Linked bibliography for the SEP article "George Boole" by Stanley Burris

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Primary Literature

  • Boole, G., 1841, “Researches on the Theory of Analytical Transformations, with a special application to the Reduction of the General Equation of the Second Order,” The Cambridge Mathematical Journal, 2: 64–73. (Scholar)
  • –––, 1841, “On Certain Theorems in the Calculus of Variations,” The Cambridge Mathematical Journal, 2: 97–102. (Scholar)
  • –––, 1841, “On the Integration of Linear Differential Equations with Constant Coefficients,” The Cambridge Mathematical Journal, 2: 114–119. (Scholar)
  • –––, 1847, The Mathematical Analysis of Logic, Being an Essay Towards a Calculus of Deductive Reasoning, Originally published in Cambridge by Macmillan, Barclay, & Macmillan. Reprinted in Oxford by Basil Blackwell, 1951. (Scholar)
  • –––, 1848, “The Calculus of Logic,” The Cambridge and Dublin Mathematical Journal, 3: 183–198. (Scholar)
  • –––, 1854, An Investigation of The Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, Originally published by Macmillan, London. Reprint by Dover, 1958. (Scholar)
  • –––, 1859, A Treatise on Differential Equations, Cambridge: Macmillan. (Scholar)
  • –––, 1860, A Treatise on the Calculus of Finite Differences, Cambridge: Macmillan. (Scholar)
  • De Morgan, A., 1839, “On the foundation of algebra,” Transactions of the Cambridge Philosophical Society, VII, 174–187. (Scholar)
  • –––, 1841, “On the foundation of algebra, No. II,” Transactions of the Cambridge Philosophical Society VII, 287–300. (Scholar)
  • –––, 1847, Formal Logic: or, the Calculus of Inference, Necessary and Probable, Originally published in London by Taylor and Walton. Reprinted in London by The Open Court Company, 1926. (Scholar)
  • –––, 1966, On the Syllogism, and Other Logical Writings, P. Heath (ed.), New Haven: Yale University Press. (A posthumous collection of De Morgan's papers on logic.) (Scholar)
  • Gregory, D.F. 1839, “Demonstrations in the differential calculus and the calculus of finite differences,” The Cambridge Mathematical Journal, Vol. I, 212–222. (Scholar)
  • –––, 1839, “I.–On the elementary principles of the application of algebraical symbols to geometry,” The Cambridge Mathematical Journal, Vol. II, No. VII, 1–9. (Scholar)
  • –––, 1840, “On the real nature of symbolical algebra.” Transactions of the Royal Society of Edinburgh, 14: 208–216. Also in [Gregory 1865, pp. 1–13]. (Scholar)
  • –––, 1865, The Mathematical Writings of Duncan Farquharson Gregory, M.A., W. Walton (ed.), Cambridge, UK: Deighton, Bell. (Scholar)
  • Jevons, W.S., 1864, Pure Logic, or the Logic of Quality apart from Quantity: with Remarks on Boole's System and on the Relation of Logic and Mathematics, London: Edward Stanford. Reprinted 1971 in Pure Logic and Other Minor Works, R. Adamson and H.A. Jevons (eds.), New York: Lennox Hill Pub. & Dist. Co. (Scholar)
  • Lacroix, S.F, 1797/1798, Traité du calcul différentiel et du calcul integral, Paris: Chez Courcier. (Scholar)
  • Lagrange, J.L., 1797, Théorie des fonctions analytique, Paris: Imprimerie de la Republique. (Scholar)
  • –––, 1788, Méchanique Analytique, Paris: Desaint. (Scholar)
  • Peacock, G., 1830, Treatise on Algebra, 2nd ed., 2 vols., Cambridge: J.&J.J. Deighton, 1842/1845. (Scholar)
  • –––, 1833, “Report on the Recent Progress and Present State of certain Branches of Analysis”, In Report of the Third Meeting of the British Association for the Advancement of Science held at Cambridge in 1833, pp. 185-352. London: John Murray. (Scholar)
  • Schröder, E., 1890–1910, Algebra der Logik, Vols. I–III. Leipzig, B.G. Teubner; reprint Chelsea 1966. (Scholar)

