Theophrastus on Lyngurium: Medieval and Early Modern Lore from the Classical Lapidary Tradition

The ancient philosopher Theophrastus (c. 371-285 BC) described a gemstone called lyngurium, purported to be solidified lynx urine, in his work De lapidibus ('On Stones'). Knowledge of the stone passed from him to other classical authors and into the medieval lapidary tradition, but there it was almost always linked to the 'learned master Theophrastus'. Although no physical example of the stone appears to have been seen or touched in ancient, medieval, or early modern times, its physical and medicinal properties were continually reiterated and elaborated as if it did 'exist'. By the seventeenth century, it began to disappear from lapidaries, but with no attempt to explain previous authors' errors since it had never 'existed' anyway. In tracing the career of lyngurium, this study sheds some light on the transmission of knowledge from the classical world to the Renaissance and the changing criteria by which such knowledge was judged.     

The Role of Geometrical Construction in Theodosius’s <Emphasis Type="Italic">Spherics</Emphasis>

This paper is a contribution to our understanding of the constructive nature of Greek geometry. By studying the role of constructive processes in Theodoius’s Spherics, we uncover a difference in the function of constructions and problems in the deductive framework of Greek mathematics. In particular, we show that geometric problems originated in the practical issues involved in actually making diagrams, whereas constructions are abstractions of these processes that are used to introduce objects not given at the outset, so that their properties can be used in the argument. We conclude by discussing, more generally, ancient Greek interests in the practical methods of producing diagrams.     

Boyle’s teleological mechanism and the myth of immanent teleology

According to recent commentators, medieval natural philosophers endorsed immanent teleology, the view that natural agents possess immanent active powers to achieve certain ends. Moreover, some scholars have argued that Robert Boyle, despite his intentions, failed to eliminate immanent teleology from his natural philosophy. I argue in this paper that it is not at all clear that immanent teleology was widely endorsed in the medieval period. Moreover, I argue that a proper understanding of immanent teleology, and why it was rejected by mainstream medieval natural philosophers, reveals that Boyle did not fail to eliminate immanent teleology from his natural philosophy. I conclude that any attempt to describe the break between medieval and early modern natural philosophy in terms of a break with immanent teleology is likely not on target.     

Newtonianism and information control in Rome at the wake of the eighteenth century

ABSTRACT

This paper offers an opportunity to ponder the way the Catholic Church and its methods of information control reshaped, and paradoxically even enabled, the dissemination and practice of science in early modern Italy. Focusing on the activities of Newtonian scholars operating in Rome in the First half of the eighteenth century – especially the Celestine monk Celestino Galiani (1681–1753) and prelate Francesco Bianchini (1662–1729) – I will argue that major contributions to the spread of Newtonianism in Italy came from individuals operating within the Church, acting more-or-less independently from the Church’s oversight. These scholars realized they were witnessing an inexorable transition and that the medieval scholastic cosmology and physics could not survive. In order to rescue the Church – and to avoid further embarrassment, especially after the Galileo Affair – renewal was needed. Counterintuitively, the dissemination of Italian Newtonianism was largely a Catholic effort.     

Master Georg Dörffel and the rise of cometary astronomy

This paper examines the purport of epact tables encountered on scientific instruments, and explains their use. The epact is a valuable chronological aid for calculating the age of the moon. In handbooks of chronology, usually two types of epacts are distinguished: the epact used in medieval times, and the so-called Lilian epact used after 1582 in the Gregorian perpetual calendar. By examining the rules for calculating the age of the moon, it turns out that the Julian and Gregorian epacts encountered on instruments must be distinguished from the medieval and Lilian epacts. It is shown that the Julian epact was already in use in 1478, and that, by adjusting for the shift of ten days in the date of the vernal equinox, the Gregorian epact was derived from it in 1582. The common association of the latter with the Lilian epact employed in the Gregorian perpetual calendar is incorrect. It is further shown that in contrast to the medieval and Lilian epacts, which served purely ecclesiastical purposes, the Julian and Gregorian epacts were mainly used to calculate the true age and zodiacal position of the moon. This knowledge was applied to secular interests such as ‘lunar astrology’, tidal computations, and the conversion of lunar into solar time.     

