I work on the late Pythagorean mathematicians, Aristotle, and the tradition of Greek commentators on Aristotle. My interests extend from Greek science to metaphysics, with a concentration on Greek science and natural philosophy. I wrote the book ARISTOTLE AND PHILOPONUS ON LIGHT (1991 & reissue Routledge UK 2015) and my book, ARISTOTLE'S EMPIRICISM: EXPERIENCE AND MECHANICS IN THE FOURTH CENTURY BC, appeared in 2014. I am interested in exploring the continuity in kinematics and in mechanics generally from ancient times to 1900. I also investigate issues in cognitive history and cognitive science that connect science, theater, and art in antiquity.
Modern commentators have doubts about the authenticity and cogency of the early propositions of A... more Modern commentators have doubts about the authenticity and cogency of the early propositions of Archimedes' On Equilibrium of Planes Book 1. Ernst Mach famously said that the proof of Prop. 6, the so-called law of the lever, assumes what is to be proven. Comparing the initial text in Heiberg's modern edition (1881, 1913) to the first propositions in Eutocius' commentary on EP 1, J. L. Berggren ([1976]. 'Spurious Theorems in Archimedes' Equilibrium of Planes: Book I', Archive for History of Exact Sciences 16.2 (1976), 87-103.) claimed that the propositions up through Proposition 3 of the standard modern edition are schoolbook additions written by an ancient author inferior to Archimedes. The present paper argues for the logical connectedness of Postulates 1-5 to Props. 1-6, by means of a detailed examination of the course of the argument and a re-examination of Eutocius' remarks. The paper reinterprets the role of the empirical in the early propositions and offers a reading of the contribution of Archimedes' mechanics to the method of EP 1.
Texts and Contexts in Ancient and Medieval Science, 1997
Written in honor of John E. Murdoch's seventieth birthday, the essays collected here focus on... more Written in honor of John E. Murdoch's seventieth birthday, the essays collected here focus on the interpretation of ancient and scientific texts not just as isolated intellectual productions but as responses to particular settings or contexts.
Philoponus on Separating the Three-Dimensional in Optics, 1991
Philoponus' separation of three-dimensionality in optics is considered in the context of his comm... more Philoponus' separation of three-dimensionality in optics is considered in the context of his commentary on Physics 2.2. Notably, Philoponus includes the mode of separation of the essences (e.g., to sarki einai) of physical things given in De Anima 3.4 and reconciles it with the account in Physics 2.2.
Abstract: This paper traces the significance of first principles (archai) in Greek philosophy to ... more Abstract: This paper traces the significance of first principles (archai) in Greek philosophy to cognitive developments in colonial Greek Italy in the late fifth century BC. Conviction concerning principles comes from the power to make something true by action. Pairing and opposition, the forerunners of metonymy, are shown to structure disparate cultural phenomena—the making of figured numbers, the sundial, and the production, with the aid of device, of fear or panic in the spectators of Greek tragedy. From these starting points, the function of the gnômôn in knowledge is explored.
Proceedings of the American Catholic Philosophical Assocition, 2007
Examples are presented of Aristotle's use of non-idealized mathematics. Distinctions Husserl make... more Examples are presented of Aristotle's use of non-idealized mathematics. Distinctions Husserl makes in Crisis help to delineate the features of this empirical mathematics, which include the non-persistence of mathematical aspects of things and the selective application of mathematical traits and proper accidents. In antiquity , non-abstracted mathematics was involved with practical sciences that treat motion. The suggestion is made that these sciences were incorporated by Aristotle into natural philosophy without first being abstracted as pure mathematics-a state of affairs not envisioned by Husserl, for whom science recast natural ontol-ogy by means of the idealization of pure mathematics. The relation of empirical mathematics to life-world ontology is considered.
Modern commentators have doubts about the authenticity and cogency of the early propositions of A... more Modern commentators have doubts about the authenticity and cogency of the early propositions of Archimedes' On Equilibrium of Planes Book 1. Ernst Mach famously said that the proof of Prop. 6, the so-called law of the lever, assumes what is to be proven. Comparing the initial text in Heiberg's modern edition (1881, 1913) to the first propositions in Eutocius' commentary on EP 1, J. L. Berggren ([1976]. 'Spurious Theorems in Archimedes' Equilibrium of Planes: Book I', Archive for History of Exact Sciences 16.2 (1976), 87-103.) claimed that the propositions up through Proposition 3 of the standard modern edition are schoolbook additions written by an ancient author inferior to Archimedes. The present paper argues for the logical connectedness of Postulates 1-5 to Props. 1-6, by means of a detailed examination of the course of the argument and a re-examination of Eutocius' remarks. The paper reinterprets the role of the empirical in the early propositions and offers a reading of the contribution of Archimedes' mechanics to the method of EP 1.
