The Great Math Mystery Mario Livio (1950 - ) Astrophysicist and Writer Astrofísico Y Escritor Astrophysicien Et Écrivain Space Telescope Science Institute

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“How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?” “¿Cómo es posible que la matemática, un producto del pensamiento humano independiente de la experiencia, se adapte tan admirablemente a los objetos de la realidad?”1 Albert Einstein (1879-1955) “Intelligent people would never say, ‘I don’t care about art, or music. But it is totally okay to say, ‘I hate math.’” The Great Math Mystery Mario Livio (1950 - ) Astrophysicist and writer Astrofísico y escritor Astrophysicien et écrivain Space Telescope Science Institute

LIVIO, Mario, “The Great Math Mystery”. This is a Nova Production for WGBF Boston. © 2015 WGBF Educational Foundation. All rights reserved. This program was produced by WGBF, which is solely responsible for its content. Cf.: https://www.youtube.com/watch?v=pPUTrIgdCZI

1 JAMMER, Max, Einstein and Religion, Princeton University Press, 1921, p. 124. The Great Math Mystery Documentary New 2015 HD http://docuwiki.net/index.php?title=T... The Great Math Mystery Documentary New 2015 HD NOVA leads viewers on a mathematical mystery tour –a provocative exploration of math’s astonishing power across the centuries. We discover math’s signature in the swirl of a nautilus shell, the whirlpool of a galaxy, and the spiral in the center of a sunflower. Math was essential to everything from the first wireless radio transmissions to the successful landing of rovers on Mars. But where does math get its power? Astrophysicist and writer Mario Livio, along with a colorful cast of mathematicians, physicists, and engineers, follow math from Pythagoras to Einstein and beyond, all leading to the ultimate riddle: Is math an invention or a discovery? Humankind’s clever trick or the language of the universe? Whether we think we’re good with numbers or not, we all use math in our daily lives. The Great Math Mystery sheds fascinating light on how math works in our brains and ponders the ultimate mystery of why it works so well when decoding the universe. LIVIO, Mario, “The Great Math Mystery”, Nova, April 15, 2015 on PBS. Cf.: http://www.pbs.org/wgbh/nova/physics/great-math-mystery.html The Great Math Mystery Is math invented by humans, or is it the language of the universe? Airing April 15, 2015 at 9 pm on PBS Aired April 15, 2015 on PBS Program Description Join NOVA on a mathematical mystery tour—a provocative exploration of math’s astonishing power across the centuries. We discover math’s signature in the swirl of a nautilus shell, the whirlpool of a galaxy, and the spiral in the center of a sunflower. Math was essential to everything from the first wireless radio transmissions to the prediction and discovery of the Higgs boson and the successful landing of rovers on Mars. Astrophysicist and writer Mario Livio, along with a colorful cast of mathematicians, physicists, and engineers, follow math from Pythagoras to Einstein and beyond. It all leads to the ultimate riddle: Is math a human invention or the discovery of the language of the universe? LIVIO, Mario, « Le grand mystère des mathématiques », Arte.tv, Vendredi 15 janvier 2016 22h25 (53’). Cf. : http://www.arte.tv/guide/fr/061655-000-A/le-grand-mystere-des-mathematiques Détails Documentaire: Omniprésentes dans les sciences et les technologies, les mathématiques sont parvenues à décrypter les orbites elliptiques des planètes, à prédire la découverte du boson de Higgs ou à faire atterrir le robot Curiosity sur Mars. De tout temps, l’homme, en quête de cycles et de motifs, les a utilisées pour explorer le monde physique et pour comprendre les règles de la nature, du nombre de pétales de fleurs (répondant à des « suites ») à la symétrie de notre corps. La réalité possède-t-elle une nature mathématique inhérente ou les mathématiques sont-elles des outils précieux créés par l’esprit humain ? Voyage visuel Depuis l’Antiquité grecque, leur universalité et leur efficacité ont nourri débats philosophiques et métaphysiques. Sur les traces de Pythagore (qui avait notamment établi des liens entre mathématiques et musique), Platon, Galilée, Newton ou Einstein, le film, ludique, sonde leur fascinant mystère et leur évolution au fil des siècles, en compagnie de Mario Livio, astrophysicien américain renommé, et de nombreux mathématiciens, physiciens et ingénieurs. Une enquête captivante, formidablement illustrée d’exemples, en même temps qu’un voyage visuel vertigineux. Entre construction neuronale et ordre cosmique, à la frontière de

l’invention et de la découverte, les mathématiques, extraordinaire énigme, n’ont pas fini de révéler, d’anticiper et de surprendre. LIVIO, Mario, Brilliant Blunders. From Darwin to Einstein. Colossal Mistakes by Great Scientists That Changed Our Understanding of Life and the Universe, New York: Simon & Schuster, 2013, pp. 352. Cf.: http://www.amazon.com/Brilliant-Blunders-Einstein-Scientists- Understanding/dp/1439192367/ref=mt_hardcover?_encoding=UTF8&me= http://www.amazon.com/Brilliant-Blunders-Einstein-Scientists- Understanding/dp/1439192367/ref=mt_hardcover?_encoding=UTF8&me=#reade r_1439192367 WE ALL MAKE MISTAKES. Nobody’s perfect. Not even some of the greatest geniuses in history, as Mario Livio tells us in this marvelous story of scientific error and breakthrough. Charles Darwin, William Thomson (Lord Kelvin), Linus Pauling, Fred Hoyle, and Albert Einstein were all brilliant scientists. Each made groundbreaking contributions to his field—but each also stumbled badly. Darwin’s theory of natural selection shouldn’t have worked, according to the prevailing beliefs of his time. Not until Gregor Mendel’s work was known would there be a mechanism to explain natural selection. How could Darwin be both wrong and right? Lord Kelvin, Britain’s leading scientific intellect at the time, gravely miscalculated the age of the earth. Linus Pauling, the world’s premier chemist (who would win the Nobel Prize in chemistry) constructed an erroneous model for DNA in his haste to beat the competition to publication. Astrophysicist Fred Hoyle dismissed the idea of a “Big Bang” origin to the universe (ironically, the caustic name he gave to this event endured long after his erroneous objections were disproven). And Albert Einstein, whose name is synonymous with genius, speculated incorrectly about the forces that hold the universe in equilibrium—and that speculation opened the door to brilliant conceptual leaps. These five scientists expanded our knowledge of life on earth, the evolution of the earth itself, and the evolution of the universe, despite and because of their errors. As Mario Livio luminously explains, the scientific process advances through error. Mistakes are essential to progress. Brilliant Blunders is a singular tour through the world of science and scientific achievement – and a wonderfully insightful examination of the psychology of five fascinating scientists. ***** “It is said that genius is the ability to make all possible mistakes in the least amount of time. Livio’s genius is to show us just how much those mistakes have taught us.” –Adam Riess, Thomas Barber Professor of Physics and Astronomy, Johns Hopkins University, Nobel Laureate in Physics 2011 Astrophysicist and award-winning author Livio (The Golden Ratio) analyzes ruinous errors of five great scientific minds in the wake of their most prominent discoveries and how those errors have not only propelled scientific breakthroughs, but provide “insights... into the operation of the human mind.” Summoning Charles Darwin, Lord Kelvin, Linus Pauling, Fred Hoyle, and Albert Einstein, Livio argues there is no progress without lessons in humility. These thinkers succumbed to moments of fear, pride, stubbornness, and doubt common to all “mere mortals”—to the benefit of elucidating the evolution of life and the universe. Two-time Nobel prize-winning chemist Pauling’s flub of basic chemistry catalyzed the discoveries of Watson and Crick; Hoyle, a cosmologist who displayed “pigheaded, almost infuriating refusal” to give up his thoroughly refuted “steady state theory”, energized advanced studies of how we exist in space with his controversial ideas; and Einstein, “the embodiment of genius”, refused to give up on his cosmological constant, “the most famous fudge factor in the history of science.” With humor and precision, Livio reminds us: “Even the most impressive minds are not flawless; they merely pave the way for the next level of understanding.” —From Publishers Weekly, May.

LIVIO, Mario, Is God a Mathematician?, New York: Simon & Schuster, 2010, pp. 320. ISBN: 978-0743-2940-65. Cf.: http://books.simonandschuster.com/Is-God-a-Mathematician/Mario- Livio/9780743294065 Mario Livio is an internationally known astrophysicist, a bestselling author, and a popular speaker. He is a Fellow of the American Association for the Advancement of Science. Dr. Livio is the author of The Golden Ratio, a highly acclaimed book for which he received the International Pythagoras Prize and the Peano Prize; The Equation That Couldn’t Be Solved; Is God A Mathematician?; the national bestseller Brilliant Blunders; and The Accelerating Universe. “Is God a mathematician? In his new book Mario Livio delves into this question, putting it into a scientific, historical and philosophical context. He steers skillfully through deep and tricky waters, but writes with clarity and ease... Read the book and decide for yourself what the answer is.” – Sir Michael Atiyah, recipient of the Fields Medal, 1966, and the Abel Prize, 2004. “This highly readable book explores one of the most fascinating questions that lies at the heart of fundamental physics – why is mathematics so effective in describing nature and is mathematics an invention of the human mind or part of the fabric of physical reality? Livio provides a wonderful review of the various issues, presents a wide variety of opinions, and in addition some fascinating insights of his own. I strongly recommend this volume to anyone interested in these questions.” – David Gross, 2004 Nobel Prize Winner in Physics, Frederick W. Gluck Professor of Theoretical Physics and Director, Kavli Institute For Theoretical Physics, University of California, Santa Barbara. “All science proceeds from the assumption that the cosmos is ordered in an intelligible way. Beneath the bewildering richness of natural phenomena there lies an elegant mathematical unity. How astonishing that the human mind is attuned to this hidden subtext of nature! With elegance and clarity, Mario Livio charts how, through science and mathematics, we have come to glimpse the fundamental rules on which the universe runs.” – Paul Davies, author of The Goldilocks Enigma and Director of the Beyond Center for Fundamental Concepts in Science, Arizona State University. LIVIO, Mario, ¿Es Dios un matemático?, Barcelona: Ariel, 2011, pp. 320. Cf.: http://www.casadellibro.com/libro-es-dios-un- matematico/9788434469518/1819691?utm_source=criteo&utm_campaign=Criteo &utm_medium=retargeting COSTA, Rebecca, “The Costa Report. Mario Livio”, YouTube. Interview 2013 (53:50). Cf.: https://www.youtube.com/watch?v=YmX9ZkrVNE0 LIVIO, Mario, “Why Math Works?”, Scientific American, August 1, 2011, pp. 81-83. Cf.: http://www.cs.virginia.edu/~robins/Why_Math_Works.pdf Mario Livio is a theoretical astrophysicist at the Space Telescope Science Institute in Baltimore which operates the Hubble Space Telescope. He has studied a wide range of cosmic phenomena, ranging from dark energy and supernova explosions to extrasolar planets and accretion onto white dwarfs, neutron stars and black holes. Mario Livio is an author of works that popularize science and mathematics. He is perhaps best known for his book on the irrational number phi: The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number (2002). The book won the Peano Prize and the International Pythagoras Prize for popular books on mathematics.

LIVIO, Mario [Space Telescope Science Institute], Is God a Mathematician?, 2009. Cf.: http://hubblesite.org/about_us/public_talks/presentations/livio_2009_01_06.pdf

LIVIO, Mario [Space Telescope Science Institute], Is God a Mathematician? New York: Simon and Schuster, 2009, pp. 320. ISBN-13: 978-0743294058 (Hardback edition). Reviewed by Marianne FREIBERGER. Cf.: http://www.brophy.net/Downloads/AIL%20Class%20on%20Reality%20&%20U nreality/READING%20MATERIAL%20IN%20PDF%20FORMAT/12%20is%2 0god%20a%20mathematician.pdf LIVIO, Mario [Space Telescope Science Institute], Is God a Mathematician? New York: Simon and Schuster, 2010 [2009], pp. 320. ISBN-13: 978-0743294065 (Paperback edition). Cf.: http://books.simonandschuster.com/Is-God-a-Mathematician/Mario- Livio/9780743294065# http://www.amazon.com/Is-God-Mathematician-Mario-Livio/dp/0743294068 Stephen WOLFRAM, Director General of Wolfram Research (46:40) Derek ABBOTT, The University of Adelaide (47:57) Sylvester James, GATES, University of Maryland (51:22) LIVIO, Mario, The Equation that couldn’t Be Solved: How Mathematical Genius Discovered the Language of Symmetry, New York: Simons & Schuster, reprinted edition, 2006 [2005], pp. 368. Cf.: (paperback) http://www.amazon.com/Equation-That-Couldnt-Solved- Mathematical/dp/0743258215/ref=asap_bc?ie=UTF8 http://www.amazon.com/Equation-That-Couldnt-Solved- Mathematical/dp/0743258215/ref=asap_bc?ie=UTF8#reader_0743258215 The idea of symmetry has been heavily deployed in recent science popularizations to introduce advanced subjects in math and physics. This approach usually backfires—mathematical symmetry is much too difficult for most laypeople to understand. But this engaging treatise soft-pedals it in a crowd-pleasing way. The title’s formula is the “quantic” equation (involving x raised to the fifth power), the analysis of which gave rise to “group theory,” the mathematical apparatus scientists use to explore symmetry. Inevitably, the author’s attempts to explain group theory and its applications in particle physics and string theory to a general audience fall sadly short, so readers will just have to take his word for the Mozartean beauty of it all. Fortunately, astrophysicist Livio (The Golden Ratio) keeps the hard stuff to a minimum, concentrating instead on interesting digressions into human interest (e.g., the founder of group theory, Evariste Galois, was a revolutionary firebrand who died in 1832 at age 20 in a duel over “an infamous coquette”), pop psychology (women have more orgasms when their partners have symmetrical faces), strategies for finding a soul mate and some easy math puzzles readers might actually solve. The result is a somewhat shapeless but intriguing excursion. Photos. —From Publishers Weekly (© Reed Business Information, a division of Reed Elsevier Inc.). ***** The so-called quintic equation resisted solution for three centuries, until two brilliant young mathematicians independently discovered that it could not be solved by any of the usual methods — and thereby opened the door to a new branch of mathematics known as group theory. This book is the story of these two early 19th-century mathematicians— a Norwegian, Niels Henrik Abel, and a Frenchman, Evariste Galois, both of whom died tragically, Galois in a duel at the age of 20. Livio, an astrophysicist now at the Space Telescope Science Institute