Secondary Literature

Cited Works

  • Brown, F.W, 2009, “ George Boole's deductive system”, Notre Dame Journal of Logic, 50: 303–330. (Scholar)
  • Burris, S. and Sankappanavar, H.P., 2013, “The Horn theory of Boole's partial algebras”, The Bulletin of Symbolic Logic, 19: 97–105. (Scholar)
  • Ewald, W. (ed.), 1996, From Kant to Hilbert. A Source Book in the History of Mathematics, 2 Vols, Oxford: Oxford University Press. (Scholar)
  • Grattan-Guiness, I., 2001, The Search for Mathematical Roots, Princeton, NJ: Princeton University Press. (Scholar)
  • Hailperin, T., 1976, Boole's Logic and Probability, (Series: Studies in Logic and the Foundations of Mathematics, 85), Amsterdam, New York, Oxford: Elsevier North-Holland. 2nd edition, Revised and enlarged, 1986. (Scholar)
  • –––, 1981, “Boole's algebra isn't Boolean algebra”, Mathematics Magazine, 54: 172–184. (Scholar)
  • Jourdain, P.E.B., 1914, “The development of the theories of mathematical logic and the principles of mathematics. William Stanley Jevons”, Quarterly Journal of Pure and Applied Mathematics, 44: 113–128. (Scholar)
  • MacHale, D., 1985, George Boole, His Life and Work, Dublin: Boole Press. (Scholar)

Other Important Literature

  • Couturat, L., 1905, L'algèbre de la Logique, 2d edition, Librairie Scientifique et Technique Albert Blanchard, Paris. English translation by Lydia G. Robinson: Open Court Publishing Co., Chicago & London, 1914. Reprinted by Dover Publications, Mineola, 2006. (Scholar)
  • Dummett, M., 1959, “Review of Studies in Logic and Probability by George Boole”, Watts & Co., London, 1952, edited by R. Rhees. The Journal of Symbolic Logic, 24: 203–209. (Scholar)
  • Frege, G., 1880, “Boole's logical calculus and the concept-script”, in Gottlob Frege: Posthumous Writings, Basil Blackwell, Oxford, 1979. English translation of Nachgelassene Schriften, vol. 1, edited by H. Hermes, F. Kambartel, and F. Kaulbach, Felix Meiner, Hamburg, 1969. (Scholar)
  • Kneale, W., and M. Kneale, 1962, The Development of Logic, The Clarendon Press, Oxford. (Scholar)
  • Lewis, C. I., 1918, A Survey of Symbolic Logic, University of California Press, Berkeley. Reprinted by Dover Publications, Inc., New York, 1960. Chap. II, “The Classic, or Boole-Schröder Algebra of Logic.” (Scholar)
  • Peirce, C. S., 1880, “On the Algebra of Logic”, American Journal of Mathematics, 3: 15–57. (Scholar)
  • Smith, G. C., 1983, “Boole's annotations on The Mathematical Analysis of Logic”, History and Philosophy of Logic, 4: 27–39. (Scholar)
  • Styazhkin, N. I., 1969, Concise History of Mathematical Logic from Leibniz to Peano, Cambridge, MA: The MIT Press. (Scholar)
  • van Evra, J. W., 1977, “A reassessment of George Boole's theory of logic”, Notre Dame Journal of Formal Logic, 18: 363–77. (Scholar)
  • Venn, J., 1894, Symbolic Logic, 2d edition, Macmillan, London. Reprinted, revised and rewritten. Bronx: Chelsea Publishing Co., 1971. (Scholar)
  • Whitney, H., 1933, “Characteristic functions and the algebra of logic”, Annals of Mathematics, Second Series, 34: 405–414. (Scholar)

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