Leibniz speaks, in a variety of contexts, of there being two realms—a "kingdom of power or efficient causes" and "a kingdom of wisdom or final causes." This essay explores an often overlooked application of Leibniz's famous "two realms doctrine." The first part turns to Leibniz's work in optics for the roots of his view that nature can be seen as being governed by two complete sets of equipotent laws, with one set corresponding to the efficient causal order of the world, (...) and the other to its teleological order. The second part offers an account of how this picture of lawful over-determination is to be reconciled with Leibniz's mature metaphysics. The third addresses a line of objection proposed by David Hirschmann to the effect that Leibniz's doctrine undermines his stated commitment to an efficient, broadly mechanical account of the natural world. Finally, the fourth part suggests that Leibniz's thinking about the harmony of final and efficient causes in connection with corporeal nature may help to shed light on his understanding of the teleological unfolding of monads as well. (shrink)

In a situation in which several explanations compete, is the one that is better qua explanation also the one we should regard as the more likely to be true? Realists usually answer in the affirmative. They then go on to argue that since realism provides the best explanation for the success of science, realism can be inferred to. Nonrealists, on the other hand, answer the above question in the negative, thereby renouncing the inference to realism. In this paper I separate (...) the two issues. In the first section it is argued that a rationale can be provided for the inference to the best explanation; in the second, that this rationale cannot justify an inference to realism. The defence of the inference rests on the claim that our standards of explanatory power are subject to critical examination, which, in turn, should be informed by empirical considerations. By means of a comparison of the realist's explanation for the success of science with that of conventionalism and instrumentalism it is then shown that realism does not offer a superior explanation and should not, therefore, be inferred to. (shrink)

This article explores the metaphor of Science as provider of sharp images of our environment, using the epistemological framework of Objective Cognitive Constructivism. These sharp images are conveyed by precise scientific hypotheses that, in turn, are encoded by mathematical equations. Furthermore, this article describes how such knowledge is pro-duced by a cyclic and recursive development, perfection and reinforcement process, leading to the emergence of eigen-solutions characterized by the four essential properties of precision, stability, separability and composability. Finally, this article discusses (...) the role played by ontology and metaphysics in the scientific production process, and in which sense the resulting knowledge can be considered objective. (shrink)

Consider the distinctive qualitative property grass visually appears to have when it visually appears to be green. This property is an example of what I call sensuous color. Whereas early modern mechanists typically argue that bodies are not sensuously colored, Margaret Cavendish (1623–73) disagrees. In cases of veridical perception, she holds that grass is green in precisely the way it visually appears to be. In defense of her realist approach to sensuous colors, Cavendish argues that (i) it is impossible to (...) conceive of colorless bodies, (ii) the very possibility of color experience requires that bodies are sensuously colored, and (iii) the attribution of sensuous colors to bodies provides the best explanation of color constancy. Although some passages might suggest that Cavendish endorses a reductive account of sensuous color, according to which sensuous color reduces to a body's microscopic surface texture (or some other mechanistically respectable property), I argue that she accepts a nonreductive account, on which sensuous color is not thus reducible. (shrink)