Texts and Contexts in Ancient and Medieval Science, 1997
Written in honor of John E. Murdoch's seventieth birthday, the essays collected here focus on... more Written in honor of John E. Murdoch's seventieth birthday, the essays collected here focus on the interpretation of ancient and scientific texts not just as isolated intellectual productions but as responses to particular settings or contexts.
Philoponus on Separating the Three-Dimensional in Optics, 1991
Philoponus' separation of three-dimensionality in optics is considered in the context of his comm... more Philoponus' separation of three-dimensionality in optics is considered in the context of his commentary on Physics 2.2. Notably, Philoponus includes the mode of separation of the essences (e.g., to sarki einai) of physical things given in De Anima 3.4 and reconciles it with the account in Physics 2.2.
Abstract: This paper traces the significance of first principles (archai) in Greek philosophy to ... more Abstract: This paper traces the significance of first principles (archai) in Greek philosophy to cognitive developments in colonial Greek Italy in the late fifth century BC. Conviction concerning principles comes from the power to make something true by action. Pairing and opposition, the forerunners of metonymy, are shown to structure disparate cultural phenomena—the making of figured numbers, the sundial, and the production, with the aid of device, of fear or panic in the spectators of Greek tragedy. From these starting points, the function of the gnômôn in knowledge is explored.
Proceedings of the American Catholic Philosophical Assocition, 2007
Examples are presented of Aristotle's use of non-idealized mathematics. Distinctions Husserl make... more Examples are presented of Aristotle's use of non-idealized mathematics. Distinctions Husserl makes in Crisis help to delineate the features of this empirical mathematics, which include the non-persistence of mathematical aspects of things and the selective application of mathematical traits and proper accidents. In antiquity , non-abstracted mathematics was involved with practical sciences that treat motion. The suggestion is made that these sciences were incorporated by Aristotle into natural philosophy without first being abstracted as pure mathematics-a state of affairs not envisioned by Husserl, for whom science recast natural ontol-ogy by means of the idealization of pure mathematics. The relation of empirical mathematics to life-world ontology is considered.
This is an unpublished paper on Aristotle's De Anima given a few years ago. It analyzes Prof. Kur... more This is an unpublished paper on Aristotle's De Anima given a few years ago. It analyzes Prof. Kurt Pritzl's understanding of that text as a whole. The talk deals with properties belonging to soul by itself and how Aristotle arrives at a determination of those. It also presents Pritzl's identity version of hylomorphism.
The complete paper is entitled , "Traits Proper to the Soul Itself: A Posteriori Reasoning in Aristotle's De Anima."
This book is the editio princeps, together with a French translation and introduction, of the old... more This book is the editio princeps, together with a French translation and introduction, of the oldest known Arabic manuscript of a hydrostatic treatise by Menelaus (first century CE), who was an important figure in the astronomy and mechanics of the Hellenistic Greek world. Menelaus is mentioned by Ptolemy, Pappus of Alexandria, Proclus, and others. None of Menelaus' works survive in their original Greek, but some do survive in Arabic translations. The editor/translator Comments BMCR provides the opportunity to comment on reviews in order to enhance scholarly communication. Comments are moderated. We ask that comments be substantive in content and civil in tone and those that do not adhere to these guidelines will not be published. Expressions of thanks or praise should be sent directly to the reviewer, using the email address in the review.
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Papers by Jean De Groot
action. Pairing and opposition, the forerunners of metonymy, are shown to structure disparate cultural phenomena—the making of figured numbers, the sundial, and the production, with the aid of device, of fear or panic in the spectators of Greek tragedy. From these starting points, the function of the gnômôn in knowledge is explored.
action. Pairing and opposition, the forerunners of metonymy, are shown to structure disparate cultural phenomena—the making of figured numbers, the sundial, and the production, with the aid of device, of fear or panic in the spectators of Greek tragedy. From these starting points, the function of the gnômôn in knowledge is explored.
The complete paper is entitled , "Traits Proper to the Soul Itself: A Posteriori Reasoning in Aristotle's De Anima."