Studies on reductio ad absurdum and its Application in Indian Propositional Logic

反证法研究及其在印度命题逻辑中的应用

• 批准号: 10610016
• 负责人: YOSHIMIZU Kiyotaka
• 金额: $ 0.96万
• 依托单位: Hokkaido University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10610016/
• 关键词: reductio ad absurdum; arthapatti; Kumarila; Mimamsa; arthapath; ミーマーンサー; arthaapatti

The way of proof with the help of reductio ad absurdum was called arthapatti and distinguished from inference (anumana) in the hermeneutical school in India, Mimamsa. If we define "A" "B" and "C" as propositions of the following sense : A="Caitra is present in his house" ; B="Caitra is present in outside" ; C="Caitra is living", and if we presuppose that Caitra is present either in his house or in outside as far as he is living, we can formulate the example of arthapatti assuming that Caitra is present in outside as follows : ((C⊃(A∨B)) Λ (CΛ¬A )) ⊃B.This formula can be proven formally by means of natural deduction. Kumarila remarks that it is not a defect of an arthapatti that the conclusion to be proved is implied in the reason which proves it (Arthapattipariccheda k.29). Kumarila calls the relation between "absence of a living person in house" and "his presence in outside" expressed in the universal proposition "inseparable relation" (avinabhavita). It is sure that this inseparable relation is there before we realize Caitra's presence in outside. But we do not realize it on the basis of the former. The inseparable relation is rather assumed when we realize Caitra's presence in outside (Arthapattipariccheda k.30). Though Kumarila did not establish an axiomatic method of propositional logic, he brought up a unique question on Logic. He maintained that it must be possible to derive a proposition from another ones in which it is implied without recourse to the universal relation between two terms. Caitra's presence in outside can be deduced from a combination of propositions of which subject is restricted to Caitra. Therefore we can safely say that this type of arthapatti cannot be reduced to an anumana.

借助Reaductio Ad Adurdum的证明方式被称为Arthapatti，与Mimamsa的印度诠释学学校中的推论（Anumana）区别开来。如果我们将“ A”“ B”和“ C”定义为以下意义的建议：A =“ Caitra在他的房子里”； b =“凯特拉在外面”； c =“凯特拉（Caitra）的生活”，如果我们以凯特拉（Caitra）存在在他的房子或外面的生活为前提，那么我们可以提出Arthapatti的例子，假设Caitra在外部存在如下：（（c⊃（a∨b）λ（cλ-）λ（cλ-）λ（cλ-）λ（cλ-））。库马里拉（Kumarila）提醒人们，这不是arthapatti的缺陷，即在证明这一点的原因中暗示了要证明的结论（arthapattipariccheda k.29）。库马里拉（Kumarila）称之为“室内有活着的人”与普遍命题“不可分割的关系”（Avinabhavita）中表达的“在外面”之间的关系。可以肯定的是，这种密不可分的关系就在我们意识到凯特拉在外面的存在之前就存在。但是我们没有根据前者意识到这一点。当我们意识到Caitra在外部的存在时，就可以假定这种不可分割的关系（Arthapattipariccheda K.30）。尽管Kumarila没有建立命题逻辑的公理方法，但他提出了关于逻辑的独特问题。他坚持认为，必须从另一个命题中得出一个命题，在该命题中暗示它，而无需求助于两个术语之间的普遍关系。 Caitra在外部的存在可以从命题的组合中推导出来，该主题仅限于Caitra。因此，我们可以肯定地说，这种类型的Arthapatti不能简化为动物。

项目成果

藤井教公: "天台と三論-その異質性と類似性-"印度哲学仏教学. 15. 203-216 (2000)

Noriko Fujii：“Tendai 和 Sanron - 它们的异质性和相似性”印度哲学和佛教 15. 203-216 (2000)。

細田典明: "『アーラニヤカ・ウハニシャッド』と『ダンマパダ』-樹の比喩について"印度哲学仏教学. 14. 102-111 (1999)

Noriaki Hosoda：“Aranyaka Uhanishad 和 Dhammapada - 关于树的隐喻”印度哲学和佛教 14. 102-111 (1999)

藤井教公: "天台智〓における四悉檀の意義"印度学仏教学研究. 47-2. 27-35 (1999)

藤井纪子：《天台地中四天坛的意义》《印度研究与佛教研究》47-2（1999）。

YOSHIMIZU,Kiyotaka: "On the Object of Cognition by srutarthapatti"Bukkyo-gaku (Journal of Buddhist Studies). vol.40. 1-22 (1999)

吉水清隆：“斯鲁塔塔帕蒂论认知的对象”《佛学学报》。

吉水清孝: "ミーマーンサー・スートラにおける " arthapatti " と " anumana ""印度学仏教学研究. 48-2. 38-44 (2000)

Kiyotaka Yoshimizu：《Mimamsa Sutras》中的“Arthapatti”和“anumana”，《印度研究和佛教研究》48-2 38-44（2000）。