The purpose of this dissertation is to defend Pierre Fermat and Gottfried Wilhelm Leibniz against the charge of error made against them by Pierre Maupertuis that they errantly applied final causes to physics. This charge came in Maupertuis’ 1744 speech to the Paris Academy of Sciences, later published in different versions, entitled Accord Between Different Laws Which at First Seemed Incompatible. It is in this speech that Maupertuis lays claim to one of the most important discoveries in the history of (...) physics and science, The Principle of Least Action. From the date of this speech up until the end of the twentieth century, Maupertuis was credited with this discovery. Fermat discovered least time in optical physics, and Leibniz co-discovered infinitesimal calculus. When the credited discoverer of least action in physics accuses the discoverer of least time in optics and the co-discoverer of infinitesimal calculus of error before and audience of mathematicians, physicists and scientists, it is an event that calls out for investigation. The idea of final causes in physics is the idea that bodies move for an end purpose. During the early modern period, this challenged the intellectual establishment of the day with the idea of thinking in nature. The question which fueled the research for this dissertation is why such a man would accuse two other prominent intellects with such an unprovable metaphysical assumption. The research for this project started with a study of the positions of all three of these men regarding final causes in physics. The second phase was to research the historical context in which Accord Between Different Laws Which at First Seemed Incompatible was written and delivered. This context included the life of Maupertuis as member of the Paris Academy of Sciences and as later President of the Berlin Academy of Sciences. It also included the workings of three highly competitive, state funded, academies of science in Berlin, London and Paris. Research showed that no formal positions were held on the subject of final causes by either Maupertuis or Fermat. Only Leibniz demonstrated an established and well thought out position on the subject. Research did reveal the story of an ambitious man in Maupertuis, who made it the fulfillment of his ambition to rise in the ranks of math and science within the academies and establish himself as an intellectual great in European culture. Consequently, the life and career of Maupertuis illustrates the sociological dimension of scientific achievement. Accord Between Different Laws Which at First Seemed Incompatible turned out to be a politically calculated speech delivered for the purpose of career advancement. In 1744, Maupertuis was being considered by the King of Prussia, Frederick the Great, and the leadership of the Berlin Academy of Science for the presidency of that institution. Maupertuis knew this. Therefore, the work must be interpreted in this context. Consequently, the charge of error against Fermat and Leibniz by Maupertuis must be interpreted likewise. Discovery was made in contextual and Leibnizian research that Maupertuis was aware of Leibniz’s idea of action from 1738 on, and knowingly claimed to have discovered a generalized notion of action in physics which was not his. It is the story of ambition clouding human judgment. The Leibnizians attacked Maupertuis on this matter, led by a member of the Berlin Academy named Samuel Konig. In the “Konig Affair”, Konig accused Maupertuis of what is essentially plagiarism, and Maupertuis countered with charging Konig with forgery for claiming to have in his possession a letter from Leibniz to Jacob Hermann demonstrating Leibniz’s knowledge of least action. Maupertuis buries Konig in legal proceedings, but loses his reputation in the process. During the final stages of the Konig affair, Maupertuis admits to Patrick d’Arcy, a member of the Paris academy, that he had used Leibniz’s theory of action. Having lost his effective leadership as President of the Berlin Academy, Maupertuis spends the last years of his life in his native France without ever relinquishing his title and office. When at first examining the charge of error, the immediate notion is that this is a cause and effect argument. It appears to be an argument about the order of metaphysics before physics. This turns out not to be the case. Maupertuis agrees with Fermat and Leibniz at every turn. The charge is all about career success. (shrink)

The ArugmentThis essay answers a single question: what was Robert Hooke, the Royal Society's curator of experiments, doing in his well-known 1665 work,Micrographia?Hooke was articulating a “universal cure of the mind” capable of bringing about a “reformation in Philosophy,” a change in philosophy's interpretive practices and organization. The work explicated the interpretive and political foundations for a community of optical instrument users coextensive with the struggling Royal Society. Standard observational practices would overcome the problem of using nonstandard instruments, while inherent (...) inrepresentation– the interpretive practice championed in the text – were important theological and political meanings. Hooke's kind of experimental philosophy undermined the claims made by “atheists” and “enthusiasts” – the enemies of the restored church and state – while also producing useful knowledge. Equally important, Hooke modeled the community described inMicrographiaupon the classicalres publica, but his community made important concessions to Restoration political realities, especially the growing role of commercial or transactional relationships. (shrink)

ABSTRACTÉmilie du Châtelet’s recently-discovered Essai sur l’optique offers new insights into her early natural philosophy. Here I analyse the Essai in detail, focusing on Du Châtelet’s use of attr...

