During the period of national isolation, a mathematical tradition called wasan flourished in Japan. Though virtually unknown to Europeans before the Meiji Restoration, its practitioners, the wasanka, produced some results comparable to (and sometimes in advance of) those of mathematicians of the European Enlightment. This volume, a companion to Unger's earlier translation of solutions by Aida Yasuaki (1747-1817), focuses on problems that Aida most likely used as a teacher. Unger explains the reasons for believing this, and sheds further light on the intellectual milieu in which Aida worked by discussing other books by Aida, including one in which he describes Dutch techniques of navigation.

Towards Non-Being presents an account of the semantics of intentional language-verbs such as 'believes', 'fears', 'seeks', 'imagines'. Graham Priest tackles problems concerning intentional states which are often brushed under the carpet in discussions of intentionality, such as their failure to be closed under deducibility. Priest's account draws on the work of the late Richard Routley (Sylvan), and proceeds in terms of objects that may be either existent or non-existent, at worlds that may be either possible or impossible. Since Russell, non-existent objects have had a bad press in Western philosophy; Priest mounts a full-scale defence. In the process, he offers an account of both fictional and mathematical objects as non-existent. The book will be of central interest to anyone who is concerned with intentionality in the philosophy of mind or philosophy of language, the metaphysics of existence and identity, the philosophy or fiction, the philosophy of mathematics, or cognitive representation in AI. This updated second edition adds ten new chapters to the original eight. These further develop the ideas of the first edition, reply to critics, and explore new areas of relevance. New topics covered include: conceivability, realism/antirealism concerning non-existent objects, self-deception, and the verb to be.

This is the first complete English translation of Bernard Bolzano's four-volume Wissenschaftslehre or Theory of Science, a masterwork of theoretical philosophy. Bolzano (1781-1848), one of the greatest philosophers of the nineteenth century, was a man of many parts. Best known in his own time as a teacher and public intellectual, he was also a mathematician and logician of rare ability, the peer of other pioneers of modern mathematical logic such as Boole, Frege, and Peirce. As Professor of Religion at the Charles University in Prague from 1805, he proved to be a courageous and determined critic of abuses in church and state, a powerful advocate for reform. Dismissed by the Emperor in 1819 for political reasons, he left public life and spent the next decade working on his "theory of science," which he also called logic. The resulting Wissenschaftslehre, first published in 1837, is a monumental, wholly original study in logic, epistemology, heuristics, and scientific methodology. Unlike most logical studies of the period, it is not concerned with the "psychological self-consciousness of the thinking mind." Instead, it develops logic as the science of "propositions in themselves" and their parts, especially the relations between these entities. It offers, for the first time in the history of logic, a viable definition of consequence (or deducibility), and a novel view of probability. Giving constant attention to Bolzano's predecessors and contemporaries, with particular emphasis on Kant, this richly documented work is also a valuable source for the history of logic and philosophy. Each volume of the edition is accompanied by a detailed introduction, which alerts the reader to the historical context of Bolzano's work and illuminates its continued relevance.

This book analyses the straw man fallacy and its deployment in philosophical reasoning. While commonly invoked in both academic dialogue and public discourse, it has not until now received the attention it deserves as a rhetorical device. Scott Aikin and John Casey propose that straw manning essentially consists in expressing distorted representations of one’s critical interlocutor. To this end, the straw man comprises three dialectical forms, and not only the one that is usually suggested: the straw man, the weak man and the hollow man. Moreover, they demonstrate that straw manning is unique among fallacies as it has no particular logical form in itself, because it is an instance of inappropriate meta-argument, or argument about arguments. They discuss the importance of the onlooking audience to the successful deployment of the straw man, reasoning that the existence of an audience complicates the dialectical boundaries of argument. Providing a lively, provocative and thorough analysis of the straw man fallacy, this book will appeal to postgraduates and researchers alike, working in a range of fields including fallacies, rhetoric, argumentation theory and informal logic.

This publication includes an unabridged and annotated translation of two works by Johann Heinrich Lambert (1728-1777) written in the 1760s: Vorlaufige Kenntnisse fur die, so die Quadratur und Rectification des Circuls suchen and Memoire sur quelques proprietes remarquables des quantites transcendentes circulaires et logarithmiques. The translations are accompanied by a contextualised study of each of these works and provide an overview of Lambert's contributions, showing both the background and the influence of his work. In addition, by adopting a biographical approach, it allows readers to better get to know the scientist himself. Lambert was a highly relevant scientist and polymath in his time, admired by the likes of Kant, who despite having made a wide variety of contributions to different branches of knowledge, later faded into an undeserved secondary place with respect to other scientists of the eighteenth century. In mathematics, in particular, he is famous for his research on non-Euclidean geometries, although he is likely best known for having been the first who proved the irrationality of pi. In his Memoire, he conducted one of the first studies on hyperbolic functions, offered a surprisingly rigorous proof of the irrationality of pi, established for the first time the modern distinction between algebraic and transcendental numbers, and based on such distinction, he conjectured the transcendence of pi and therefore the impossibility of squaring the circle.

