Jean De Groot

It is shown that Aristotle’s references to automata in his biological treatises are meant to invoke the principle behind the ancient conception of the lever, i.e. that points on the rotating radius of a circle all move at different speeds proportional to their distances from the center. This principle is mathematical and explains a phenomenon taken as whole. Automata do not signify for him primarily a succession of material movers in contact, the modern model for mechanism. For animal locomotion and embryological development, Aristotle models his dunamis concept on the idea of mechanical potential that the lever principle displays.

Examples are presented of Aristotle’s use of non-idealized mathematics. Distinctions Husserl makes in Crisis help to delineate the features of this empiricalmathematics, 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 ontology by means of the idealization of pure mathematics. The relation of empirical mathematics to life-world ontology is considered

In the introduction to An Approach to Aristotle’s Physics, David Bolotin presents an exceptionally clear account of the difficulties of making a claim for Aristotle’s natural philosophy as a contemporary teacher about nature. Modern science has repudiated the chief elements of the Aristotelian cosmos—the geocentric universe, the account of projectile motion—and so the contemporary interpreter treats Aristotle as a brilliant expositor of the world “as it appears.” Alternatively, the interpreter may say there is no final truth in the matter of nature, so Aristotle’s cosmos within its own perspective was as compelling as our modern science is within its own perspective. Neither of these interpretations suits Aristotle, Bolotin says, since the philosopher’s conception of science included its being a true account of nature itself.

QUINE'S DOCTRINE of the indeterminacy of translation is made possible by the principle of substitution characteristic of extensional logic. The same characteristic makes it impossible, in philosophy of science, to choose among theoretical models no one of which is obviously best suited to explain the facts. Hilary Putnam achieved a sort of closure to the problem of reference in philosophy of science, when he pointed out the implications of the Skolem-Löwenheim theorem. He said that besides the facts a theory is designed to explain, there are any number of unintended interpretations of the same theory that assign the correct truth values to all sentences of the theory. There can be no sound basis for deciding upon the sole interpretation for a theory. Following Putnam, some philosophers have abandoned the problem of reference in the context of axiomatic systems. Ian Hacking, for instance, prefers a notion of reference "that is not tied by any specific, binding theory about what is referred to." He has turned to the study of approximations and practical models, spurred on by the difficulty of reconciling axiomatic systems to scientific practice.

This paper examines geometrical arguments from Galileo's Mechanics and Two New Sciences to discern the influence of the Aristotelian Mechanical Problems on Galileo's dynamics. A common scientific procedure is found in the Aristotelian author's treatment of the balance and lever and in Galileo's rules concerning motion along inclined planes. This scientific procedure is understood as a development of Eudoxan proportional reasoning, as it was used in Eudoxan astronomy rather than simply as it appears in Euclid's Elements. Topics treated include the significance of the circle in Galileo's demonstrations, the substitution of rectilinear elements for heterogeneous factors like weight and curvilinear distance, and the way in which elements of a motion are used to measure other elements of the same motion. The indirectness of Galileo's proofs, his conception of speed as relative and comparative, and the meaning of his concept of moment all come into clearer focus. Conclusions are drawn about Galilean idealization, and also about the contrast of literal versus figural modes of explanation in Galileo's science

This paper examines geometrical arguments from Galileo's Mechanics and Two New Sciences to discern the influence of the Aristotelian Mechanical Problems on Galileo's dynamics. A common scientific procedure is found in the Aristotelian author's treatment of the balance and lever and in Galileo's rules concerning motion along inclined planes. This scientific procedure is understood as a development of Eudoxan proportional reasoning, as it was used in Eudoxan astronomy rather than simply as it appears in Euclid's Elements. Topics treated include the significance of the circle in Galileo's demonstrations, the substitution of rectilinear elements for heterogeneous factors like weight and curvilinear distance, and the way in which elements of a motion are used to measure other elements of the same motion. The indirectness of Galileo's proofs, his conception of speed as relative and comparative, and the meaning of his concept of moment all come into clearer focus. Conclusions are drawn about Galilean idealization, and also about the contrast of literal versus figural modes of explanation in Galileo's science.

This paper traces the significance of first principles 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.

"This book collects essays by leading scholars, both American and European, on the American understanding of nature from Emerson to Dewey and beyond. The volume features essays on Emerson and Thoreau, Royce, Peirce, Wright, James, Holmes, Tocqueville, and Dewey. Topics include the role of nature in American idealism, the influence of Darwin, naturalism in psychology, and human nature in political thought. The final essay presents a comprehensive taxonomy of views of nature in relation to expressions of nature in American art." "With its focus on philosophy of nature, this book fills a gap in the ongoing reassessment of nineteenth-century American philosophy, and it opens the way to further study of the role played by reflection on nature in the emergence of the American mind."--Jacket.

QUINE'S DOCTRINE of the indeterminacy of translation is made possible by the principle of substitution characteristic of extensional logic. The same characteristic makes it impossible, in philosophy of science, to choose among theoretical models no one of which is obviously best suited to explain the facts. Hilary Putnam achieved a sort of closure to the problem of reference in philosophy of science, when he pointed out the implications of the Skolem-Löwenheim theorem. He said that besides the facts a theory is designed to explain, there are any number of unintended interpretations of the same theory that assign the correct truth values to all sentences of the theory. There can be no sound basis for deciding upon the sole interpretation for a theory. Following Putnam, some philosophers have abandoned the problem of reference in the context of axiomatic systems. Ian Hacking, for instance, prefers a notion of reference "that is not tied by any specific, binding theory about what is referred to." He has turned to the study of approximations and practical models, spurred on by the difficulty of reconciling axiomatic systems to scientific practice.

Examples are presented of Aristotle’s use of non-idealized mathematics. Distinctions Husserl makes in Crisis help to delineate the features of this empiricalmathematics, 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 ontology by means of the idealization of pure mathematics. The relation of empirical mathematics to life-world ontology is considered.