The model of a closed linear measure space, which can be used to model Aristotle’s treatment of motion (kinesis), can be analogically extended to the qualitative ‘spaces’ implied by his theory of contraries in Physics I and in Metaphysics Iota, and to the dimensionless ‘space’ of the unity of matter and form discussed in book Eta of the Metaphysics. By examining Aristotle’s remarks on contraries, the subject of change, continuity, and the unity of matter and form, Aristotle’s thoughts on motion, (...) on contraries, and on the unity of substance can be brought together under a single interpretive framework, which can provide an approach to interpreting his ontology. (shrink)

At least since Socrates, philosophy has been understood as the desire for acquiring a special kind of knowledge, namely wisdom, a kind of knowledge that human beings ordinarily do not possess. According to ancient thinkers this desire may result from a variety of causes: wonder or astonishment, the bothersome or even painful realization that one lacks wisdom, or encountering certain hard perplexities or aporiai. As a result of this basic understanding of philosophy, Greek thinkers tended to regard philosophy as an (...) activity of inquiry (zētēsis) rather than as a specific discipline. Discussions concerning the right manner of engaging in philosophical inquiry – what methodoi or routes of inquiry were best suited to lead one to wisdom – became an integral part of ancient philosophy, as did the question how such manners or modes of inquiry are related to, and differ from, other types of inquiry, for instance medical or mathematical. In this special issue of History of Philosophy & Logical Analysis, we wish to concentrate in particular on ancient modes of inquiry. (shrink)

How does Newton approach the challenge of mechanizing gravity and, more broadly, natural philosophy? By adopting the simple machine tradition’s mathematical approach to a system’s co-varying parameters of change, he retains natural philosophy’s traditional goal while specifying it in a novel way as the search for impressed forces. He accordingly understands the physical world as a divinely created machine possessing intrinsically mathematical features, and mathematical methods as capable of identifying its real features. The gravitational force’s physical cause remains an outstanding (...) problem, however, as evidenced by Newton’s onetime reference to active principles as the “genuine principles of the mechanical philosophy”. (shrink)

I present a systematic interpretation of the foundational purpose of constructions in ancient Greek geometry. I argue that Greek geometers were committed to an operationalist foundational program, according to which all of mathematics—including its entire ontology and epistemology—is based entirely on concrete physical constructions. On this reading, key foundational aspects of Greek geometry are analogous to core tenets of 20th-century operationalist/positivist/constructivist/intuitionist philosophy of science and mathematics. Operationalism provides coherent answers to a range of traditional philosophical problems regarding classical mathematics, such (...) as the epistemic warrant and generality of diagrammatic reasoning, superposition, and the relation between constructivism and proof by contradiction. Alleged logical flaws in Euclid can be interpreted as sound operationalist reasoning. Operationalism also provides a compelling philosophical motivation for the otherwise inexplicable Greek obsession with cube duplication, angle trisection, and circle quadrature. Operationalism makes coherent sense of numerous specific choices made in this tradition, and suggests new interpretations of several solutions to these problems. In particular, I argue that: Archytas’s cube duplication was originally a single-motion machine; Diocles’s cissoid was originally traced by a linkage device; Greek conic section theory was thoroughly constructive, based on the conic compass; in a few cases, string-based constructions of conic sections were used instead; pointwise constructions of curves were rejected in foundational contexts by Greek mathematicians, with good reason. Operationalism enables us to view the classical geometrical tradition as a more unified and philosophically aware enterprise than has hitherto been recognised. (shrink)

Ptolemy wrote the Planetary Hypotheses for both astronomers and instrument-makers. Most studies of this text concentrate on its meaning for the former, but there remain many questions surrounding its meaning for the latter.1 This article investigates the purpose of Ptolemy’s Planetary Hypotheses in light of what he says about instrument-making. It takes up the following questions: what kind of instrument does Ptolemy describe? And, could such an instrument have been constructed? I argue that he did not have one specific design (...) in mind, but instead he offered craftsmen options for the content, design, and operational methods. In addition to exhibiting his astronomical models and estimating planetary positions, the... (shrink)

What causes winds was regarded as one of the most difficult questions of early modern natural philosophy. Vitruvius, the ancient Roman architectural author, put forth an alternative to Aristotle’s theory by likening the generation of wind to the actions of the aeolipile, which he believed made artificial winds. As Vitruvius’s work proliferated during the sixteenth and seventeenth centuries, numerous natural philosophers, including Descartes, used the aeolipile as a model for nature. Yet, interpretations of Vitruvius’s text and of the relation of (...) the aeolipile to natural winds varied according to definitions and conceptions of air, wind, rarefaction, condensation, and vapor. (shrink)

Biton’s Construction of Machines of War and Catapults describes six machines by five engineers or inventors; the fourth machine is a rolling elevatable scaling ladder, named sambukē, designed by one Damis of Kolophōn. The first sambukē was invented by Herakleides of Taras, in 214 BCE, for the Roman siege of Syracuse. Biton is often dismissed as incomprehensible or preposterous. I here argue that the account of Damis’ device is largely coherent and shows that Biton understood that Damis had built a (...) machine that embodied Archimedean principles. The machine embodies three such principles: (1) the proportionate balancing of the torques on a lever (from Plane Equilibria, an early work); (2) the concept of specific gravity or density (from Floating Bodies, a late work); and (3) the κοχλίας, i.e., a worm drive (invented ca 240 BCE), with the toothed wheel functioning as the horizontal axis of rotation of the elevated ladder. Moreover, the stone-thrower of Isidoros of Abydos (the second machine in Biton) also embodies the κοχλίας. (shrink)

