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)

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 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)

Institutional corruption is a normative concept of growing importance that embodies the systemic dependencies and informal practices that distort an institution’s societal mission. An extensive range of studies and lawsuits already documents strategies by which pharmaceutical companies hide, ignore, or misrepresent evidence about new drugs; distort the medical literature; and misrepresent products to prescribing physicians. We focus on the consequences for patients: millions of adverse reactions. After defining institutional corruption, we focus on evidence that it lies behind the epidemic of (...) harms and the paucity of benefits. (shrink)

Over the past 35 years, patients have suffered from a largely hidden epidemic of side effects from drugs that usually have few offsetting benefits. The pharmaceutical industry has corrupted the practice of medicine through its influence over what drugs are developed, how they are tested, and how medical knowledge is created. Since 1906, heavy commercial influence has compromised congressional legislation to protect the public from unsafe drugs. The authorization of user fees in 1992 has turned drug companies into the FDA's (...) prime clients, deepening the regulatory and cultural capture of the agency. Industry has demanded shorter average review times and, with less time to thoroughly review evidence, increased hospitalizations and deaths have resulted. Meeting the needs of the drug companies has taken priority over meeting the needs of patients. Unless this corruption of regulatory intent is reversed, the situation will continue to deteriorate. We offer practical suggestions including: separating the funding of clinical trials from their conduct, analysis, and publication; independent FDA leadership; full public funding for all FDA activities; measures to discourage R&D on drugs with few, if any, new clinical benefits; and the creation of a National Drug Safety Board. (shrink)

As of January 1, 2008, over 98,000 people are waiting for organ transplants in the United States of America. Of those, nearly 75,000 are waiting for a kidney. In this calendar year, fewer than 15,000 will receive a kidney transplant from a deceased donor. The average waiting time for a deceased donor kidney now exceeds five years in virtually all metropolitan areas. Sadly, nearly as many people die waiting as there are deceased donors each year, despite monumental efforts by the (...) entire transplant community to increase both the number of organ donors and the number of organs recovered from each donor. The imbalance between demand and supply has led to considerable efforts to expand the criteria for what is considered an acceptable organ donor by the Organ Procurement and Transplant Network, thereby hoping somewhat to assuage the shortfall of donor organs. So-called Expanded Criteria Donors may be older than 50, have history of hypertension, or have died from intracerebral hemorrhage and/or have impaired renal function. ECDs now make up nearly 40% of the donor population. (shrink)

The author recounts his experience with an uDCD program that ran for three years at the Washington Hospital I Center in Washington, D.C. in the 1990s. Challenges, I benefits, and lessons learned are considered in depth. A I primary focus is the importance of community education, Organ Procurement Organization support, and the need for immediate in-situ preservation of organs.

This paper evaluates the existing research on Stand Your Ground (SYG) laws in terms of the extent to which it has accounted for gender. In particular, we address (a) what the available evidence suggests are the gender-based impacts of SYG laws and (b) where, how, and why considerations of gender may be missing in available studies.

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)

What might it be to write a post-colonial social science? And how might the intellectual legacy of Chinese classical philosophy—for instance Sun Tzu and Lao Tzu—contribute to such a project? Reversing the more usual social science practice in which EuroAmerican concepts are applied in other global locations, this paper instead considers how a “Chinese” term, _shi_ might be used to explore the UK’s 2001 foot-and-mouth epidemic. Drawing on anthropological insights into mis/translation between different worlds and their alternative ways of knowing (...) and being, the paper explores that epidemic in three differently inspired _shi_-inflected “empirical” accounts. The first uses Sun Tzu’s strategic understanding of _shi_ to tell a conventionally representational story. The second resists the causes and background factors implied in standard social science by offering a “light” and _shi_-inflected form of knowing. And the third combines the referentiality of social science with a Lao Tzu-informed commitment to the paradoxes of normative epigram. This third narrative thus illustrates the possible features of a situated and _shi_-inflected social science that recognizes that it participates in the contexted and immanent flows and counterflows of things in the world. The paper concludes by noting that such a _shi_-inflected social science is experimental, and suggests that it is important to explore a range of ways of reversing the flow of concepts between EuroAmerica and other global locations. (shrink)

In 1672, inspired by the wave theory of Ignace Gaston Pardies, Christiaan Huygens made his first attempt to explain the sine law of refraction, but in 1673 he abandoned his plans owing to difficulties concerning double refraction. Huygens was able to explain double refraction on 6 August 1677 after his discoveries of the axis of symmetry of the crystal and of ‘Huygens's principle’. On 6 August 1679, he wrote: ‘I have found the confirmation of my theory of (...) light and of refraction’, and then described an ‘experimentum crucis’ to decide between his theory and a rival hypothesis. A study of caustics may have led Huygens to the discovery of ‘Huygens's principle’. (shrink)

