Mathematics, Reason & Religion.

Referencias bibliográficas

• PRIYA HEMENWAY, Divine Proportion: Phi In Art, Nature, and Science, Sterling Publishing Company Inc. , 2005, p. 56.
• RUSSELL W. HOWELL and W. JAMES BRADLEY (eds. ), Mathematics in a Postmodern Age: A Christian Perspective, Wm. Eerdmans Publishing Co. , 2001;
• JOHN BYL, The Divine Challenge: on Matter, Mind, Math and Meaning, Banner of Truth Trust, 2004.
• GEORG HENRIK VON WRIGHT, «Norms, Truth and Logic», in GEORG HENRIK VON WRIGHT, Philosophical Papers I. Practical Reason, Blackwell, Oxford, 1983;
• trans. by CARLOS CABRERA ALARCÓN, Normas, verdad y lógica, Fontamara, México, 1997.
• Gottlob Frege (1848-1925) & Bertrand Russell are the best known advocates of this logistical movement.
• The principle of excluded middle asserts that given a statement A, A is either false or true. Constructivist logic does not accept that one of the two possibilities A or not A is inevitably true, only that the two possibilities cannot be true at the same time, as we would be faced with a contradiction. Constructivist logicians can only assert A when A can be proved and can only assert not A when not A can be proved, but if neither A nor not A can be proved, we cannot assert: «A or not A».
• In order to understand these ideas it is important to distinguish between the excluded middle principle that states that «A or not A» is true and the principle of no-contradiction that states that «A and not A» cannot be both true.
• HOWARD EVES, An Introduction to the History of Mathematics, Ed. Saunders College Publishing, 1992, p. 9.
• ARISTOTLE, Metaphysics, 1011b25.
• GALILEO GALILEI, Opere, 4, 171 (translation into English as quoted by Machamer in the Cambridge Companion to Galileo, p. 64f).
• Laplace developed Newton's mechanics. Laplace's equations are important, as is his partial differential equation.
• GEORGE BOOLE, The mathematical analysis of logic, New York: Philosophical Library, 1948 (first published in 1847. Cambridge: Macmillan, Barclay, & Macmillan; London: George Bell);
• GEORGE BOOLE, An Investigation of the Laws of Thought, Prometeus Books, New York, 2000 (first published in 1854).
• GOTTLOB FREGE, Begriffsschrift: eine der arithmetischen nachgebildete Formelsprache des reinen Denkens, Halle, 1879.
• DAVID HILBERT (1926), «Über das Unendliche», Mathematische Annalen, 95: 161-90. Lecture given Münster, 4 June 1925.
• L. E. J. BROUWER, On the significance of the principle of excluded middle in mathematics, especially in function theory, 1923.
• S. WALTER, The non-Euclidean style of Minkowskian relativity. The Symbolic Universe, J. Gray (ed. ), Oxford University Press, 1999.