¿Es Dios un Matemático? (41 page)

Entonces, ¿hemos resuelto definitivamente el misterio de la inexplicable eficacia de la matemática? Dudo mucho que los argumentos que he expuesto en este libro hayan dejado completamente convencidas a todas las personas. Sin embargo, puedo citar a Bertrand Russell en
Los problemas de la filosofía
:
^[291]

Para resumir nuestro análisis sobre el valor de la filosofía: la filosofía debe ser estudiada, no por las respuestas concretas a los problemas que plantea, puesto que, por lo general, ninguna respuesta precisa puede ser garantizada como verdadera, sino más bien por el valor de los problemas mismos; porque estos problemas amplían nuestra concepción de lo posible, enriquecen nuestra imaginación intelectual y disminuyen la seguridad dogmática que cierra el espíritu a la investigación; pero, ante todo, porque por la grandeza del Universo que la filosofía contempla, el espíritu se hace a su vez grande, y llega a ser capaz de la unión con el Universo que constituye su supremo bien.

Aczel, A. D. 2000,
The Mystery of the Aleph: Mathematics, the Kabbalah and the Search for Infinity
(Four Walls Eight Windows, Nueva York).

—, 2004,
Chance: A Guide to Gambling, Love, the Stock Market, and Just about Everything Else
(Thunder's Mouth Press, Nueva York).

—, 2005,
Descartes ' Secret Notebook
(Broadway Books, Nueva York).

Adams, C. 1994,
The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots
(W. H. Freeman, Nueva York).

Adam, C. y Tannery, P. 1897-1910,
Oeuvres des Descartes.
Edición revisada 1964-1976 (París: Vrin/CNRS). La traducción al inglés más exhaustiva es: (Nottingham, J., Stoothoff, R. y Murdoch, D. 1985,
The Philosophical Writing of Descartes
(Cambridge University Press, Cambridge).

Alexander, J. W. 1928,
Transactions of the American Mathematical Society,
30, 275.

Applegate, D. L., Bixby, R. E., Chvátal, V. y Cook, W.J. 2007,
The Traveling Salesman Problem
(Princeton University Press, Princeton).

Archibald, R. C. 1914,
American Mathematical Society Bulletin,
vol. 20, 409.

Aronoff, M. y Rees-Miller, J. 2001,
The Handbook of Linguistics
(Blackwell Publishing, Oxford).

Ashley, C. W. 1944,
The Ashley Book of Knots
(Doubleday, Nueva York).

Atiyah, M. 1990,
The Geometry and Physics of Knots
(Cambridge University Press, Cambridge).

—, 1993,
Proceedings of the American Philosophical Society,
vol. 137, num. 4, 517.

—, 1994,
Supplement to Royal Society Netos,
vol. 7, num. 12.

—, 1995,
Times Higher Education Supplement,
29 de septiembre.

Atiyah, M. F. 1989,
Publications Mathématiques de Uns t. des Hautes Eludes

Scientifiques,
Paris, 68, 175. Baillet, A. 1691, La Vie de M. Des-Cartes (Daniel Horthemels, Paris). Un  facsímil fotográfico se publicó en 1972 (Olms, Hildesheim) y 1987

(Garner, Nueva York). Balz, A. G. A. 1952,
Descartes and the Modem Mind
(Yale University Press, New Haven).

Barnes, J. y Lawrence, G. (trad.) 1984, Aristóteles ca. 350 a.C,
Metaphysics,
en
The Complete Works of Aristotle,
ed. J. Barnes (Princeton University Press, Princeton).

Barrow, J. D. 1992,
Pi in the Sky: Counting, Thinking, and Being
(Clarendon Press, Oxford).

—, 2005,
The Infinite Booh: A Short Guide to the Boundless, Timeless and Endless
(Pantheon, Nueva York).

Beaney, M. 2003, en N. Griffin (ed.).
The Cambridge Companion to Bertrand Russell
(Cambridge University Press, Cambridge).

Begsadde, M. 1993, en
Essays on the Philosophy and Science of René Descartes,
ed. S. Voss (Oxford University Press, Oxford).

Bell, E. T. 1937,
Men of Mathematics: The Lives and Achievements of the Great Mathematicians from Zeno to Poincaré
(Touchstone, Nueva York).

—, 1940,
The Development of Mathematics
(McGraw-Hill, Nueva York).

—, 1951,
Mathematics: Queen and Servant of Science
(McGraw-Hill, Nueva York).

Bel tran Mari, A. 1994, en la introducción al
Diálogo Sobre los Dos Máximos Sistemas del Mundo
(Alianza Editorial, Madrid).

Bennett, D. 2004,
Logic Made Easy: How to Know When Language Deceives You
(W. W. Norton, Nueva York).

Berger. E. B. y Starbird, M. 2005,
Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas
(W. W. Norton, Nueva York).

