failed to construct advanced telescopes, while practitioners who successfully constructed telescopes good for terrestrial and naval usage, were unable to improve the performance of these devices? The construction of a high-quality telescope requires theories for determining the interplay among material and optical features and methods for controlling these relations. Such methods are based on optical theories which are categorically different from the “hands on” skills applied in the spectacle craft industry. We exhibit the properties of spectacle and telescope lenses which Sirtori used and discuss the optical setups of his telescopes. We ask: what is an optical theory? Did Sirtori have a theory to explain how telescopes function? We argue that Sirtori’s Telescopium is grounded in empirically derived rules of thumb from the spectacle-making craft and did not develop into a coherent instrumental theory capable of advancing telescope construction.

In 1646, Francesco Fontana (1580–1656) published his Novae Coelestium Terresriumque Rerum Observationes which includes discussions of optical properties of systems of lenses, e.g., telescope and microscope. Our study of the Novae Coelestium shows that the advance Fontana made in optics could not have been accomplished on the basis of the traditional spectacle optics which was the dominant practice at his time. Though spectacle and telescope making share the same optical elements, improving eyesight and constructing telescope are different practices based on different principles. The production of powerful astronomical telescopes demanded objective lenses with much longer focal length and eyepiece lenses with much shorter focal length than the range of focal length of lenses used for spectacles, respectively. Moreover, higher standard of precision and purity of the glass was required. The transition from the practice by which optical components were chosen from ready-made spectacle lenses to lenses which were produced according to predetermined specifications (e.g., calculation of focal length) was anything but straight forward. We argue that Fontana developed the optical knowledge necessary for improving the performance of optical systems. Essentially, he formulated—based on rich practical experience—a set of rules of calculation by which optical properties of a lens system could be determined and adjusted as required.

We call attention to the historical fact that the meaning of symmetry in antiquity—as it appears in Vitruvius’s De architectura—is entirely different from the modern concept. This leads us to the question, what is the evidence for the changes in the meaning of the term symmetry, and what were the different meanings attached to it? We show that the meaning of the term in an aesthetic sense gradually shifted in the context of architecture before the image of the balance was attached to the term in the middle of the 18th century and well before the first modern scientific usage by Legendre in 1794.Keywords: Symmetry; Vitruvius; Claude Perrault; Charles-Louis de Secondat Baron de Montesquieu; Balance in architecture.

The optical works of Giambattista Della Porta (ca. 1535-1615) have mostly received mixed if not negative appraisals in the historiography of early modern optics. However, these optical studies contained significant contributions to the understanding of the functioning of optical elements. The articles comprising this volume assess the epistemological background, merits, and failures of Della Porta’s scholarship in a critical yet balanced way. The novel insights thus obtained may facilitate further studies aimed at redressing Della Porta's optics and the impact he had on contemporaries and successors.

Logically, generating knowledge requires a fixed set of presuppositions, anchored in a given conceptual framework. Scientists may or may not be aware of all the elements that are involved in the process of generating knowledge but, whether the elements are assumed explicitly or implicitly, they have to be fixed for the production of knowledge to be coherent. I distinguish between two sets of elements of knowledge, which I call a “baseline” and a “snapshot.” The baseline represents the sum of what is, in principle, available to the community of practitioners in the field. In contrast, a snapshot is personal, that is, it is the result of applying some rules of selection to the baseline. A snapshot includes, in addition to the selected elements, idiosyncratic assessments of the elements; such assessments may not be found in the standard literature. I analyze two case studies, theoretical and experimental, in which the practitioners themselves presupposed the distinction here proposed. I show that the distinction is an effective tool in the presentation of case studies with the goal of throwing light on how scientific knowledge is modified and changed. What is illuminating in the cases at hand is the fact that the scientists themselves exhibited in their works the dynamics of “baseline” and “snapshot,” in parallel to the practice of the historians and the philosophers of science.

This volume contains essays that examine the optical works of Giambattista Della Porta, an Italian natural philosopher during the Scientific Revolution. Coverage also explores the science and technology of early modern optics. Della Porta's groundbreaking book, Magia Naturalis, includes a prototype of the camera. Yet, because of his obsession with magic, Della Porta's scientific achievements are often forgotten. As the contributors argue, his work inspired such great minds as Johanes Kepler and Francis Bacon. After reading this book, researchers, historians, and students will have a better appreciation of this influential scientist. They will also gain a greater understanding of an important period in the history of optics. Readers will learn about Della Porta's experimental method, a process governed by the protocols, aims, and theoretical assumptions of natural magic. Coverage also discusses the material properties and limitations of optical technology in the early 17th century, based on a recently discovered Dutch spyglass. It also demonstrates how diagrams were instrumental in the discovery of the sine law of refraction. In addition, the book includes an in-depth analysis of previously untranslated Latin sources. This makes the material useful to historians of optics unfamiliar with the language. More than 70 illustrations complement the text.