and author of The Golden Ratio, interweaves their story with fascinating examples of how mathematics illuminates a wide swath of our world. —Editors of Scientific American LIVIO, Mario, The Golden Ratio: The Story of PHI, the World’s Most Astonishing Number, Broadways Book, reprint edition, 2003 [2002], pp. 294. Cf.: (paperback) http://www.amazon.com/The-Golden-Ratio-Worlds- Astonishing/dp/0767908163/ref=pd_sim_14_1?ie=UTF8&dpID=51nOpMy5leL& dpSrc=sims&preST=_AC_UL160_SR103%2C160_&refRID=0NE8NNZSZCX1G Z77C1MP http://www.amazon.com/The-Golden-Ratio-Worlds- Astonishing/dp/0767908163/ref=pd_sim_14_1?ie=UTF8&dpID=51nOpMy5leL& dpSrc=sims&preST=_AC_UL160_SR103%2C160_&refRID=0NE8NNZSZCX1G Z77C1MP#reader_0767908163 Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887... This curious mathematical relationship, widely known as “The Golden Ratio,” was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci’s Mona Lisa to Salvador Dali’s The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market! The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist. ***** Most readers will have at least dim memories from geometry class of the irrational number pi. Theoretical astrophysicist Livio gives pi’s overlooked cousin phi its due with this lively account, the first on the subject written for the layperson. Phi is the golden ratio of antiquity (1.6180339887), a never-ending number so lauded for its harmonious qualities that in the 16th century it was dubbed the divine proportion. It is related to phenomena as diverse as the petal arrangements of roses, the breeding patterns of rabbits and the shape of our galaxy. Phi is also claimed to have been crucial in the design of the Great Pyramids, the composition of the Mona Lisa and the construction of Stradivarius violins. Livio (The Accelerating Universe) carefully investigates these and other claims and does not hesitate to debunk myths perpetuated by overzealous enthusiasts he calls “Golden Numberists.” This is an engaging history of mathematics as well, addressing such perennial questions as the geometric basis of aesthetic pleasure and the nature of mathematical objects. Useful diagrams and handsome illustrations of works under discussion are amply provided. Livio is gifted with an accessible, entertaining style: one typical chapter bounds within five pages from an extended discourse on prime numbers to a clever Oscar Wilde quote about beauty to an amusing anecdote about Samuel Beckett and finally to an eminently clear explanation of Gödel’s incompleteness theorem. With a guide to the history of ideas as impassioned as Livio, even the math-phobic can

experience the shock and pleasure of scientific discovery. This thoroughly enjoyable work vividly demonstrates to the general reader that, as Galileo put it, the universe is, indeed, written in the language of mathematics. — From Publishers Weekly LIVIO, Mario, The Accelerating World. Infinite Expansion, the Cosmological Constant, and the Beauty of the Cosmos, New York: John Wiley & Sons, 2000, pp. 292. Cf.: (paperback) http://www.amazon.com/Accelerating-Universe-Infinite-Expansion- Cosmological/dp/0471399760/ref=la_B001IU4RI2_1_5?s=books&ie=UTF8&qid= 1453994078&sr=1-5&refinements=p_82%3AB001IU4RI2 http://www.amazon.com/Accelerating-Universe-Infinite-Expansion- Cosmological/dp/0471399760/ref=mt_paperback?_encoding=UTF8&me=#reader _0471399760 One of the most important recent discoveries in cosmology--and science in general--is that the expansion rate of the universe is not staying steady or getting slower, as most scientists had assumed; on the contrary, it is accelerating. Something is counteracting gravity and making it so that in billions of years, the universe will be an even vaster, emptier realm, filled with stars and galaxies flickering out one by one until there is only darkness. In this book, Livio, a senior scientist at Baltimore’s Space Telescope Science Institute, evaluates current theories about the universe in terms of whether or not they are “beautiful.” Livio defines beauty for purely scientific purposes: a beautiful scientific theory, he explains, must be symmetric and simple (reductionist), and it must follow the Copernican principle that man is not the center of the universe –it need not be elegant. Livio’s discussion, however, carefully constructed (like a well-laid-out mathematical proof), certainly is elegant. Readers who only hazily remember high school math and science classes will enjoy the author’s clear, jargon-free explanation of such complicated astronomical concepts as inflationary theory, “pocket” or multiple universes and the anthropic principle. Although the opening chapters are weighed down with extraneous references to art and literature, once Livio gets into his subject, he employs such references more selectively. Any educated individual interested in current theories about the past and future of the universe will want to read this lucid book. 10 b&w photos and drawings. (Mar.) – (© 2000 Reed Business Information, Inc.). ***** Like Donald W. Goldsmith’s The Runaway Universe (LJ 1/00), this is a survey of modern cosmology, with an emphasis on recent observations that the universe is expanding at an ever- accelerating speed. But while Goldsmith focuses on the techniques of astronomical research, Livio, a scientist at the Space Telescope Science Institute in Baltimore, concentrates on scientific aesthetics. He argues that a fundamental theory of the universe must be beautiful-- symmetrical, reductionist, and compliant with the generalized Copernican principle (i.e., assuming no special circumstances)--even though an eternally expanding universe appears to violate the requisites for scientific beauty. Along the way, Livio often digresses, recounting sometimes irrelevant anecdotes about astronomers or works of art. Superbly accessible explanations of physical and astronomical concepts compensate, however. More appropriate for general readers than Goldsmith’s book, this is recommended for public and academic libraries. –Nancy Curtis, Univ. of Maine Lib., Orono. (© 2000 Reed Business Information, Inc.). §♦♦♦♦♦§

Galileo Galilei (1564-1642)

“The Laws of Nature are written in the language of mathematics” “No me siento obligado a creer que un Dios que nos hubiera dotado de inteligencia, sentido común y raciocinio, tuviera como objetivo privarnos de su uso”. “I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use” “Creo que en la discusión de los problemas naturales deberíamos comenzar no con las escrituras, sino con experimentos y demostraciones”

Ma ch’io sia per voler portare la toga, Come s’io fussi qualche Fariseo, O qualche scriba o archisinagoga, Non lo pensar. Io son contento dir la mia ragione, E che tu stessa la sentenza dia: so che tu a giudizio e discrezione. Galileo, Capitolo contra il portar la toga, 1590. “Galileo Galilei”, Biografías y vidas. La Enciclopedia Biográfica en Línea. Cf.: http://www.biografiasyvidas.com/monografia/galileo/ensayador.htm GALILEO GALILEI (1564-1642), “Obras de Galileo Galilei, Parte 3, Volumen 15, Astronomía: El Ensayador”, Biblioteca Digital Mundial. Cf: §♦♦♦♦♦§ https://www.wdl.org/es/item/4184/

GALILEO GALILEI, El Ensayador, Wikipedia. Cf.: https://es.wikipedia.org/wiki/El_ensayador [Español. Última actualización: 31 de octubre de 2015] GALILEO GALILEI, The Assayer, Wikipedia. Cf.: §♦♦♦♦♦§ https://en.wikipedia.org/wiki/The_Assayer [English. Las modified: 11 December 2015] GALILEO GALILEI, L’Essayeur, Wikipedia. Cf.: https://fr.wikipedia.org/wiki/L%27Essayeur [Français. Dernière modification: 2 juillet 2015] GALILEO GALILEI, Il Saggiatore, Wikipedia. Cf.: https://it.wikipedia.org/wiki/Il_Saggiatore_(trattato) [Italiano. Modificata per ultima volta: [Italiano: Modificata per l’ultima volta: 9 novembro 2015] GALILEO GALILEI, O ensaidor, Wikipedia. Cf.: [Português. Modificada pela última vez: 3 de janeiro de 2015] §♦♦♦♦♦§ https://pt.wikipedia.org/wiki/Il_Saggiatore GALILEO GALILEI, Wikipedia. Cf. [Italiano] https://it.wikiquote.org/wiki/Galileo_Galilei GALILEO GALILEI, Wikipedia. Cf. [English] https://en.wikiquote.org/wiki/Galileo_Galilei GALILEO GALILEI, Wikiquote. Cf. [Spanish] https://es.wikiquote.org/wiki/Galileo_Galilei GALILEO GALILEI, Amazon. Cf.: http://www.amazon.fr/s/?ie=UTF8&keywords=galil%C3%A9o+galil%C3%A9i &tag=googhydr0a8- 21&index=stripbooks&hvadid=56674197779&hvpos=2o1&hvexid=&hvnetw=g& hvrand=17432648036324554433&hvpone=&hvptwo=&hvqmt=b&hvdev=c&ref= pd_sl_7qnmi7dxyj_b GALILEO GALILEI, Il Saggiatore, 1623, pp. 236. Cf. [Biblioteca Nazionale Centrale di Firenze] http://teca.bncf.firenze.sbn.it/ImageViewer/servlet/ImageViewer?idr=BNCF0003 623344#page/26/mode/2up GALILEO GALILEI, Opere, Biblioteca Nacionale Centrale di Firenze. Cf.: https://www.wdl.org/es/search/?institution=national-central-library-of-florence (Anónimo). “La fe y creencia en Dios de científicos y personajes históricos. Galileo Galilei ‘La Escritura no puede errar, sus intérpretes sí’”, CreyentesIntelectuales.blogspot, Miércoles, 20 de junio de 2012. Cf.: http://creyentesintelectuales.blogspot.fr/2012/06/retrato-de-galileo-galilei-por- justus.html ÁLVAREZ GARCÍA, J.L., “Luz y sombra de Galileo Galilei”, Revista Mexicana de Física, Vol. 55, n.º 2, diciembre de 2009, pp. 221-227. Cf.: http://www.scielo.org.mx/pdf/rmfe/v55n2/v55n2a10.pdf GRATON, Fausto, “Un Linceo y su visión del mundo físico: Galileo Galilei”, en ARCHIDEO, Lila Blanca (coordinadora), Epistemología de las ciencias. La visión del mundo del investigador y la incidencia en su trabajo científico, Buenos Aires: 9

CIAFIC Ediciones (Centro de Investigaciones en Antropología Filosófica y Cultural de la Asociación Argentina de Cultura), 2007, pp. 99-137. Cf.: http://www.ciafic.edu.ar/documentos/04_Simposio_Naturales_2006_Gratton_pp_ 99-137.pdf [Lotario Sarsi] forse stima che la filosofia sia un libro e una fantasia d’un uomo, come l’Iliade e l’Orlando Furioso, libri ne’ quali la meno importante cosa è che quello che vi è scritto sia vero. Signor Sarsi, la cosa non istà così. La filosofia è scritta in questo grandissimo libro che continuamente ci sta aperto innanzi a gli occhi (io dico l’universo), ma non si può intendere se prima non s’impara a intender la lingua, e conoscer i caratteri, ne’ quali è scritto. Egli è scritto in lingua matematica, e i caratteri son triangoli, cerchi, ed altre figure geometriche, senza i quali mezi impossibile a intenderne umanamente parola; senza questi è un aggirarsi vanamente per un oscuro laberinto. (Galileo Galilei, sesto capitolo del Saggiatore). http://www.oilproject.org/lezione/galileo-saggiatore-metodo-scientifico-sistema- tolemaico-urbano-VIII-orazio-grassi-9419.html HERNÁNDEZ GONZÁLEZ, Francisco Javier y Sebastián SALGADO GONZÁLEZ, “El Renacimiento y la nueva ciencia”, Duererías. Cuadernos de Filosofía, 2010- 2011, pp. 18. Cf.: http://guindo.pntic.mec.es/ssag0007/filosofica/renacimientoynuevaciencia%20cop ia.pdf MARQUINA, José E., Rosalía RIDAURA, José Luis Álvarez y Manuel QUINTANA [Departamento de Física, Facultad de Ciencias, UNAM] “Il Saggiatore. Un libro poco recordado”, Ciencias (México), n.º 41,enero-marzo 1996, pp. 4-8. Cf.: http://www.ejournal.unam.mx/cns/no41/CNS04102.pdf http://www.revistacienciasunam.com/es/148-revistas/revista-ciencias-41/1218-il- saggiatore-un-libro-poco-recordado.html MAS TORRES, Salvador [Universidad Complutense de Madrid], “Matemáticas, Técnica e Instrumentos en la obra de Galileo”, Teorema (Universidad Complutense de Madrid), vol. VIII, n.º 1-2, 1983, pp. 94-107. Cf.: http://www.google.fr/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja &uact=8&ved=0ahUKEwi9yPLF4bHKAhUDAxoKHaWyC1IQFggpMAE&url= http%3A%2F%2Fdialnet.unirioja.es%2Fdescarga%2Farticulo%2F2043862.pdf &usg=AFQjCNFZJicwPuECOtMTQDLVxb47mKbI4g&sig2=Py0tAlP1AKgQIC 6lOPCV4w PÉREZ TAMAYO, Ruy, “¿Existe el método científico? Historia y realidad”, Biblioteca digital Galileo Galilei”, Biblioteca digital. Cf.: http://bibliotecadigital.ilce.edu.mx/sites/ciencia/volumen3/ciencia3/161/html/meto do.html PÉREZ TAMAYO, Ruy, “II.3 Galileo Galilei”, Ibid. ant. Cf.: http://bibliotecadigital.ilce.edu.mx/sites/ciencia/volumen3/ciencia3/161/html/sec_1 3.html

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Evandro Agazzi (1934- )

AGAZZI, Evandro (1934- ), Wikipedia. Cf.: https://it.wikipedia.org/wiki/Evandro_Agazzi [Italiano, modificata per l’ultima volta il 26 gennaio 2016]

AGAZZI, Evandro, “Works by Evandro Agazzi”, philpapers. Cf.: [123 references] http://philpapers.org/autosense.pl?searchStr=Evandro%20Agazzi

