The Logic of Uddyotakara The conflict with Buddhist logic and his achievement

Transcription

1 1 The Logic of Uddyotakara The conflict with Buddhist logic and his achievement 0 Introduction 1 The Framework of Uddyotakara s Logic 1.1 Nyāya system and Uddyotakara 1.2 The Framework of Uddyotakara s Logic 2 Aspects of Uddyotakara s Logic 2.1 Dharma-Dharmin-Framework 2.2 Trairūpya-Theory and Logical Necessity 2.3 The Usage and the Logical Structure of vyatirekin 3 An Aspect of Prasaṅga-demonstration A Genealogy of Avīta 3.1 The Development of Vīta and Āvīta Theory 3.2 Uddyotakara s Theory of Avīta 4 Conclusion Appendix Japanese Translation and Elucidation of Nyāyavārttika A Theory of Inference: under NS B Theory of Demonstration: under NS C Theory of Debate: under NS D Theory of Fallacy: under NS E General Introduction to NV: under NS The aim of this article is to clarify Uddyotakara s theories of inference and demonstration by examining mainly from the logical point of view, their position in the development of early Indian logic. In this article I devote attention to the following two points: 1 the relation between an inferential object and its valid reason, or the conditions for the valid reasons, 2 the demonstrative schemata called vyatirekin or avīta. In the case of Uddyotakara, the relation between an inferential object and its valid reason has been sometimes said to be samavāya. This view would be based on Uddyotakara s criticism of Diṅnāga s avinābhāva and Uddyotakara s unique interpretation of the inference of fire. However, I disagree on the grounds that the above portions must be interpreted in other way, and that the relation called avyabhicāra should afford the key to understanding the validity of reason in Uddyotakara s logical system. The vyatirekin has been generally said to be a reason having no similar instance sapakṣa or an inference based on such a reason. This explanation is due to Uddyotakara s definition. On the other hand, the vyatirekin that is listed in Uddyotakara s three types of inferences or sixteen classification of valid and invalid reasons has a strange form. Its reason is represented in terms of -prasaṅgāt it would be absurdity that... It is parallel to reductio ad absurdum. In the tradition of Indian logic, this kind of demonstration is hardly found in the five-membered or three-membered demonstrative schemata, and has

2 2 Summary called the attention of some scholars, for example, Hadano, Katsura and Matilal. However, we are still dubious as to whether the vyatirekin alway has such a form. Even if it is true, the theoretical basis for vyatirekin and its historical background must be clarified. In preparation for the above investigation, I have examined the historical context of Nyāyavārttika, and clarified the framework of his descriptions of logic in the 1st chapter. Firstly I have examined the historical context of Nyāyavārttika. He sometimes criticizes Vātsyāyana s interpretations of Nyāya doctrine, and alters them. These facts imply Uddyotakara s re-systematization of Nyāya, which includes the integration of Vaiśeṣika ontology into Nyāya system. Secondly I have investigated the framework of Uddyotakara s logic. I have traced the historical development of the relation between the means of valid knowledge pramāṇa and the demonstration throughout this investigation. It also concerns the integration of vāda debate -tradition and pramāṇa the means of valid knowledge -tradition. From historical point of view, it can be classified into two groups: 1 integrating the means of valid knowledge into the demonstration, 2 integrating the demonstrative schema into the theory of inference. The view 2 might be originated with Diṅnāga. He divides the inference into inference for myself svārthānumāna and that for others parārthānumāna. The former is the inference as a means of knowledge, and the latter is the demonstration. This view finally have prevailed over the later Indian logicians, although there are some varieties of this view. Uddyotakara, however, does not adopt this view. Rather he seems to follow Vātsyāyana who would belong to 1. They maintain that each means of valid knowledge corresponds to the formula of demonstrative schema respectively. In this view, the reason is connected with inference, and the most important member of demonstration, although it differs from the view, which is advocated by Carakasaṃhitā or Asaṅga, that every means of valid knowledge are integrated into the reason. Therefore, the inference described under NS and the demonstration under NS must be treated in different way. The further treats the epistemological or psychological process of inference, the latter does the validity of demonstration, which was concluded by my investigation. The trairūpya-theory three conditions for valid reason concerns the latter. Both the inference and the demonstration, however, have the common basic structure. It is the dharma-dharmin property and its substratum -structure. I have begun 2nd chapter by examining the dharma-dharmin-structure. In the history of Nyāya school, the dharma-dharmin-structure might be used in the description of the demonstration or the debate since early times. Especially, Vātsyāyana s description of five-membered demonstrative schema is clearly based on this structure, but that of the inference does not make reference to it. The first Nyāya scholar who describes

