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**The Mathematical and Physical Theory of Rational Human Intelligence: Complete Empirical-Digital Properties; Full Electrochemical-Mechanical Model (Part I: Mathematical Foundations)** ()

The design of this paper is to present the first
installment of a complete and final theory of rational human intelligence. The
theory is *mathematical* in the
strictest possible sense. The mathematics involved is strictly digital—not
quantitative in the manner that what is usually thought of as mathematics is
quantitative. It is anticipated at this time that the exclusively digital nature
of rational human intelligence exhibits four flavors of digitality, apparently
no more, and that each flavor will require a lengthy study in its own right. (For more information,please refer to the PDF.)

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*Advances in Pure Mathematics*, Vol. 3 No. 5, 2013, pp. 491-561. doi: 10.4236/apm.2013.35071.

Conflicts of Interest

The authors declare no conflicts of interest.

[1] | L. Depuydt, “Questions and Related Phenomena in Coptic and in General: Final Definitions Based on Boole’s Laws of Thought,” In: J. E. Goehring and J. E. Timbie, Eds., The World of Ancient Christianity, The Catholic University of America Press, Washington DC, 2007, pp. 72-94. |

[2] | L. Depuydt, “The Other Mathematics,” Gorgias Press, Piscataway, 2008, pp. 307-321. |

[3] | L. Depuydt, “The Conjunctive in Egyptian and Coptic: Towards a Final Definition in Boolean Terms,” In: C. G. Haberl, Ed., Proceedings of the 35th Annual Meeting of the North American Conference on Afroasiatic Linguistics (NACAL 35), Cambridge Scholars Publishing, Newcastle Upon Tyne, 2009, pp. 13-30. |

[4] | L. Depuydt, “Towards the Full Digitalization of Grammar: The Case of the Egyptian and Coptic Nominal Sentence,” Lingua Aegyptia, Vol. 17, 2010, pp. 27-50. |

[5] | L. Depuydt, “From ‘My Body’ to ‘Myself’ to ‘Me Too’: Philological and Digital Analysis of a Triple Shift in Egyptian,” Journal of the American Research Center in Egypt, Vol. 45, 2009, pp. 247-290. |

[6] | L. Depuydt, “Zur unausweichlichen Digitalisierung der Sprachbetrachtung: ‘allein’, ‘anderer’, ‘auch’, ‘einziger’, ‘(seiner)seits’, und ‘selbst’ als digitales Wortfeld im Agyptisch-Koptischen und im Allgemeinen,” In: A. I. Blobaum, K. Butt and I. Kohler, Eds., Lexical Fields, Semantics and Lexicography, Aegyptiaca Monasteriensia, Vol. 7, Shaker Verlag, Aachen, 2011, pp. 5-38. |

[7] | J. C. Maxwell, “Matter and Motion,” Dover Publications Inc., New York, 1991 (first published in 1877). |

[8] | J. C. Maxwell, “A Treatise on Electricity and Magnetism,” 2 Vols., 3rd Edition, Clarendon Press, Oxford, 1904 (1st Edition: 1873), vol. 1, p. xi. |

[9] | G. Boole, “An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities,” Walton and Maberly, London, 1854, pp. 24-27. |

[10] | J. Venn, “Symbolic Logic,” 2nd Edition, Macmillan and Co., London and New York, 1894, pp. 453-476. |

[11] | J. Venn, “Symbolic Logic,” 2nd Edition, Macmillan and Co., London and New York, 1894, pp. 499-500. |

[12] | G. W. Leibniz, “Opera Philosophica Quae Extant Latina Gallica Germanica Omnia,” Scientia, Aalen, 1959 (facsimile of the original edition of 1840, supplemented with additional texts and a preface by R. Vollbrecht), p. 96. |

[13] | G. Boole, “An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities,” Walton and Maberly, London, 1854, p. 400. |

[14] | L. Carroll, “Symbolic Logic,” edited, with annotations and an introduction, by W. W. Bartley, III, Clarkson N. Potter, Inc., New York, 1977 (original edition of Part I: 1896; of Part II: 1977), Part I, p. 150, No. 60 (Example), p. 180, No. 60 (Solution). |