A discussion of Lloyd's Tarner Lectures at Trinity College. The importance of Lloyd's previous scholarship is characterized and these sweeping, erudite lectures are placed in the context of that scholarship. In the broadest terms, the lectures are a call to culturally and historically comparative study of human reasoning. At their heart is a comparative history of scientific theorizing from the ancients through to modern science. Lloyd rejects the positivist picture, and the view of modern and ancient science as discontinuous; he (...) urges scholars to undertake comparative work on the ancient sciences in different traditions. This critical notice evaluates Lloyd's view and raises several questions for further reflection. (shrink)

From the first century BCE onwards, philosophers started to write commentaries on those Aristotle’s treatises that were meant for the internal use of his school. Plato’s works had been commented on already earlier, the first reported commentary originates in the 300s BCE. Commentaries are treatises that follow an object text in a more or less linear fashion. The format was not unknown before the first century BCE but new in extensive philosophical use. This review essay focuses on authors who commented (...) on Aristotle’s works. The commentaries emerged when Platonists and Aristotelians observed the need to teach the philosophy of these ancient masters to their students and to systematise their philosophy to respond to rival schools. In the late ancient schools, Plato and Aristotle were considered great thinkers, whose views needed to be studied carefully when considering any matter at hand. Many also argued that, despite the initial appearance to the contrary, there is no deep disagreement between Plato and Aristotle but, rather, a division of labour; Aristotle is dominant in natural philosophy and Plato in theology. However, this harmony thesis was not universally accepted. Despite their respect for Plato and Aristotle, the commentators were not mere followers of these authors. They developed, criticised and transformed the doctrines in significant ways, not only by suggesting different answers to the same questions but also by transforming the questions themselves. (shrink)

Aristotle has traditionally been cast as the arch-enemy of all things mechanistic. Given the dichotomy long thought to exist between mechanistic and teleological schools of thought, there is a satisfying irony in discovering veins of apparently ‘mechanistic’ thought within the work of the definitive teleologist. Several waves of scholarship in the past century have argued, from different angles, for mechanistic interpretations of Aristotle’s natural philosophy. The present generation is no exception: in the last decade, Jean De Groot, Monte Johnson, and (...) Tiberiu Popa have variously argued that a mechanistic vein can be found in Aristotle’s work, despite his undeniable teleological credentials. This paper explores the assumptions—some of them open to question—that accompany such advocacy. It will urge some terminological refinements, and turn a skeptical lens on some aspects of these projects. Nonetheless, it will stress that they open promising lines of inquiry, avoiding some of the limitations of earlier ventures into this territory. (shrink)

Scholarship on Plato's Timaeus has paid relatively little attention to Tim. 77a–81, a seemingly disjointed passage on topics including plants, respiration, blood circulation, and musical sounds. Despite this comparative neglect, commentators both ancient and modern have levelled a number of serious charges against Timaeus' remarks in the passage, questioning the coherence and explanatory power of what they take to be a theory of respiration. In this paper, I argue that the project of 77a–81e is not to sketch theories of respiration, (...) circulation, and digestion, but to explain how the human body is maintained in light of and despite constant environmental depletion. Further, I argue that in order to understand this account of “the replenishing system,” we need to understand Timaeus' striking analogy of the fish trap or nassa. Commentators have generally focused directly on the workings of the bodily construction that Timaeus likens to a fish trap, but without considering how we should understand the analogy qua analogy. I develop a functional reading of the analogy that yields a coherent account of the replenishing system on which previous criticisms of Timaeus' remarks on respiration do not arise. Aside from lending greater unity to the passage, both internally and within its immediate context in the dialogue, this account of the replenishing system contributes to our understanding of Timaeus' reason-and-necessity explanatory framework as applied to the human body and has noteworthy implications for specific explanatory principles, in particular like-to-like motion and circular thrust. (shrink)

RESUMO O objetivo deste trabalho é indicar como a exploração estilística de Margaret Cavendish responde às particularidades do conceito de natureza dela, por exemplo, a tese de que a natureza é uma matéria viva, infinita, mutável e heterogênea. Primeiramente, mostrarei o modo pelo qual a autora está presente em seus escritos, como ela escreve de uma perspectiva de primeira pessoa sobre sua própria experiência e de quem ela é. Resumirei brevemente sua biografia e o contexto no qual ela praticou filosofia. (...) Dado que suas escolhas de estilo são bastante numerosas, apresentarei somente algumas poucas, entre as peculiaridades estilísticas dela. Em segundo lugar, desenvolverei uma visão geral do seu conceito de natureza, ao contrário do proposto pelas teorias mecanicistas de seu tempo. Esclarecerei que tal conceito é expresso adequadamente pela diversidade estilística à qual Cavendish se volta em suas investigações. ABSTRACT This paper aims at indicating how Margaret Cavendish's stylistic exploration answer to the particularities of her concept of nature, i.e. the thesis that nature is live, infinite, changing and heterogeneous matter. I will first show the way in which the author is present in her writings, as she writes from a first person perspective about her own experience and from who she is. I will briefly summarise her biography and the context in which she practiced philosophy. Given that her stylistic choices are quite numerous, I will only present a few of her stylistic particularities. Secondly, I will develop the general outline of her concept of nature, as opposed to the one proposed by the mechanistic theories of her time. I will make it clear that said concept is adequately expressed in the stylistic diversity to which Cavendish turns in her investigations. (shrink)

We argue that Isaac Newton really is best understood as being in the tradition of the Mechanical Philosophy and, further, that Newton saw himself as being in this tradition. But the tradition as Newton understands it is not that of Robert Boyle and many others, for whom the Mechanical Philosophy was defined by contact action and a corpuscularean theory of matter. Instead, as we argue in this paper, Newton interpreted and extended the Mechanical Philosophy's slogan “matter and motion” in reference (...) to the long and distinguished tradition of mixed mathematics and the study of simple machines. (shrink)