3 3 the inference in the framework of dharma-dharmin can be placed in the period of pre-uddyotakara. Uddyotakara, succeeding to his or their thought, has established a basis for the description of inference and demonstration. In his theory, a property of reason sādhanadharma and its substratum dharmin are always perceptible, but the property of the inferential object sādhyadharma is not. I have made it possible to interpret the inference of fire in this framework. Although most of the dharma and dharmin can be interpreted as conjunctional or inherent relata saṃyogin/samavāyin, these concepts seems to be used in epistemological sense. Uddyotakara s threefold classifications of the inferences are mainly concerned with the variety of the property of inferential objects sādhyadharma. It must be especially noticed that Uddyotakara divides the property of inferential object into three types: 1 affirmative vidhīyamāna, 2 negative pratiṣidhyamāna and 3 independent svatantra. This classification makes us possible to enlarge the concept of dharma, and also to develop the possibilities of the inference and the demonstration. Secondly, I have examined the influence of the trairūpya-theory upon Uddyotakara s interpretations on Nyāyasūtra. It is well-known that he incorporated the trairūpya-theory or its developed version into the threefold classification of inference under NS He classifies the inferences into three on the basis of the developed trairūpya-theory and interpreted the three word in Nyāyasūtra as the three conditions of trairūpya-theory In this case, however, his interpretation seems to be tentative, at least one of the interpretations on Nyāsūtra. On the other hand, his interpretation on NS and 35 is clearly influenced from the trairūpya-theory, and his own fixed view. As a matter of fact, we can not find other interpretations on them. This fact that the trairūpya-theory or its developed version is used in the definition of the reason implies that Uddyotakara s logical basis for the validity of demonstration is the developed version of trairūpya-theory, because the validity of reason warrants it. In addition, the reason is directly concerned with the relation between an inferential object and its reason in the context of early Nyāya logic. The relation named avyabhicāra is used in Uddyotakara s explanation of the negative reason vyatirekin under NS He says that the affirmative reason anvayin is not based on mere association anvaya but on the infallibility of association anvayāvyabhicāra, and that the negative reason is not based on mere dissociation vyatireka but on the infallibility of dissociation vyatirekāvyabhicāra. It follows from this description that avyabhicāra is the relation similar to vyāpti pervasion, warranting the validity of reason. Besides the same view is shown under NS To clarify the conditions for valid reason, we should firstly grasp the concept of avyabhicāra and verify the conditions that follow from the definition of avyabhicāra in the sixteen classification of valid and invalid reasons, which is a check list of valid reason.

4 4 Summary It is not difficult to define the concept of avyabhicāra, since we can easily collect the descriptions concerning vyabhicāra and its antonym from Nyāyavārttika under NS the definition of doubt and the definition of savyabhicāra-pseudo reason. To sum up those descriptions, we can define S-avyabhicārin H as H is limited to S or H exists in S and its similar instances but not in others. The latter forms the conjunction of three conditions for valid reason trairūpya advocated by Buddhist logicians. It can be formulated as follows: x Hx Sx x Hx Sx (1) If S and H stand for the property of an inferential object and that of its reason respectively, the formula 1 functions as one condition for valid reason in the sixteen classification of valid and invalid reasons. The four reasons, two affirmative-negative reasons anvayavyatirekin and two affirmative reasons anvayin only fulfill this condition. We can safely say that the formula 1 is the meaning of anvayāvyabhicāra. For convenience, I will, henceforth, express formula 1 in term of H S On the other hand, there remains the meaning of vyatirekāvyabhicāra. The discussion about an unique pseudo reason asādhāraṇa-hetvāsa under NS and NS offers the key to solve this problem. An unique pseudo reason is described as follows: ad NS H is fallibly concluded with both S and non-s. ad NS H is excluded from both S and non-s. If the latter means that both S H and S H hold, vyatirekāvyabhicāra means that S H holds but S H not. This functions as the other conditions for valid reason. As a matter of fact, only the three reasons listed in the sixteen classification of valid and invalid reasons, two anvayavyatirekin and one vyatirekin fulfill this condition. To sum up our discussion, the conditions for the valid reasons are summarized as follows: anvayāvyabhicāra H S holds vyatirekāvyabhicāra S H holds but S H not Thirdly, I have examined the formulae and schemata that named vyatireka or avīta in Nyāyavārttika, which resulted in the followings: 1 The statements pratijñā are mainly expressed in negative or double-negative form. 2 The reasons have prasaṅga-form or a somewhat negative form. It follows from these facts and my logical analysis that we can regard each vyatirekin or avīta as reductio ad absurdum. In addition, I have found an example of demonstration that is called vyatirekin but not kevalavyatirekin. This means that the term vyatirekin mainly refers to the sort of demonstrative form or logical structure, but not the reason without similar instances. The reasons without similar instances are always vyatirekin, but its converse is not true.

5 5 In the 3rd chapter, I have examined the historical background of avīta. First of all I have examined some examples of classical Sāṃkhya. Having observed them cited in Jaina Dvādaśāraṃ Nayacakra and its commentary, we can guess the process of āvīta as follows: 1st stage 2nd stage 3rd stage 4th stage 5th stage 6th stage 7th stage To illustrate the absurdity in the case when the hypothetical proposition is supposed To explain the reason why the absurdity is concluded Re-illustration of the absurdity To illustrate the inapplicability to this subject The conclusion that the hypothetical proposition is negated The deduction based on elimination pariśeṣa The final conclusion In classical Sāṃkhya, especially Ṣaṣṭitantra, the following points must be noticed. The āvīta is subordinate to vīta, which is positive and consists of five formulae. The concept of pariśeṣa plays an important role in the āvīta. On the other hand, it contains prasaṅga formulation, and defined as a negation of other s view. These two points are common to Uddyotakara s vyatirekin The most significant difference between Uddyotakara s avīta and Sāṃkhya s one lies on the independency of āvīta. In the 3rd chapter of Pramāṇasamuccayavṛtti, Diṅnāga criticizes āvīta. The āvīta cited in Pramāṇasamuccayavṛtti consists three formulae, and contains a negative statement and a prasaṅga-form reason. We can regards it as an independent three membered demonstrative schema. Diṅnāga insists that the negative statement and the prasaṅga-form reason must be transformed to positive ones. He argues that the cited āvīta does not fulfill the first condition for valid reason(pakṣadharmatā: being a property of inferential object), and that the association does not hold in some cases. Uddyotakara solves these criticized points by introducing the concept of vyatirekāvyabhicāra and the negative property. Then, differing from Diṅnāga, he accepts āvīta as its original form. Uddyotakara s contribution to Indian logic is establishing a theory where prasaṅga-form demonstration is possible.