Philosophy of Space-Time in Early Jaina Thought: Quantification as a Means of Knowing
Issued Date: 27 Dec 2017
Abstract
The aim of this article is to bring to light the determining role played by quantification for early Jain monastic intellectuals. Jaina philosophy of space-time attempts to fix in a finely elaborated numerical structure the model of the Universe and the whole system of reality. In discussions about the sophisticated mathematical practices characterizing Jaina sources, the achievements realized by highly elaborate formulae have been variously emphasized. An aspect that has been thus far disregarded by historiography is the reasoning behind mathematical modes of enquiry. Therefore, there is a need to investigate the relationship between the way Jaina thinkers expounded philosophical issues and the use of quantifying procedures. Everything imaginable that could be quantified was computed: the numbers of individuals among different kinds of beings in the various regions of the three worlds, the extent of their lifespans, the volumes of space occupied by living beings of various shapes, and other matters. I shall argue that in Jainism, mathematics is a fundamental expedient of philosophical enquiry. Textual evidence from religious-philosophical works will be presented to demonstrate that, for Jainas, quantification responds to a‘quest for order’: the intellectual and spiritual ambition to recognize in nature structured and predictable patterns.
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DOI: 10.1558/rosa.32494
References
Primary Sources
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Gommatsara Karma-Kanda of Nemicandra. 2 vols. J. L. Jaini with Brahmachari Sital Prasad (trans.). The Sacred Books of the Jainas, vols. 6 and 10. Lucknow: Central Jaina Publishing House, 1927. Repr., New Delhi: Today & Tomorrow’s Printers & Publishers, 1990.
Niyamasāra (The Perfect Law) of Kundakunda. Uggar Sain with Brahmachari Sital Prasada (original text in Prakrit, with Sanskrit renderings, trans., commentaries and Intro.). Lucknow: Pandit Ajit Prasada, Central Jaina Pubhishing House, 1931.
Pañcāstikāyasāra of Kundakunda = The Building of the Cosmos. Prakrit text, Sanskrit chāyā, English commentary, etc., along with philosophical and historical introductions by A. Chakravartinayanar and the Prakrit text, Sanskrit chāyā of the same along with the Sanskrit commentary of the Amṛtacandra and various readings. A.N.Upadhye (ed. this format). New Delhi: Bharatiya Jnanpith Publication, 1975.
Pravacana-sāra of Kunda-kunda Ācārya. Together with the commentary, Tattva-dīpikā by Amṛtacandra Sūri. Barend Faddegon (English trans.), F. W. Thomas (ed. and Intro.). 1935. Repr., New York: Cambridge University Press, 2014.
Sarvārthasiddhi of Pūjyapāda. Phoolchandra Siddhāntaśāstri (Sanskrit text with Hindi trans.). 8th edn. Delhi: Bhāratīya Jñānapīṭha, 1998. S. A. Jain (English trans.), Reality. Calcutta: Vira Sasana Sangha, 1960.
Tattvārthavārtika (Rājavārtikam) of Akalaṅkadeva. 2 vols. Jñānapīṭha Mūrtidevī Jaina Granthamālā, Sanskrit Grantha, Nos. 10 and 20. Delhi: Bhāratīya Jñānapīṭha, 1953–1957. Repr. 1982.
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Tiloyapannatti (Trilokaprajñapti) of Yativṛṣabha. 3 vols. Dashrath Jain and P. C. Jain (trans.). In Acharya Yati Brishabha’s Tiloya Pannatti. Delhi: Jain Granthāgār, 2012.
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Uttarādhyayana-sūtra with the Ṭīkā of Lakṣmīvallabhagaṇi. 2 vols. Ahmedabad: Śāradā Prakāśana Kendra, 1984. Rājendra Muni Śāstrī (Hindi trans. and annotation). Jināgama Granthamālā, No. 19. Beawar: Āgama Prakāśan Samiti, 1984.
