Abstract
The present chapter aims to clarify the logical structure of the fundamental concept of Indian logic for inference, i.e., invariable concomitance or pervasion (vyāpti), with the help of a new device, i.e., diagrams. Gaṅgeśa, who was active in the fourteenth century and the consolidater of New Logic (Navya-Nyāya), provided 21 provisional definitions of this concept. His definitions greatly influenced later Indian logic. Past research has illustrated that the third and fifth definitions are logically equivalent, but has not claimed that their logical structure is the same or not. As a result, it has failed to explain why Gaṅgeśa presented both definitions. The chapter attempts to illustrate that they differ in logical structure in spite of being equivalent to one another. This task has been done with the diagrams. The chapter also demonstrates that this device, as well as symbolic notations, helps us present logical structure of other concepts.
I am delighted to be contributing to the present book on the thought of Professor J.L. Shaw. He has offered me his constant encouragement in my study of Sanskrit texts and Indian philosophy. He has devoted his life to research on Western and Indian philosophies and the comparative study of both. It is not an easy task for me to review or refer to his research directly, but here I would like to address a Western concept utilised in the analysis of Sanskrit texts, that concept being ‘logical structure’. Shaw, like other Western philosophers, uses notations of symbolic logic to represent the logical structure of propositions, etc., while I propose another method of representing the structure of Sanskrit expressions. This is not to say that one method is superior to the other, but that there are multiple means of accomplishing the same goal. I wish to thank Dr. Charles Pain for correcting my English.
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Notes
- 1.
On the date of Navya-Nyāya authors, see Potter and Bhattacharyya (1993, pp. 10–13). When I have not followed this work, I have given the source.
- 2.
In that chapter Gaṅgeśa lists twenty-one provisional definitions, and the twenty-second conclusive (siddhānta) definition. To this he adds eight conclusive definitions applicable to an invariable concomitance between particulars (viśeṣavyāpti).
- 3.
Ingalls (1951, p. 93) symbolises the first definition as “−o1└l − s┘P̄̄h,” but unfortunately he does not symbolise the other four. On the Sanskrit expression of this definition and its translation, see the second section of the present paper. On his system of the symbols, see Ingalls (1951, pp. 84–85).
- 4.
Staal (1988, pp. 71–72) compares his system with that of Bocheński and claims that Bocheński’s formalisation can be transferred to his formalisation. He states that Bocheński’s formulae for the five definitions can be rewritten as his formulae, and that the former formulae also indicate that the third and fifth definitions are equivalent. On his purpose of using symbols, Staal (p. 17) says “I was careful not to introduce concepts of western logic into my language but symbols that stand in one-to-one correspondence to the original expressions. This symbolism was introduced in such a manner that it became possible to automatically replace Sanskrit expressions by symbols and visa versa.” Hence, it may not be proper to refer to Staal here as one who uses symbols to express the logical structure of Sanskrit expressions.
- 5.
nāpi sādhyāsāmānādhikaraṇyānadhikaraṇa-tvaṃ sādhyavaiyadhikaraṇyānadhikaraṇatvaṃ vā, tadubhayam api sādhyānadhikaranānadhikaraṇatvaṃ tac ca tatra yatkiñcitsādhyānanādhikaraṇādhikaraṇe dhūme cāprasiddham. (Trans.: [Invariable concomitance is] neither (1) the state [possessed by a probans] of not being the locus of the property of having no common locus with the probandum nor (2) the state [possessed by a probans] of not being the locus of the property of having a locus different from that of the probandum. Both states [are equivalent to] the state [possessed by a probans] of not having for a locus a non-locus of the probandum. This state is not obtained [in a probans] in the case [of the inference whose probandum is unnegatable] and in smoke which has for a locus the non-locus of one of the probanda [in the valid inference that the mountain possesses fire because it possesses smoke].) For an analysis of this section, see Wada (1995 b, pp. 279–282; 2007, pp. 69–73).
- 6.
There is another possibility: though Gaṅgeśa considered both definitions to have the same structure, he listed them separately. I will refer to this possibility in the concluding section of the present paper.
- 7.
- 8.
- 9.
Goekoop (1967, pp. 30–34) provides the transformation of the formula for invariable concomitance to these three formulae.
- 10.