[15] | Ch. Petzold, “The Hidden Language of Computer Hardware and Software,” Microsoft Press, Redmond, Washington, 2000, p. 87. |

[16] | L. Depuydt, “Synchrony and Diachrony: The Speaker/Observer Dichotomy,” Gottinger Beitrage zur Sprachwissenschaft, Vol. 5, 2001, pp. 21-31. |

[17] | G. Boole, “An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities,” Walton and Maberly, London, 1854. |

[18] | Ch. Petzold, “The Hidden Language of Computer Hardware and Software,” Microsoft Press, Redmond, Washington, 2000, p. 87. |

[19] | Ch. Petzold, “The Hidden Language of Computer Hardware and Software,” Microsoft Press, Redmond, Washington, 2000, p. 87. |

[20] | |

[21] | G. Boole, “An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities,” Walton and Maberly, London, 1854, pp. 114-149. |

[22] | J. Venn, “Symbolic Logic,” 2nd Edition, Macmillan and Co., London and New York, 1894, p. 396. |

[23] | L. Carroll, “Symbolic Logic,” Clarkson N. Potter, Inc., New York, 1977, p. 30. |

[24] | G. Boole, “An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities,” Walton and Maberly, London, 1854. |

[25] | J. Venn, “Symbolic Logic,” 2nd Edition, Macmillan and Co., London and New York, 1894. |

[26] | J. Venn, “Symbolic Logic,” 2nd Edition, Macmillan and Co., London and New York, 1894, p. 177. |

[27] | J. Venn, “Symbolic Logic,” 2nd Edition, Macmillan and Co., London and New York, 1894, p. 176, Note 2. |

[28] | G. W. Leibniz, “Opera Philosophica Quae Extant Latina Gallica Germanica Omnia,” Scientia, Aalen, 1959, p. 102. |

[29] | G. W. Leibniz, “Opera Philosophica Quae Extant Latina Gallica Germanica Omnia,” Scientia, Aalen, 1959, p. 102. |

[30] | G. W. Leibniz, “Opera Philosophica Quae Extant Latina Gallica Germanica Omnia,” Scientia, Aalen, 1959, p. 103. |

[31] | On J. H. Lambert’s logical studies, see J. Venn, “Symbolic Logic,” 2nd Edition, Macmillan and Co., London and New York, 1894, pp. xxxi-xxxvii. |

[32] | J. Venn, “Symbolic Logic,” 2nd Edition, Macmillan and Co., London and New York, 1894, p. xxxi. |

[33] | G. Boole, “An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities,” Walton and Maberly, London, 1854, p. 120. |

[34] | G. Boole, “An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities,” Walton and Maberly, London, 1854, pp. 120-121. |

[35] | G. Boole, “An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities,” Walton and Maberly, London, 1854, pp. 99-113. |

[36] | L. Carroll, “Symbolic Logic,” Clarkson N. Potter Inc., New York, 1977, p. 67. |

[37] | L. Carroll, “Symbolic Logic,” Clarkson N. Potter Inc., New York, 1977, pp. 67-68. |

[38] | L. Carroll, “Symbolic Logic,” Clarkson N. Potter Inc., New York, 1977, p. 68. |

[39] | G. Boole, “An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities,” Walton and Maberly, London, 1854, pp. 31, 37. |

[40] | T. Hailperin, “Boole’s Logic and Probability,” North-Holland Publishing Company, Amsterdam, New York, Oxford, 1976, p. 85. |

[41] | P. E. B. Jourdain, “The Development of Theories of Mathematic Logic and the Principles of Mathematics,” The Quarterly Journal of Pure and Applied Mathematics, Vol. 44, 1913, pp. 113-128. |

[42] | Ph. E. B. Jourdain, “The Development of Theories of Mathematic Logic and the Principles of Mathematics,” The Quarterly Journal of Pure and Applied Mathematics, Vol. 41, 1910, pp. 324-352 (about G. Boole and some on G. W. Leibniz). |

[43] | Ph. E. B. Jourdain, “The Development of Theories of Mathematic Logic and the Principles of Mathematics,” The Quarterly Journal of Pure and Applied Mathematics, Vol. 43, 1912, pp. 219-314 (on H. McColl, G. Frege, and G. Peano). |