It is likely that internal factors play an important role in restricting the possible avenues of evolutionary change from any starting point. Internal selective processes operating on premutational disturbances, on mutations, and on developmental phases may usefully be separated from the adaptive selection of phenotypes. The precise structural and morphological consequences of internal factors should soon become an isolable problem owing to a) the observational correlation of definite changes in hereditary specificity with particular developmental consequences; and b) the progressive theoretical (...) identification of the coordinative conditions in organisms. Increasing clarity regarding the coordinative conditions should throw light on the “mutational selection rules” and on the differentiative mutations which led to the most important steps in the past history of evolution.Die Wege der Evolution können sowohl durch innere Auslese der Genotypen wÄhrend der Entwicklung als auch durch die Äussere Darwinische Auslese der Phenotypen bestimmt werden. Seit 1949 haben sich zumindest fünf Forscher mit dieser Möglichkeit befasst. Es ist zur Zeit möglich, zwischen den beiden Arten von Zuchtwahl theoretisch und experimentell zu unterscheiden.Les chemins de l'évolution peuvent Être déterminés non seulement par la sélection extérieure Darwinienne des phénotypes mais aussi par la sélection intérieure des genotypes pendant le développement. Depuis 1949 aux moins cinq investigateurs en ont considéré la possibilité. Il est possible à présent de faire la distinction entre les deux types de sélection dans la théorie comme dans l'expérience. (shrink)

This chapter contains sections titled: Introduction The Shipwreck of the Richmond and the Duty to Rescue The Ethics of Global Access to Essential Medicines Conclusion References.

Let AC be a ray coming from the medium DC into the medium CE, and let the density of the former to the latter be as d to e. It is asked, how should the ray ACB be directed so that it is the easiest path of all, or that (AC x d) + (CB x e) is a minimum. Let DC = l, and EC = m. It is given also that FG = f, and let AD = FC (...) = x, CG = EB = f – x. Therefore, AC = √(l2 + x2) and CB = √(m2 + f2 +x2 – 2fx). 2 It will then be the case that d√(l2 + x2) + e√(m2 + f2 + x2 – 2fx is equal to a minimum. Therefore, through my method of tangents it is the case that: (2dx/(√(l2 +x2)(AC))) + ((2ex -2ef)/ (√(m2 +f2 +x2 +2fx)(BC))) = 0. That is, it will be the case that AC/BC = dx/e(f-x). Now if we suppose that AC and BC are equal, it will be the case that f – x is to x, as d to e. Therefore, if a circle, with its center at C, is described by the ray CA or CB, AD or “x,” – the sine of the angle of incidence – will be to BE or “f – x,” – the sine of the angle of refraction – as e, the density of the medium of refraction, will be to d, the density of the medium of incidence, that is, the sines of the angles will be in reciprocal relation to the mediums or densities. (shrink)

Physical activity and sedentary behaviour have been linked to the mental health of children and adolescents, yet the timing of behaviours may play a role in this relationship and clarifying this could inform interventions. We explored cross-sectional associations of PA and SED in varying time segments throughout the school day with the mental health of school-aged children and adolescents from rural Northeastern Ontario, Canada. A total of 161 students wore accelerometers for 8 days and completed a self-report survey. Mental health (...) was measured using the Strengths and Difficulties Questionnaire. Accelerometer-measured SED, light PA, and moderate and vigorous PA were estimated in the time-segments before school, school time, after school, and evenings. Associations were tested with multilevel linear regressions while adjusting for confounding factors. Students spent 72.6 min in MVPA, 209.0 min in LPA, and 621.0 min in SED per day. Daily SED was associated with less conduct problems. Evening LPA was inversely associated with hyperactivity, while SED was associated with hyperactivity and with peer problems before school, and during school. No associations were observed for MVPA, emotional symptoms, or prosocial behaviour. In conclusion, displacing SED with LPA in some specific periods of the day may benefit the mental health of students; taking this into account could strengthen interventions. (shrink)

This article assesses Jerome Zanchi’s theory of natural law in relation to that of Richard Hooker’s by arguing three theses. First, Zanchi’s view of natural law is generally Thomistic, but he expands upon it in a manner similar to his contemporaries, thereby providing further evidence against the increasingly discredited narrative of a Protestant voluntarism dominating early Reformed scholastic thought. Second, Zanchi’s commitment to the Reformed doctrine of total depravity does not represent as drastic a departure from Thomas as might first (...) appear. Third, Hooker’s disagreement with Zanchi on this last point does not, as often argued, result from his own diluted commitment to total depravity, but denotes a more coherent and elegant way of reaching the same Reformed Thomistic synthesis. The historical record suggests that Hooker’s approach proved more influential than Zanchi’s. (shrink)