The history of the Parallelogram Rule for composing physical quantities, such as motions and forces, is marked by conceptual difficulties leading to false starts and halting progress. In particular, authors resisted the required assumption that the magnitude and the direction of a quantity can interact and are jointly necessary to represent the quantity. Consequently, the origins of the Rule cannot be traced to Pseudo-Aristotle or Stevin, as commonly held, but to Fermat, Hobbes, and subsequent developments in the latter part of (...) the seventeenth century. (shrink)

Philosophy and Memory Traces defends two theories of autobiographical memory. One is a bewildering historical view of memories as dynamic patterns in fleeting animal spirits, nervous fluids which rummaged through the pores of brain and body. The other is new connectionism, in which memories are 'stored' only superpositionally, and reconstructed rather than reproduced. Both models, argues John Sutton, depart from static archival metaphors by employing distributed representation, which brings interference and confusion between memory traces. Both raise urgent issues about control (...) of the personal past, and about relations between self and body. Sutton demonstrates the role of bizarre body fluids in moral physiology, as philosophers from Descartes and Locke to Coleridge struggled to control their own innards and impose cognitive discipline on 'the phantasmal chaos of association'. Going on to defend connectionism against Fodor and critics of passive mental representations, he shows how problems of the self are implicated in cognitive science. (shrink)

O artigo procura avaliar a consolidação e os desdobramentos da função heurística e simbólica ocupada pelo Ungeheuer [o monstro ou o monstruoso] na filosofia kantiana, tendo em vista a emergência do horizonte da racionalidade moderna. Uma reconfiguração dessas imagens do Monstro e da Monstruosidade parece ter lugar no momento mesmo em que a filosofia moderna procurou pensar sua identidade e seus limites. O pensamento de Kant, que ocupa - de fato ou de direito - um lugar central nessa ruptura, apresentaria (...) de modo exemplar, embora não evidente, o percurso dessa transformação. This work intends to evaluate the origins and developments of the symbolic and heuristic function at stake in the term Ungeheuer [the monster or the monstrous] within Kant's philosophy, regarding the rising horizon of modern rationality. A reconfiguration of the Monster and Monstrous imagery seems to take place right at the moment when modern philosophy had to reflect upon its own identity and limits. Kant's thought, that occupies - de jure or de facto - a central place within this rupture could exemplarily, but not obviously, show the path of such transformation. (shrink)

It is well known that Hooke's wave theory of light, set forth in his Micrographia of 1665, is viewed as a step towards Huygens's famous theory of light. This view depends mostly on some short remarks given by Huygens in his Traité de la Lumi`ere and the earlier Projet du Contenu de la Dioptrique . Huygens's personal copy of Micrographia was believed to be lost until found at Braunschweig University Library by the author three years ago. It is annotated at (...) Observ. IX only, where Hooke deals with his wave theory of light and colours. This article provides a short review of Hooke's theory, and an interpretation of Huygens's annotations, which show clearly the first steps towards the opinions he was to express in his Traité de la lumi`ere, particularly methodological ones. Furthermore, a short comparison is here drawn with Huygens's annotations in his copy of Ango's L'optique divisée en trois livres, which show similar patterns of reasoning. (shrink)

Leibniz’s mature philosophical understanding of the laws of nature emerges rather suddenly in the late 1670’s to early 1680’s and is signaled by his embrace of three central theses.1 The first, what I’ll call the thesis of Contingency, suggests that the laws of nature are not only contingent, but, in some sense, paradigmatically contingent; they are supposed to provide insight into the very nature of contingency as Leibniz comes to understand it. The second, what I’ll call the thesis of Providence, (...) suggests that the laws of nature provide a basis for a new argument from design by showing how reflection on God’s ends can be positively useful in the practice of natural philosophy. The third, what I’ll call thesis of .. (shrink)

This paper aims both to tackle the technical issue of deciphering Hobbes’s derivation of the sine law of refraction and to throw some light to the broader issue of Hobbes’s mechanical philosophy. I start by recapitulating the polemics between Hobbes and Descartes concerning Descartes’ optics. I argue that, first, Hobbes’s criticisms do expose certain shortcomings of Descartes’ optics which presupposes a twofold distinction between real motion and inclination to motion, and between motion itself and determination of motion; second, Hobbes’s optical (...) theory presented in Tractatus Opticus I constitutes a more economical alternative, which eliminates the twofold distinction and only admits actual local motion, and Hobbes’s derivation of the sine law presented therein, which I call “the early model” and which was retained in Tractatus Opticus II and First Draught, is mathematically consistent and physically meaningful. These two points give Hobbes’s early optics some theoretical advantage over that of Descartes. However, an issue that has baffled commentators is that, in De Corpore Hobbes’s derivation of the sine law seems to be completely different from that presented in his earlier works, furthermore, it does not make any intuitive sense. I argue that the derivation of the sine law in De Corpore does make sense mathematically if we read it as a simplification of the early model, and Hobbes has already hinted toward it in the last proposition of Tractatus Opticus I. But now the question becomes, why does Hobbes take himself to be entitled to present this simplified, seemingly question-begging form without having presented all the previous results? My conjecture is that the switch from the early model to the late model is symptomatic of Hobbes’s changing views on the relation between physics and mathematics. (shrink)