[44] | P. E. B. Jourdain, “The Development of Theories of Mathematic Logic and the Principles of Mathematics,” The Quarterly Journal of Pure and Applied Mathematics, Vol. 44, 1913, pp. 113-128, at p. 117. |

[45] | See now also I. Grattan-Guinness, “The Correspondence between George Boole and Stanley Jevons, 1863-1864,” History and Philosophy of Logic, Vol. 12, 1991, pp. 15-35, at p. 30. |

[46] | G. Boole, “An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities,” Walton and Maberly, London, 1854, pp. 130-131. |

[47] | G. Boole, “An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities,” Walton and Maberly, London, 1854, p. 139. |

[48] | D. MacHale, “George Boole: His Life and Work,” Boole Press, Dublin, 1985, p. 71. |

[49] | J. Venn, “Symbolic Logic,” 2nd Edition, Macmillan and Co., London and New York, 1894, pp. 175, 269. |

[50] | J. Venn, “Symbolic Logic,” 2nd Edition, Macmillan and Co., London and New York, 1894, pp. xxxiii-xxxiv. |

[51] | E. Schroder, “Vorlesungen über die Algebra der Logik (Exakte Logik),” J. C. Hinrichs, Leipzig, Vol. 2, 1891/ 1905, p. x. E. Schroder died in 1902. Part 2 of Vol. 2 was edited by E. Müller on behalf of the Deutsche Mathematiker-Vereinigung. All three volumes of E. Schroder’s “Vorlesungen über die Algebra der Logik” have been reprinted in 2001 by Thoemmes Press, Bristol, England. |

[52] | E. Schroder, “Vorlesungen über die Algebra der Logik (Exakte Logik),” J. C. Hinrichs, Leipzig, Vol. 1, 1890, p. 460. |

[53] | E. Schroder, “Vorlesungen über die Algebra der Logik (Exakte Logik),” J. C. Hinrichs, Leipzig, Vol. 1, 1890, p. 481. |

[54] | E. Schroder, “Vorlesungen über die Algebra der Logik (Exakte Logik),” J. C. Hinrichs, Leipzig, Vol. 2, 1891/ 1905; E. Schroder, “Vorlesungen über die Algebra der Logik (Algebra und Logik der Relative),” J. C. Hinrichs, Leipzig, 1895, Vol. 3. |

[55] | E. Schroder, “Vorlesungen über die Algebra der Logik (Exakte Logik),” J. C. Hinrichs, Leipzig, Vol. 2, 1891/ 1905, p. 402. |

[56] | E. Schroder, “Vorlesungen über die Algebra der Logik (Algebra und Logik der Relative),” J. C. Hinrichs, Leipzig, 1895, Vol. 3, p. 1. |

[57] | I. Grattan-Guinness, “The Search for Mathematical Roots, 1870-1940: Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Godel,” Princeton University Press, Princeton and Oxford, 2000. |

[58] | I. Grattan-Guinness, “The Search for Mathematical Roots, 1870-1940: Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Godel,” Princeton University Press, Princeton, 2000, p. 176. |

[59] | Review of G. Frege, “Begriffsschrift: Eine der arithmetischen nachgebildete Formelsprache des reinen Denkens,” L. Nebert, Halle, 1879, in Zeitschrift für Mathematik und Physik, Vol. 25, 1880, pp. 81-94. |

[60] | G. Boole, “An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities,” Walton and Maberly, London, 1854, p. 72. |

[61] | G. Boole, “An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities,” Walton and Maberly, London, 1854, p. 123. |

[62] | G. Boole, “An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities,” Walton and Maberly, London, 1854, pp. 138-140. |

[63] | L. Depuydt, “Higher Variations of the Monty Hall Problem (3.0, 4.0) and Empirical Definition of the Phenomenon of Mathematics, in Boole’s Footsteps, as Something the Brain Does,” Advances in Pure Mathematics, Vol. 2, No. 4, 2012, pp. 243-273, at pp. 268-272. www.scirp.org/journal/apm |

[64] | On the reception of G. Boole’s ideas, see several papers in J. Gasser, Ed., “A Boole Anthology: Recent and Classical Studies in the Logic of George Boole,” Kluwer Academic Publishers, Dordrecht, Boston, and London, 2000. |

