文学研究融入数学思想方法论

Integrating Mathematical Thought and Methods Into Literary Research

无论文学研究还是数学,都是人类认识主客观世界的方式。两者解决问题的手段相异,却都遵循共同的逻辑法则。人类的许多知识体系,往往类似数学推演,由几条基本命题经逻辑推演而成为一个体系。文学研究的一些领域,组成基础的命题有些是无可置疑的客观事实,有些却并非公理式的存在。基础命题一旦被抛弃,就会引发体系震荡。文学研究中被广泛使用的排中律,适用于内涵与外延都明确的概念。对概念内涵清楚而外延不明确的文学史问题,需要借助模糊数学的思想方法求解。比如考察明清之际通俗小说由改编逐步过渡到独创的历程,学者借用模糊数学方法,引入隶属度概念,能够解决许多争执不休的问题。精细的数据统计,能够展示文学史上文体的起伏态势。数学突变论则有助于解释文学语言领域内的一些现象,如中国古代诗歌从四言到五言的发展历程、古体诗到近体诗的演变历程。数学的概率论可用于考察作家的写作特征,如分析不受写作内容影响的虚字分布概率,帮助判断文本的作者,开辟一条作者考证的新途径。考察文学研究体系的自身发展,融入数学思想方法后也可理解得更深刻。

Both literary research and mathematics are ways for human beings to understand the subjective and objective world.They follow the common rules of logic despite their different methods of solving problems.Many human knowledge systems,like mathematical deduction,are often logically deduced from several basic propositions into a system.In some fields of literary research,some of the propositions that form the basis are unquestionable objective facts,but some are not axiomatic existence.The abandonment of the basic proposition will cause system shock.The law of the excluded middle,which is widely used in literary research,applies to concepts with clear connotation and denotation.The problem of history of literature with clear connotation and unclear denotation needs to be solved by the thought method of fuzzy mathematics.For example,scholars have solved many controversial problems by using fuzzy mathematics and introducing the concept of membership degree in the process of investigating the gradual transition of popular novels from adaptation to originality during Ming and Qing dynasties.Fine statistics can show the ups and downs of literary styles in the history of literature.The sudden change theory in mathematics helps to explain some phenomena in the field of literary language,such as the development process of ancient Chinese poetry from four words to five words,and the evolution process of ancient poetry to modern poetry.Mathematical probability theory can be used to investigate the writing characteristics of writers,such as analyzing the distribution probability of function words that are not affected by the writing content,helping to judge the author of the text and opening up a new way of author verification.The development of literary research system itself also needs integration with mathematical methods.