: This paper focuses on Princess Elisabeth of Bohemia's philosophical views as exhibited in her early correspondence with René Descartes. Elisabeth's criticisms of Descartes's interactionism as well as her solution to the problem of mind-body interaction are examined in detail. The aim here is to develop a richer picture of Elisabeth as a philosophical thinker and to dispel the myth that she is simply a Cartesian muse.

The polarity of light and dark in the treatment of the Newtonian spectrum and the inverse spectrum is studied further and the validity of heterogeneity of light and darkness in relation to Goethe’s views is examined. In order to clarify the reality of the “darkness rays”, theexperimentum crucisis re-evaluated. It is shown that the commonly accepted analysis contains assumptions in the choice of the spectrum and background, which mask the inherent dynamic of the spectrum. The relation between colour and wavelength (...) is re-examined with respect to the immutability and specific refrangibility of colour. It is then shown that both these properties are approximations that apply under the specific conditions that have later become standardized in spectroscopy, leading to a consensus regarding the relation of wavelength to colours of one particular spectrum. This consensus has resulted in the study of colour diverging into spectroscopy and colour physiology. As an alternative, the basis of the dichotomy postulated by Müller is studied, leading to the realization that the resolution of this dichotomy was begun by Goethe with the idea of turbidity. A further study shows that turbidity resolves the apparent incompatibility of light and dark. (shrink)

Johannes Kepler dedicated much of his work to discover a law for the refraction of light. Unfortunately, he formulated an incorrect law. Nevertheless, it was useful for anticipating the behavior of light in some specific conditions. Some believe that Kepler did not have the elements to formulate the law that was later accepted by the scientific community, that is, the Snell–Descartes law. However, in this paper, we propose a model that agrees with Kepler’s heuristics and that is also successful in (...) anticipating the behavior of light when it passes through a surface that separates two media with different optical densities. This model adopts strategies that were recommended by Kepler in two types of analogies. The obstacles that led to the failure of the two types of analogies are presented in the article, and we argue that the model proposed here could overcome these specific obstacles. Finally, we show how the proposed model could be articulated with Kepler’s metaphysics of light. (shrink)

This essay examines one of the cornerstones of Leibniz's defense of teleology within the order of nature. The first section explores Leibniz's contributions to the study of geometrical optics, and argues that his "Most Determined Path Principle" or "MDPP" allows him to bring to the fore philosophical issues concerning the legitimacy of teleological explanations by addressing two technical objections raised by Cartesians to non-mechanistic derivations of the laws of optics. The second section argues that, by drawing on laws such as (...) the MDPP, Leibniz is able to introduce a thin notion of teleology that gives him the resources to respond to the most pressing charges of his day against teleological explanations within natural philosophy. Finally, the third section argues that contemporary philosophers have been overly hasty in their dismissal of Leibniz's account of natural teleology, and indeed that their own generally thin conceptions of teleology have left them with few well-motivated resources for resisting his elegant position. (shrink)

Simon Schaffer has published a constructivist analysis of the acceptance of Newton’s theory of color that focuses on Newton’s experiments, the continual controversies over them, and his power and authority. In this article, I show that Schaffer’s account does not agree with the historical evidence. Newton’s theory was accepted much sooner than Schaffer holds, when and in places where Newton had little power; many successfully repeated the experiments and few contested them; and theory mattered more than experiment in acceptance. I (...) also present an alternative account of the acceptance of Newton’s theory that shows that, despite criticism when it was first published in 1672, the theory, or parts of it, gradually came to be accepted by mathematical scientists—including Huygens and Leibniz—and Scottish natural philosophers by the time of the publication of the Opticks in 1704. On the Continent, it was coming to be accepted within a decade or so after its publication, that is, before 1716, when Newton replied to a challenge, purportedly by Leibniz, that Schaffer sees as the crucial conflict that at last gave Newton’s experiments their authority. (shrink)