[65] | G. Boole, “An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities,” Walton and Maberly, London, 1854, pp. 125-126. |

[66] | J. Venn, “Symbolic Logic,” 2nd Edition, Macmillan and Co., London, 1894, p. 301. |

[67] | J. Venn, “Symbolic Logic,” 1st Edition, Macmillan and Co., London, 1881, pp. 222-239. Copies of the first edition are not easily to locate. An electronic copy is available at archive.org/details/symboliclogic00venniala (Accessed January 14, 2013); it is a scan of a copy kept at the University of California at San Diego. |

[68] | E. Schroder, “Vorlesungen über die Algebra der Logik (Exakte Logik),” J. C. Hinrichs, Leipzig, Vol. 1, 1890, p. 533. |

[69] | J. Venn, “Symbolic Logic,” 2nd Edition, Macmillan and Co., London and New York, 1894, p. 301, Note 1. |

[70] | E. Schroder, “Vorlesungen über die Algebra der Logik (Exakte Logik),” J. C. Hinrichs, Leipzig, Vol. 1, 1890, p. 489. |

[71] | E. Schroder, “Vorlesungen über die Algebra der Logik (Exakte Logik),” J. C. Hinrichs, Leipzig, Vol. 1, 1890, p. 481. |

[72] | E. Schroder, “Vorlesungen über die Algebra der Logik (Exakte Logik),” J. C. Hinrichs, Leipzig, Vol. 1, 1890, p. 489. |

[73] | E. Schroder, “Vorlesungen über die Algebra der Logik (Exakte Logik),” J. C. Hinrichs, Leipzig, Vol. 1, 1890, p. 480. |

[74] | A. Macfarlane, “Principles of the Algebra of Logic,” David Douglas, Edinburgh, 1879, pp. 76-77. |

[75] | G. Boole, “An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities,” Walton and Maberly, London, 1854, pp. 90, 92. |

[76] | G. Boole, “An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities,” Walton and Maberly, London, 1854, p. 124. |

[77] | G. Boole, “The Mathematical Analysis of Logic, Being an Essay towards a Calculus of Deductive Reasoning,” Macmillan, Barclay, & Macmillan, Cambridge and George Bell, London, 1847. Reprinted with different pagination, though with references to the pagination of the original edition, in G. Boole, “Studies in Logic and Probability,” Watts & Co., London, 1952. |

[78] | J. Venn, “Symbolic Logic,” 2nd Edition, Macmillan and Co., London and New York, 1894, p. 393, Note 1. |

[79] | G. Boole, “An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities,” Walton and Maberly, London, 1854, p. 139. |

[80] | First in J. C. Maxwell, “A Dynamical Theory of the Electromagnetic Field,” edited and introduced by Th.F. Torrance, with an appreciation by A. Einstein, Scottish Academic Press, Edinburgh, 1982 (1st publication: 1865), described as “forever one of the finest of all man’s scientific accomplishments” in B. Mahon, “The Man Who Changed Everything: The Life of James Clerk Maxwell,” Wiley, Chichester, West Sussex, 2003, p. 119; later comprehensively in J. C. Maxwell, “A Treatise on Electricity and Magnetism,” 2 Vols., 3rd Edition, Clarendon Press, Oxford, 1904 (1st Edition: 1873). |

[81] | D. J. Griffiths, “Introduction to Electrodynamics,” Prentice Hall, Upper Saddle River, N.J., p. xii. |

[82] | B. Mahon, “The Man Who Changed Everything: The Life of James Clerk Maxwell,” Wiley, Chichester, 2003, p. 121. |

[83] | B. Mahon, “The Man Who Changed Everything: The Life of James Clerk Maxwell,” Wiley, Chichester, 2003, p. 96. |

[84] | B. Mahon, “The Man Who Changed Everything: The Life of James Clerk Maxwell,” Wiley, Chichester, 2003, p. 104. |

[85] | B. Mahon, “The Man Who Changed Everything: The Life of James Clerk Maxwell,” Wiley, Chichester, 2003, p. 110. |