AGAZZI, Evandro, “Investigadores”, Universidad Panamericana (México). Cf.: http://www.up.edu.mx/es/investigador/26101/dr-evandro-agazzi

AGAZZI, Evandro, “Table de matières des publications” [Table of content of the publications – Índice de las publicaciones], Les Académies. Cf.: http://www.lesacademies.org/en/iaps/publications/aips-tables-of- contents?showall=1&limitstart=

AGAZZI, Evandro, Helveticat. 50 titles. Cf.: http://www.helveticat.ch/search/query?match_1=PHRASE&field_1=a&term_1= Agazzi,+Evandro++&theme=Helveticat

AGAZZI, Evandro, Biblioteca Evandro Agazzi, 10 luglio 2014. Cf.: http://www.dicom.uninsubria.it/centrocattaneopreti/allegati/Biblioteca_Evandro_Agazzi _luglio_2014_schedatura.pdf

AGAZZI, Evandro, “Curriculum Vitae and List of Publications (as of 31.10.2013). Cf.: §♪♪♪♪♪§ http://www.dif.unige.it/epi/hp/agazzi/agazzipub.html

AGGAZI, Evandro, “Publicaciones”, Findeen. Cf.: http://www.findeen.es/agazzi_evandro_la_l%C3%B3gica_simb%C3%B3lica_pdf.html

AGAZZI, Evandro. Books and CD Roms: 11 Results. Books & CD Roms: 11 Results. Online contents: 335 Results. Webpages: 1. Springer. Cf.: https://www.springer.com/?SGWID=0-102-24-0- 0&searchType=EASY_CDA&queryText=evandro+agazzi&submit=Soumettre+l a+requ%C3%AAte

TAROZZI, G., Marco BUZZONI and Mario ALAI, Science between Truth and Ethical Responsibility – Evandro AGAZZI in the Contemporary and Philosophical Debate, Springer International Publishing, 2015, xiii + 337, Cf.: http://www.springer.com/us/book/9783319163680#aboutBook  Download Preface 1 PDF (1.5 MB)  Download Sample pages 2 PDF (160.6 KB)  Download Table of contents PDF (1.5 MB) This book offers the most complete and up-to-date overview of the philosophical work of Evandro Agazzi, presently the most important Italian philosopher of science and one of the most influential in the world. Scholars from seven countries explore his contributions in areas ranging from philosophy of physics and general philosophy of science to bioethics, philosophy of mathematics and logic, epistemology of the social sciences and history of science, philosophy of language and artificial intelligence, education and anthropology, metaphysics and philosophy of religion. Agazzi developed a complete and coherent philosophical system, anticipating some of the turns in the philosophy of science after the crisis of logical empiricism and exerting an equal influence on continental hermeneutic philosophy. His work is characterized by an original synthesis of contemporary analytic philosophy, phenomenology and classical philosophy, including the scholastic tradition and these threads are reflected in the different backgrounds of the contributors to this book. While upholding the epistemological value of science against scepticism and relativism, Agazzi eschews scientism by stressing the equal importance of non-scientific forms of thought, such as metaphysics and religion. While defending the freedom of research as a cognitive enterprise, he argues that as a human and social practice it must nonetheless respect ethical constraints. AGAZZI, Evandro [University of Fribourg, Switzerland; University of Genova, Italy, and President of the International Academy of Philosophy of Science] and Gerhard HEINZMANN [Professor of Philosophy at the University of Lorraine, Nancy, France] (Edited by), The Practical Turn in Philosophy of Science: Proceedings of the Annual Meeting of the International Academy of Science 2014, Milano (Italy): FrancoAngeli, 2015, pp. 203 (collana Epistemologia, diretta da Evandro Agazzi). Cf.: http://www.francoangeli.it/Ricerca/Scheda_libro.aspx?ID=22894&Tipo=Libro&s trRicercaTesto=&titolo=the+practical+turn+in+philisophy+of+science++ http://www.francoangeli.it/Area_PDFDemo/490.109_demo.pdf (pp. 1-19) After Gödel’s results the limitations of the three principal “foundational schools” became more and more evident, while the “working scientists” continued their activity caring more for the acquisition of “results” than for logical rigor. This “pragmatic turn” was perceivable also in philosophy of science due to an influence of pragmatism that replaced the previous influence of logical empiricism and analytic philosophy.

Philosophy of science as a specialized discipline was born at the beginning of the twentieth century as a reaction to the “crisis” that was affecting especially mathematics and physics in their conceptual and logical “foundations”. The philosophical investigation on the said foundations took the shape of an epistemology and methodology of science and, for historical reasons, the tools used were those of linguistic analysis and mathematical logic. This was in keeping with the formalistic approach to science inspired by the primacy attributed to the axiomatic method not only in mathematics, but also ideally in all rigorous sciences. After Gödel’s results the limitations of the three principal “foundational schools” became more and more evident, while the “working scientists” continued their activity caring more for the acquisition of “results” than for logical rigor. This “pragmatic turn” was perceivable also in philosophy of science due to an influence of pragmatism that replaced the previous influence of logical empiricism and analytic philosophy. Evandro Agazzi is the current President of the International Academy of Philosophy of Science. He was Professor at the Universities of Fribourg (Switzerland), Genoa (Italy) and at present at the Panamerican University of Mexico City. His contributions concern particularly the philosophy of logic and mathematics, the philosophy of physics, general philosophy of science, the ethics of science and technology. He has published more than 80 books and over 1000 papers.

Gerhard Heinzmann is professor of philosophy at the University of Lorraine in Nancy. Director and founder (1992-2007) of the research group “Laboratoire d’Histoire des Sciences et de Philosophie – Archives Henri Poincaré”, he was director of the “Lorrain Institute for Humanities and Social Sciences” (MSH Lorraine) from 2007 to 2014. Editor of the “Publications of the Henri Poincaré Archives” (Birkhäuser/Springer) and of the journal “Philosophia Scientiae” (Kimé), his areas of specialization are: Poincaré Studies, Philosophy of Mathematics, Philosophy of Logic, French Philosophy of Science in the 20th century. Indice Evandro Agazzi, Gerhard Heinzmann, Introduction Evandro Agazzi, Truth Between Semantics and Pragmatics Alberto Cordero, Pragmatism: The Good, the Bad, and the Ugly Fabio Minazzi, Pragmatism and Objectivity Lena Soler, Shifts Introduced by the Practice Turn in Philosophy, History, and Social Studies of Science Marco Buzzoni, The Practice Turn in Philosophy of Science: The Discovery/Justification Distinction, and the Social Dimension of Scientific Objectivity Gerhard Heinzmann, Pragmatism and the Practical Turn in Philosophy of Mathematics: Explanatory Proofs Paul Weingartner, Pragmatic Aspects of Tarski’s Truth Condition Hans Lenk, An Epistemological and Action-theoretical Approach to Pragmatic Realism Vincenzo Fano, Giovanni Macchia, Robustness and The Rejection of Wegener’s Continental Drift in the Thirties Reinhard Kahle, After Hilbert and Brouwer: Bourbaki and Bishop.

AGAZZI, Evandro, Scientific Objectivity and Its Contexts, Switzerland: Springer Science + Business Media, 2014, pp. 482. Cf.: https://books.google.fr/books?id=TzDABAAAQBAJ&printsec=frontcover&hl=fr &source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false The first part of this book is of an epistemological nature and develops an original theory of scientific objectivity, understood in a weak sense (as intersubjective agreement among the specialists) and a strong sense (as having precise concrete referents). In both cases it relies upon the adoption of operational criteria designed within the particular perspective under which any single science considers reality. The “object” so attained has a proper ontological status, dependent on the specific character of the criteria of reference (regional ontologies). This justifies a form of scientific realism. Such perspectives are also the result of a complex cultural-historical situation. The awareness of such a “historical determinacy” of science justifies including in the philosophy of science the problems of ethics of science, relations of science with metaphysics and social dimensions of science that overstep the traditional restriction of the philosophy of science to an epistemology of science. It is to this “context” that the second part of the book is devoted. Evandro Agazzi completed his studies in Philosophy at the Catholic University of Milan and in Physics at the State University of the same city. He became full professor of Philosophy of Science at the University of Genoa in 1970 and also held the chair of Philosophical Anthropology, Philosophy of Nature and Philosophy of Science at the University of Fribourg in Switzerland (1979-1998) and a chair in Philosophy in the Department of Humanities of the Autonomous Metropolitan University/Campus of Cuajimalpa of Mexico City (2009-2013). He taught as a visiting professor at the Universities of Düsseldorf, Berne, Pittsburgh, Stanford and Geneva, as well as at other universities for shorter times. At present he is Emeritus Professor of Philosophy at the University of Genoa and full Professor in the Department of Bioethics of the Universidad Panamericana of Mexico City. Professor Agazzi is President of the International Academy of Philosophy of Science (Brussels). He was also President, and is now Honorary President, of the International Federation of the Philosophical Societies (FISP), the International Institute of Philosophy (Paris). He has received many honors. He has been elected as a member of the Russian Academy of Sciences (2012) and the Mexican Academy of Sciences (2012). His publications include more than 70 books, of which he is the author and/or editor and almost 1000 papers and articles, including contributions to books, anthologies, encyclopedias and journals. He is the editor of Epistemologia, an Italian journal for the philosophy of science and is a consulting editor for several international journals.

AGAZZI, Evandro, Science, Metaphysics, Religion, Milano: Franco Angeli, 2014, pp. 218. Cf.: http://www.lesacademies.org/en/iaps/publications/aips-tables-of- contents?showall=1&limitstart http://www.ebay.it/itm/8891709247-SCIENCE-METAPHYSICS-RELIGION- EVANDRO-AGAZZI-FRANCOANGELI- /181964950743?hash=item2a5df4ccd7:g:rfkAAOSwUdlWctct The contributions of this book investigate systematically and historically many aspects of the relations between science, metaphysics and religion. The search for the autonomy of different domains of human culture is one of the essential traits of Modernity, but the exaggerations of this process count among the causes of our present cultural uneasiness. Today the problem consists in counterbalancing the reciprocal isolation between different fields of human life, without going back to some new hierarchy, for example by inverting the ancient order and putting science at the summit, considering it as the only genuine form of knowledge, that is at variance, in particular, with metaphysics and

religion. This is the attitude of "scientism" that has produced as a reaction an attitude of anti- science. The appreciation of the great merits of science and technology, along with the awareness of the kind of human problems and aspirations that they are unable to satisfy, imposes the search for an integration that must rely upon the recognition of the specificity of the different domains bound to their delimited perspective, but at the same time on the analysis of the mutual links that subsist among them. The contributions of this book investigate systematically and historically many aspects of the relations between science, metaphysics and religion. AGAZZI, Evandro (ed.), Representation and Explanation in the Sciences, Milano: FrancoAngeli, 2013, pp. 243 [pp. 55-69]. Cf.: [Papers presented at the Conference of the International Academy of Philosophy of Science -Louvain-la-Neuve, 26-28 April 2011]. https://www.francoangeli.it/Area_PDFDemo/490.103_demo.pdf http://www.lesacademies.org/en/iaps/publications/aips-tables-of- contents?showall=1&limitstart Representation and explanation are distinct notions in the philosophy of science, since the first can be defined as an answer to a how-question, and the second as an answer to a why- question. In particular, the task of providing explanations has been traditionally attributed to scientific theories. These notions, however, are also strictly interrelated, like shown by the variety of the approaches offered by the papers included in this volume. Representation and explanation are distinct notions in the philosophy of science, since the first can be defined as an answer to a how-question, and the second as an answer to a why- question. In particular, the task of providing explanations has been traditionally attributed to scientific theories. These notions, however, are also strictly interrelated, especially because in more recent times the role of theories has been sometimes downgraded to that of simply offering representations or images of physical phenomena and, correspodingly, the role of representations was upgraded to the capability of offering explanations. Several philosophically interesting issues are implicit in these relationships, going from the permanent dispute on scientific realism, to other methodological and even metaphysical, ontological and semantic questions. In order to investigate this topic certain historical reconstructions are very useful, and, in addition, the consideration of different contexts is almost indispensable. These reasons explain the variety of the approaches offered by the papers included in this volume. They can be put in some organic order (as it has been attempted in giving them a particular disposition in the volume), but the greater interest probably resides in the articulated difference of their optics. Becoming acquainted with this variety can constitute a real intellectual enrichment for the reader interested in the philosophy of science. AGAZZI, Evandro (Edited by.), The Legacy of A.M. Turing, Milano: Franco Angeli, 2013, pp. 197. http://www.lesacademies.org/en/iaps/publications/aips-tables-of- contents?showall=1&limitstart

The papers collected in the present book deal with some of the most salient aspects of Turing’s whole work. The exceptional value of Turing’s work consists in the confirmation of a fundamental role played by mathematics in the development of science, that of a tool for the rigorous analysis of concepts. Indeed his characterization of the general concept of computation opened new vistas in several fields of research and also started the must typical technologies of our time.