In this essay the authors explore the nature of efficient causal explanation in Newton’s "Principia and The Opticks". It is argued that: (1) In the dynamical explanations of the Principia, Newton treats the phenomena under study as cases of Hall’s second kind of atypical causation. The underlying concept of causation is therefore a purely interventionist one. (2) In the descriptions of his optical experiments, Newton treats the phenomena under study as cases of Hall’s typical causation. The underlying concept of causation (...) is therefore a mixed interventionist/mechanicist one. (shrink)

Descartes’s most extensive discussion of the law of refraction and the shape of the anaclastic lens is contained in Rule 8 of "Rules for the Direction of the Mind". Few reconstructions of Descartes’s discovery of the law of refraction take Rule 8 as their basis. In Rule 8, Descartes denies that the law of refraction can be discovered by purely mathematical means, and he requires that the law of refraction be deduced from physical principles about natural power or force, the (...) nature of the action of light, and the behavior of light rays in a variety of transparent media. For over a century, however, there has been broad agreement that Descartes discovered the law of refraction by purely mathematical means, and that he only later provided the relevant physical rationale (via comparisons or analogies) in Dioptrics II. I execute each step in Descartes’s proposed deduction of the law of refraction and the shape of the anaclastic lens in Rule 8 and concretely show how Descartes could have discovered the law of refraction and the shape of the anaclastic by its means. Rule 8, I argue, reflects Descartes’s actual path to the discovery of the law of refraction and the shape of the anaclastic lens. (shrink)

This paper reconstructs the development of Mersenne's reflections concerning optics. I argue that Mersenne's optical writings provide crucial insights into Mersenne's Aristotelianism. I reconstruct Mersenne's attempt of explaining the new ideas on light, which were advanced by Kepler, Descartes and Hobbes within Aristotle's natural philosophy. Mersenne explained Kepler's work on light within the Scholastic tradition. In the 1640s, Mersenne was stimulated by the debate concerning Descartes' theory of light, which he accepted only in 1648. Indeed, Mersenne first explained Descartes' law (...) of refraction by means of Hobbes physics. However, Mersenne always wanted to remain faithful to Aristotle. (shrink)

Newton claims to have proven the heterogeneity of light through his experimentum crucis. However, Olaf Müller has worked out in detail Goethe’s idea that one could likewise prove the heterogeneity of darkness by inverting Newton’s famous experiment. Müller concludes that this invalidates Newton’s claim of proof. Yet this conclusion only holds if the heterogeneity of light and the heterogeneity of darkness is logically incompatible. This paper shows that this is not the case. Instead, in Quine’s terms, we have two logically (...) compatible theories based on mutually irreducible theoretical terms. From a Quinean point of view, this does no harm to the provability of the corresponding statements. (shrink)

This article attends to “questionnaires” in linguistic fieldwork defined by the inclusion of sensory stimuli. It shows that such non-verbal protocols have been used to help elucidate and compare semantic content, which has generally been subordinated to formal analysis in the history of linguistics. To explain and exemplify this relationship, I target the color questionnaire developed by Hugo Magnus, which included ten standardized color chips and a long list of interview questions on language use. Magnus’s questionnaire (Fragebogen) decoupled perception and (...) denotation in its day, though similar protocols have recently been employed to restore the connection between meaning and form. (shrink)

The ArgumentThe inclusion of an item within a theory may be essential or accidental, and if the former then the explanation of its meaning and of its inclusion in the theory cannot be by accidental events and circumstances. Since all events and circumstances – be they social, political, religious, psychological, etc. – are accidental vis-à-vis the ideas they occasion, they cannot serve as explanation of these ideas. The only way to explain the ideas is by showing their essentiality to the (...) theory rather than their importance to the people. Thus, the place of spirits and souls within seventeenth-century science is explained by Platonic ideology.This demands a concept of nature which is thoroughly efficient causative, and a concept of explanation which is thoroughly informative. This means that theories must explain any given effect by a cause which is separable from it and is conceptually heterogeneous to it. Such a nature and such an explanation are inherently paradoxical and irrational, which explains the preponderance of these traits in seventeenth-century science as created by Kepler, through Galileo and Descartes to Newton.The primary efficient-causal and explanatory agency is force, which is ontically distinct from matter and from the motion it causes in matter. Soul, spirit and active principle are mere variants of force. Thus, their presence in seventeenth-century science is explained only by their being conceptually essential to any Platonic philosophy of nature. (shrink)

