Download or read book The Argument of Mathematics written by Andrew Aberdein and published by Springer Science & Business Media. This book was released on 2013-07-01 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics. ​

Download or read book Deduction Computation Experiment written by Rossella Lupacchini and published by Springer Science & Business Media. This book was released on 2008-09-25 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is located in a cross-disciplinary ?eld bringing together mat- matics, logic, natural science and philosophy. Re?ection on the e?ectiveness of proof brings out a number of questions that have always been latent in the informal understanding of the subject. What makes a symbolic constr- tion signi?cant? What makes an assumption reasonable? What makes a proof reliable? G ̈ odel, Church and Turing, in di?erent ways, achieve a deep und- standing of the notion of e?ective calculability involved in the nature of proof. Turing’s work in particular provides a “precise and unquestionably adequate” de?nition of the general notion of a formal system in terms of a machine with a ?nite number of parts. On the other hand, Eugene Wigner refers to the - reasonable e?ectiveness of mathematics in the natural sciences as a miracle. Where should the boundary be traced between mathematical procedures and physical processes? What is the characteristic use of a proof as a com- tation, as opposed to its use as an experiment? What does natural science tell us about the e?ectiveness of proof? What is the role of mathematical proofs in the discovery and validation of empirical theories? The papers collected in this book are intended to search for some answers, to discuss conceptual and logical issues underlying such questions and, perhaps, to call attention to other relevant questions.

Download or read book Analysis and Synthesis in Mathematics written by Michael Otte and published by Springer Science & Business Media. This book was released on 1997 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses the main interpretations of the classical distinction between analysis and synthesis with respect to mathematics. In the first part, this is discussed from a historical point of view, by considering different examples from the history of mathematics. In the second part, the question is considered from a philosophical point of view, and some new interpretations are proposed. Finally, in the third part, one of the editors discusses some common aspects of the different interpretations.

Download or read book The Growth of Mathematical Knowledge written by Emily Grosholz and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics has stood as a bridge between the Humanities and the Sciences since the days of classical antiquity. For Plato, mathematics was evidence of Being in the midst of Becoming, garden variety evidence apparent even to small children and the unphilosophical, and therefore of the highest educational significance. In the great central similes of The Republic it is the touchstone ofintelligibility for discourse, and in the Timaeus it provides in an oddly literal sense the framework of nature, insuring the intelligibility ofthe material world. For Descartes, mathematical ideas had a clarity and distinctness akin to the idea of God, as the fifth of the Meditations makes especially clear. Cartesian mathematicals are constructions as well as objects envisioned by the soul; in the Principles, the work ofthe physicist who provides a quantified account ofthe machines of nature hovers between description and constitution. For Kant, mathematics reveals the possibility of universal and necessary knowledge that is neither the logical unpacking ofconcepts nor the record of perceptual experience. In the Critique ofPure Reason, mathematics is one of the transcendental instruments the human mind uses to apprehend nature, and by apprehending to construct it under the universal and necessary lawsofNewtonian mechanics.

Download or read book Kant Studien written by Hans Vaihinger and published by . This book was released on 1999 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1904-26 (includes lists of members)

Download or read book Real Mechanical Experimental written by Francesco G. Sacco and published by Springer Nature. This book was released on 2020-06-29 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This original work contains the first detailed account of the natural philosophy of Robert Hooke (1635-1703), leading figure of the early Royal Society. From celestial mechanics to microscopy, from optics to geology and biology, Hooke’s contributions to the Scientific Revolution proved decisive. Focusing separately on partial aspects of Hooke’s works, scholars have hitherto failed to see the unifying idea of the natural philosophy underlying them. Some of his unpublished papers have passed almost unnoticed. Hooke pursued the foundation of a real, mechanical and experimental philosophy, and this book is an attempt to reconstruct it. The book includes a selection of Hooke's unpublished papers. Readers will discover a study of the new science through the works of one of the most known protagonists. Challenging the current views on the scientific life of restoration England, this book sheds new light on the circulation of Baconian ideals and the mechanical philosophy in the early Royal Society. This book is a must-read to anybody interested in Hooke, early modern science or Restoration history.

Download or read book Revue internationale de philosophie written by and published by . This book was released on 1996 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Philosophical Review written by and published by . This book was released on 1996 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Review of Metaphysics written by and published by . This book was released on 1996 with total page 1022 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Bibliografisch repertorium van de wijsbegeerte written by and published by . This book was released on 2000 with total page 1162 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mind written by and published by . This book was released on 1996 with total page 804 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues for 1896-1900 contain papers of the Aristotelian Society.

Download or read book Philosophica written by and published by . This book was released on 1995 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book International Philosophical Quarterly written by and published by . This book was released on 1995 with total page 1114 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Communication Cognition written by and published by . This book was released on 1996 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Historical Abstracts written by Eric H. Boehm and published by . This book was released on 1999 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Philosopher s Index written by and published by . This book was released on 1996 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Humanities Index written by and published by . This book was released on 1998 with total page 1494 pages. Available in PDF, EPUB and Kindle. Book excerpt: