Representation and Productive Ambiguity in Mathematics and the Sciences 电子书下载
Emily Grosholz offers an original investigation of demonstration in mathematics and science, examining how it works and why it is persuasive. Focusing on geometrical demonstration, she shows the roles that representation and ambiguity play in mathematical discovery. She presents a wide range of case studies in mechanics, topology, algebra, logic, and chemistry, from ancient Greece to the present day, but focusing particularly on the seventeenth and twentieth centuries. She argues that reductive methods are effective not because they diminish but because they multiply and juxtapose modes of representation. Such problem-solving is, she argues, best understood in terms of Leibnizian "analysis"--the search for conditions of intelligibility. Discovery and justification are then two aspects of one rational way of proceeding, which produces the mathematician`s formal experience.Grosholz defends the importance of iconic, as well as symbolic and indexical, signs in mathematical representation, and argues that pragmatic, as well as syntactic and semantic, considerations are indispensable fore mathematical reasoning. By taking a close look at the way results are presented on the page in mathematical (and biological, chemical, and mechanical) texts, she shows that when two or more traditions combine in the service of problem solving, notations and diagrams are subtly altered, multiplied, and juxtaposed, and surrounded by prose in natural language which explains the novel combination. Viewed this way, the texts yield striking examples of language and notation that are irreducibly ambiguous and productive because they are ambiguous. Grosholtz`s arguments, which invoke Descartes, Locke, Hume, and Kant, will be of considerable interest to philosophers and historians of mathematics and science, and also have far-reaching consequences for epistemology and philosophy of language.
尊敬的读者:
欢迎您访问我们的网站。本站的初衷是为大家提供一个共享学习资料、交换知识的平台。每位用户都可以将文件上传至网盘并分享。
然而,随着用户上传的资料增多,我们发现部分不宜或版权问题的书籍被分享到了本站。
为此,我们已经关闭了分享入口,并进行了多次书籍审查,但仍有部分内容未能彻底审查到位。
在此,我们恳请广大读者与我们共同监督,如发现任何不宜内容,请 点击此处 进行举报,我们会第一时间处理并下架相关内容。
希望我们能共建一个文明社区!感谢您的理解与支持!
猜你喜欢
- 《于丹论语心得》于丹文字版 电子书下载
- 《一间只属于自己的房间》弗吉尼亚・伍尔夫文字版 电子书下载
- 《乡下人的悲歌》[美]J.D.万斯中文版 电子书下载
- 《隐性逻辑:教你快速切换思考方式》卡尔・诺顿文字版 电子书下载
- A Tour of C++ 2nd Edition - Bjarne Stroustrup 电子书下载
- 《写在人生边上》钱钟书 电子书下载
- 《能力都是逼出来的》[美]布兰登·伯查德纽约时报畅销书作家、高效能学院创始人布兰登·伯查德作品!文字版 电子书下载
- 《投资者的未来》杰里米 J·西格尔中文修订版 电子书下载
- 《别让猴子跳回背上》威廉•安肯三世 电子书下载
- 《汗青堂欧洲史第一辑(套装共6册)》菲利普·帕克 等全译典藏版 电子书下载
- 《重新发现日本》矶达雄 / 宫泽洋 电子书下载
- 《宋明理学与文学》马积高最新版 电子书下载