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Cort, John E. 2001. Jains in the World. Religious Values and Ideology in India. New York: Oxford University Press.
—2009. ‘The Cosmic Man and the Human Condition.’ In Granoff 2009a: 34–47.
Datta, Bibhutibhushan. 1935. ‘Mathematics of Nemicandra.’ The Jaina Antiquary 1 (2): 25–44.
—1993 [1932]. Ancient Hindu Geometry: The Science of the Sulba. New Delhi: Cosmo Publications.
Datta, Bibhutibhushan, and Avadhesh Narayan Singh. 1962 [1935]. History of Hindu Mathematics: A Source Book. 2 vols. Bombay: Asia Publishing House.
Dundas, Paul. 2005. ‘Jain Cosmology.’ In Lindsay Jones (ed.), Encyclopedia of Religion: 3.2022–26. 2nd edn. Detroit: Thomson Gale.
—2007. History, Scripture and Controversy in a Medieval Jain Sect. London: Routledge.
Glasenapp, Helmuth von. 1942. The Doctrine of Karman in Jain Philosophy. English trans. of Die Lehre vom Karma in der Philosophie der Jainas (Leipzig: Otto Harrassowitz 1915) by G. Barry Gifford, rev. the Author, and ed. Hiralal R. Kapadia. Bombay: Bai Vijibhai Jivanlal Panalal Charity Fund.
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Salvation. Delhi: Motilal Banarsidass. (Jainismus, eine Indische Erlösungsreligion. Trans. Shridhar B. Shrotri.)
Granoff, Phyllis (ed.) 2009a. Victorious Ones: Jain Images of Perfection, New York: Ahmedabad: Ocean Township, NJ: Rubin Museum of Art Mapin; Grantha.
Granoff, Phyllis. 2009b. ‘Contemplating the Jain Universe: Visions of Order and Chaos.’ In Granoff 2009a: 48–63.
Gupta, R. C. 1992a. ‘Jaina Cosmography and Perfect Numbers.’ Arhat Vacana 4: 69–94.
—1992b. ‘The First Innumerable Number in Jaina Mathematics.’ Gaṇita Bhāratī 14: 11–24.
Hanaki, Taiken (trans.). 1970. Aṇuogaddārāiṃ. Vaishali (Muzaffarpur), Bihar: Research Institute of Prakrit, Jainology and Ahimsa.
Hegewald, Julia A. B. 2000. ‘Oceans, Islands and Sacred Mountains: Representations of Cosmic Geography in Jaina Art and Architecture.’ Cosmos 16 (1) 2000: 3–43.
Jadhav, Dipak. 2015. ‘A Specific Rule in India for Common Difference as Found in the Gommaṭasāra of Nemicandra (c. 981).’ International Journal of Jaina Studies (Online) 11 (2): 1–21.
Jaini, Padmanabh S. 1980a. The Jaina Path of Purification. Berkeley: University of California Press.
—1980b. ‘Karma and the Problem of Rebirth in Jainism.’ In Wendy Doniger O’Flaherty (ed.), Karma and Rebirth in Classical Indian Traditions: 217–38. Berkeley: University of California Press.
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Krümpelmann. K. 2006. ‘The Sthānāṅgasūtra an Encyclopaedic Text of the Vetāmbara Canon.’ International Journal of Jaina Studies (Online) 2 (2): 1–13.
Malvania, Dalsukh, and Jayendra Soni (eds.). 2007. Encyclopaedia of Indian Philosophies, vol. 10: Jain Philosophy (Part I). Delhi: Motilal Banarsidass.
Morice-Singh, Catherine. 2015. ‘Mathématiques et cosmologie Jaina: Nombres et algorithmes dans le Gaṇitasārasaṃgraha et la Tiloyapaṇṇattī.’ PhD dissertation, Universite Sorbonne Nouvelle, Paris 3.
Ohira, Suzuko. 1994. A Study of the Bhagavatīsūtra: A Chronological Analysis. Ahmedabad: Prakrit Text Society 28.