Moreover, these new views also had a strong resonance in philosophy and outlined interesting approaches in biology and quantum physics. Owing to his “operational” approach to concepts, and to his ability to find technological implementations of abstract models, his work can also be considered as the foundation of computer science and of the artificial intelligence program. For the general public the name of Turing is associated with the idea of the “machine” that is named after him, but this happens because the abstract concept of a machine wa shown by him to be the most suitable means for making clear and precise two concepts (that of computability and that of an “effective procedure” for solving any mathematical problem) that were at the core of the research on the foundations of mathematics at that time. Turing’s goal, however, was that of representing by his machine the general mechanical process carried out by human beings in their resoning. In this way he opened the way to the program of artificial intelligence, in which he also brought interesting contributions of a technical kind. Yet he went beyond the purely technical problem, by addressing also the philosophical problem of the possibility of distinguishing human intelligence from machine intelligence, by proposing his famous “test” that still constitutes a matter of debate among the specialists of artificial intelligence and philosophy of mind. The papers collected in the present book touch upon some of the most salient aspects of the wide spectrum of his work. AGAZZI, Evandro (Editor), Probability in the Sciences, Netherlands: Springer, 2013 [1988], pp. x + 269 (Synthese Library / Volume 201). Cf.: http://www.booklooker.de/B%C3%BCcher/Agazzi+Probability-in-the- Sciences/id/A022IplN01ZZk http://www.springer.com/gb/book/9789027728081 Probability has become one of the most characteristic concepts of modern culture, and a ‘probabilistic way of thinking’ may be said to have penetrated almost every sector of our intellectual life. However it would be difficult to determine an explicit list of ‘positive’ features, to be proposed as identification marks of this way of thinking. One would rather say that it is characterized by certain ‘negative’ features, i.e. by certain attitudes which appear to be the negation of well-established traditional assumptions, conceptual frameworks, world outlooks and the like. It is because of this opposition to tradition that the probabilistic approach is perceived as expressing a ‘modern’ intellectual style. As an example one could mention the widespread diffidence in philosophy with respect to self-contained systems claiming to express apodictic truths, instead of which much weaker pretensions are preferred, that express ‘probable’ interpretations of reality, of history, of man (the hermeneutic trend). An analogous example is represented by the interest devoted to the study of different patterns of ‘argumentation’, dealing with reasonings which rely not so much on the truth of the premisses and stringent formal logic links, but on a display of contextual conditions (depending on the audience, and on accepted standards, judgements, and values), which render the premisses and the conclusions more ‘probable’ (the new rhetoric). AGAZZI, Evandro and Massimo PAURI [Department of Physics (Theoretical Division), University of Parma, Italy], The Reality of the Unobservable: Observability, Unobservability and Their Impact on the Issue of Scientific Realism, Dordrecht: Springer Science + Business Media, 2013 [2000], pp. 378 (Boston Studies in the Philosophy and History of Science Volume 215). Cf.: https://books.google.fr/books?id=Hr3wCAAAQBAJ&printsec=frontcover&hl=fr &source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false Introduction. Observability and Scientific Realism

It is commonly thought that the birth of modern natural science was made possible by an intellectual shift from a mainly abstract and speculative conception of the world to a carefully elaborated image based on observations. There is some grain of truth in this claim, but this grain depends very much on what one takes observation to be. In the philosophy of science of our century, observation has been practically equated with sense perception. This is understandable if we think of the attitude of radical empiricism that inspired Ernst Mach and the philosophers of the Vienna Circle, who powerfully influenced our century’s philosophy of science. However, this was not the attitude of the founders of modern science: Galileo, for example, expressed in a famous passage of the Assayer the conviction that perceptual features of the world are merely subjective, and are produced in the ‘anima!’ by the motion and impacts of unobservable particles that are endowed uniquely with mathematically expressible properties, and which are therefore the real features of the world. Moreover, on other occasions, when defending the Copernican theory, he explicitly remarked that in admitting that the Sun is static and the Earth turns on its own axis, ‘reason must do violence to the sense’, and that it is thanks to this violence that one can know the true constitution of the universe. AGAZZI, Evandro, El impacto epistemológico de la tecnología, Slideshare, 27 de febrero de 2013. Transcripción de un seminario del mismo título impartido por el autor en la Facultad de Filosofía de la Universidad de Sevilla los días 7 y 8 de abril de 1997. Cf.: http://fr.slideshare.net/bitocchi/agazzi-el-impacto-epistemolgico-de-la-tecnologia AGAZZI, Evandro, Ragioni e limiti del formalismo. Saggi di filosofia della logica e della matematica. A cura e con una prefazione di Fabio MINAZZI, Milano: FrancoAngeli, 2012, pp. 326 . Cf.: Ver: p. 301 con una bibliografía de E.A, muy bien hecha. See: p. 301 with a well-done bibliography of E.A. https://books.google.fr/books?id=9PH9CQAAQBAJ&pg=PA301&lpg=PA301&d q=AGAZZI,+Evandro,+Temi+e+problemi+di+Filosofia+della+Fisica,+Milano:+ Manfredi+Editore,+1969&source=bl&ots=id9Ixd- cBi&sig=6XvKaXvPCZm9aLrW11lj_Go3zNw&hl=fr&sa=X&ved=0ahUKEwjgk oeBwsrKAhXJ2BoKHZYmDAUQ6AEIIzAA#v=onepage&q=AGAZZI%2C%20 Evandro%2C%20Temi%20e%20problemi%20di%20Filosofia%20della%20Fisi ca%2C%20Milano%3A%20Manfredi%20Editore%2C%201969&f=false La prospettiva formale ha dominato la cultura logico-matematica del Novecento. I primi volumi di Evandro Agazzi (Introduzione ai problemi dell’assiomatica, 1961 e La logica simbolica, 1964) sviluppavano una riflessione capace di indicare sia le ragioni storico- concettuali che hanno condotto all’egemonia del formalismo, sia i rilievi che fanno emergere – attraverso un’accurata analisi delle sue caratteristiche– le ragioni dell’impossibilità di assolutizzarlo. Questa riflessione è proseguita per tutto l’arco della carriera scientifica di Agazzi, il quale ha sviluppato analisi critiche addentratesi specialmente in problemi di teoria del significato e di ontologia, tradottesi in alcune proposte originali la cui correttezza, nonostante il loro ardimento, è stata riconosciuta nelle sedi tecnicamente più autorevoli. L’articolo “Consistency, Truth and Ontology”, apparso su “Studia Logica” nel 2011, testimonia, a mezzo secolo dall’opera prima, il permanere di questi interessi di ricerca e l’attualità che viene loro riconosciuta. Il presente volume raccoglie alcuni dei principali saggi (difficilmente reperibili perché apparsi su riviste o in volumi collettivi, pubblicati, in parte, in lingua straniera) che hanno scandito questo itinerario. Un’apposita “Introduzione” e un’organica distribuzione degli studi conferiscono unità all’intera raccolta, arricchita da una prefazione del curatore e da una bibliografia per ulteriori approfondimenti critici. http://www.ibs.it/code/9788820408626/agazzi-evandro/ragioni-limiti-del.html

AGAZZI, Evandro (Edited by), Modern Logic. A Survey: Historical, Philosophical and Mathematical aspects of Modern Logic and Its Applications, Dordrecht: Holland/Boston: USA/London: England: D. Reidel Publishing Company, 2012 [1981], pp. 483 (Synthese Library/Volume 149). Cf.: https://books.google.fr/books?id=Ky30CAAAQBAJ&printsec=frontcover&hl=fr &source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false Logic has attained in our century a development incomparably greater than in any past age of its long history, and this has led to such an enrichment and proliferation of its aspects, that the problem of some kind of unified recomprehension of this discipline seems nowadays unavoidable. This splitting into several subdomains is the natural consequence of the fact that Logic has intended to adopt in our century the status of a science. This always implies that the general optics, under which a certain set of problems used to be considered, breaks into a lot of specialized sectors of inquiry, each of them being characterized by the introduction of specific viewpoints and of technical tools of its own. The first impression, that often accompanies the creation of one of such specialized branches in a discipline, is that one has succeeded in isolating the ‘scientific core’ of it, by restricting the somehow vague and redundant generality of its original ‘philosophical’ configuration. But, after a while, it appears that some of the discarded aspects are indeed important and a new specialized domain of investigation is created to explore them. By following this procedure, one finally finds himself confronted with such a variety of independent fields of research, that one wonders whether the fact of labelling them under a common denomination be nothing but the contingent effect of a pure historical tradition. AGAZZI, Evandro and György DARVAS, Philosophy of Mathematics Today, Springer Science + Business, 2012 [1997], pp. 361 (Episteme 22). Cf.: https://books.google.fr/books?id=zMZ9CAAAQBAJ&printsec=frontcover&hl=fr &source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false Mathematics is often considered as a body of knowledge that is essentially independent of linguistic formulations, in the sense that, once the content of this knowledge has been grasped, there remains only the problem of professional ability, that of clearly formulating and correctly proving it. However, the question is not so simple, and P. Weingartner’s paper (Language and Coding-Dependency of Results in Logic and Mathematics) deals with some results in logic and mathematics which reveal that certain notions are in general not invariant with respect to different choices of language and of coding processes. Five example are given: 1) The validity of axioms and rules of classical propositional logic depend on the interpretation of sentential variables; 2) The language dependency of verisimilitude; 3) The proof of the weak and strong anti inductivist theorems in Popper’s theory of inductive support is not invariant with respect to limitative criteria put on classical logic; 4) The language- dependency of the concept of provability; 5) The language dependency of the existence of ungrounded and paradoxical sentences (in the sense of Kripke). The requirements of logical rigour and consistency are not the only criteria for the acceptance and appreciation of mathematical propositions and theories. AGAZZI, Evandro, The Problem of Reductionism in Science (Colloquium of the Swiss Society of Logic and Philosophy of Science, Zurich,, May 18-19, 1990, Dordrecht: Springer Science + Business, 2012 [1991], pp. 361 (Episteme 18). Cf.: https://books.google.fr/books?id=eRArBgAAQBAJ&printsec=frontcover&hl=fr &source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false

The topic to which this book is devoted is reductionism, and not reduction. The difference in the adoption of these two denominations is not, contrary to what might appear at first sight, just a matter of preference between a more abstract (reductionism) or a more concrete (reduction) terminology for indicating the same subject matter. In fact, the difference is that between a philosophical doctrine (or, perhaps, simply a philosophical tenet or claim) and a scientific procedure. Of course, this does not mean that these two fields are separated; they are only distinct, and this already means that they are also likely to be interrelated. However it is useful to consider them separately, if at least to better understand how and why they are interconnected. Just to give a first example of difference, we can remark that a philosophical doctrine is something which makes a claim and, as such, invites controversy and should, in a way, be challenged. A scientific procedure, on the other hand, is something which concretely exists, and as such must be first of all described, interpreted, understood, defined precisely and analyzed critically; this work may well lead to uncovering limitations of this procedure, or of certain ways of conceiving or defining it, but it does not lead to really challenging it. AGAZZI, Evandro and Alberto CORDERO [Department of Philosophy, Queen’s College; City University of New York, USA], Philosophy and the Origin and Evolution of Universe, Dordrecht-Boston-London: Springer Science+Business Media, B.V., 2012 [1991], pp. 466 (Synthese Library Volume 217). Papers from the Annual Meeting of the International Academy of Philosophy of Science, Lima, Peru, August 1988. Cf.: https://books.google.fr/books?id=mFXtCAAAQBAJ&printsec=frontcover&hl=fr &source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false It has often been noted that a kind of double dynamics characterizes the development of science. On the one hand the progress in every discipline appears as the consequence of an increasing specialization, implying the restriction of the inquiry to very partial fields or aspects of a given domain. On the other hand, an opposite (but one might better say a complementary) trend points towards the construction of theoretical frameworks of great generality, the aim of which seems to correspond not so much to the need of providing «explanations» for the details accumulated through partial investigation, as to the desire of attaining an horizon of global comprehension of the whole field. This intellectual dialectics is perceivable in every discipline, from mathematics, to physics, to biology, to history, to economics, to sociology, and it is not difficult to recognize there the presence of the two main attitudes according to which human beings try to make «intelligible» the world surrounding them (including themselves), attitudes which are sometimes called analysis and synthesis. They correspond respectively to the spontaneous inclination which pushes us to try to understand things by seeing «how they are made», in the sense of «looking into them» and breaking them into their constitutive parts, or rather to encompass things in a global picture, where they are accounted for as occupying a place, or playing a role, which are understandable from the point of view of the whole. AGAZZI, Evandro and Fabio MINAZZI (eds.), Evolutionism and Religion. Proceedings of the Meeting in Florence, 19-21 November 2009. Milano-Udine: Mimesis Edizioni, 2011, pp. 320. Cf.: http://www.lesacademies.org/en/iaps/publications/aips-tables-of- contents?showall=1&limitstart

19 http://mimesisedizioni.it/libri/filosofia/centro-internazionale- insubrico/evolutionism-and-religion.html The theory of evolution has been often used in the last decades as a weapon in the atheistic fight against religion. This is in way strange, since peaceful relations between evolutionism and religion had been quickly attained already in the nineteenth century, after a few initial but isolated polemics. Moreover, not only the “compatibility” of evolutionism and religion has been defended by many scholars on the ground of different arguments, but even theological perspectives explicitly “incorporating” evolution in a Christian worldview have been elaborated by such prominent figures as Drummond, Theilard de Chardin and Maritain. Yet a legal controversy lasted more than half a century in the courts of the USA has determined the revival of a dispute that has gradually acquired the overtones of an ideological confrontation. Therefore, an unbiased analysis of this issue appears of significant cultural importance, and two sister Academies (the International Academy of Philosophy of Science and the International Academy of Religious Sciences) have intended to propose a modest contribution to this analysis in a joint meeting devoted to the theme Evolutionism and Religion that took place in Florence in 2009. The papers published in the present book offer four different approaches to evolutionism: the scientific one, the philosophical-epistemological one, the cultural one and the religious one. Finally a concluding section deals with the controversial issue of the “Intelligent Design”. Through this separate analysis several ambiguities can be dissipated, and the correct, delimited and specific points of view from which evolution can be considered are clarified. Within each one of these approaches, concepts and principles regarding evolutionism receive distinct but legitimate meanings. Since distinction does not entail separation, however, the intellectual effort of correlating such approaches appears as an intellectual challenge of undeniable difficulty but also of great cultural importance. ***** Le colloque organisé conjointement par l’Académie Internationale de Philosophie des Sciences et l’Académie Internationale des Sciences religieuses, à l’occasion de l’anniversaire de Darwin s’inscrit dans la perspective d’une recherche interdisciplinaire où la philosophie tient une place importante. La première partie donne des informations scientifiques avec le souci d’une ouverture philosophique. Werner Arber part de la métaphore de la « mère nature » pour situer les sciences de la vie, Jacques Ricard est attentif à la tension entre les concepts de sélection et d’auto-organisation, Peter Schuster s’interroge sur les concepts impliqués dans les débats sur l’origine de la vie et Paul Weingartner traite du concept de hasard dans la théorie de l’évolution. La deuxième partie du colloque est consacrée à l’épistémologie en abordant successivement la question de la prédiction dans la théorie darwinienne (par Alberto Cordero), celle du réalisme en sciences (Marco Buzzoni) et de la philosophie de Darwin lui-même (Fabio Minazzi). L’attention se porte minutieusement sur le sens de l’hésitation de Darwin à recourir au terme « évolution » (Jean-Guy Meunier, Maxime Sainte-Marie et Jean-François Chartier). La troisième partie s’attache aux aspects culturels du débat en relevant la dimension symbolique et sociale du propos. Trois étapes dans cette réflexion sur l’incidence du darwinisme sur la culture (Wenceslao Gonzalez), la société (Ramon Queralto) et les passions religieuses soulevées à ce propos (Peter Kemp). La partie suivante donne la parole aux théologiens en situant l’accueil du darwinisme par les théologiens de son temps (Alasdair Heron), et par deux études bibliques, d’abord sur les premières pages de la Genèse (Jean- Marie Van Cangh) et l’hymne aux Colossiens (Michel Gourgues). La dernière partie entre dans une étude de théologie plus spéculative dans le souci de se situer par rapport à la démarche de la théologie naturelle. La question de la finalité est posée par Jesus Zamora Bonilla. Une très remarquable étude des textes personnels de Darwin est faite par Antonello La Vergata ; celui-ci montre combien la présence du mal dans la nature est à l’origine de l’agnosticisme de Darwin et de son rejet de la théologie naturelle anglo-saxonne. Jean-Michel Maldamé traite du renouveau de cette tradition dans le mouvement dit « Dessein intelligent », courant de pensée étudié au plan métaphysique par Evandro Agazzi.

