v. 1. Language.--v. 2. Mythical thought.--v. 3. The phenomenology of knowledge.--v. 4. The metaphysics of symbolic forms.

In sixteenth century Paris a circle of mathematicians produced texts of the most advanced kind of algebra. This "French algebraic tradition" will be the context for Viete's symbolic algebra. Comparing French algebraic texts with Italian and German, and examining the publishing context , I establish a periodization in two phases. ;Jacques Peletier stands for the introduction of the abacus tradition and algebra at the court. Peletier's algebraic program is connected to his theory of rhetoric. He establishes a genre of texts (...) devoted to algebra in vernacular, promoting French as a scientific language. Rhetorical criteria order L'Algebre, emphasizing structure and theory . He innovates on Cardano's and Stifel's treatments of equations in several unknowns. ;Phase two changes style and content; Guillaume Gosselin is representative. Manuals shift focus from problems and questions to equations and classification. Solution of equations becomes the purpose of algebra. Problems are no longer addressed as such, but conceived in their most general form as corresponding equations. Algebrists connect with a milieu of jurists important in politics and scholarship. This erudite milieu favored the recovery of Diophantus' Arithmetic, which provides a set of theoretical problems on numbers. Diophantus solved problems by transforming them into particular cases; Gosselin reaches a general solution by transforming them into equations. Gosselin's notation makes the difference. The algebrists create an illustrious genealogy for algebra, deriving it from Greece rather than abacus schools. ;Three features of this tradition can be traced back to Italian humanism: Cardano's and Tartaglia's algebra, imitatio , and the construction of a history for the discipline. The French algebrists radically transformed all three. Their translatio authorized them to abandon links to the medieval tradition and to build a new discipline that they could see as national. Preparing the adoption of this discipline by the legal elite was the rhetorical interpretation of logic developed in Paris at the time. This provided a theoretical frame in which generalized algebraic problems were seen as Cicero's quaestiones infinitae, i.e. scientific questions. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Ernst Cassirer occupies a unique space in Twentieth-century philosophy. A great liberal humanist, his multi-faceted work spans the history of philosophy, the philosophy of science, intellectual history, aesthetics, epistemology, the study of language and myth, and more. The Philosophy of Symbolic Forms is Cassirer's most important work. It was first published in German in 1923, the third and final volume appearing in 1929. In it Cassirer presents a radical new philosophical worldview - at once rich, creative and controversial - of (...) human beings as fundamentally "symbolic animals," placing signs and systems of expression between themselves and the world. This major new translation, the first for over fifty years, brings Cassirer's magnum opus to a new generation of students and scholars. Volume 1: Language is a fascinating examination of arguably the most fundamental of these systems of expression: human language. Cassirer traces the problem of language and expression far back in the history of philosophy, considering the work of the early Greek rationalists. He then examines the later empiricist tradition, up to the romantic tradition in the nineteenth century tackling fundamental questions about representation, signification and expression as well as language and conceptual thought in mathematics and science. Correcting important errors in previous English editions, this translation reflects the contributions of significant advances in Cassirer scholarship over the last twenty to thirty years. Each volume includes a new introduction and translator's notes by S. G. Lofts, a foreword by Peter Gordon, a glossary of key terms, and a thorough index. (shrink)

In Paradigms and Barriers Howard Margolis offers an innovative interpretation of Thomas S. Kuhn's landmark idea of "paradigm shifts," applying insights from cognitive psychology to the history and philosophy of science. Building upon the arguments in his acclaimed Patterns, Thinking, and Cognition, Margolis suggests that the breaking down of particular habits of mind—of critical "barriers"—is key to understanding the processes through which one model or concept is supplanted by another. Margolis focuses on those revolutionary paradigm shifts— such as the switch (...) from a Ptolemaic to a Copernican worldview—where challenges to entrenched habits of mind are marked by incomprehension or indifference to a new paradigm. Margolis argues that the critical problem for a revolutionary shift in thinking lies in the robustness of the habits of mind that reject the new ideas, relative to the habits of mind that accept the new ideas. Margolis applies his theory to famous cases in the history of science, offering detailed explanations for the transition from Ptolemaic to cosmological astronomy, the emergence of probability, the overthrow of phlogiston, and the emergence of the central role of experiment in the seventeenth century. He in turn uses these historical examples to address larger issues, especially the nature of belief formation and contemporary debates about the nature of science and the evolution of scientific ideas. Howard Margolis is a professor in the Harris Graduate School of Public Policy Studies and in the College at the University of Chicago. He is the author of Selfishness, Altruism, and Rationality and Patterns, Thinking, and Cognition, both published by the University of Chicago Press. (shrink)