Petrocchi, Alessandra. 2015. ‘A New Theoretical Approach to Sample Problems and Deductive Reasoning in Sanskrit Mathematical Texts.’ Journal of the British Society for the History of Mathematics 30 (1) 2–19. https://doi.org/10.1080/17498430.2014.976805
—2016. ‘Early Jaina Cosmology, Soteriology, and Theory of Numbers in the Aṇuogaddārāiṃ: An Interpretation.’ Journal of Indian Philosophy 45 (2): 233–55. https://doi.org/10.1007/s10781-016-9305-z
Plofker, Kim. 2007. ‘Mathematics in India.’ In Victor J. Katz (ed.), A Sourcebook in the Mathematics of Egypt, Mesopotamia, China, India, and Islam: 385–514. Princeton, NJ: Princeton University Press.
—2009. ‘The Mathematics of the Jain Cosmos.’ In Granoff 2009a: 64–69.
Satinsky, Ruth. 2015. ‘What Can the Lifespans of Ṛṣabha, Bharata, Śreyāṃsa, and Ara Tell Us about the History of the Concept of Mount Meru?’ International Journal of Jaina Studies (Online) 11 (1): 1–24.
Schubring, Walther. 2000 [1935, 1962]. The Doctrine of the Jainas Described after the Old Sources. Trans. from rev. German edn. by Wolfgang Beurlen with Three Indices enlarged and added by Willem Bollée and Jayandra Soni. 2nd rev. edn. Delhi: Motilal Banarsidas (Lala Sundarlal Jain Research Series 15).
Sen, S. N., and A. K. Bag. 1983. The Śulbasūtras. New Delhi: Indian National Science Academy.
Shah, U. P., and M. A. Dhaky (eds.). 1975. Aspects of Jaina Art and Architecture. Ahmedabad: Gujarat State Committee for the Celebration of the 2500th Anniversary of Bhagavan Mahavira Nirvana.
Srinivasiengar, C. N. 1967. The History of Ancient Indian Mathematics. Calcutta: World Press.
Thomson, William. 1891. ‘Electrical Units of Measurement.’ Popular Lectures and Addresses 1: 25–88. London: Macmillan.
Wiley, Kristi L. 1999. ‘Gotra Karma: A Contrast in Views.’ In N. K. Wagle and Olle Qvarnström (eds.), Approaches to Jaina Studies: Philosophy, Logic, Rituals and Symbols: 113–30. Toronto: University of Toronto, Centre for South Asian Studies.
—2000. ‘Aghātiyā Karmas: Agents of Embodiment in Jainism.’ PhD dissertation, University of California, Berkeley.
—2003. ‘The Story of King Śreṇika: Binding and Modification of Āyu Karma.’ In Olle Qvarnström (ed.), Jainism and Early Buddhism: Essays in Honor of Padmanabh S. Jaini: 337–58. Fremont, CA: Asian Humanities Press.
Aṇuogaddārāim. M. Puṇyavijaya, D. Mālavaṇiyā, and A. M. Bhojaka (eds.). Siridevavāyagaviraiyam Nandisuttam: Siriajjarakkhiyatheraviraiyāim Aṇuogaddārāim ca. Bambaī: Śrī Mahāvīra Jaina Vidyālaya, 1968.
Dravyasaṃgraha by Nemichandra Siddhānta-chakravartī, with a commentary by Brahma-deva. Sarat Chandra Ghoshal (ed., intro., trans., and English Commentary). Kumar: Devendra Prasada, 1917.
Gaṇita-sāra-sangraha of Mahāvīrācārya. M. Raṅgācārya (trans.). Madras: Printed by the Superintendent, Government Press, 2011 [1912].
Gommatsara Jiva-kanda of Nemicandra. J. L. Jaini with Brahmachari Sital Prasad (trans.). The Sacred Books of the Jainas, vol. 5. Lucknow: Central Jaina Publishing House, 1927. Repr., New Delhi: Today & Tomorrow’s Printers & Publishers, 1990.