Berkeley, G. 1734,
The Analyst: Or a Discourse Addressed to an Infidel Mathematician,
D. R. Wilkins (ed),
http://www.maths.tcd.ie/pub/HistMath/People/Berkeley/Analyst/Analyst.html
.

Berlin ski, D. 1996,
A Tour of the Calculus
(Pantheon Books, Nueva York).

Bernardini, G. y Fermi, L. (trad.) 1965,
The Little Balance,
en
Galileo and the Scientific Revolution
(Nueva York; Fawet Premier). Se trata de una traducción de 1890-1909,
Le Opere di Galileo Galilei,
ed. A. Favaro (G. Barbero, Florencia).

Bernoulli,J 1713,
Ars Conjectandi
(Thamisiorum, Basilea).

Black, F. y Scholes, M. 1973,
Journal of Political Economy,
81 (3), 637.

Bloom, A. (trad.) 1968, Platon,
The Republic
(Basic Books, Nueva York).

Blumberg, R. B.,
Mendel's Paper in English,
http://www.mendelweb.org/Mendel.plain.html
.

Bodanis, D. 2000,
E = me: A Biography of the World's Most Famous Equation
(Walker, Nueva York).

Bonola, R. 1955,
Non-Euclidean Geometry,
H. S. Carshaw (trad.) (Dover Publications, Nueva York). Se trata de una reedición de la traducción de 1912 (publicada por Open Court Publishing Company).

Boole, G. 1847,
The Mathematical Analysis of Logic, Being an Essay totoards a Calculus of Deductive Reasoning,
reproducido en Ewald 1996.

—, 1854.
An Investigation of the Laws of Thought on Which Are Founded the Mathematical Theories of Logic and Probabilities
(Macmillan, Londres). Reimpreso en 1958 (Dover Publications, Mineóla, NY).

Boolos, G. 1985,
Mind,
94, 331.

—, 1999,
Logic, Logic, Logic
(Harvard University Press, Cambridge, MA).

Borovik, A. 2006,
Mathematics under the Microscope,
http://www.maths
.
manchester.ac.uk/~avb/micromathematics/downloads
.

Brewster. D. 1831,
The Life of Sir Isaac Netuton
(John Murray, Albemarle Street, Londres).

Bukowski. J. 2008,
The College Mathematics Journal,
vol. 39, num. 1, 2.

Burkert, W. 1912,
Lore and Science in Ancient Pythagoreanism
(Harvard University Press, Cambridge, MA).

Cajori, F. 1926,
The American Mathematical Monthly,
vol. 33, num. 8, 397.

—, 1928, en
Sir Isaac Newton 1727-1927: A Bicentenary Evaluation of His Work,
The History of Science Society (The Williams & Wilkins Company, Baltimore).

Cardano, G. 1545,
Artis Magnae, sive de regulis algebraices,
editado en 1968 con el título
The Great Art or the Rules of Algebra,
T. R. Witmer (trad, y ed.) (MIT Press, Cambridge, MA).

Caspar, M. 1993,
Kepler,
C. D. Hellman (trad.) (Dover Publications, Mineóla, NY).

Chandrasekhar, S. 1995,
Newton's Principia for the Common Reader
(Clarendon Press, Oxford).

Changeaux, J.-P. y Connes, A. 1995,
Conversations on Mind, Matter, and Mathematics
(Princeton University Press, Princeton).

Cherniss, H. 1945,
The Riddle of the Early Academy
(University of California Press Berkeley), reimpreso en 1980 (Garland, Nueva York).

—, 1951,
Review of Metaphysics,
4, 395.

Chomsky, N. 1957,
Syntactic Structures
(Mouton & Co., The Hague).

Clark, M. 2002,
Paradoxes from A to Z
(Routledge, Londres).

Clarke, D. M. 1992, en
The Cambridge Companion to Descartes,
ed. J. Cot-

tingham (Cambridge University Press, Cambridge). Cohen, I. B. 1982, en
Contemporary Newtonian Research,
ed. Z. Bechler

(Reidel, Dordrecht). —, 2006,
The Triumph of Numbers
(W. W. Norton
8c
Company, Nueva York).

Cohen, I. B. y Whitman, A. (con la asistencia de J. Budenz) 1999,
The Principia: Mathematical Principles of Natural Philosophy
(University of California Press, Berkeley).

Cohen, P.J. 1966,
Set Theory and the Continuum Hypothesis
(W. A. Benjamin, Nueva York).

Cole, J. R. 1992,
The Olympian Dreams and Youthful Rebellion of René Descartes
(University of Illinois Press, Champaign, IL).

Connor, J. A. 2006,
Pascal's Wager: The Man Who Played Dice with God
(Harper Collins, Nueva York).

Conway, J. H. 1970, en
Computational Problems in Abstract Algebra,
ed. J. Leech (Pergamon Press, Oxford), 329.