Cet ensemble a le mérite d’être plus que les autres colloques centré sur la philosophie de la nature, un point souvent méconnu et pourtant bien nécessaire pour un dialogue science-foi. Ces trois ouvrages, parmi bien d’autres, montrent comment les questions anthropologiques ne sauraient aujourd’hui se contenter d’un discours intemporel sur l’essence humaine ou sur la prise en compte de la seule expérience spirituelle. Il y a ainsi une quête plus large des fondements ; la difficulté d’y accéder ne saurait être une raison de l’éluder comme le font hélas trop de moralistes et de théologiens attentifs à la spiritualité. Jean-Michel Maldamé http://moodle-adae.ict-toulouse.fr/module_paiement/recensions.php?id=52 AGAZZI, Evandro, “«Intelligent Design» as a Scientific and Metaphysical Concept”, in Agazzi, Evandro and Fabio Minazzi (eds.), Evolutionism and Religion…, pp. 239- 314. http://www.uam.mx/sah/pre-pa/tema04/Informe%202011_cuaji.pdf §♦♦♦♦♦§* AGAZZI, Evandro, “Conocimiento científico y fe cristiana con especial consideración de las teorías de la evolución”, Persona y Cultura (Universidad Católica San Pablo, Arequipa, Perú), año 9, n.º 9, 2011, pp. 90-119. Cf.: http://ucsp.edu.pe/personaycultura/archivos/Evandro-Agazzi-Conocimiento- cientifico-y-fe-cristiana.pdf AGGAZI, Evandro, La ciencia y el alma de Occidente, Madrid: Tecnos, 2011, pp. 343. Cf.: http://www.casadellibro.com/libro-la-ciencia-y-el-alma-de- occidente/9788430952243/1862173 La ciencia es un revolucionaria invención griega, tal vez la más típica contribución legada por Occidente a la civilización. Desde la antigüedad las distintas “revoluciones” en la concepción y práctica de la ciencia han tenido reflejo en todos los aspectos de la cultura. Esto es paladino en la modernidad co n la revolución científica que alumbró la física matemático-experimental primero y toda una serie de ciencias después. La nueva ciencia se convirtió a los ojos de muchos filósofos e intelectuales no ya en la forma emblemática del saber, sino en su forma exclusiva. A partir de ahí se dieron profundos cambios de mentalidad y de costumbres, además de los de índole política y social, cuyo ejemplo más palmario fue la revolución industrial. Asimismo en el campo de las humanidades el surgimiento de las ciencias humanas no fue menos significativo. La consecuencia de ello fue un difuso “cientificismo”, que extendió la convicción de que las ciencias tendrían la capacidad de resolver todos los problemas de la humanidad. Esto se ha revelado como una ilusión: a la par que asistimos al vertiginoso crecimiento de la tecnociencia es creciente la preocupación por su pérdida de control. Ello explica la búsqueda de valores-guía para la orientación de la nueva civilización tecnológica y el renovado interés por las temáticas de frontera entre tecnociencia, ética y religión. AGAZZI, Evandro and Giuliano Di BERNARDO, Relations Between Natural Sciences and Human Sciences – Relations entre les sciences naturelles et les sicences humaines, Genova: Casa Editrice Tilgher, 2010, pp. 352 (Special Issues of Epistemologia, n.º 15). Cf.: http://www.lesacademies.org/en/iaps/publications/aips-tables-of- contents?showall=1&limitstart AGAZZI, Evandro, Filosofía de la naturaleza, ciencia y cosmología, México: Fondo de Cultura Económica de España, 2010 [1995, italiano; 2000, español], pp. 146 (prólogo de Francisco Miró Quesada C.). Cf.: http://www.casadellibro.com/libro-filosofia-de-la-naturaleza-ciencia-y- cosmologia/9789681661793/1708021

El autor aborda la relación entre ciencia y filosofía a la luz de disciplinas como la física cuántica y la cosmología: las dificultades técnicas que implica experimentar con las supercuerdas del espacio-tiempo, por ejemplo; o la variación que ha sufrido el concepto de lo directamente observable, que ha hecho que muchos físicos importantes consideren que la ciencia y la metafísica están ahora más cerca que nunca. También plantea que la filosofía analítica –predominante desde la Segunda Guerra Mundial hasta los años setenta– se ha estancado, por lo cual es necesario una apertura de horizonte o comprensión global del universo –tal cual es la filosofía de la naturaleza–, con procedimientos analíticos ya indispensables. AGAZZI, Evandro, “La evolución entre ciencia e ideología”, ArtefaCTos, vol. 2, n.º 1, diciembre de 2009, pp. 38-63. Cf.: http://gredos.usal.es/jspui/bitstream/10366/72717/1/La_evolucion_entre_ciencia_e _ideologia.pdf AGAZZI, Evandro, Javier ECHEVERRÍA and Amparo GÓMEZ RODRÍGUEZ (Edited by), Epistemology and the Social, Amsterdam-New York: Editions Rodopi, 2008, pp. 231 (Poznan Studies in the Philosophy of the Sciences and Humanities 96). Cf.: https://books.google.fr/books?id=xBvbQgWtgjsC&printsec=frontcover&hl=fr&s ource=gbs_ge_summary_r&cad=0#v=onepage&q&f=false Epistemology had to come to terms with “the social” on two different occasions. The first was represented by the dispute about the epistemological status of the “social” sciences, and in this case the already well established epistemology of the natural sciences seemed to have the right to dictate the conditions for a discipline to be a science. But the social sciences could successfully vindicate the legitimacy of their specific criteria for scientificity. More recently, the impact of social factors on the construction of our knowledge (including scientific knowledge) has reversed, in a certain sense, the old position and promoted social inquiry to the role of a criterion for evaluating the purport of cognitive (including scientific) statements. But this has undermined the traditional characteristics of objectivity and rigor that seem constitutive of science. Moreover, in order to establish the real extent to which social conditionings have an impact on scientific knowledge one must credit sociology with a sound ground of reliability, and this is not possible without a preliminary “epistemological” assessment. These are some of the topics discussed in this book, both theoretically and with reference to concrete cases. AGAZZI, Evandro and Fabio MINAZZI [Professor of Philosophy at the University of the Salento (Lecce)] (eds.), Science and Ethics. The Axiological Contexts of Science, Brussels (Belgium): Peter Lang, 2008, pp. 296 (Collection “Philosophy and Politics” Nº 14). Papers presented at the joint meeting of the International Academy for Religious Sciences, with the support of the Dipartimento di filologia classica e di Scienze filosophique dell’Università del Salento, held in Lecce on 17- 21 October 2003. Cf.: https://books.google.fr/books?id=RWysX- QC_C8C&printsec=frontcover&hl=fr&source=gbs_ge_summary_r&cad=0#v=o nepage&q&f=false Philosophy of science used to be identified with the logical and methodological analysis of scientific theories, and any allusion to values was considered as a deplorable intromission in a philosophical investigation that should remain strictly epistemological. As a reaction against this view, an opposite –sociological– approach

downplayed the usual virtues of scientific knowledge (such as logical rigor and empirical adequacy) as artificial imageries that cover the actual nature of science, that is a social product submitted to all the kinds of social conditionings and compromises. A more balanced view is badly needed today, when technoscience is permeating all aspects of our civilization and wise persons understand that we cannot survive without using science and technology but at the same time we need to steer their development in view of the real benefit of humankind. We must investigate how science, technology and values are legitimately interconnected and, in particular, how the discourses of ethics, politics and religion can enter a fruitful dialogue with science. The essays presented in this volume offer a valuable contribution to this interdisciplinary study. AGAZZI, Evandro e Giuseppe BERTAGNA, Scienza. Intervista di Giuseppe Bertagna, Brescia: La Scuola Editrice, 2008, pp. 112 (Collana Interviste). L’intervista a Evandro Agazzi si trasforma in queste pagine in una vera e propria “autobiografia culturale” che affronta i problemi della scienza nella prospettiva di una vita spesa a cercare di capire i limiti e le possibilità della “conoscenza” moderna. Per Agazzi, filosofo della scienza, la logica matematica ha portato all’esigenza di affrontare la filosofia della scienza e, di conseguenza, la filosofia generale nella prospettiva di analizzare i problemi nella loro intrinseca complessità.

AGAZZI, Evandro, Le rivoluzioni scientifiche e il mondo moderno, Fondazione Achille e Giulia Boroli, 2008, pp. 304. (Collana Homo Sapiens). Cf.: http://www.fondazioneaegboroli.it/fondazione/collana_XIII.html La scienza è forse il contributo più tipico che l’Occidente ha recato alla civiltà umana. Già a partire dall’antichità le diverse “rivoluzioni” nel modo di concepire e praticare la scienza si sono riflesse su tutti gli aspetti della civiltà occidentale. Ciò fu particolarmente chiaro nell’età moderna, alle cui radici sta la rivoluzione scientifica da cui è nata dapprima la fisica matematico-sperimentale e poi una serie di altre scienze. La nuova scienza è diventata agli occhi di molti filosofi e intellettuali non solo la forma emblematica del sapere, ma addirittura la forma esclusiva di esso. La massa di applicazioni che la nuova scienza ben presto permise, determinò il passaggio dalla semplice tecnica alla ben più complessa “tecnologia”. Ne son venuti cambiamenti profondi di mentalità e di costumi, oltre che di assetto sociale e politico, il cui esempio più evidente fu la rivoluzione industriale. Anche nel campo delle discipline umanistiche il sorgere delle scienze umane non è stato meno significativo. La conseguenza fu un diffuso “scientismo”, ossia la convinzione che le scienze sarebbero state in grado di risolvere tutti i problemi dell’umanità. Questa si è rivelata un’illusione: mentre il Novecento assisteva a un vertiginoso progresso delle tecnoscienze, con l’esplorazione e lo sfruttamento tecnologico dell’infinitamente piccolo, crescenti preoccupazioni si sono venute svegliando a proposito di una crescita della tecnoscienza che sembra ormai fuori controllo. Pertanto la ricerca di valori-guida per l’orientamento della nuova civiltà tecnologica e per la ricerca di un senso della vita stanno suscitando rinnovati interessi per le tematiche di frontiera tra scienza, tecnologia, filosofia, etica e religione. AGAZZI, Evandro, Right, Wrong and Science. The Ethical Dimensions of the Techno- Scientific Enterprise, Edited by Craig Dilworth, Amsterdam-New York: Rodopi, 2004, pp. 354 (Poznań Studies in the philosophy of the sciences and the humanities Volume 81). Cf.: https://books.google.fr/books?id=0ZtkBFEJ_pIC&printsec=frontcover&hl=fr&s ource=gbs_ge_summary_r&cad=0#v=onepage&q&f=false Solving the problem of the negative impact of science and technology on society and the environment is indeed the greatest challenge of our time. To date, this challenge

has been taken up by few professional philosophers of science, making this volume a welcome contribution to the general debate. Agazzi’s treatment involves viewing modern science and technology as each constituting systems. Against the background of this approach, he provides a penetrating analysis of science, technology and ethics, and their interrelations. Agazzi sees the solution to the problem as lying in the moral sphere and including a multilateral assumption of responsibility on the part of decision makers both within and outside of science. AGAZZI, Evandro (a cura di), Valore e limiti del senso comune, Milano: FrancoAngeli, 2004, pp. 544. Cf.: http://www.francoangeli.it/Ricerca/Scheda_libro.aspx?CodiceLibro=490.83 Il concetto di senso comune non ha un significato univoco e ciò ha indotto a darne valutazioni molto diverse. Inteso come sinonimo di “buon senso” (ossia come innata disposizione “pratica” a comportarsi ragionevolmente nelle circostanze ordinarie della vita) esso viene di solito apprezzato positivamente. Se gli si attribuisce un significato conoscitivo (intendendolo come un bagaglio di conoscenze, giudizi, convinzioni e principi largamente condivisi anche da chi non ha particolari competenze) può essere valutato in modi opposti. Infatti è possibile vederlo come atteggiamento ingenuo, acritico e molto spesso fallace (cui vengono contrapposte le conoscenze precise e criticamente vagliate del sapere specialistico e in particolare scientifico). Questo atteggiamento svalutativo è stato assunto dai primi filosofi greci, e poi da molti filosofi della modernità. Tuttavia sin dall’antichità è stata presente anche una tendenza opposta: il fatto che certe convinzioni e principi appaiano condivisi dalla stragrande maggioranza degli uomini è visto come una garanzia della loro validità, che diverse filosofie hanno cercato di giustificare. L’età moderna ha “tematizzato” il problema del senso comune: sin dal Settecento sono così apparse sistematiche difese del senso comune, che si sono ripresentate anche in seno alla filosofia contemporanea, chiarendo per un verso la sua natura e, per altro verso, la insopprimibilità della sua funzione in quanto presupposto necessario per ogni discorso filosofico e per la stessa scienza. I saggi raccolti in questo volume offrono una panoramica abbastanza completa su questo insieme di problemi, analizzando dapprima i principali tentativi di caratterizzare il senso comune e le vicende della sua considerazione nella storia del pensiero filosofico. Vengono in seguito studiati i rapporti che il senso comune intrattiene con la filosofia da un punto di vista sistematico, ossia con le principali branche in cui la filosofia stessa si suddivide. Segue una parte dedicata allo studio dei rapporti fra senso comune e scienza, sia da un punto di vista generale, sia rispetto ad alcune discipline specializzate. Come conclusione, si considera il ruolo che la credenza e la certezza (che sono le caratteristiche salienti del senso comune) ricoprono in qualunque conoscenza umana. In un momento storico come il nostro, in cui si avverte l’urgenza di poter fare affidamento su una qualche base “comune” per affrontare i problemi che incalzano “globalmente” l’umanità, questa complessa riflessione sul valore del senso comune (che non esclude la presa di coscienza anche dei suoi limiti rispetto ai saperi disciplinari) appare ricca di significato e attualità. Indice Evandro Agazzi, Introduzione Sezione I Caratterizzazioni del senso comune Evandro Agazzi, Il senso comune e l’unità dell’esperienza Craig Dilworth, Il senso comune, i princìpi e la scienza Luisa Montecucco, Il senso comune come “teoria” e come “limite”