[86] | B. Mahon, “The Man Who Changed Everything: The Life of James Clerk Maxwell,” Wiley, Chichester, 2003, p. 120. |

[87] | D. J. Griffiths, “Introduction to Electrodynamics,” Prentice Hall, Upper Saddle River, N.J., p. xii. |

[88] | D. J. Griffiths, “Introduction to Electrodynamics,” 3rd Edition, Prentice Hall, Upper Saddle River, p. 343. |

[89] | J. C. Maxwell, “A Dynamical Theory of the Electromagnetic Field,” Scottish Academic Press, Edinburgh, 1982, p. 31. |

[90] | Th. F. Torrance, in J. C. Maxwell, “A Dynamical Theory of the Electromagnetic Field,” Scottish Academic Press, Edinburgh, 1982, p. ix. |

[91] | J. Venn, “Symbolic Logic,” 2nd Edition, Macmillan and Co., London and New York, 1894, p. xxviii. |

[92] | D. MacHale, “George Boole: His Life and Work,” Boole Press, Dublin, 1985, p. 256. |

[93] | B. Mahon, “The Man Who Changed Everything: The Life of James Clerk Maxwell,” Wiley, Chichester, West Sussex, 2003, back cover. |

[94] | J. C. Maxwell, “A Dynamical Theory of the Electromagnetic Field,” Scottish Academic Press, Edinburgh, 1982. |

[95] | D. MacHale, “George Boole: His Life and Work,” Boole Press, Dublin, 1985, p. 300. |

[96] | D. MacHale, “George Boole: His Life and Work,” Boole Press, Dublin, 1985, pp. 34-38. |

[97] | For bibliography, see D. MacHale, “George Boole: His Life and Work,” Boole Press, Dublin, pp. 281-282. |

[98] | B. Mahon, “The Man Who Changed Everything: The Life of James Clerk Maxwell,” Wiley, Chichester, 2003, pp. 90-127. |

[99] | D. MacHale, “George Boole: His Life and Work,” Boole Press, Dublin, 1985, p. 222. |

[100] | J. C. Maxwell, “A Dynamical Theory of the Electromagnetic Field,” 1982, p. ix. |

[101] | D. MacHale, “George Boole: His Life and Work,” Boole Press, Dublin, 1985, pp. 281-282. |

[102] | D. MacHale, “George Boole: His Life and Work,” Boole Press, Dublin, 1985, pp. 240-243. |

[103] | A. Macfarlane, “Principles of the Algebra of Logic,” David Douglas, Edinburgh, 1879. |

[104] | A. Macfarlane, “Lectures on Ten British Physicists of the Nineteenth Century,” Mathematical Monographs, Vol. 20, John Wiley & Sons, Inc., New York; Chapman & Hall, Limited, London, 1919, p. 11. |

[105] | B. Mahon, “The Man Who Changed Everything: The Life of James Clerk Maxwell,” Wiley, Chichester, 2003, p. 21. |

[106] | G. C. Smith, “The Boole-De Morgan Correspondence,” Clarendon Press, Oxford, 1982. |

[107] | D. MacHale, “George Boole: His Life and Work,” Boole Press, Dublin, 1985, p. 225. |

[108] | B. Mahon, “The Man Who Changed Everything: The Life of James Clerk Maxwell,” Wiley, Chichester, 2003. |

[109] | D. MacHale, “George Boole: His Life and Work,” Boole Press, Dublin, 1985. |

[110] | J. Venn, “Symbolic Logic,” 2nd Edition, Macmillan and Co., London and New York, 1894, p. xii. |

[111] | J. C. Maxwell, “Matter and Motion,” Dover Publications, Inc., New York, 1991. |

[112] | C. B. Boyer, “A History of Mathematics,” 2nd Edition, John Wiley & Sons Inc., New York, 1989, p. 490. |

[113] | B. Mahon, “The Man Who Changed Everything: The Life of James Clerk Maxwell,” Wiley, Chichester, 2003, p. 121. |

[114] | D. MacHale, “George Boole: His Life and Work,” Boole Press, Dublin, 1985, p. 67. |

[115] | B. Mahon, “The Man Who Changed Everything: The Life of James Clerk Maxwell,” Wiley, Chichester, 2003, p. 20. |

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