数学:一种人类学现象——后期维特根斯坦数学哲学思想探析

Mathematics, An Anthropological Phenomenon:Remark on Later Wittgenstein's Philosophy of Mathematics

数学哲学经过长期的演化,形成了罗素的逻辑主义、希尔伯特的形式主义、布劳威尔的直觉主义、欧内斯特的社会建构主义等流派。在数学哲学中,一个不容忽略的哲学家就是维特根斯坦。他的后期数学哲学思想对后世影响深远。维特根斯坦反对数学柏拉图主义,认为数学仅仅是基于生活形式上的约定,是公共性质的。数学计算只不过是语言游戏活动,而语言游戏之所以能进行下去,是因为它是基于生活形式的一致性,这显然脱离不了各种社会因素的影响。

After long evolution, philosophy of mathematics has formed the following schools: Russell's logicism, Hilbert's formalism,Brouwer's intuitionism, Ernest's social constructivism, etc.A famous philosopher of mathematics who cannot be neglected is LudwigWittgenstein, whose later philosophy of mathematics has great influence on future generations.Wittgenstein opposes to mathematicalPlatonism, and believes that math is based on the agreement of the form of life, its nature being public.Math is just an activity of languagegame, which can be carried out because it is based on the consistency of the form of life.It depends on the influence of various social factors.