Gommatsara Karma-Kanda of Nemicandra. 2 vols. J. L. Jaini with Brahmachari Sital Prasad (trans.). The Sacred Books of the Jainas, vols. 6 and 10. Lucknow: Central Jaina Publishing House, 1927. Repr., New Delhi: Today & Tomorrow’s Printers & Publishers, 1990.
Niyamasāra (The Perfect Law) of Kundakunda. Uggar Sain with Brahmachari Sital Prasada (original text in Prakrit, with Sanskrit renderings, trans., commentaries and Intro.). Lucknow: Pandit Ajit Prasada, Central Jaina Pubhishing House, 1931.
Pañcāstikāyasāra of Kundakunda = The Building of the Cosmos. Prakrit text, Sanskrit chāyā, English commentary, etc., along with philosophical and historical introductions by A. Chakravartinayanar and the Prakrit text, Sanskrit chāyā of the same along with the Sanskrit commentary of the Amṛtacandra and various readings. A.N.Upadhye (ed. this format). New Delhi: Bharatiya Jnanpith Publication, 1975.
Pravacana-sāra of Kunda-kunda Ācārya. Together with the commentary, Tattva-dīpikā by Amṛtacandra Sūri. Barend Faddegon (English trans.), F. W. Thomas (ed. and Intro.). 1935. Repr., New York: Cambridge University Press, 2014.
Sarvārthasiddhi of Pūjyapāda. Phoolchandra Siddhāntaśāstri (Sanskrit text with Hindi trans.). 8th edn. Delhi: Bhāratīya Jñānapīṭha, 1998. S. A. Jain (English trans.), Reality. Calcutta: Vira Sasana Sangha, 1960.
Tattvārthavārtika (Rājavārtikam) of Akalaṅkadeva. 2 vols. Jñānapīṭha Mūrtidevī Jaina Granthamālā, Sanskrit Grantha, Nos. 10 and 20. Delhi: Bhāratīya Jñānapīṭha, 1953–1957. Repr. 1982.
Tattvārtha-sūtra of Umāsvāti. Nathmal Tatia (English trans.), Tattvārtha Sūtra: That Which Is. London: Harper Collins, 1994.
Tiloyapannatti (Trilokaprajñapti) of Yativṛṣabha. 3 vols. Dashrath Jain and P. C. Jain (trans.). In Acharya Yati Brishabha’s Tiloya Pannatti. Delhi: Jain Granthāgār, 2012.
Trilokasāra (Trailokyasāra) of Nemicandra. Prakrit text, English translation and commentary. Laxmi Chandra Jain with Prabha Jain (eds.). In The Exact Sciences in the Karma Antiquity, vol. 2: Mathematical Contents of the Trilokasāra (The Essential Information about the Three Universes). Jabalpur: Sanjay Kumar Jain, 2003.
Ṭhāṇaṃgasuttaṃ and Samavāyaṃgasuttaṃ. M. Jambūvijaya (ed.). Jaina-Āgama - Series 3. Bombay: Śrī Mahāvīra Jaina Vidyālaya, 1985.
Uttarādhyayana-sūtra with the Ṭīkā of Lakṣmīvallabhagaṇi. 2 vols. Ahmedabad: Śāradā Prakāśana Kendra, 1984. Rājendra Muni Śāstrī (Hindi trans. and annotation). Jināgama Granthamālā, No. 19. Beawar: Āgama Prakāśan Samiti, 1984.
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Appleton, Naomi. 2014. Narrating Karma and Rebirth: Buddhist and Jain Multi-Life Stories. Cambridge: Cambridge University Press.
Balcerowicz, Piotr, and Karl H. Potter (eds.). 2013. Encyclopaedia of Indian Philosophies, vol. 14: Jain Philosophy (Part II). Delhi: Motilal Banarsidass.
