Unpopular in its day, David Hume's sprawling, three-volume 'A Treatise of Human Nature' (1739-40) has withstood the test of time and had enormous impact on subsequent philosophical thought. Hume's comprehensive effort to form an observationally grounded study of human nature employs John Locke's empiric principles to construct a theory of knowledge from which to evaluate metaphysical ideas. A key to modern studies of eighteenth-century Western philosophy, the Treatise considers numerous classic philosophical issues, including causation, existence, freedom and necessity, and morality. (...) Unabridged republication of the edition originally published by Oxford at the Clarendon Press, London, 1888. (shrink)

Traditional geometry concerns itself with planimetric and stereometric considerations, which are at the root of the division between plane and solid geometry. To raise the issue of the relation between these two areas brings with it a host of different problems that pertain to mathematical practice, epistemology, semantics, ontology, methodology, and logic. In addition, issues of psychology and pedagogy are also important here. To our knowledge there is no single contribution that studies in detail even one of the aforementioned areas.

This paper aims at understanding the concept of convention in mechanics as a notion transferred from the field of jurisprudence. This enables us to clarify it as a new epistemic category having a pertinent role in the transformation of mechanics in the nineteenth century. Such understanding permits a separation from linguistic and arbitrary conventions, thus highlighting its epistemic features and not transforming fundamental principles into mere arbitrary agreements. After addressing the main references in the literature discussing the role of convention (...) in mechanics, we analyze its classical use as a concept originating from law. Then we explain its use by Carl G. Jacobi, Ferdinand F. Reech, and J. Henri Poincaré. Here we also show how their uses conform to the features analyzed regarding conventions in jurisprudence. Finally, we try to explain how the use of this concept, among other factors, contributed to the transformation of mechanics. (shrink)

'To think often, and never to retain it so much as one moment, is a very useless sort of thinking' In An Essay concerning Human Understanding, John Locke sets out his theory of knowledge and how we acquire it. Eschewing doctrines of innate principles and ideas, Locke shows how all our ideas, even the most abstract and complex, are grounded in human experience and attained by sensation of external things or reflection upon our own mental activities. A thorough examination of (...) the communication of ideas through language and the conventions of taking words as signs of ideas paves the way for his penetrating critique of the limitations of ideas and the extent of our knowledge of ourselves, the world, God, and morals. Locke's masterpiece laid the foundation of British empiricism and is of enduring interest to anyone exploring the development of philosophical thought. This sensitive abridgement uses P. H. Nidditch's authoritative text, and together with an illuminating introduction and other features, makes Locke's arguments more accessible. (shrink)

Henri Poincaré was not just one of the most inventive, versatile, and productive mathematicians of all time--he was also a leading physicist who almost won a Nobel Prize for physics and a prominent philosopher of science whose fresh and surprising essays are still in print a century later. The first in-depth and comprehensive look at his many accomplishments, Henri Poincaré explores all the fields that Poincaré touched, the debates sparked by his original investigations, and how his discoveries still contribute to (...) society today. Math historian Jeremy Gray shows that Poincaré's influence was wide-ranging and permanent. His novel interpretation of non-Euclidean geometry challenged contemporary ideas about space, stirred heated discussion, and led to flourishing research. His work in topology began the modern study of the subject, recently highlighted by the successful resolution of the famous Poincaré conjecture. And Poincaré's reformulation of celestial mechanics and discovery of chaotic motion started the modern theory of dynamical systems. In physics, his insights on the Lorentz group preceded Einstein's, and he was the first to indicate that space and time might be fundamentally atomic. Poincaré the public intellectual did not shy away from scientific controversy, and he defended mathematics against the attacks of logicians such as Bertrand Russell, opposed the views of Catholic apologists, and served as an expert witness in probability for the notorious Dreyfus case that polarized France. Richly informed by letters and documents, Henri Poincaré demonstrates how one man's work revolutionized math, science, and the greater world. (shrink)