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George Boole’s Laws of Thought and Indian Logic
This note explores an important problem of the history of science, namely the influence of Indian logic on George Boole’s The Laws of Thought. The theories that have been proposed to explain the origins of Boole’s algebra have ignored his wife Mary’s claim that he was deeply influenced by Indian logic. This note examines this claim and argues that Boole’s focus was more than a framework for propositions and that he was trying to mathematize cognitions as is assumed in Indian logic and to achieve this, he believed an algebraic approach was the most reasonable. By exploring parallels between his work and Indian logic, we can explain several peculiarities of his algebraic system.
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- Boole, G., An Investigation of the Laws of Thought on which are Founded the Mathematical Theories of Logic and Probabilities, Dover Publications Inc., New York, USA, 1854 (reprint 1958).
- Corsi, G. and Gherardi, G., The basis of Boole’s logical theory, 2017; arXiv: 1710.01542.
- De Morgan, A., Formal Logic or The Calculus of Inference, Necessary and Probable, Taylor & Walton, London, UK, 1847.
- De Morgan, A., Trigonometry and Double Algebra, Taylor, Walton & Malbery, London, UK, 1849.
- Smith, G. C. (ed.), The Boole–De Morgan Correspondence, 1842–1864, Oxford University Press, Oxford, UK, 1982.
- Boole, M., In Boole, Mary Everest Collected Works (eds Cobham, E. M. and Dummer, E. S.), Daniel, London, UK, 1931, pp. 947–967.
- Blakely, R., Historical Sketch of Logic, H. Baillière, London, UK, 1851.
- De Morgan, A., Syllabus of a Proposed System of Logic, Walton & Malbery, London, UK, 1860.
- Boole, G., Cambridge Dublin Math. J., 1848, 3, 183–198.
- Hailperin, T., Math. Mag., 1981, 54, 172–184.
- Jevons, W. S., The Substitution of Similars, The True Principle of Reasoning, Macmillan & Co, 1869.
- Peirce, C. S., Am. J. Math., 1885, 7, 180–196.
- Vidyabhusana, S. C., A History of Indian Logic, University of Calcutta, Calcutta, 1921.
- Potter, K. H. (ed.), Indian Metaphysics and Epistemology: The Tradition of Nyaya-Vaisesika Up to Gangesa Motilal Banarsidass, Delhi and Princeton University Press, Princeton, USA, 1977.
- Kak, S., Aristotle and Gautam on Logic and Physics, 2005; arXiv:physics/0505172.
- Matilal, B. K., The Word and the World, Oxford University Press, Oxford, UK, 1990.
- Potter, K. H. and Bhattacharyya, S. (eds), Indian Philosophical Analysis: Nyaya-Vaisesika from Gangesa to Raghunatha Siromani, Motilal Banarsidass, Delhi and Princeton University Press, Princeton, USA, 1993.
- Bhattacharyya, S., Philos. East West, 1974, 24, 329–342.
- Chakrabarti, K. K., Philos. Phenomenol. Res., 1976, 36, 554–563.
- Ganeri, J., In Logic, Navya-Nyāya & applications homage to Bimal Krishna Matilal, Studies in Logic (eds Chakraborti, M. et al.), College Publications, London, 2008, vol. 15, pp. 105–138.
- Kak, S., In Logic in Religious Discourse (ed. Schumann, A.), Ontos Verlag, Frankfurt, Germany, 2009, pp. 20–33.
- Staal, F., Universals: Studies in Indian Logic and Linguistics, University of Chicago Press, Chicago, USA, 1988.
- Kak, S., In Learning as Self-Organization (eds Pribram, K. and King, J.), Lawrence Erlbaum Associates, Mahwah, NJ, USA, 1996, pp. 185–219.
- Kak, S., The Nature of Physical Reality, Mt Meru Publishing, Mississanga, Canada, 2016.
- Schrödinger, E., What is Life? and Mind and Matter, Cambridge University Press, Cambridge, UK, 1967.
- Kak, S., Found. Phys., 1999, 29, 267–279.
- Kak, S., Int. J. Theor. Phys., 2007, 46, 860–876.
- Kak, S., Matter and Mind, Mt. Meru Publishing, Mississanga, Canada, 2016.
- Heisenberg, W., Physics and Philosophy: the Revolution in Modern Science, George Allen & Unwin, London, 1971.
- Boole, G., A Mathematical Analysis of Logic, Dover Publications, New York, USA, 1847.
- Sheffer, H. M., Trans. Am. Math. Soc., 1913, 14, 481–488.
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