In Bk. 17, Ch. 4 of Magia Naturalis (1589) Giambattista Della Porta (ca. 1535–1615) reported his experiments on concave spherical mirrors arranged in various setups. Della Porta identified two critical points: (1) the point of inversion (punctum inversionis) in reference to the place where the magnified image is turned upside down and seen blurred, and (2) the point of burning (punctum incensionis) in reference to the place where the reflected rays concentrate and ignite fire. Opticians and practitioners of the time distinguished between the two points but considered them to occupy the same spatial location.Della Porta inferred from his studies of concave spherical mirrors that the position of the point of inversion and that of the point of burning occupy different spatial locations. He associated the point of inversion with a locus where the image is seen magnified, turned upside down and blurred—a matter of visual perception. He defined the point of burning as a physical, optical position associated with a geometrical point in which the converging rays ignite fire. Consequently, throughout Bk. 17, Della Porta discarded the point of inversion from his optical nomenclature and referred only to the point of burning, the real—so to speak—optical point. In so doing, Della Porta contributed fundamentally towards the technological management of sets of optical elements.In this paper we follow the experimental practice of Della Porta as presented by the optical demonstrations in Bk. 17, Ch. 4. We discuss the theoretical principles Della Porta developed to clarify whether his claim concerning concave spherical mirror is hypothetical or was it based on an inference from experience. We offer novel insights into the development of the theory of reflection in concave spherical mirrors as it was pursued by Della Porta. He eliminated perceptual considerations from his optics and considered only geometrical-physical aspects. This approach was most useful in the development of the telescope where the critical aspect is not perception but rather ratio of spatial angles.

The claim that Galileo Galilei transformed the spyglass into an astronomical instrument has never been disputed and is considered a historical fact. However, the question what was the procedure which Galileo followed is moot, for he did not disclose his research method. On the traditional view, Galileo was guided by experience, more precisely, systematized experience, which was current among northern Italian artisans and men of science. In other words, it was a trial-and-error procedure—no theory was involved. A scientific analysis of the optical properties of Galileo’s first improved spyglass shows that his procedure could not have been an informed extension of the traditional optics of spectacles. We argue that most likely Galileo realized that the objective and the eyepiece form a system and proceeded accordingly.

In 1768, Kant published a short essay in which he inquired into the possibility of determining the directionality of space. Kant's central argument invokes the strategy that if one were to demonstrate directionality, then the relational view of space that Leibniz propounded would be refuted. This paper has been considered a major turning point in Kant's philosophical development towards his critical philosophy of transcendental idealism. I demonstrate that in this study, Kant came very close to the modern concept of symmetry. His novel construction of incongruent counterpart (inkongruentes Gegenstück) contains elements essential to the modern notion of symmetry. However, Kant does not consider the incongruent counterparts, which he designates as ‘Right’ and ‘Left’, symmetric; rather, he holds the French encyclopaedist view that symmetry is a kind of balance. This study convinced Kant that the solution to the problem of the nature of space lies not in mathematics but in metaphysics. He was wrong in this conclusion, at least with respect to symmetry. The solution was found within the framework of mathematics, that is, solid geometry. In 1794, Legendre recast the traditional encyclopaedist concept of symmetry by calling a certain property of polyhedra symmetrical. The view of Kant is contrasted with that of Legendre by comparing their usages of mirror image as an aid for understanding. While in both cases mirror images are not considered illusions—perhaps for the first time in the history of mirror reflections—the differences are substantial, highlighting the limitation of Kant's position and the great potential of Legendre's new concept of symmetry.

In addition to his scientific achievements, James Clerk Maxwell was an innovator in methodologies in physics. In fact, in his hands methodology and theory mutually inform one another, an aspect of his work that has not been properly appreciated. We examine closely from a methodological perspective Maxwell’s contributions to electromagnetism and uncover a trajectory of great interest, which we call Maxwell’s methodological odyssey. There are four principal stations along the fifteen-year trajectory of Maxwell’s published writings devoted to electromagnetism. These contributions form a sequence of different methodologies which culminated in 1873 in his Treatise on Electricity and Magnetism. Tracing the path leading to his magnum opus yields novel insights into the various methodologies which Maxwell applied in the course of constructing his epoch-making electrodynamic theory. Indeed, we claim that the framework of the theory is just as important as the empirical facts in this physical domain. Thus, we are persuaded that Maxwell's formulation and application of novel scientific methodologies is no less a feat than proposing a fundamental theory.

According to the received view, the first spyglass was assembled without any theory of how the instrument magnifies. Galileo, who was the first to use the device as a scientific instrument, improved the power of magnification up to 30 times. How did he accomplish this feat? Galileo does not tell us what he did. We hold that such improvement of magnification is too intricate a problem to be solved by trial and error, accidentally stumbling upon a complex procedure. We construct a plausibility argument and submit that Galileo had a theory of the telescope. He could develop it by analogical reasoning based on the phenomenon of reflection in mirrors—as it was put to use in surveying instruments—and applied to refraction in sets of lenses. Galileo could appeal to this analogy and assume Della Porta’s theory of refraction. He could thus turn the spyglass into a revolutionary scientific instrument—the telescope.