Jewish theologies of space in the scientific revolution: Henry More,Joseph Raphson,Isaac Newton and their predecessors

Theological speculations on God's relation to place and space were introduced into the Jewish tradition by the early rabbis, initially in response to the previous appearance of words like māqôm (place) in Biblical literature. In the Middle Ages, Jewish philosophers modified these rabbinical ideas in the context of Aristotelian, Neoplatonic, and anti-Aristotelian currents within Jewish thought. One development in medieval Jewish thought of special interest for the development of ideas of space was the rise of Cabala, which Christian thinkers of the Renaissance and early modern periods saw as a sacred and primeval deposit of wisdom akin to prisca theologia. Both Henry More and, under More's influence, Joseph Raphson made use of Cabalist ideas in developing their own theologies of space. Isaac Newton was aware of these Jewish ideas but for the most part repudiated them, while making some use of māqôm as an expression of God's omnipresence.     

A Framework for Defining the Generality of Diophantos' Methods in ``Arithmetica'

Diophantos' solutions to the problems of Arithmetica have been the object of extensive reading and interpretation in modern times, especially from the point of view of identifying ``hidden steps' or ``general methods'. In this paper, after examining the relevance of various interpretations given for the famous problem II 8 in the context of modern algebra or geometry, we focus on a close reading of the ancient text of some problems of Arithmetica in order to investigate Diophantos' solving practices. This inquiry reveals certain pointers, which enable us to create a framework for defining the generality of Diophantos' methods. An erratum to this article can be found at     

The scholastic pendulum

The history of the physics of pendular motion rightly begins with Galileo's discovery of the isochronous character of that motion. There is, however, a ‘pre-history’ of the pendulum, centering on its initial recognition as a significant special case requiring explanation. This occurred in the writings of Jean Buridan and Nicole Oresme in the middle of the fourteenth century. Earlier works that might have been construed as discussing pendular motion are considered, as are the explanations for the scholastic ‘discovery’ of pendular motion put forth by Thomas Kuhn and Piero Ariotti. In contrast to these writers, this paper seeks to account for the pendulum's emergence with reference to an imaginary experiment concerning a body moving past the earth's center, medieval theories of impetus, and the proximate physical model of pendular motion, the late medieval heavy suspended church bell.     

Polynomials and equations in arabic algebra

It is shown in this article that the two sides of an equation in the medieval Arabic algebra are aggregations of the algebraic “numbers” (powers) with no operations present. Unlike an expression such as our 3x + 4, the Arabic polynomial “three things and four dirhams” is merely a collection of seven objects of two different types. Ideally, the two sides of an equation were polynomials so the Arabic algebraists preferred to work out all operations of the enunciation to a problem before stating an equation. Some difficult problems which involve square roots and divisions cannot be handled nicely by this basic method, so we do find square roots of polynomials and expressions of the form “A divided by B” in some equations. But rather than initiate a reconsideration of the notion of equation, these developments were used only for particularly complex problems. Also, the algebraic notation practiced in the Maghreb in the later middle ages was developed with the “aggregations” interpretation in mind, so it had no noticeable impact on the concept of polynomial. Arabic algebraists continued to solve problems by working operations before setting up an equation to the end of the medieval period. I thank Mahdi Abdeljaouad, who provided comments on an earlier version of this paper, and Haitham Alkhateeb, for his help with some of the translations. Notes on references: When page numbers are separated by a “ / ”, the first number is to the Arabic text, and the second to the translation. Also, a semicolon separates page number from line number. Example: [Al-Khwārizmī, 1831, 31;6/43] refers to page 31 line 6 of the Arabic text, and page 43 of the translation.     

The Foundations of Projective Geometry in Italy from De Paolis to Pieri

 In this paper we examine the contributions of the Italian geometrical school to the Foundations of Projective Geometry. Starting from De Paolis' work we discuss some papers by Segre, Peano, Veronese, Fano and Pieri. In particular we try to show how a totally abstract and general point of view was clearly adopted by the Italian scholars many years before the publication of Hilbert's Grundlagen. We are particularly interested in the interrelations between the Italian and the German schools (mainly the influence of Staudt's and Klein's works). We try also to understand the reason of the steady decline of the Italian school during the twentieth century. (Received Febuary 25, 2000)     

Pictures and pedagogy: The role of diagrams in Feynman's early lectures

This paper aims to give a substantive account of how Feynman used diagrams in the first lectures in which he explained his new approach to quantum electrodynamics. By critically examining unpublished lecture notes, Feynman's use and interpretation of both “Feynman diagrams” and other visual representations will be illuminated. This paper will discuss how the morphology of Feynman's early diagrams were determined by both highly contextual issues, which molded his images to local needs and particular physical characterizations, and an overarching common diagrammatic style, which facilitated Feynman's movement between different diagrams despite their divergent forms and significance.     