En los Discorsi Galileo afirma haber realizado un experimento, cuyo resultado fue negativo, para determinar si la luz tarda tiempo en propagarse. En este trabajo analizo ese experimento como crucial entre las hipótesis rivales según las cuales la luz se propaga con velocidad infinita o con velocidad finita. Procuro determinar las hipótesis auxiliares y la carga teórica que presupone el diseño experimental. Argumento que las hipótesis presupuestas son razonables y que la carga teórica es muy baja. Sostengo que en principio (...) es posible un experimento crucial exitoso, esto es, con resultado positivo, como el concebido por Galileo. Concluyo que la hipótesis de que la luz se propaga con velocidad finita no es refutable mediante un experimento de esta clase, por lo cual cualquier resultado negativo es compatible con ambas hipótesis rivales. Como consecuencia de ello, la hipótesis de que la luz, o cualquier otra interacción física, se propagan con velocidad infinita resulta inverificable. (shrink)

Analogies between hearing and seeing already existed in ancient Greek theories of perception. The present paper follows the evolution of such analogies until the rise of 17th century optics, with due regard to the diversity of their origins and nature but with particular emphasis on their bearing on the physical concepts of light and sound. Whereas the old Greek analogies were only side effects of the unifying concepts of perception, the analogies of the 17th century played an important role in (...) constructing optical theories by imitation of acoustic theories, or vice versa. This transition depended on several factors including the changing relations between optics, music, mathematics, and physics, the diversity of early modern concepts of sound, and the rise of a new physics based on experimentation and mechanical explanation. (shrink)

In 1626, René Descartes and Claude Mydorge worked closely together on the problem of refraction, apparently discovering what is now known as the sine law of refraction. They constructed a plano-hyperbolic lens in order to test out the truth of this mathematical relationship. In 1637, Descartes finally published the sine method of determining refractions in his Dioptrique, which also demonstrated, on the basis of this relationship, that the hyperbola and ellipse were anaclastic lines (that is, that a lens with their (...) profile would refract rays perfectly to a single point) without mentioning Mydorge. Mydorge himself wrote a short manuscript on the subject of refraction and lenses, which is found in a copy among Mersenne’s papers. Scholars have usually assumed that this treatise was written as Mydorge and Descartes worked together in 1626. However, other evidence shows that only the first part of the treatise records the two men’s early collaboration. Subsequently, Mydorge and Descartes completed their arguments separately, Descartes with the help of Isaac Beeckman. (shrink)

Positivism and, especially, Max Weber's vision of the modern disen chantment of the world are incoherent because they separate human culture from the environment in which human agents pursue their life- projects. The same problem is manifested, more blatantly, in current social studies of science, which take the project of disenchantment further by disenchanting science itself. A different image of science is traced to classical empiricism, whose paradigm of learning is belief and, more specifically, the practical nature of the believer's (...) experience of the environment of his or her actions. The believer's ecological imagery of the world, as it was elaborated by classical empiricism, provides the means to transcend the disenchanted image of the world and its prob lems. (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)

Attempts in antiquity and the Middle Ages to determine the mathematical law of refraction are well known. In view of the movement toward the mathematization of physical laws, which has made great gains since the beginning of the seventeenth century, and of the efforts of Hariot, Kepler, Snell, and Descartes to determine the true mathematical ratio between the angles of incidence and refraction, it is understandable that historians of pre-seventeenth-century science should concentrate on the quantitative aspects of refraction. But to (...) do so is to gain a distorted picture of early optical thought, for as much effort was actually devoted to understanding the cause of refraction as to finding the mathematical law of refraction. (shrink)