A contemporary reader of Buddhist scriptures is often challenged by immense numbers and long series in Indic numerals, finding them superfluous, impractical, and inscrutable. These tedious lists are the focus of the current study which is aiming at understanding the message behind those counting sequences built into teachings in Buddhist scriptures. Tracing the concrete instances of such extended reckoning took us from the Avataṃsaka to the Dàzhìdù lùn, to the Abhidharma treatise of Kātyāyanīputra’s disciples, the Mahāvibhāṣā, and the Abhidharmakośa by Sautrāntika Vasubandhu, to a later recension of the Lalitavistara sutra, to the Buddhavaṃsa, Cariyāpiṭaka, and the Buddha-apadāna in Pāli as well as their traditional commentaries, then back to the Dàzhìdù lùn which led us finally again to the Avataṃsaka. Though most of the texts we are working with are available only in Chinese translations, we look at them as edifices of the Indian literary tradition, and follow an Indian approach in our study. For each scripture we investigate the context in which the counting occurs, after which we etymologize and interpret the corresponding number-terms. On one hand, this investigation allowed us to unearth and give shape to diverse arithmetic discourses entertained by Indian sages of yore, and on the other hand it helped to throw, from a rather unexpected angle, light on different aspects of a bodhisattva’s cultivation.
目次
ABSTRACT i 摘要 iii ACKNOWLEDGEMENTS iv CONTENTS v ABBREVIATIONS 1 INTRODUCTION 2 CHAPTER 1: A HISTORY OF ANCIENT INDIAN NUMBERS THROUGH THE PRISM OF RELIGIOUS SCRIPTURES 11 1.1. Importance of Powers of Ten and Epistemological Principles Behind the Numerical Elaborations 17 1.2. Apophatic Terms and Numbers Read Through Nyāya Inference 22 CHAPTER 2: A CONCEPT OF A BODHISATTVA IN THE DÀZHÌDÙ LÙN: ABHIDHARMIC PERSPECTIVE 31 2.1. Definition of a Bodhisattva in the Dàzhìdù lùn 31 2.2. Bodhisattva Concept Amongst Disciples of Kātyāyanīputra as Related by the Dàzhìdù lùn 35 CHAPTER 3: NUMBERS AMONG DISCIPLES OF KĀTYĀYANĪPUTRA 49 3.1. Jñānaprasthāna 51 3.2. Mahāvibhāṣā 53 3.2.1. A remark on mathematical quandary behind the numerical sequences 61 3.3. The Second Counting Alternative: Traits of Mahāyāna Numbers 62 3.4. The Third Numerical System 72 3.4.1. Idiom of the third reckoning convention 74 CHAPTER 4: ABHIDHARMAKOŚA: ASAṂKHYEYA AS ONE OF SIXTY BIG NUMBERS 87 4.1. Three Asaṃkhyeya Kalpas in the Kośa 90 4.2. Asaṃkhyeya: Finite Number or Entity Beyond Wit of Counting 99 CHAPTER 5: LALITAVISTARA: ASAṂKHYEYA AS DESIGNATION OF SUPRA-MUNDANE NUMERICAL PROWESS 102 5.1. The Earliest Recension 103 5.2. Later Recensions 107 5.2.1. Locution of numerical progression 109 CHAPTER 6: ASAṄKHYEYYA IN PĀLI TRADITION 121 6.1. Asaṅkhyeyya Across Traditions: Extent of Sāriputta’s Recollection of Past Lives, and Duration of the Bodhisattva’s Cultivation 121 6.2. Asaṅkhyeyya in Pāḷi Treatises 131 6.3. Asaṅkhyeyya in the Buddhavaṃsa-Aṭṭhakathā 132 6.4. Asaṅkhyeyya in the Cariyāpiṭaka-Aṭṭhakathā 137 6.5. Asaṅkhyeyya in the Apadāna-Aṭṭhakathā 142 6.5.1. Asaṅkhiyā of Buddhas in the Buddhāpadāna-Aṭṭhakathā 147 6.6. Bridging Different Linguistic and Scholastic Conventions of the Duration of a Bodhisattva’s Cultivation 161 CHAPTER 7: BODHISATTVA AND MAHĀSATTVA ACCORDING TO THE DÀZHÌDÙ LÙN: IMMEASURABLE KALPAS OF CULTIVATION AND INFINITE SCALE OF ASPIRATION 166 7.1. Refutation of the Abhidharma Premises 166 7.2. Mahāsattva 174 CHAPTER 8: NUMBERS IN BUDDHABHADRA’S TRANSLATION OF THE AVATAṂSAKA 179 8.1. Asaṃkhyeya Chapter 181 8.2. Merit of the Initial Determination for Enlightenment Chapter 206 8.3. Gaṇḍavyūha: Bhikṣu Meghaśrī Vision of an “Ineffable Ineffables” Buddhas 212 8.4. Gaṇḍavyūha: Upāsikā Āśā’s Teaching on Giving Rise to Bodhicitta 215 8.5. Gaṇḍavyūha: Prince Indriyeśvara’s Teaching on Prominence of Counting in Bodhisattvas’ Career 218 8.6. Number-terms Subject to Translation or Transcription 221 CONCLUSION 228 BIBLIOGRAPHY 243 Primary Sources 243 Secondary Sources 243 APPENDICES 247 Appendix A: Comparative Translation of the Counting Contest in the Two Recensions of the Lalitavistara Available in Chinese 247 Appendix B: Abhidharma-type Numbers: Comparision of Number-terms in the Mahāvibhāṣā, Various Recensions of the Abhidharmakośa and the Lalitavistara 263 Appendix C: Three Types of Counting in Buddhist Scriptures: saṃkhyānaṃ, gaṇanāṃ, mudrāṃ 268 Appendix D: Cariyāpiṭaka-Aṭṭhakathā: A Traslation of an Excerpt 272 Appendix E: Mindking Bodhisattva Requests [a Teaching] on Asaṃkhyeya Chapter: A Translation of an Excerpt 277 Appendix F: Avataṃsaka-type Numbers in Different Sources 281 Appendix G: Comparative Transaltion of the Opening Section of Merit of the Initial Determination for Enlightenment Chapter 287 Appendix H: Bhikṣu Meghaśrī’s Teaching in the Gaṇḍavyūha 290 Appendix I: Upāsikā Āśā’s Teaching on Giving Rise to Bodhicitta 294 Appendix J: Indiryeśvara’s Teaching 310 Appendix K: Categorization of Numbers and Types of Infinities in Jain Scriptures 314 Appendix L: Counting in the Abhidharmakośa 317 Appendix M: Kātyāyanīputra’s Bodhisattva Doctrine Related in the Dàzhìdù lùn 321 Appendix N: Three Types of Reckoning into an Asaṃkhyeya in the Mahāvibhāṣā 324