This book subjects the traditional concept of law of nature to critical examination. There are two kinds of reasons that invite this reexamination, one deriving from philosophical concerns over the traditional concept, the other motivated by theoretical and practical changes in science. One of the philosophical worries is that the idiom of law of nature, especially when combined with the notion of laws 'governing' individual events and processes, is no longer as intelligible as it used to be in the theistic (...) context in which the formulation of laws became central to science. The traditional concept is also challenged in various ways by contemporary scientific theories such as quantum mechanics, chaos theory and the general theory of relativity. It is no longer clear that there are any universal laws, laws do not always guarantee predictability, and the border between physical and mathematical considerations is constantly shifting. The most difficult challenge, perhaps, is to come up with a scientific explanation of the origin of laws. Wrestling with these intriguing problems, the papers in this volume broaden both our understanding of the natural order and our desiderata of scientific explanation. (shrink)

On April 30, 1982, the Eleventh Session of the Third United Nations Conference on the Law of the Sea endorsed the final version of the Draft Convention of the Law of the Sea by a vote of 130 to 4, with 17 abstentions.1 The Session met at UN Headquarters in New York from March 8 to April 30.2.

A stable classification of practical principles into mutually exclusive types is foundational to Kant’s moral theory. Yet, other than a few brief hints on the distinction between maxims and laws, he does not provide any elaborate discussion on the classification and the types of practical principles in his works. This has led Onora O’Neill and Lewis Beck to reinterpret Kant’s classification of practical principles in a way that would clarify the conceptual connection between maxims and laws. In this paper I (...) argue that the revised interpretations of O’Neill and Beck stem from a mistaken reading of the fundamental basis of the classification of practical principles. To show this, I first argue that Kant distinguishes between maxims and laws on the bases of validity and reality. I then argue that although a practical principle necessarily has the feature of validity, its reality in actually moving the agents to action sufficiently makes a principle a practical principle. If this is so, I argue that the classification of practical principles must be based on the extent to which they are effective in human agents. Such a classification yields us three exhaustive and mutually exclusive types namely, “maxims that are not potential laws”, “maxims that are potential laws” and “laws that are not maxims”. (shrink)

It is often claimed (most recently by Michael Friedman) that Kant intended to justify Newton’s most fundamental claims expressed in the Principia, such as his laws of motion and the law of universal gravitation. In this article, I argue that the differences between Newton’s laws of motion and Kant’s laws of mechanics are not superficial or merely apparent. Rather, they reflect fundamental differences in their respective projects. This point can be seen especially clearly by considering the nature of the various (...) projects undertaken in Germany prior to Kant that discuss the laws of motion. Wolff and his followers qua metaphysicians were especially interested in providing nonempirical justifications of their laws of motion as well as an intelligible account of the fundamental properties of bodies in terms of substance, accident, and force. Maupertuis and Euler, despite often being seen as Newtonians, both drew on traditions other than Newton’s. Physics textbooks (by figures such as Erxleben, Karsten, ‘s Gravesande, and Musschenbroek) vary considerably in their aims, but in none of these cases is Newton’s main argument of the Principia presented. In light of the fact that these projects are distinct in significant ways from Newton’s project, the differences between Newton’s laws of motion and Kant’s laws of mechanics are most likely not merely apparent but reflect the fact that Kant, too, was pursuing a project fundamentally distinct from Newton’s. (shrink)

Rene Descartes (1596 – 1650) is considered the founder of modern philosophy. Profoundly influenced by the new physics and astronomy of Kepler and Galileo, Descartes was a scientist and mathematician whose most long-lasting contributions in science were the invention of Cartesian coordinates, the application of algebra to geometry, and the discovery of the law of refraction, what we now call Snell’s law.His most important books on philosophy were The discourse on method(1637) and The meditations(1642). Descartes’ writings display an exemplary (...) degree of clarity and an aversion to pedantry. I explore Descartes' break with Aristotle, but also shine a light on the intellectual continuity Descartes had with Aristotle's thought. I also draw attention to some overlooked but interesting possibilities for an experimental test of a dualistic theory of mind. (shrink)

