中文摘要 (Chinese summary of Chapter 1)

jiuzhang

第一章The Veil小摘要, more precisely.  I can’t read that, I’m afraid, even though I’m convinced that the most interesting problem currently facing philosophy of mathematics is to clarify how or whether Chinese and European mathematics differ and how or whether these differences reflect differences in the respective metaphysical traditions.  One of the peculiarities of my own education is that I was exposed to classical Chinese philosophy (in translation!) before I read any of the canonical texts of European philosophy, so perhaps when I did come to the latter my philosophical bearings were already slightly askew.

Anyway, I was pleased to see that a summary — a “little summary,” as my recent Ph.D. student Lin Jie tells me the more precise title should be translated — has appeared on the website of a Chinese bookseller.   Here it is.

尽管希尔伯特认为历史告诉我们科学的发展是连贯的,我们如今已经不相信这种连贯性。并且,即便揭开未来的面纱,我们也未必知道我们的目标何在。我们今天大多相信科学的发展是由一连串的范式革命构成的。数学也是如此,如克罗内克所说的,新现象会推翻旧假说并且以新假说取而代之。但数学中的变化剧烈程度要小,因为数学不必为适应新发现而调适自身,而是可以改变旧的假说或者改变我们所认为可以接受的标准。康托尔说数学之为自由学问,其题中之义在是。
史学家Jeremy Gray认为职业自治(professional autonomy)是数学线代主义的标志。前现代的数学家的想象受限于数学-哲学和数学-科学之间的关系。在Gray看来,没有职业自治性,数学的现代转向就不会发生。现代主义之成为主流,是因为它恰当表述了数学家所在的新处境:数学被吸纳到现代研究型大学的结构(从而形成职业数学家的国际群体),数学的目标和主题的新形式得以形成。
如果本书是关于什么的话,那么本书是关于过一种数学家的双重人生是何种感觉:一方面数学家在这种职业自治之中的生活,只需要向同事负责;另一个是更广阔的世界中的生活。要解释数学家到底做什么是一件很难的事情,正如David Mumford所说的:“作为一个职业数学家,我已经习惯于生活在一种真空之中,这种真空的周围是那些以对数学一无所知而自豪的人。”这种困难使得后面的问题不被问出来:什么是数学家的目标?为什么要做数学?
为什么做数学?这个问题一般有三个回答,其中两个明显是错的。第一个是数学没有实际应用,第二是数学能确定地证明真理。这两者不论有多少可信度,都不无法为纯数学——不旨在解决特定范围的实际问题的数学——的提供驱动力。两者都在数学之外寻求数学的驱动力,并且暗示着,数学家要么是失败的工程师,要么是失败的哲学家。
第三个理由是美学的,其经典表达见于哈代。但这个理由仍旧受到贫乏和自我陷溺的责难,而数学之被容忍,不过是因为它有可能的实际用处和大学仍需要数学来训练真正有用的公民。
本书一开始主要是讨论为什么做数学,但见于一本数学书不讨论何谓数学是说不通的,所以也讨论何谓数学。又因为本书是为无数学训练背景的人写作的,因此更多是关于“作为一种生活方式的数学”。
本书并不追求得出定论,而是如 Herbert Mehrtens所说的,以“如何做数学”来说明“数学是什么”

The site book.douban.com also cites this passage from the Preface to MWA, which specifically refers to the cross-cultural comparative study of mathematics.

One of the most exciting trends in history of mathematics  is  the  comparative  study across  cultures,  especially between European (and Near Eastern) mathematics and the  mathematics of East Asia. These studies, which are occasionally (too  rarely) accompanied by no  less exciting comparative philosophy, is  necessarily  cautious  and  painstaking,  because  its  authors  are  trying  to  establish  a reliable basis for future comparisons.

Advertisements

One thought on “中文摘要 (Chinese summary of Chapter 1)

  1. Jack Morava

    In Western languages, Joseph Needham’s Science & Civilization in China (Vol 3: Mathematics and the Sciences of the Heavens and the Earth) is useful background.

    Like

    Reply

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s