This book introduces the reader to Serres' unique manner of 'doing philosophy' that can be traced throughout his entire oeuvre: namely as a novel manner of bearing witness. It explores how Serres takes note of a range of epistemologically unsettling situations, which he understands as arising from the short-circuit of a proprietary notion of capital with a praxis of science that commits itself to a form of reasoning which privileges the most direct path (simple method) in order to expend minimal efforts while pursuing maximal efficiency. In Serres' universal economy, value is considered as a function of rarity, not as a stock of resources. This book demonstrates how Michel Serres has developed an architectonics that is coefficient with nature. Mathematic and Information in the Philosophy of Michel Serres acquaints the reader with Serres' monist manner of addressing the universality and the power of knowledge - that is at once also the anonymous and empty faculty of incandescent, inventive thought. The chapters of the book demarcate, problematize and contextualize some of the epistemologically unsettling situations Serres addresses, whilst also examining the particular manner in which he responds to and converses with these situations.

I first had a quick look, then I started reading it. I couldn't stop. -Gerard 't Hooft (Nobel Prize, in Physics 1999) This is a book about the mathematical nature of our Universe. Armed with no more than basic high school mathematics, Dr. Joel L. Schiff takes you on a foray through some of the most intriguing aspects of the world around us. Along the way, you will visit the bizarre world of subatomic particles, honey bees and ants, galaxies, black holes, infinity, and more. Included are such goodies as measuring the speed of light with your microwave oven, determining the size of the Earth with a stick in the ground and the age of the Solar System from meteorites, understanding how the Theory of Relativity makes your everyday GPS system possible, and so much more. These topics are easily accessible to anyone who has ever brushed up against the Pythagorean Theorem and the symbol , with the lightest dusting of algebra. Through this book, science-curious readers will come to appreciate the patterns, seeming contradictions, and extraordinary mathematical beauty of our Universe.

Is anything truly random? Does infinity actually exist? Could we ever see into other dimensions?

In this delightful journey of discovery, David Darling and extraordinary child prodigy Agnijo Banerjee draw connections between the cutting edge of modern maths and life as we understand it, delving into the strange would we like alien music? and venturing out on quests to consider the existence of free will and the fantastical future of quantum computers. Packed with puzzles and paradoxes, mind-bending concepts and surprising solutions, this is for anyone who wants life s questions answered even those you never thought to ask.

From an infant's first grasp of quantity to Einstein's theory of relativity, the human experience of number has intrigued researchers for centuries. Numeracy and mathematics have played fundamental roles in the development of societies and civilisations, and yet there is an essential mystery to these concepts, evidenced by the fear many people still feel when confronted by apparently simple sums. Including perspectives from anthropology, education and psychology, The Nature and Development of Mathematics addresses three core questions: Is maths natural? What is the impact of our culture and environment on mathematical thinking? And how can we improve our mathematical ability? Examining the cognitive processes that we use, the origins of these skills and their cultural context, and how learning and teaching can be supported in the classroom, the book contextualises each issue within the wider field, arguing that only by taking a cross-disciplinary perspective can we fully understand what it means to be numerate, as well as how we become numerate in our modern world. This is a unique collection including contributions from a range of renowned international researchers. It will be of interest to students and researchers across cognitive psychology, cultural anthropology and educational research.

Mathematical platonism is the view that mathematical statements are true of real mathematical objects like numbers, shapes, and sets. One central problem with platonism is that numbers, shapes, sets, and the like are not perceivable by our senses. In contemporary philosophy, the most common defense of platonism uses what is known as the indispensability argument. According to the indispensabilist, we can know about mathematics because mathematics is essential to science. Platonism is among the most persistent philosophical views. Our mathematical beliefs are among our most entrenched. They have survived the demise of millennia of failed scientific theories. Once established, mathematical theories are rarely rejected, and never for reasons of their inapplicability to empirical science. Autonomy Platonism and the Indispensability Argument is a defense of an alternative to indispensability platonism. The autonomy platonist believes that mathematics is independent of empirical science: there is purely mathematical evidence for purely mathematical theories which are even more compelling to believe than empirical science. Russell Marcus begins by contrasting autonomy platonism and indispensability platonism. He then argues against a variety of indispensability arguments in the first half of the book. In the latter half, he defends a new approach to a traditional platonistic view, one which includes appeals to a priori but fallible methods of belief acquisition, including mathematical intuition, and a natural adoption of ordinary mathematical methods. In the end, Marcus defends his intuition-based autonomy platonism against charges that the autonomy of mathematics is viciously circular. This book will be useful to researchers, graduate students, and advanced undergraduates with interests in the philosophy of mathematics or in the connection between science and mathematics.

This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ++++ The below data was compiled from various identification fields in the bibliographic record of this title. This data is provided as an additional tool in helping to ensure edition identification: ++++ Cours D'analyse De L'ecole Polytechnique, Volume 1; Cours D'analyse De L'ecole Polytechnique; Camille Jordan 2 Camille Jordan s.n., 1893 Calculus; Calculus of variations; Curves, Plane; Differential equations; Functions; Mathematical analysis; Series, Infinite

This book is an attempt to change our thinking about thinking. Anna Sfard undertakes this task convinced that many long-standing, seemingly irresolvable quandaries regarding human development originate in ambiguities of the existing discourses on thinking. Standing on the shoulders of Vygotsky and Wittgenstein, the author defines thinking as a form of communication. The disappearance of the time-honoured thinking-communicating dichotomy is epitomised by Sfard's term, commognition, which combines communication with cognition. The commognitive tenet implies that verbal communication with its distinctive property of recursive self-reference may be the primary source of humans' unique ability to accumulate the complexity of their action from one generation to another. The explanatory power of the commognitive framework and the manner in which it contributes to our understanding of human development is illustrated through commognitive analysis of mathematical discourse accompanied by vignettes from mathematics classrooms.