There are certain standards of legal interpretation. Interpretive directives are heterogeneous—both in terms of the issues they address and of the form. Not all authors consider the canons of interpretation to be norms like any other ones. Moreover, some claim that the term “incorrect interpretation” refers only to an arbitrarily chosen concept. I intend to investigate whether, despite the objections raised, interpretative directives can be said to have the status of legal norms. I wonder whether the so-called law of interpretation (...) (LoI), can provide a normative key to assess the correctness of the interpretation of legal texts. Text raises important questions concerning LoI. Firstly, the question of the status of interpretative directives and the problem of their defeasibility. Second, it refers to the problem of compliance with interpretative directives and the consequences of their violation, drawing attention to the two contexts of legal interpretation (the context of discovery and justification) and to the fact that canons of interpretation can constitute a standard for the correctness of the interpretative procedure and for its result. Third, this paper refers to the problem of vagueness of interpretative directives, analysing the advantages of maintaining it to a certain extent, as well as the possibilities of reducing it in the rest. The fourth issue analysed is the multiplicity of canons and the lack of a defined hierarchy of them. I conclude by pointing out that LoI should provide a model by which to assess the correctness of an interpretation. (shrink)

Discovering laws of nature was a way to worship a law-giving God, during the Scientific Revolution. So why should we consider it worthwhile now, in our own more secularized science? For historical perspective, I examine two competing early modern theological traditions that related laws of nature to different divine attributes, and their secular legacy in views ranging from Kant and Nietzsche to Humean and ‘governing’ accounts in recent analytic metaphysics. Tracing these branching offshoots of ethically charged God-concepts sheds light (...) on how our ethical ideals and ideas of natural order can still be valuably integrated. Early modern intellectualists valued the law-governed order of nature as a sign of divine Reason. In turn, Reason traditionally ascribed to God has now been partly reclaimed for humans, reframing the value of natural order anthropocentrically, in terms of the value of our own intelligence. Alternatively, Reason may be reclaimed for nature itself, as in an ‘objective’ idealism or metaphysical rationalism. However, beyond divine Reason, an influential voluntarist tradition in theology stressed a connection between laws of nature and God’s Power or free Will. Tracking how divine Power has been reinvested in human beings provides a broader context for instrumentalism and related lineages of empiricism. But secularization can also transfer Power from God to the impersonal natural world. In this light, current scientific interest in lawlike order may also reflect the inherent value of brute necessity or inhuman causal power in nature: this is a deeper way to reject anthropocentrism and to show our respect for the environment. (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)

Certain results, most famously in classical statistical mechanics and complex systems, but also in quantum mechanics and high-energy physics, yield a coarse-grained stable statistical pattern in the long run. The explanation of these results shares a common structure: the results hold for a 'typical' dynamics, that is, for most of the underlying dynamics. In this paper I argue that the structure of the explanation of these results might shed some light --a different light-- on philosophical debates on the (...) laws of nature. In the explanation of such patterns, the specific form of the underlying dynamics is almost irrelevant. The conditions required, given a free state-space evolution, suffice to account for the coarse-grained lawful behaviour. An analysis of such conditions might thus provide a different account of how regular behaviour can occur. This paper focuses on drawing attention to this type of explanation, outlining it in the diverse areas of physics in which it appears, and discussing its limitations and significance in the tractable setting of classical statistical mechanics. (shrink)

Certain results, most famously in classical statistical mechanics and complex systems, but also in quantum mechanics and high-energy physics, yield a coarse-grained stable statistical pattern in the long run. The explanation of these results shares a common structure: the results hold for a ‘typical’ dynamics, that is, for most of the underlying dynamics. In this paper I argue that the structure of the explanation of these results might shed some light—a different light—on philosophical debates on the laws of (...) nature. In the explanation of such patterns, the specific form of the underlying dynamics is almost irrelevant. The constraints required, given a free state-space evolution, suffice to account for the coarse-grained lawful behaviour. An analysis of such constraints might thus provide a different account of how regular behaviour can occur. This paper focuses on drawing attention to this type of explanation, outlining it in the diverse areas of physics in which it appears, and discussing its limitations and significance in the tractable setting of classical statistical mechanics. (shrink)

How should we assess the appeal of multiple scientific theories when they can all explain a particular empirical phenomenon of interest? We contrast Huygens' and Fermat's explanations of the law of refraction of light and find that neither dominates the other when considering multiple criteria for assessing the overall appeal of a scientific theory. The absence of teleology in Huygens' account is a strong plus compared to Fermat's. But Huygens' wave theory scores less well with respect to other (...) desiderata for a scientific theory. In this case, there does not appear to be a clear winner, nor need there be one. (shrink)