Bossche, Frank van den. 2007. Elements of Jaina Geography: The Jambūdvīpasaṃgrahaṇī of Haribhadra Sūri. Critically ed. and trans. with the commentary of Prabhānanda Sūri. Delhi: Motilal Banarsidass.
Caillat, Colette, and Ravi Kumar. K. R. Norman (trans.). 1981. The Jaina Cosmology. Basel and Bombay: R. Kumar and Jaico Publishing House.
Cort, John E. 2001. Jains in the World. Religious Values and Ideology in India. New York: Oxford University Press.
—2009. ‘The Cosmic Man and the Human Condition.’ In Granoff 2009a: 34–47.
Datta, Bibhutibhushan. 1935. ‘Mathematics of Nemicandra.’ The Jaina Antiquary 1 (2): 25–44.
—1993 [1932]. Ancient Hindu Geometry: The Science of the Sulba. New Delhi: Cosmo Publications.
Datta, Bibhutibhushan, and Avadhesh Narayan Singh. 1962 [1935]. History of Hindu Mathematics: A Source Book. 2 vols. Bombay: Asia Publishing House.
Dundas, Paul. 2005. ‘Jain Cosmology.’ In Lindsay Jones (ed.), Encyclopedia of Religion: 3.2022–26. 2nd edn. Detroit: Thomson Gale.
—2007. History, Scripture and Controversy in a Medieval Jain Sect. London: Routledge.
Glasenapp, Helmuth von. 1942. The Doctrine of Karman in Jain Philosophy. English trans. of Die Lehre vom Karma in der Philosophie der Jainas (Leipzig: Otto Harrassowitz 1915) by G. Barry Gifford, rev. the Author, and ed. Hiralal R. Kapadia. Bombay: Bai Vijibhai Jivanlal Panalal Charity Fund.
—1999. Jainism: An Indian Religion of
Salvation. Delhi: Motilal Banarsidass. (Jainismus, eine Indische Erlösungsreligion. Trans. Shridhar B. Shrotri.)
Granoff, Phyllis (ed.) 2009a. Victorious Ones: Jain Images of Perfection, New York: Ahmedabad: Ocean Township, NJ: Rubin Museum of Art Mapin; Grantha.
Granoff, Phyllis. 2009b. ‘Contemplating the Jain Universe: Visions of Order and Chaos.’ In Granoff 2009a: 48–63.
Gupta, R. C. 1992a. ‘Jaina Cosmography and Perfect Numbers.’ Arhat Vacana 4: 69–94.
—1992b. ‘The First Innumerable Number in Jaina Mathematics.’ Gaṇita Bhāratī 14: 11–24.
Hanaki, Taiken (trans.). 1970. Aṇuogaddārāiṃ. Vaishali (Muzaffarpur), Bihar: Research Institute of Prakrit, Jainology and Ahimsa.
Hegewald, Julia A. B. 2000. ‘Oceans, Islands and Sacred Mountains: Representations of Cosmic Geography in Jaina Art and Architecture.’ Cosmos 16 (1) 2000: 3–43.
Jadhav, Dipak. 2015. ‘A Specific Rule in India for Common Difference as Found in the Gommaṭasāra of Nemicandra (c. 981).’ International Journal of Jaina Studies (Online) 11 (2): 1–21.
Jaini, Padmanabh S. 1980a. The Jaina Path of Purification. Berkeley: University of California Press.
—1980b. ‘Karma and the Problem of Rebirth in Jainism.’ In Wendy Doniger O’Flaherty (ed.), Karma and Rebirth in Classical Indian Traditions: 217–38. Berkeley: University of California Press.
Johnson, William J. 1995. Harmless Souls: Karmic Bondage and Religious Change in Early Jainism with Special Reference to Umāsvāti and Kundakunda. Delhi: Motilal Banarsidass Publishers.
Kāpadīā, Hiralal Rasikdas. 1941. A History of the Canonical Literature of the Jainas. Gopipura, Surat: Hiralal Rasikdas Kapadia.