Here the term ‘dharma’ is used in a limited sense. In a wider sense it means a component of the world, such as a thing, a property, a relation, or a state. On this, see Tachikawa (1981, p. 3).
- 11.
In Navya-Nyāya the property-possessor is not always the locus of its property.
- 12.
They are ‘viśeṣaṇa’ (qualifier), ‘nirūpaka’ (describer), and ‘avacchedaka’ (delimitor). On these concepts, see Wada (1990, pp. 45–98). On how these three concepts are related to one another, see Wada (1990, pp. 59, 66, 76). On how the latter two concepts are related to each other, see Wada (2001, pp. 521–527; 2007, pp. 27–35).
- 13.
- 14.
The present paper does not require us to discuss the relation between absence and its counterpositive (pratiyogin), so I will refer to this relation here only briefly. According to the Navya-Nyāya, absence functions as the describer of its counterpositive. A describer is a relatum which is designated as a factor determining the function of the other relatum. In the case of absence, something can be regarded as a counterpositive by postulating absence, so absence is the explaining factor of what is its counterpositive. For a more detailed explanation of describer, see Wada (1990, pp. 66–80; 2001, pp. 524–526).
- 15.
The discussion by these two commentators is found in the following texts respectively: ‘Tattvacintāmāṇiprabhā,’ p. 61,14–16) and ‘Tattvacintāmaṇiprakāśa,’ pp. 43,5–44,9.
- 16.
nanu tadanyonyābhāvādhārādhikaraṇatvābhāva iti spaṣṭam eva paunaruktyam. (Trans.: Indeed, [the fifth definition is:] an absence [possessed by a probans] of the state of having a locus for a container of a mutual absence of that [possessor of the probandum, and this is] nothing but an apparent repetition [of the third definition].) Since this Sanskrit sentence does not explicitly mention these two definitions, it is from the context that I have read the sentence as expressing the relation between them. For an analysis of the above sentence of the TCS, see Wada (2004, p. 54 text 5b). On an analysis of the whole “Five difinitions of Invariable Concomitance Section” of the TCS, see Wada (2003, 2004).
- 17.
- 18.
na caivaṃ pañcamābhedaḥ, tatra sādhyavattvtāvacchinna-pratiyogikānyonyābhāvattvena praveśaḥ atra tu tādṛsānyonyābhāvādhikaraṇatvenety adhikaraṇatvapraveśāpraveśābhyām eva bhedāt. akhaṇḍābhāvaghaṭakatayā ca nādhikaraṇatvāṃśasya vaiyadhikaraṇyam iti na ko ’pi doṣa iti dik. For a translation of this, see Ingalls (1951, p. 136). The third definition is interpreted by Mathurānātha as “an absence [possessed by a probans] of occurrence described by the locus of a mutual absence whose counterpositive is the possessor of the probandum” (sādhyavat-pratiyogikānyonyābhāvādhikaraṇanirūpitavṛttitvābhāvaḥ) (Ingalls 1951, p. 134 text 93.5–8]), while the fifth one is interpreted as “an absence [possessed by a probans] of occurrence in the possessor of an absence whose counterpositiveness is delimited by the state of being the possessor of the probandum and is described by a mutual absence.” (anyonyābhāvanirūpitasādhyavattvāvacchinnapratiyogitākābhāvavadvṛttitvābhāvaḥ). This interpretation of the fifth definition is constructed from Mathurānātha’s commentary on the fifth, which is included in Ingalls (1951, p. 148 text 100.1–7).
- 19.
- 20.
- 21.
We can demonstrate a case in which Gaṅgeśa lists two definitions of invariable concomitance having the same structure in the “Lion and Tiger Definitions of Invariable Concomitance Section” of the TC. This means that he does not take into account only the structure of the definitions. On the Sanskrit text and translation of the section, see fn. 5.
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Wada, T. (2016). The Logical Structure of the Third and Fifth Definitions in the Vyāptipañcaka Section of Gaṅgeśa’s Tattvacintāmaṇi . In: Bilimoria, P., Hemmingsen, M. (eds) Comparative Philosophy and J.L. Shaw. Sophia Studies in Cross-cultural Philosophy of Traditions and Cultures, vol 13. Springer, Cham. https://doi.org/10.1007/978-3-319-17873-8_13
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