Sezione II Il senso comune nella storia del pensiero occidentale Domenico Antonino Conci, Alla ricerca delle origini della nozione di senso comune: una prospettiva di antropologia fenomenologica Letterio Mauro, Il senso comune nel pensiero classico Gordon Graham, La filosofia del senso comune e la sua ricezione Franca D’Agostini, Il senso comune nella filosofia analitica Claudio Ciancio, Il senso comune nel pensiero ermeneutico Carmine Di Martino, Il senso comune nella fenomenologia Sezione III Senso comune e filosofia Antonio Livi, Il senso comune e i "presupposti" della costruzione filosofica Matteo Negro, Teoria della conoscenza e senso comune Paul Gochet, Senso comune e logica Barry Smith, L’ontologia del senso comune Antonio Livi, Dalle certezze del senso comune alla problematicità della metafisica Roberto Mordacci, Etica e senso comune Sezione IV Senso comune e discipline specialistiche Evandro Agazzi, Continuità e discontinuità fra scienza e senso comune Mariano Artigas, Conoscenza ordinaria e scienza empirica Jan Faye, Senso comune e sensatezza della scienza Giuseppe Del Re, Evidenze intuitive, principi universali e conoscenza del mondo fisico Paolo Musso, Senso comune e complessità Roberto Casati, Achille Varzi, Senso comune, appartenenza e realtà Javier Echeverría, Armando Menéndez, Senso comune e tecnologie Lucio Iannotta, Osservazione e ricostruzione delle vicende giuridiche: il caso emblematico del diritto amministrativo Antonio Palma, Il riferimento alla giustizia nell’elaborazione del diritto: l’esempio emblematico del diritto romano Thomas F. Torrance, Senso comune e certezze ultime: dalla scienza alla religione e alla teologia https://books.google.fr/books?id=maUxyXSmz3sC&printsec=frontcover&hl=fr#v =onepage&q&f=false Il concetto di senso comune non ha un significato univoco e ciò ha indotto a darne valutazioni molto diverse. I saggi raccolti in questo volume analizzano dapprima i principali tentativi di caratterizzare il senso comune e le vicende della sua considerazione nella storia del pensiero filosofico. Vengono in seguito studiati i rapporti che il senso comune intrattiene con la filosofia da un punto di vista sistematico, ossia con le principali branche in cui la filosofia si suddivide. Segue una parte dedicata allo studio dei rapporti fra senso comune e scienza. Come conclusione, si considera il ruolo che la credenza e la certezza (che sono le caratteristiche salienti del senso comune) ricoprono in qualunque conoscenza umana.

AGAZZI, Evandro, “Ética y técnica”, Estudios (Instituto Tecnológico Autónomo de México), n.º 67, invierno 2003, pp. 25-36. Cf.: http://biblioteca.itam.mx/estudios/60-89/67/67.PDF

AGAZZI, Evandro (a cura di), Corrente elettriche e illuminismo scientifico, Milano: FrancoAngeli, 2002, pp. 247. Il volume si articola in quattro parti: la prima delinea la complessa e tortuosa evoluzione della “filosofia naturale” dalle grandiose intuizioni dell’Antichità, del

Medioevo e del primo Rinascimento alla grande sintesi newtoniana tra fisica terrestre e fisica celeste; la seconda si incentra sulla concezione voltiana di indagine teorica ed esperimento; la terza mostra come le grandi trasformazioni delle “discipline fisiche” abbiano permeato anche la più alta speculazione filosofica; la quarta esamina l’eredità di Volta cercando di riconfigurare l’odierna contrapposizione tra naturale e artificiale e indagando la dialettica tra realizzazione tecnica e pratica scientifica alla luce della nuova rivoluzione informatica. AGAZZI, Evandro and Luisa MOTECUCCO [University of Genoa, Italy], Complexity and Emergence, New Jersey-London-Singapore-Hong Kong: World Scientific Publ., 2002, pp. XIX + 210. Proceedings of the Annual Meeting of the International Academy of the Philosophy of Science, Bermago (Italy), 10-12 May 2001. Cf.: https://books.google.fr/books?id=4b3UCgAAQBAJ&printsec=frontcover&hl=fr &source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false http://www.lesacademies.org/en/iaps/publications/aips-tables-of- contents?showall=1&limitstart Complexity has become a central topic in certain sectors of theoretical physics and chemistry (for example, in connection with nonlinearity and deterministic chaos). Also, mathematical measurements of complexity and formal characterizations of this notion have been proposed. The question of how complex systems can show properties that are different from those of their constituent parts has nurtured philosophical debates about emergence and reductionism, which are particularly important in the study of the relationship between physics, chemistry, biology and psychology. This book offers a good presentation of those topics through a truly interdisciplinary approach in which the philosophy of science and the specialized topics of certain sciences are put in a dialogue. Contents: The Notions of Complexity and Emergence: What is Complexity? (E. Agazzi) On Levels and Types of Complexity and Emergence (H. Lenk & A. Stephan) Formal Metatheoretical Criteria of Complexity and Emergence (C. U. Moulines) Beyond Reductionism and Holism. The Approach of Synergetics (B. Kanitscheider) Kolmogorov Complexity (J. Mosterín) Modèles de Structures Émergentes dans les Systèmes Complexes (J. Petitot) Complexity and Emergence in Natural Science: Emergence in Physics: The Case of Classical Physics (R. Omnés) Classical Properties in a Quantum-Mechanical World (A. Cordero) Reduction, Integration, Emergence and Complexity in Biological Networks (J. Ricard) The Emergence of the Mind:Complexity and the Emergence of Meaning: Toward a Semiophysics (F. Tito Arecchi) Complexity and the Emergence of Intentionality: Some Misconceptions (M. Casartelli) Can Supervenience Save the Mental? (L. Montecucco) From Complexity Levels to the Separate Soul (G. Del Re) AGAZZI, Evandro, “Filosofía ténica y filosofía práctica”, en VEGA, A. Marga., Carlos MALDONADO y Alfredo MARCOS (coords.), Racionalidad científica y racionalidad humana, Valladolid (España): Universidad de Valladolid y Universidad El Bosque (Bogotá), 2001, pp. 35-52. Cf.: http://www.fyl.uva.es/~wfilosof/webMarcos/JF99.html AGAZZI, Evandro, “Prólogo”, en DUFOUR, Adrián, Ciencia y lógica de mundos posibles, Berna (Suiza): Peter Lang, 2001, pp. 321. Cf.:

http://www.amazon.es/Ciencia-Logica-Mundos-Posibles- Hochschulschriften/dp/3906758168/ref=sr_1_6?s=books&ie=UTF8&qid=1453914 228&sr=1-6 AGAZZI, Evandro and Jan FAYE [University of Copenhagen], (Editors), The Problem of the Unity of Science: Proceedings of the Annual Meeting of the International Academy of the Philosophy of Science, Copenhagen-Aarhus, Denmark, 31 May-3 June 2000. New Jersey-London-Singapore-Hong Kong: World Scientific, 2001, pp. XVI + 194. Cf.: https://books.google.fr/books?id=qLxUGXO2SVIC&printsec=frontcover&hl=fr &source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false The unity of science has been a widely discussed issue both in the philosophy of science and within several sciences. Reductionism has often been seen as the means of bringing the different sciences to a fundamental unity by reference to some basic science, but it shows many limitations. Multidisciplinarity and interdisciplinarity have also been proposed as methodologies for attaining unity without underestimating the diversity of the sciences. This volume starts with a clarification of the possible meanings of this unity and then discusses the features of the mentioned approaches to unity, evaluating the success and the shortcomings of the unification programme among different sciences and within a single science. Contents: The General Framework: What Does “The Unity of Science” Mean? (E. Agazzi); The Unity of Disunity (J. Faye); Sciences of Nature and Sciences of Man: On a Difference between Natural Science and the Interpretive Sciences of Man (F. Collin); Natural Sciences and Human Sciences (G. M. Prosperi); Overcoming Reductionism: Complexity, Reductionism, and the Unity of Science (J. Ricard); The Consilience Approach to the Unity of Science (B. Kanitscheider); The Unity Within a Single Science: The Problem of Unity in a Single Field of Science (A. Cordero); The Unity of Particle Physics and Cosmology? The Case of the Cosmological Constant (J. Mosterín); Is Quantum Mechanics a Universal Theory ? (B. d’Espagnat); and other papers. Readership: Graduate students and academics in the philosophy of science. AGAZZI, Evandro, Carlos ANGELINO e Michele MARSONET, Il concetto di verità nel pensiero occidentale, Genova: Università de Genova, 2000, pp. 176. AGAZZI, Evandro, Paidéia, verità, educazione, Brescia: La Scuola Editrice, 1999, pp. 144 (Collana Filosofia dell’educazione). AGAZZI, Evandro e Dario PALLADINO, Le geometrie non euclidee e i fondamenti della geometria dal punto di vista elementare, Brescia: La Scuola Editrice, 1998, pp. 352. AGAZZI, Evandro e Nicia VASSALLO (a cura di), George Boole Filosofia, Logica, Matemtica, Milano: Franco Angelli, 1998, pp. 300. AGAZZI, Evandro, El bien, el mal y la ciencia. Las dimensiones éticas de la empresa científico-tecnológica, Madrid: Tecnos, 1996, pp. 386. Edición, traducción y referencias bibliográficas españolas a cargo de Ramón Queraltó. Cf.: [Disponible en formato “.PDF”] http://documents.mx/documents/agazzi-evandro-el-bien-el-mal-y-la- cienciaepistemologia-sociologia-ensayopdfpdf.html ¿Qué es la ciencia? / Ciencia y Sociedad / ¿Neutralidad de la Ciencia? / Ciencia, técnica y tecnología / La ideología científico-tecnológica / El sistema científico-tecnológico / Normas y

valores en el obrar humano / El papel de los valores en las ciencias humanas / Racionalidad teorética y racionalidad práctica / El juicio moral sobre la ciencia y la técnica / El problema del riesgo / La responsabilidad de la ciencia en un planteamiento sistémico / La dimensión ética / Una ética para la ciencia y la técnica / Bibliografía. AGAZZI, Evandro, Le bien, le mal et la science: les dimensions éthiques de l’entreprise techno-scientifique, Paris: Presses Universitaires de France, 1996, pp. IX + 277. Traduction de: Isolda Agazzi. AGAZZI, Evandro, “Ciencia y racionalidad para el futuro del ser humano”, Contrastes. Revista Interdisciplinar de Filosofía (Universidad de Málaga, España), vol. I, 1996, pp. 7-18. Cf.: http://www.uma.es/contrastes/pdfs/001/Contrastes001-02.pdf AGAZZI, Evandro, Cultura scientifica e interdisciplinarietà, Brescia: Editrice La Scuola, 1994, pp. 142. AGAZZI, Evandro (a cura di), Bioetica e persona, Milano: FrancoAngeli, 1993, pp. 229. AGAZZI, Evandro, Il bene, il male e la scienza: le dimensione etiche dell’impresa scientifico-tecnologica, Milano: Rusconi, 1992, pp. 372. AGAZZI, Evandro (edited by), Science et Sagesse. Entretiens de L’Académie Internationale de Philosophie des Sciences – Science and Wisdom. Meeting of the International Academy of Philosophy of Science, 1990, Fribourg (Suisse): Éditions Universitaires, 1991, pp. 236. Cf.: http://catalog.hathitrust.org/Record/006741659 AGAZZI, Evandro, Introduzione: “Le frontiere della conoscenza scientifica e l’ipotesi del trascendente”, en Un Dibattito sulla dimensione etica e religiosa nella comunità scientifica internationale, vol. 2, Torino: Fondazione Giovanni Angelli, 1990, pp. 1-12 [total págs. 265]. AGAZZI, Evandro, Fabio MINAZZI e Ludovico GEYMONAT, Filosofia, scienza e verità, Milano: Rusconi, 1989, pp. 274. AGAZZI, Evandro, Philosophie, science, métaphisique, 2e éd., Fribourg: Éditions Universitaires, 1989 [1987], pp. 85. AGAZZI, Evandro, Marco BUZZONI e Guido SERVALLI, Linguaggio comune e linguaggio scientifico, Milano: FrancoAngeli, 1987, pp. 97.

AGAZZI, Evandro, La lógica simbólica, Barcelona: Editorial Herder, 1986 [1967], pp. 356 [La logica simbolica, Brescia: La Scuola. 1964, pp.396; 4th revised and enlarged edition 1990, pp. 384].