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Augustus De Morgan was a British mathematician and logician. He formulated De Morgan's laws and introduced the term mathematical induction, making its idea rigorousFrom the introduction:"If I had before me a fly and an elephant, having never seen more than one such magnitude of either kind; and if the fly were to endeavor to persuade me that he was larger than the elephant, I might by possibility be placed in a difficulty. The apparently little creature might use such arguments about (...) the effect of distance, and might appeal to such laws of sight and hearing as I, if unlearned in those things, might be unable wholly to reject. But if there were a thousand flies, all buzzing, to appearance, about the great creature; and, to a fly, declaring, each one for himself, that he was bigger than the quadruped; and all giving different and frequently contradictory reasons; and each one despising and opposing the reasons of the others-I should feel quite at my ease. I should certainly say, My little friends, the case of each one of you is destroyed by the rest. I intend to show flies in the swarm, with a few larger animals, for reasons to be given.In every age of the world there has been an established system, which has been opposed from time to time by isolated and dissentient reformers. The established system has sometimes fallen, slowly and gradually: it has either been upset by the rising influence of some one man, or it has been sapped by gradual change of opinion in the many.I have insisted on the isolated character of the dissentients, as an element of the a priori probabilities of the case. Show me a schism, especially a growing schism, and it is another thing. The homeopathists, for instance, shall be, if any one so think, as wrong as St. John Long; but an organized opposition, supported by the efforts of many acting in concert, appealing to common arguments and experience, with perpetual succession and a common seal, as the Queen says in the charter, is, be the merit of the schism what it may, a thing wholly different from the case of the isolated opponent in the mode of opposition to it which reason points out.During the last two centuries and a half, physical knowledge has been gradually made to rest upon a basis which it had not before. It has become mathematical. The question now is, not whether this or that hypothesis is better or worse to the pure thought, but whether it accords with observed phenomena in those consequences which can be shown necessarily to follow from it, if it be true. Even in those sciences which are not yet under the dominion of mathematics, and perhaps never will be, a working copy of the mathematical process has been made. This is not known to the followers of those sciences who are not themselves mathematicians and who very often exalt their horns against the mathematics in consequence. They might as well be squaring the circle, for any sense they show in this particular.". (shrink)

This is the first volume of the first ever comprehensive edition of the works of Immanuel Kant in English translation. The eleven essays in this volume constitute Kant's theoretical, pre-critical philosophical writings from 1755 to 1770. Several of these pieces have never been translated into English before; others have long been unavailable in English. We can trace in these works the development of Kant's thought to the eventual emergence in 1770 of the two chief tenets of his mature philosophy: the (...) subjectivity of space and time, and the phenomena-noumena distinction. The volume has been furnished with substantial editorial apparatus, including a general introduction to the main themes of Kant's early thought, introduction to the individual works and résumés of their contents, linguistic and factual notes, bibliographies, a glossary of key terms, and biographical-bibliographical sketches of persons mentioned by Kant. (shrink)

This is the first volume of the first ever comprehensive edition of the works of Immanuel Kant in English translation. The eleven essays in this volume constitute Kant's theoretical, pre-critical philosophical writings from 1755 to 1770. Several of these pieces have never been translated into English before; others have long been unavailable in English. We can trace in these works the development of Kant's thought to the eventual emergence in 1770 of the two chief tenets of his mature philosophy: the (...) subjectivity of space and time, and the phenomena-noumena distinction. The volume has been furnished with substantial editorial apparatus, including a general introduction to the main themes of Kant's early thought, introduction to the individual works and résumés of their contents, linguistic and factual notes, bibliographies, a glossary of key terms, and biographical-bibliographical sketches of persons mentioned by Kant. (shrink)