Kirfel, Willibald. 1920. Die Kosmographie der Inder: Nach den Quellen dargestellt. Bonn and Leipzig: K. Schroeder.
Krümpelmann. K. 2006. ‘The Sthānāṅgasūtra an Encyclopaedic Text of the Vetāmbara Canon.’ International Journal of Jaina Studies (Online) 2 (2): 1–13.
Malvania, Dalsukh, and Jayendra Soni (eds.). 2007. Encyclopaedia of Indian Philosophies, vol. 10: Jain Philosophy (Part I). Delhi: Motilal Banarsidass.
Morice-Singh, Catherine. 2015. ‘Mathématiques et cosmologie Jaina: Nombres et algorithmes dans le Gaṇitasārasaṃgraha et la Tiloyapaṇṇattī.’ PhD dissertation, Universite Sorbonne Nouvelle, Paris 3.
Ohira, Suzuko. 1994. A Study of the Bhagavatīsūtra: A Chronological Analysis. Ahmedabad: Prakrit Text Society 28.
Petrocchi, Alessandra. 2015. ‘A New Theoretical Approach to Sample Problems and Deductive Reasoning in Sanskrit Mathematical Texts.’ Journal of the British Society for the History of Mathematics 30 (1) 2–19. https://doi.org/10.1080/17498430.2014.976805
—2016. ‘Early Jaina Cosmology, Soteriology, and Theory of Numbers in the Aṇuogaddārāiṃ: An Interpretation.’ Journal of Indian Philosophy 45 (2): 233–55. https://doi.org/10.1007/s10781-016-9305-z
Plofker, Kim. 2007. ‘Mathematics in India.’ In Victor J. Katz (ed.), A Sourcebook in the Mathematics of Egypt, Mesopotamia, China, India, and Islam: 385–514. Princeton, NJ: Princeton University Press.
—2009. ‘The Mathematics of the Jain Cosmos.’ In Granoff 2009a: 64–69.
Satinsky, Ruth. 2015. ‘What Can the Lifespans of Ṛṣabha, Bharata, Śreyāṃsa, and Ara Tell Us about the History of the Concept of Mount Meru?’ International Journal of Jaina Studies (Online) 11 (1): 1–24.
Schubring, Walther. 2000 [1935, 1962]. The Doctrine of the Jainas Described after the Old Sources. Trans. from rev. German edn. by Wolfgang Beurlen with Three Indices enlarged and added by Willem Bollée and Jayandra Soni. 2nd rev. edn. Delhi: Motilal Banarsidas (Lala Sundarlal Jain Research Series 15).
Sen, S. N., and A. K. Bag. 1983. The Śulbasūtras. New Delhi: Indian National Science Academy.
Shah, U. P., and M. A. Dhaky (eds.). 1975. Aspects of Jaina Art and Architecture. Ahmedabad: Gujarat State Committee for the Celebration of the 2500th Anniversary of Bhagavan Mahavira Nirvana.
Srinivasiengar, C. N. 1967. The History of Ancient Indian Mathematics. Calcutta: World Press.
Thomson, William. 1891. ‘Electrical Units of Measurement.’ Popular Lectures and Addresses 1: 25–88. London: Macmillan.
Wiley, Kristi L. 1999. ‘Gotra Karma: A Contrast in Views.’ In N. K. Wagle and Olle Qvarnström (eds.), Approaches to Jaina Studies: Philosophy, Logic, Rituals and Symbols: 113–30. Toronto: University of Toronto, Centre for South Asian Studies.
—2000. ‘Aghātiyā Karmas: Agents of Embodiment in Jainism.’ PhD dissertation, University of California, Berkeley.
—2003. ‘The Story of King Śreṇika: Binding and Modification of Āyu Karma.’ In Olle Qvarnström (ed.), Jainism and Early Buddhism: Essays in Honor of Padmanabh S. Jaini: 337–58. Fremont, CA: Asian Humanities Press.
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