AGAZZI, Evandro (diretta da), Storia delle scienze, Volume 1, Dal mondo antico al secolo XVIII, Roma: Città Nuova Editrice, 1984, pp. 398. http://www.booklooker.de/B%C3%BCcher/E-Agazzi+Storia-delle-Scienze-dal-mondo- antico-al-secolo-XVIII/id/A01vmLJ601ZZJ?zid=9cb627988f0f807f4206187bd4924fd4

AGAZZI, Evandro (diretta da), Storia delle scienze, Volume 2, Dal secolo XIX. al mondo contemporaneo, Roma: Città Nuova Editrice, 1984, pp. 480. Cf.:

http://www.booklooker.de/B%C3%BCcher/E-Agazzi+Storia-delle-Scienze-dal- secolo-XIX-al-mondo-contemporaneo-Volume- secondo/id/A01vmvWd01ZZv?zid=9cb627988f0f807f4206187bd4924fd4 http://www.ebay.it/itm/Evandro-Agazzi-STORIA-DELLE-SCIENZE-2-Voll- /361458833022?hash=item5428a0167e:g:ExAAAOSw3KFWg~1w La scienza è senza dubbio il tratto più ca-ratteristico della civiltà contemporanea; ma, paradossalmente, ad atteggiamenti di affascinata ammirazione ed entusiastica ac-cettazione si accompagnano spesso reazioni di diffidenza, paura e rigetto; stati d’animo dovuti ad una insufficiente comprensione della scienza, al linguaggio tecnico sempre più inaccessibile, all’isolamento e alla settorializzazione che spesso ha accompagnato gli uomini e le varie discipline scientifiche. Ecco perché, da alcuni anni, si assiste ad un interesse crescente per la storia della scienza, non come un resoconto complicato dei vari settori specialistici, ma come il cammino di una grande impresa intellettuale che, lungo i secoli, l’umanità ha percorso per conoscere, interpretare e comprendere il mondo che ci circonda e l’uomo stesso. Ma la scienza non è mai stata sola in questa impresa; ad essa hanno posto mano contemporaneamente anche le filosofie, le religioni, le lettere e le arti, e si è sempre realizzata in situazioni storiche ben precise e in diverse condizioni politiche, sociali e materiali, oltre che ideali e spirituali. È ovvio quindi che una storia della scienza debba tener conto di questi vari elementi e, nello stesso tempo, guardarsi dal dissolvere lo specifico dell’impresa scientifica nel semplice gioco di questi altri fattori. Questo è l’obiettivo che si è posta la presente Storia delle Scienze e questo rimane il suo tratto più caratteristico. Il lettore troverà in essa, naturalmente, anche un resoconto dei « risultati », delle « scoperte », dei « progressi » via via susseguitisi nella storia delle discipline scientifiche fondamentali; ma vedrà sottolineato in modo particolare lo sviluppo delle idee, l’apertura di nuovi spazi concettuali, il mutamento di prospettive generali, i cambiamenti delle condizioni politico-sociali che hanno accompagnato e determinato il corso di questa storia.

AGAZZI, Evandro, “La natura del modello”, in G. Dalle FRATTE (editor), Teoria dei modelli in pedagogia, Trento: Federazione Provinciale Scuole Materne, 1984, pp. 31-64; 234-242.

AGAZZI, Evandro, “Analogicità del concetto di scienza. Il problema del rigore e dell’oggettività nelle scienze umane”, en POSENTI, V. (ed.), Epistemologia e scienze umane, Milano: Editrice Massimo, 1979, pp. 57-76.

AGAZZI, Evandro, Temas y problemas de filosofía de la física, Barcelona: Herder, 1978, pp. 470. [Temi e problemi di Filosofia de la Fisica, Milano: Manfredi Editore, 1969, pp. XIX + 395].

AGAZZI, Evandro, I Sistemi Tra Scienza e Filosofia, Torino: Societè Editrice, 1978, pp. 368.

AGAZZI, Evandro, Il concetto di progresso nella scienza, Milano: Feltrinelli, 1976, pp. 176.

ALAI, Mario, “Conversazione con Evandro Agazzi”, AphEx (Portale Italiano di Filosofia Analitica. Giornale di filosofia), n.º 6, Gennaio, 2012, pp. 26. Cf.: http://labont.it/wordpress/wp- content/uploads/2012/06/APhEx6IntervisteAgazziAlai.pdf

ALAI, Mario (a cura di), “Il realismo scientifico di Evandro Agazzi”, Isonomia (Istituto de Filosofia “Arturo Massolo”, Università degli Studi di Urbino “Carlo Bo”,

Urbino, Italia). Numero Speciale 2009: Atti del convegno di studi Urbino, 17 novembre 2006, pp. 172. Cf.: ***** http://www.uniurb.it/Filosofia/isonomia/AGAZZI-ALAI%20testo.pdf

CUÉLLAR, Hortensia, “Entrevista a Evandro Agazzi”, En-Claves del pensamiento, año IV, n.º 7, junio de 2010, pp. 177-188. Cf.: http://www.scielo.org.mx/pdf/enclav/v4n7/v4n7a11.pdf http://www.scielo.org.mx/scielo.php?pid=S1870- 879X2010000100011&script=sci_arttext

GARCÍA, Juan Alonso, La Epistemología de Evandro Agazzi, Pamplona (España): Universidad de Navarra, Facultad Eclesiástica de Filosofía, 1997. Extracto de la Tesis Doctoral. Cf.: http://www.google.fr/url?sa=t&rct=j&q=&esrc=s&source=web&cd=7&ved=0ah UKEwiN3oW_nMrKAhVMSRoKHTlvBFcQFghTMAY&url=http%3A%2F%2 Fdadun.unav.edu%2Fbitstream%2F10171%2F9659%2F1%2FCDF_VII_03.pdf &usg=AFQjCNHboCKcFUUWEcceoILbl7rQOBvs1g&sig2=x0qDHhAumKxBA G9ZAI3evg

Società Filosofica Italiana S.F.I. http://www.sfi.it/223/339/news/premio-feltrinelli-ad-evandro-agazzi.html Comunicati stampa 08/12/2015 Premio Feltrinelli ad Evandro Agazzi

Nel corso di una cerimonia che ha avuto luogo a Roma presso l’Accademia Nazionale dei Lincei nel novembre scorso, è stato conferito ad Evandro Agazzi – già Presidente della SFI – il Premio “Antonio Feltrinelli” 2015 per le Scienze Filosofiche, certamente il maggior riconoscimento che viene attribuito in Italia a un filosofo. Con esso si rende omaggio a una brillante carriera di ricerca scientifica e impegno accademico durata oltre cinquant’anni e che non accenna a concludersi. Infatti l’opera più importante di questo studioso, dal titolo Scientific objectivity and its contexts (L’oggettività scientifica e i suoi contesti), è uscita presso il prestigioso editore Springer nel 2014 ed è stata salutata in varie recensioni come uno dei maggiori contributi alla filosofia della scienza in campo internazionale. Fatto testimoniato anche dalla circostanza che presso il medesimo editore è uscito in inglese qualche mese fa un volume dal titolo La scienza tra verità e responsabilità etica. Evandro Agazzi nel dibattito scientifico e filosofico contemporaneo. Non si tratta di una delle abituali pubblicazioni di scritti “in onore” di un collega in occasione di un particolare anniversario, bensì di una raccolta di 21 saggi nei quali diversi specialisti analizzano criticamente i vari aspetti del pensiero filosofico di Agazzi, che spazia molto al di là della filosofia della scienza, toccando in particolare anche la logica, la metafisica, l’etica, la filosofia della religione, l’antropologia filosofica, la pedagogia, oltre alla storia della scienza. Fresco di stampa è pure il volume curato da Fabio Minazzi Sulla filosofia della scienza di Evandro Agazzi, che in 440 pagine raccoglie i contributi di un convegno di studi

organizzato in occasione del conferimento ad Agazzi della laurea Honoris causa da parte dell’Università dell’Insubria nel 2012. L’Accademia Russa delle Scienze ha già curato la traduzione in russo del volume di Agazzi sopra ricordato (che uscirà nel 2016), mentre la traduzione italiana è stata appena conclusa e uscirà probabilmente il prossimo anno per i tipi di Bompiani. L’edizione in lingua spagnola è in preparazione. Trattandosi di un volume di quasi 500 pagine, una simile fortuna è piuttosto eccezionale in questi tempi di crisi dell’editoria, ma si spiega con il valore intrinseco che la comunità internazionale ha riconosciuto alla filosofia di Agazzi, quale si veniva conoscendoi attraverso una linea costante di articoli in riviste, capitoli di libri e atti di congressi. La sua originale teoria dell’oggettività scientifica (fondata su una valorizzazione congiunta dei costrutti teorici e delle pratiche operazionali) giustifica la sua esplicita difesa della portata veritativa della conoscenza scientifica, accompagnata dalla sottolineatura del suo carattere delimitato. Ne scaturisce una coerente affermazione di un “realismo scientifico” che accetta l’esistenza reale degli “oggetti inosservabili” (come elettroni, particelle elementari, DNA e via dicendo) a cui la maggior parte dei filosofi della scienza si limita ancora ad attribuire il ruolo di semplici costrutti intellettuali. L’ampliamento del discorso ai “contesti” della scienza ha sempre consentito ad Agazzi di prendere in considerazione anche i rapporti fra scienza e società, fra scienza, tecnica e morale, fra scienza e religione e anche in questo volume alcuni capitoli sono dedicati a riassumere simili tematiche, alle quali per altro Agazzi ha già dedicato altre opere fortunate. Per quanto professore emerito dell’Università di Genova, Agazzi prosegue all’estero un’attività accademica a pieno titolo, essendo Presidente del Centro Interdisciplinare di Bioetica dell’università Panamericana di Città del Messico e proprio in questi mesi è uscito il primo fascicolo di una nuova rivista internazionale di Bioetica da lui fondata e diretta, Bioethics Update. MARCOS, Alfredo, Laudatio en honor del Profesor Evandro Agazzi, investido Doctor Honoris Causa de la Universidad de Valladolid el viernes 14 de noviembre de 2014. Cf.: http://www.fyl.uva.es/~wfilosof/webMarcos/textos/textos2015/A_Marcos_Laudati o_Agazzi.pdf

MINAZZI, Fabio (a cura di), Sulla filosofia de la scienza di Evandro Agazzi. De la probabilità e la logica matematica all’epistemologia realista, Milano: Mimesis, 2015, pp. 444 (Collana Centro Internazionale Insubrico). Cf.: http://mimesisedizioni.it/libri/sulla-filosofia-della-scienza-di-evandro-agazzi.html Evandro Agazzi rappresenta una delle più autorevoli e prestigiose voci filosofiche italiane a livello internazionale. La sua filosofia della scienza costituisce il fecondo nucleo critico a partire dal quale la sua stessa riflessione si è via via approfondita, giungendo a considerare ambiti sempre più articolati, spesso collocati ai confini tra differenti discipline (dalla logica matematica alla fisica quantistica, dalla bioetica all’analisi del senso comune, dall’operazionismo alla filosofia morale, etc.). La riflessione epistemologica di Agazzi ha avuto il merito e l’originalità di illustrare le ragioni del realismo, del pieno valore culturale delle tecnoscienze (e della stessa razionalità occidentale) e della funzione strategica dell’oggettività della conoscenza umana (declinata e studiata in differenti campi di ricerca).

Per analizzare questi molteplici aspetti della sua ricerca epistemologica si sono interpellati diversi studiosi, intrecciando le riflessioni di noti pensatori come Emanuele Severino, Maria Luisa Dalla Chiara, Maurizio Ferraris e Massimo Pauri, con quelle di alcuni più giovani studiosi come Marco Buzzoni, Fabio Minazzi, Gino Tarozzi e Paolo Giannitrapani. Nel volume si offre anche, per la prima volta, una disamina della inedita tesi di laurea di Agazzi sulla probabilità e il probabile. Il volume è inoltre integrato da tutto il materiale connesso con il conferimento ad Agazzi, da parte dell’Università degli Studi dell’Insubria, della laurea honoris causa in Scienze e Tecniche della Comunicazione, dalla sua laudatio e dalla sua lectio doctoralis, nonché dalla schedatura della straordinaria Biblioteca d’Autore donata da Agazzi al Centro Internazionale Insubrico.

WEINGARTNER, Paul (Ed.), Alternative Logics: Do Sciences Need Them?, Berlin-Heildelberg- New York-Hong Kong-London-Milan-Paris-Tokyo, 2004, pp. 367. Cf.: http://www.lesacademies.org/en/iaps/publications/aips-tables-of- contents?showall=&start=1

“Evandro Agazzi Filosofo della scienza”, Il Protagora (Mimesis Edizioni), Anno XXXVII, luglio- dicembre, 2010, sesta serie, n.º 14, 2010, pp. 535. Cf.: http://mimesisedizioni.it/riviste/il-protagora/vol-14-evandro-agazzi-filosofo-della- scienza.html#yt_tab_products1

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Piergiorgio Odifreddi (1950- )

ODIFREDDI, Piergiorgio. Cf.: http://www.piergiorgioodifreddi.it/ §♪♪♪♪♪§ https://it.wikipedia.org/wiki/Piergiorgio_Odifreddi [Italiano] §♦♦♦♦♦§ https://es.wikipedia.org/wiki/Piergiorgio_Odifreddi [Español] https://en.wikipedia.org/wiki/Piergiorgio_Odifreddi [English] https://fr.wikipedia.org/wiki/Piergiorgio_Odifreddi [Français] http://www.amazon.com/s?ie=UTF8&page=1&rh=n%3A283155%2Cp_27%3AP iergiorgio%20Odifreddi

ODIFREDDI, Piergiorgio, “Tutti i libri del autore”, Mondadori, 54 opere. Cf.: http://www.mondadoristore.it/libri/Piergiorgio-Odifreddi/aut00000756/

ODIFREDDI, Piergiorgio, Il giro del mondo in 80 pensieri, Rizzoli, 2015, pp. 409. Cf.: http://www.ibs.it/code/9788817083416/odifreddi-piergiorgio/giro-del-mondo- in.html Se nel romanzo di Jules Verne il motore propulsore del viaggio che spinge i protagonisti a girare il mondo in 80 giorni è il mero desiderio di vincere una scommessa, nel saggio del matematico Piergiorgio Odifreddi il carburante è costituito dal puro desiderio di conoscenza mista a un pizzico di sana curiosità. Se in Il giro del mondo in 80 giorni il lettore si imbatte in rocambolesche avventure che portano con sé l’impazienza di terminare la corsa, in Il giro del mondo in 80 pensieri quella fretta non c’è; piuttosto prevale il gusto di poter assaporare ciò che il mondo ha offerto e che continua ad offrire all’uomo attraverso otto continenti che l’autore sceglie di osservare e di condividere: Politica, Religione, Storia, Scienza, Matematica, Filosofia, Letteratura e Arte.

