It is believed in the West that logic began with Aristotle and that logic is universal. The core of Western thought – including present‐day formal mathematics and the philosophy of science – is premised on the belief that logical truths are universal, that they are necessary truths, and that logical deduction is certain and infallible. These beliefs about logic, however, are untenable, both historically and philosophically, in a larger picture which takes the rest of the world into account.
Philosophically, present‐day formal logic, like the twelfth century BCE text, Organon, attributed to Aristotle, supposes that deduction relates to two‐valued logic. In such a logic, an affirmation A conjoined with its negation (∼A) makes a contradictory pair, from which any conclusion B whatsoever can be validly inferred by the rule of inference known as reductio ad absurdum: (A ∧ ∼A ⇒ B), to put it symbolically, with “∼” denoting “not,” “∧” denoting “and,” and “⇒” denoting the usual (material)...
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Dīgha Nikāya. (Hindi trans.) Rahul Sānkrityāyana and Jagdish Kāshyapa. Delhi: Parammitra Prakashan, 2000; (English trans.) Maurice Walshe. Boston: Wisdom Publication, 1995.
For Nāgārjuna's use of the logic of four alternatives, see
Mūlamādhyamakkārikā. trans. David J. Kalupahana. Nāgārjuna. New York: SUNY Press, 1986; trans. Kenneth K. Inada. New Delhi: Sri Satguru Publications, 1993.
Dignaga's Hetucakra (The Wheel of Reason). trans. D. Chatterji. Hetucakranirnaya. Indian Historical Quarterly 9 (1933): 511–4.
For a different translation using Chinese texts, see
Chi, R. S. Y. Buddhist Formal Logic. London: The Royal Asiatic Society, 1969; Reprint. Delhi: Motilal Banarsidass, 1984.
For a quick exposition of the various other logics that were prevalent at the time of the Buddha, a good secondary source is
Baruah, B. M. A History of Pre‐Buddhistic Indian Philosophy. Calcutta: University of Calcutta, 1921; Reprint. Delhi: Motilal Banarsidass, 1970.
Haldane's account is in a journal of statistics, because of the attempt to relate syādavāda to the foundations of probability theory. See
Haldane, J. B. S. The Syadavada System of Predication. Sankhya, Indian Journal of Statistics 18 (1955): 195–200.
An interesting account of some attacks on the syādavāda position in Indian tradition, and how this helps to distinguish between the positions of syādavāda and Sañjaya the Sceptic, see
Pandya, Vijaya. Refutation of Jaina Darsana by Sankaracarya… Ed. V. N. Jha. Jain Logic and Epistemology. New Delhi: Satguru Publications, 1997.
Various books attributed to Aristotle are in
Organon. The Works of Aristotle. trans. E. Edghill, et al. Vol. 1. Chicago: Encyclopaedia Britannica, 1995.
The standard accounts of many‐valued and temporal logics are in
Prior, A. N. Past, Present and Future. Oxford: Clarendon, 1967.
Rescher, N. Many‐Valued Logic. New York: McGraw Hill, 1969.
Rescher, N. and A. Urquhart. Temporal Logic. Wien: Springer, 1971.
On the role of the empirical in mathematics, see
Proclus. A Commentary on the First Book of Euclid's Elements. trans. G. R. Morrow. Princeton: Princeton University Press, 1970. (The original source is in Friedlein, G. Procli Diadochi in primum Euclidis Elementorum commentarii. Leipzig: B. G. Teubner, 1873.)
Raju, C. K. Computers, Mathematics Education, and the Alternative Epistemology of the Calculus in the Yuktibhāṣā. Philosophy East and West 51.3 (2001): 325–62.
The concession about logic while dealing with the notion of cause is in
Al Ghazālī. Tahāfut al‐Falāsifā. trans. S. A. Kamali. Lahore: Pakistan Philosophical Congress, 1958.
For the structured‐time interpretation of quantum mechanics, see
Raju, C. K. Quantum Mechanical Time. Time: Towards a Consistent Theory. Dordrecht: Kluwer Academic, 1994.
The standard, but somewhat dated, account of Indian logic is in
Vidyabhuṣan, S. C. A History of Indian Logic. Calcutta: Calcutta University, 1921; Reprint. New Delhi: Munshiram Manoharlal, 1977.
A good starting point for the Navya–Nyaya logic is
Matilal, B. K. The Navya–Nyāya Doctrine of Negation. Cambridge, MA: Harvard University Press, 1968.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg New York
About this entry
Cite this entry
Raju, C.K. (2008). Logic. In: Selin, H. (eds) Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-4425-0_8706
Download citation
DOI: https://doi.org/10.1007/978-1-4020-4425-0_8706
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-4559-2
Online ISBN: 978-1-4020-4425-0
eBook Packages: Humanities, Social Sciences and Law