It appears that light may be thrown on the nature of moral principles if they are construed as moral laws analogous to ceteris-paribus laws of nature. Luke Robinson objects that the analogy either cannot explain how moral principles are necessary or cannot explain how obligations can be pro-tanto; and that a dispositional account of moral obligation has explanatory superiority over one in terms of moral laws. I explain the analogy, construing laws of nature as necessary relationships after the fashion (...) of William Kneale and Karl Popper. I then show that Robinson’s objections are mistaken and that if the difference between a dispositional account and a law account is not merely verbal, then it is the law account that is superior. I also dispel the common confusion between the necessity of laws and the existence of forces. (shrink)

In this paper, I discuss the problem of scientific laws in general and laws of biology in particular. After reviewing the debate around the existence of laws in biology, I examine the subject in the light of the structuralist notion of a fundamental law and argue for the law of matching as the fundamental law of genetics.

Some time in the late 1590s, the Welsh amateur mathematician John Bulkeley wrote to Thomas Harriot asking his opinion about the properties of a truly gargantuan (but totally imaginary) plano-spherical convex lens, 48 feet in diameter. While Bulkeley’s original letter is lost, Harriot devoted several pages to the optical properties of “Mr Bulkeley his Glasse” in his optical papers (now in British Library MS Add. 6789), paying particular attention to the place of its burning point. Harriot’s calculational methods in these (...) papers are almost unique in Harriot’s optical remains, in that he uses both the sine law of refraction and interpolation from Witelo’s refraction tables in order to analyze the passage of light through the glass. For this and other reasons, it is very likely that Harriot wrote his papers on Bulkeley’s glass very shortly after his discovery of the law and while still working closely with Witelo’s great Optics; the papers represent, perhaps, his very first application of the law. His and Bulkeley’s interest in this giant glass conform to a long English tradition of curiosity about the optical and burning properties of large glasses, which grew more intense in late sixteenth-century England. In particular, Thomas Digges’s bold and widely known assertions about his father’s glasses that could see things several miles distant and could burn objects a half-mile or further away may have attracted Harriot and Bulkeley’s skeptical attention; for Harriot’s analysis of the burning distance and the intensity of Bulkeley’s fantastic lens, it shows that Digges’s claims could never have been true about any real lens (and this, I propose, was what Bulkeley had asked about in his original letter to Harriot). There was also a deeper, mathematical relevance to the problem that may have caught Harriot’s attention. His most recent source on refraction—Giambattista della Porta’s De refractione of 1593—identified a mathematical flaw in Witelo’s cursory suggestion about the optics of a lens (the only place that lenses appear, however fleetingly, in the writings of the thirteenth-century Perspectivist authors). In his early notes on optics, in a copy of Witelo’s optics, Harriot highlighted Witelo’s remarks on the lens and della Porta’s criticism (which he found unsatisfactory). The most significant problem with Witelo’s theorem would disappear as the radius of curvature of the lens approached infinity. Bulkeley’s gigantic glass, then, may have provided Harriot an opportunity to test out Witelo’s claims about a plano-spherical glass, at a time when he was still intensely concerned with the problems and methods of the Perspectivist school. (shrink)

The status of the laws of nature in Hobbes’s Leviathan has been a continual point of disagreement among scholars. Many agree that since Hobbes claims that civil philosophy is a science, the answer lies in an understanding of the nature of Hobbesian science more generally. In this paper, I argue that Hobbes’s view of the construction of geometrical figures sheds light upon the status of the laws of nature. In short, I claim that the laws play the same role (...) as the component parts – what Hobbes calls the “cause” – of geometrical figures. To make this argument, I show that in both geometry and civil philosophy, Hobbes proceeds by a method of synthetic demonstration as follows: 1) offering a thought experiment by privation; 2) providing definitions by explication of “simple conceptions” within the thought experiment; and 3) formulating generative definitions by making use of those definitions by explication. In just the same way that Hobbes says that the geometer should “put together” the parts of a square to learn its cause, I argue that the laws of nature are the cause of peace. (shrink)

This volume sheds new light on modern theories of natural law through the lens of the fragmented political contexts of Italy in the eighteenth and nineteenth centuries, and the dramatic changes of the times. From the age of reforms, through revolution and the 'Risorgimento', the unification movement which ended with the creation of the unified Kingdom of Italy in 1861, we see a move from natural law and the law of nations to international law, whose teaching was introduced in (...) Italian universities of the newly created Kingdom. The essays collected here show that natural law was not only the subject of a highly codified academic teaching, but also provided a broader conceptual and philosophical framework for the 'science of man'. Natural law was also a language in which reform programmes of education and politics were formulated and were acted upon. (shrink)