Towards a Social Theory of Mathematical Knowledge
Towards a Social Theory of Mathematical Knowledge
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走向数学知识的社会理论
DOI：
10.1007/978-3-642-78542-9_12
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
M. Otte
中科院分区：
文献类型：
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作者：
M. Otte
我的主要论点非常简单，可能看起来几乎是微不足道的：没有数学和技术之间的相互作用的广泛探索，就不可能发展数学的社会理论。数学知识的社会理论的目的是什么？这种理论必须说明这种知识和一般科学知识的确定性和必要性。知识的必要性要求心灵与外部现实之间的和谐或至少是一种联系，这种和谐首先被认为是由上帝建立的。数学似乎实际上是这种和谐的表达。笛卡尔、开普勒、伽利略、牛顿、莱布尼茨和许多其他现代数学的创始人所相信的可以这样表达：自然界中有一种内在的隐藏的和谐，它以简单的数学定律的形式反映在我们的头脑中。这种和谐是自然界中的事件可以通过观察和数学分析相结合来预测的原因”（Kline 1985，第213页）。今天仍然假设数学观察可以直接将理性思维与客观自然联系起来。只是现在，这种联系的可能性并不是来自先验的预先建立的和谐，而是基于技术上的成功。作为数学知识的社会理论必须解释心灵与现实之间的联系，它必须描述数学与技术之间的关系。这个主题的意义和它是关于什么的问题同时也是对人类在数学化和技术环境中的问题和机会的探究，更具体地说，他们不是数学家或工程师，也不想成为这样的人。因此，问题不是以某种专门的方式获得数学和技术的发展和影响，而是想象数学和技术对熟悉的”普通人“的作用。“本章不追求任何狭义上的教学目标。它并不打算将某台计算机与某个人联系起来。相反，它是关于一个“全球”的接口问题，也就是说，关于我们作为人类的关系，关于我们与数学和正式知识系统的社会关系。
My main thesis is very simple and may appear almost trivially obvious: No social theory of mathematics can be developed without extensive exploration of the interaction between mathematics and technology. What is the purpose of a social theory of mathematical knowledge? Such a theory has to account for the certainty and necessity of this knowledge and of scientific knowledge in general. The necessity of knowledge requires a harmony or at least a connection between the mind and outer reality, a harmony first thought to be established by God. Mathematics seemed to be in fact an expression of this harmony." What Descartes, Kepler, Galileo, Newton, Leibniz, and many other founders of modem mathematics believed can be expressed thus: there is inherent in nature a hidden harmony that reflects itself in our minds in the form of simple mathematical laws. This harmony is the reason that events in nature are predictable by a combination of observation and mathematical analysis"(Kline 1985, p. 213). It is still assumed today that mathematical observation can directly connect the rational mind with objective nature. Only now the possibility of such a connection is not derived from an a priori pre-established harmony, but is based, I claim on technical success. As a social theory of mathematical knowledge has to explain the connection between the mind and reality it has to describe the relationship between mathematics and technology.The question of the meaning of this topic and of what it is about is simultaneously an inquiry into the problems and opportunities of humankind in a mathematized and technological environment and, more particularly, of people who are not mathematicians or engineers in any sense and do not want to become such. Thus, the problem is not one of gaining access, in some specialized mode, to the development and influence of mathematics and technology, but rather one of imagining the role of mathematics and technology for the familiar" man in the street." This chapter does not pursue any didactical goals in the narrower sense. It does not intend to relate a certain computer to a certain human being. Rather, it is about a" global" interface problem, that is, about our relations as human beings and about our social relationships with mathematics and formal knowledge systems.