An Indian Quasi-Fregean Theory of Number

• 作者: Eberhard Guhe
• 来源期刊: 复旦人文社会科学论丛:英文版
• 学科: 社会科学
• 关键词: Navya-Nyaya Natural NUMBERS FREGE Property theories Peano's AXIOMS
• 年，卷（期）: fdrwshkxlcywb_2019,（3）
• 页码范围: 329-351
• 页数: 23页
• 分类号: C

摘要

A very interesting account of the reference of number words in classical Indian philosophy was given by Mahesa Chandra (1836 -1906) in his Brief Notes on the Modern Nyaya System of Philosophy and its Technical Terms (BN), a primer on NavyaNyaya terminology and doctrines. Despite its English title, BN is a Sanskrit work. The section on"number"(samkhya) provides an exposition of a theory of number which can account for both the adjectival and the substantival use of number words in Sanskrit. According to D. H. H. Ingalls (19161999), some ideas about the reference of number words in BN are close to the FregeRussell theory of natural number. Ingalls's comparison refers to a concept of number in Navya-Nyaya which is related to the things numbered via the SO called"circumtaining relation"(paryapti). Although there is no theory of sets in Navya-Nyaya, Navya-Naiyayikas do have a realist theory of properties (dharma) and their theory of number is a theory of properties as constituents of empirical reality, anchored to their system of ontological categories. As shown by George Bealer, properties can serve the same purpose as sets in the Frege -Russell theory of natural number. In the present paper, we attempt a formal reconstruction of Mahesa Chandra's exposition of the Navya-Nyaya theory of number, which accounts for its affinity to George Bealer's neo-Fregean analysis. As part of our appraisal of the momentousness and robustness of the"circumtaining"concept of number, we show that it can be cast into a precise recursive definition of natural number and we prove property versions of Peano's axioms from this definition.