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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)

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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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Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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

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[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. |

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

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[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. |

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[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. |

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[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. |

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[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. |

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[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. |

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

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

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

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[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. |

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[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. |

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

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[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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