2000 Fiscal Year Final Research Report Summary
Studies on reductio ad absurdum and its Application in Indian Propositional Logic
| Project/Area Number |
10610016
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
印度哲学(含仏教学)
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| Research Institution | Hokkaido University |
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Principal Investigator |
YOSHIMIZU Kiyotaka Hokkaido Univ., Grad. School of Letters, Asso. Prof., 大学院・文学研究科, 助教授 (20271835)
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| Co-Investigator(Kenkyū-buntansha) |
HOSODA Noriaki Hokkaido Univ., Grad. School of Letters, Asso. Prof., 大学院・文学研究科, 助教授 (00181503)
FUJII Kyoko Hokkaido Univ., Grad. School of Letters, Prof., 大学院・文学研究科, 教授 (70238525)
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| Project Period (FY) |
1998 – 2000
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| Keywords | reductio ad absurdum / arthapatti / Kumarila / Mimamsa |
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| Research Abstract |
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.
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