The politics of environments before the environment: Biopolitics in the longue durée

Our understanding of body–world relations is caught in a curious contradiction. On one side, it is well established that many concepts that describe interaction with the outer world – ‘plasticity’ or ‘metabolism’- or external influences on the body - ‘environment’ or ‘milieu’ – appeared with rise of modern science. On the other side, although premodern science lacked a unifying term for it, an anxious attentiveness to the power of ‘environmental factors’ in shaping physical and moral traits held sway in nearly all medical systems before and alongside modern Europe. In this article, I build on a new historiography on the policing of bodies and environments in medieval times and at the urban scale to problematize Foucault's claim about biopolitics as a modern phenomenon born in the European eighteenth-century. I look in particular at the collective usage of ancient medicine and manipulation of the milieu based on humoralist notions of corporeal permeability (Hippocrates, Galen, Ibn Sīnā) in the Islamicate and Latin Christendom between the 12th and the 15th century. This longer history has implications also for a richer genealogy of contemporary tropes of plasticity, permeability and environmental determinism beyond usual genealogies that take as a starting point the making of the modern body and EuroAmerican biomedicine.     

A word of the Empirics: the ancient concept of observation and its recovery in early modern medicine

The genealogy of observation as a philosophical term goes back to the ancient Greek astronomical and medical traditions, and the revival of the concept in the Renaissance also happened in the astronomical and medical context. This essay focuses primarily on the medical genealogy of the concept of observation. In ancient Greek culture, an elaboration of the concept of observation (tērēsis) first emerged in the Hellenistic age with the medical sect of the Empirics, to be further developed by the ancient Sceptics. Basically unknown in the Middle Ages, the Empirics' conceptualisation of tērēsis trickled back into Western medicine in the fourteenth century, but its meaning seems to have been fully recovered by European scholars only in the 1560s, concomitantly with the first Latin translation of the works of Sextus Empiricus. As a category originally associated with medical Scepticism, observatio was a new entry in early modern philosophy. Although the term gained wide currency in general scholarly usage in the seventeenth century, its assimilation into standard philosophical language was very slow. In fact, observatio does not even appear as an entry in the philosophical dictionaries until the eighteenth century--with one significant exception, the medical lexica, which featured the lemma, reporting its ancient Empiric definition, as early as 1564.     

‘The long-lost truth’: Sir Isaac Newton and the Newtonian pursuit of ancient knowledge

In the 1720s the antiquary and Newtonian scholar Dr. William Stukeley (1687-1765) described his friend Isaac Newton as ‘the Great Restorer of True Philosophy’. Newton himself in his posthumously published Observations upon the prophecies of Daniel, and the Apocalypse of St. John (1733) predicted that the imminent fulfilment of Scripture prophecy would see ‘a recovery and re-establishment of the long-lost truth’. In this paper I examine the background to Newton’s interest in ancient philosophy and theology, and how it related to modern natural philosophical discovery. I look at the way in which the idea of a ‘long-lost truth’ interested others within Newton’s immediate circle, and in particular how it was carried forward by Stukeley’s researches into ancient British antiquities. I show how an interest in and respect for ancient philosophical knowledge remained strong within the first half of the eighteenth century.     

The love of truth

It is frequently said that belief aims at truth, in an explicitly normative sense—that is, that one ought to believe the proposition that p if, and only if, p is true. This truth norm is frequently invoked to explain why we should seek evidential justification in our beliefs, or why we should try to be rational in our belief formation—it is because we ought to believe the truth that we ought to follow the evidence in belief revision. In this paper, I argue that this view is untenable. The truth norm clashes with plausible evidential norms in a wide range of cases, such as when we have excellent but misleading evidence for a falsehood or no evidence for a truth. I will consider various ways to resolve this conflict and argue that none of them work. However, I will ultimately attempt to vindicate the love of truth, by arguing that knowledge is the proper epistemic goal. The upshot is that we should not aim merely to believe the truth; we should aim to know it.