Coresia, G. 1612,
Operetta intorno al galleggiare de' corpi solidi.
Reimpreso en
Le Opere di Galileo Galilei.
Favoro A. (ed.) 1968,
Le Opere di Galileo Galilei,
Edizione Nazionale, (Barbero, Florencia). Primera aparición en 1890-1909.

Cottingham,J. 1986,
Descartes
(Blackwell, Oxford).

Craig, SirJ. 1946,
Newton at the Mint
(Cambridge University Press, Cambridge).

Curley, E. 1993, en
Essays on the Philosophy and Science of René Descartes,
ed. S. Voss (Oxford University Press, Oxford).

Curzon, G. 2004,
Wotton and His Words: Spying, Science and Venetian Intrigues
(Xlibris Corporation, Filadelfia).

Davies, P. 2001,
How to Build a Time Machine
(Allen Lane, Nueva York).

Davis, P.J. y Hersh, R 1981,
The Mathematical Experience
(Birkhaüser, Boston). También 1998 (Mariner Books, Boston).

Dawkins, R. 2006,
The God Delusion
(Houghton Mifflin Company, Nueva York).

Dawson, J. 1997,
Logical Dilemmas: The Life and Work of Kurt Gödel
(A. K.

Peters, Natick, MA). De Santillana, G. 1955,
The Crime of Galileo
(University of Chicago Press, Chicago).

Dehaene, S. 1997,
The Number Sense
(Oxford University Press, Oxford).

Dehaene, S., Izard, V., Pica, P. y Spelke, E. 2006,
Science,
311, 381.

DeLong, H. 1910,
A Profile of Mathematical Logic
(Reading, MA: Addison-Wesley). Reeditado en 2004 (Dover Publications, Mineola, NY).

Demopoulos, W. у Clark, P. 2005, en S. Shapiro (ed.),
The Oxford Handbook of Philosophy of Mathematics and Logic
(Oxford University Press, Oxford).

DeMorgan, A. 1885,
Newton: His Friend: and His Niece
(Elliot Stock, Londres). Dennett, D. C. 2006,
Breaking the Spell: Religion as a Natural Phenomenon

(Viking, Nueva York). Descartes, R. 1644,
Principles of Philosophy,
II: 64, en 1985,
Philosophical

Works of Descartes,
eds. J. Cotringham, R. Stoothoff y D. Murdoch

(Cambridge University Press, Cambridge). Detlefsen, M. 2005, en
The Oxford Handbook of Philosophy of Mathematics  
and Logic,
ed. S. Shapiro (Oxford University Press, Oxford).

Deutsch, D. 1997,
The Fabric of Reality
(Allen Lane, Nueva York).

Devlin, K. 1993,
The joy of Sets: Fundamentals of Contemporary Set Theory,
segunda edición (Springer Verlag, Nueva York).

—, 2000,
The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are like Gossip
(Basic Books, Nueva York).

Dijksterhuis, E.J. 1957,
Archimedes
(The Humanities Press, Nueva York).

Dillon, J. y HershbellJ. (trad.) 1991, Jámblico ca. 300 d.C,
On the Pythagorean Life
(Scholar Press, Atlanta).

Doxiadis, A. K. 2000,
UnclePetros and Goldbach's Conjecture
(Bloomsbury, Nueva York).

Drabkin, I. E. (trad.) 1960,
On Motion
(University of Wisconsin Press, Madison, WI).

Drake, S. (trad.) 1960, Galileo 1623,
The Assayer
(título original
IlSaggia-tore)
, en
The Controversy of the Comets of 1618
(University of Pennsylvania Press, Filadelfia).

—, (trad.) 1960, Grassi, O. 1619,
Lilrra Astronómica acPhilosophica,
en
The Controversy of the Comets of 161.6
(University of Pennsylvania Press, Filadelfia).

—, (trad.) 1960,
On Mechanics
(University of Wisconsin Press, Madison, WI).

—, (trad.) 1967, Galileo 1632,
Dialogue Concerning the Tiuo Chief World Systems
(University of California Press, Berkeley.

—, (trad.) 1974, Galileo 1638,
Discourses on the TiuoNeiu Sciences
(University of Wisconsin Press, Madison, WI).

—, 1978,
Galileo at Work: His Scientific Biography
(University of Chicago Press, Chicago).

—, (trad.) 1983, Galileo 1610,
Sidereus Nuncius
(o
The Sidereal Messenger),
en
Telescopes, Tides and Tactics
(University of Chicago Press, Chicago)-

—, 1990,
Galileo: Pioneer Scientist
  (University of Toronto Press, Toronto). Dryden,J. (trad.) 1992, Plutarco ca. 75 d.C,
Marcellus,
en
Plutarch's Lives, 

ed. A. H. Clough (Modern Library, Nueva York). Dumett, M. 1978,  
Truth and Other Enigmas
(Harvard University Press, Cambridge, MA).

Dunham, W. 1994,
The Mathematical Universe. An Alphabetical journey through the Great Proofs, Problems and Personalities
(John Wiley
8c
Sons, Nueva York).