Durante lo scorrere delle pagine, si susseguono rapide fotografie scattate ai politici che dai tempi di Lincoln amano mentire e rendere il dibattito pubblico una rappresentazione vacua e ben lontana dall’originario sistema di democrazia. L’autore visita la Scienza e la Matematica dove troviamo gli scienziati/divi cool come Newton, Einstein o Nash, o ancora lo studioso Poiretti che insieme al filosofo Wittgenstein pensa all’importanza dell’aspetto ludico della matematica; ci imbattiamo in Calvino, scrittore particolarmente sensibile alla scienza e ai numeri; o in Edward Nelson che nel 2011 annuncia di voler dimostrare l’inconsistenza della matematica contemporanea. Arrivano poi le pagine dedicate alla Letteratura, dove ripercorriamo gli interrogativi che gli intellettuali si sono posti su Dante e che si sono riversati in innumerevoli opere, e alla Filosofia, alla Storia e all’Arte dove – tra i tanti personaggi – Odifreddi ricorda l’antesignano delle macchine fotografiche, Caravaggio, e il compositore tedesco Stockhausen. L’autore grazie al sui occhio razionale, logico e rigoroso ci regala un’insolita esplorazione con un itinerario bizzarro e tutto da scoprire.

ODIFREDDI, Piergiorgio, Il museo dei numeri. Da zero verso l’infinito, storie del mondo della matematica, Rizzoli, 2015 [2014], pp. 432 (collana Vintage). Cf.: http://www.ibs.it/code/9788817082174/odifreddi-piergiorgio/museo-dei-numeri- da.html “Cos’è il numero, che l’uomo lo può capire? E cos’è l’uomo, che può capire il numero?” A porsi queste domande fu nel 1960 il neurofisiologo Warren McCulloch, evidentemente insoddisfatto delle molte rigide e vuote definizioni che erano state sciorinate fino ad allora dai filosofi. In questo libro Piergiorgio Odifreddi affronta le due domande con un approccio più fluido e pratico: invece di provare inutilmente a dirci cos’è il numero in astratto, ci mostra utilmente una serie di numeri in concreto. Ne ha scelti una cinquantina tra quelli che meglio si prestano a essere raccontati, e ce li illustra come se fosse la guida di un museo, mostrandoci di ciascuno la struttura globale e i particolari locali. Passeggiando tra i quadri di questa esposizione, il lettore troverà i piccoli grandi numeri da 0 a 9, accorgendosi di non conoscerli così bene come pensava. Scoprirà il fascino di numeri che credeva senza interesse, come 42 o 1729. Proverà a immaginare numeri tanto grandi da essere quasi inafferrabili e inconcepibili E arriverà infine a intuire perché i matematici pensano che i numeri siano la cosa più vicina al divino che l’uomo possa percepire: perché lo sono.

ODIFREDDI, Piergiorgio, Sulle spalle di un gigante. Isacc Newton, TEA, 2015 [2014], pp. 238 (collana Saggistica TEA). Cf.: http://www.ibs.it/code/9788850238729/odifreddi-piergiorgio/sulle-spalle-di-un.html Chi fu, veramente, Isaac Newton? Piergiorgio Odifreddi risponde alla domanda con questo libro strutturato in due parti: la prima dedicata all’uomo, con le sue asperità di carattere, dove non mancano i riferimenti alla vasta aneddotica fiorita intorno alla sua figura; la seconda allo scienziato e all’impressionante lavoro da lui compiuto, quasi sempre in perfetta solitudine, nei più svariati campi del sapere. L’autore ce lo presenta quasi fosse un segreto compagno di viaggio, che osservi la sua mente al lavoro da un angolo della stanza al Trinity College, dove Newton visse gran parte della vita. Lo fa sembrare quasi un nostro contemporaneo, con le ossessioni e il metodo implacabile di un genio assoluto, probabilmente il più grande di ogni tempo. E così, anche le più ardue equazioni riguardanti le leggi del moto, la gravitazione universale, le orbite dei pianeti e il calcolo infinitesimale parranno al lettore meno impervie.

ODIFREDDI, Piergiorgio, Come stanno le cose.Il mio Lucrecio, la mia Venere, Rizzoli, 2014 [2013], pp. 311. Cf.: http://www.ibs.it/code/9788817077026/odifreddi-piergiorgio/come-stanno-le-cose.html Duemila anni fa un uomo guardò alla cultura del futuro, e ne anticipò una buona parte in un’opera visionaria e avveniristica: l’uomo era il poeta Lucrezio, l’opera il poema “De rerum

natura”. Tutte le grandi teorie scientifiche di oggi (l’atomismo fisico-chimico, il materialismo psicologico, l’evoluzionismo biologico) sono esposte e difese nei suoi canti. Tutte le grandi superstizioni umanistiche di ieri (la filosofia non epicurea, la letteratura non realistica, la religione non deista) sono criticate e attaccate nelle sue invettive. Il “De rerum natura” costituisce dunque, allo stesso tempo, un’opera di divulgazione scientifica e una testimonianza laica: esattamente le due chiavi di lettura del mondo alle quali ha legato il suo nome anche il “matematico impertinente” Piergiorgio Odifreddi. Ma allora chi meglio di lui potrebbe condurre il lettore nei meandri del poema antico, e mostrare che la scienza moderna è in larga misura una serie di postille a Lucrezio? “Come stanno le cose” affianca a una nuova traduzione in prosa del capolavoro di Lucrezio un commento illustrato di Odifreddi che ne mostra le connessioni ideali o fattuali con l’intera cultura, umanistica e scientifica. Si scopre così che le parole di un letterato classico e i pensieri degli scienziati contemporanei convergono nell’offrire una grandiosa visione del mondo.

ODIFREDDI, Piergiorgio, Abasso Euclide! Il gande racconto della geometria contemporanea, Mondadori, 2014 [2013], pp. 384 (collana Oscar Bestsellers). Cf.: http://www.ibs.it/code/9788804638001/odifreddi-piergiorgio/abbasso-euclide-il- grande.html Perché il grido “Abbasso Euclide!” nel titolo di un testo divulgativo sulla storia della geometria? In primo luogo, perché basta uno sguardo per accorgersi che si tratta di un libro riccamente illustrato, che si affida innanzitutto all’intuizione e alla visualizzazione. Mentre è sufficiente sfogliare i monumentali “Elementi di Euclide” per rendersi conto che il grande sistematizzatore della geometria greca usava le figure con parsimonia, e si affidava quasi soltanto alla formalizzazione e alla dimostrazione. E poi, perché il nome di Euclide è legato positivamente alla geometria classica, chiamata appunto geometria euclidea, e negativamente alle geometrie moderna e contemporanea, chiamate al contrario geometrie non euclidee. E Piergiorgio Odifreddi, che ha già raccontato la storia della prima in “C’è spazio per tutti”, e della seconda in “Una via di fuga”, in questo volume conclude la trilogia del suo “Grande racconto della geometria” affrontando la geometria contemporanea. Vediamo così scorrere, nei vari capitoli, concetti e teorie che hanno attratto l’attenzione dei matematici soltanto a partire dalla fine dell’Ottocento, e sono poi diventati il fulcro della matematica del secolo appena trascorso, ormai completamente svincolata dal retaggio euclideo: la quarta dimensione, la topologia, i frattali, le geometrie finite, e la riflessione sui fondamenti.

ODIFREDDI, Piergiorgio, Le menzogne di Ulisse. L’avventura della logica da Parmenide ad Amartya Sen, TEA, 2013, pp. 286 (collana Saggistica TEA). Cf.: http://www.ibs.it/code/9788850232987/odifreddi-piergiorgio/menzogne-di-ulisse-l- avventura.html La logica è lo studio del logos, vale a dire del pensiero e del linguaggio. E poiché le più alte vette del pensiero e gli esiti più raffinati del linguaggio trovano espressione, tra l’altro, nella filosofia e nella matematica, l’autore guida il lettore tra i sentieri ininterrotti di questo paese delle meraviglie che, in un certo senso, sta a mezza strada tra Dio e il Diavolo. Un viaggio fra le trappole del pensiero che non si nega il piacere dell’aneddoto e in cui, attraverso le pieghe e le suggestioni del passato, Odifreddi compie un’analisi critica del presente.

ODIFREDDI, Piergiorgio, Il matematico impertinente, TEA, 2013, pp. 347 (collana Saggistica TEA). Cf.: http://www.ibs.it/code/9788850233007/odifreddi-piergiorgio/matematico- impertinente.html Impertinente, in senso letterale, è chi “non appartiene”, ad esempio a una politica o a una religione, e non appartenendo, suscita i risentimenti e le stizze di coloro che, appartenendo, lo tacciano di arroganza o insolenza. Il matematico impertinente è una specie del genere, caratterizzata dal fatto di non appartenere non per partito preso ma per motivi mutuati dalla più

pura razionalità esistente: quella matematica. E l’incarnazione del matematico impertinente è Piergiorgio Odifreddi che nei saggi raccolti in questo volume su politica, religione, letteratura, filosofia e scienza – dispiega l’arsenale della ragione per argomentare che non è affatto vero che non possiamo non dirci cristiani, o che siamo tutti americani, o che la cultura è solo quella mitologica e (pseudo) filosofica sulla quale vive l’informazione. Ed è invece vero che non possiamo non dirci tecnologici, che siamo tutti africani, e che la cultura è anche (o soprattutto?) quella matematica e scientifica che informa la vita.

ODIFREDDI, Piergiorgio, Il matematico impeninente, TEA, 2013, pp. 363 (collana Saggistica TEA). Cf.: http://www.ibs.it/code/9788850233021/odifreddi-piergiorgio/matematico- impenitente.html Il titolo dà un’idea dello spirito dell’autore, che nelle sue scorribande attraversa in lungo e in largo i territori (infiniti?) della galassia logico-matematica e dei suoi pianeti. Sono saggi, articoli, riflessioni e osservazioni su temi congeniali a Odifreddi, cui si aggiungono divagazioni sulla religione, l’attualità politica, la lingua e la letteratura. L’occhio del logico e del matematico osserva i fenomeni e gli uomini, ma è un occhio freddo, che guarda le cose senza pregiudizi, osserva (e giudica) alcuni eventi socio-politici con oggettività. Lo sguardo sul presente si alterna a ricognizioni sul passato: ogni capitolo si apre con un’intervista impossibile a un grande protagonista della storia (Aristotele, Archimede, Newton... ).

ODIFREDDI, Piergiorgio, Incontri con menti straordinarie, TEA, 2013, pp. 390 (collana Saggistica TEA). Cf.: http://www.ibs.it/code/9788850233021/odifreddi-piergiorgio/matematico- impenitente.html Economia, matematica, fisica, chimica, biologia: attraverso cinquanta incontri-interviste con i maggiori protagonisti di queste cinque discipline, Odifreddi percorre un’altra tappa del suo personale viaggio lungo i sentieri del mondo scientifico contemporaneo. John Nash, Amartya Sen, Enrico Bombieri, Jean-Pierre Serre, John Archibald Wheeler, Roald Hoffmann, Ilya Prigogine, Frederick Sanger, Renato Dulbecco, Rita Levi-Montalcini, James Watson sono alcuni dei personaggi che si incontrano in queste pagine che, spaziando dalla biografia alla ricerca - con incursioni, per esempio, nella religione e nella politica - compongono nell’insieme un "ritratto" della scienza del nostro tempo.

ODIFREDDI, Piergiorgio, In principio era Darwin. La vita, il pensiero, il dibattito sull’evoluzionismo, TEA, 2013 [2009], pp. 123 (collana Saggistica TEA). Cf.: http://www.ibs.it/code/9788850233038/odifreddi-piergiorgio/in-principio-era- darwin.html Il 27 dicembre 1831 il brigantino Beagle salpò dall’Inghilterra con un passeggero d’eccezione, il giovane Charles Darwin, per un giro del mondo che durò cinque anni. Al suo ritorno le risultanze di quel viaggio spinsero il giovane naturalista a elaborare l’ardita teoria che le specie vegetali e animali non sono state create indipendentemente, ma sì sono evolute nel tempo grazie a una selezione naturale del più adatto nella lotta per la vita. Questa teoria minava alla radice la pretesa dell’uomo di essere stato creato “a immagine e somiglianza di Dio”, e faceva invece supporre una sua discendenza da qualche progenitore comune delle grandi scimmie. Non può dunque sorprendere che il darwinismo abbia scosso i fondamenti stessi delle religioni bibliche, e generato polemiche e resistenze che dividono ancor oggi l’opinione pubblica dei non addetti ai lavori. In questo agile volume Odifreddi ripercorre le tappe salienti del pensiero di Darwin, le sue ripercussioni nella cultura moderna e le reazioni che ha scatenato di là e di qua del Tevere.

ODIFREDDI, Piergiorgio e Sergio VALZANIA, La via lattea, TEA, 2013 [2008], pp. 121 (collana Saggistica TEA). Cf.:

http://www.ibs.it/code/9788850232994/odifreddi-piergiorgio-valzania-sergio/via- lattea.html In Spagna e in Portogallo la galassia che gli antichi chiamavano Via Lattea si chiama Cammino di Santiago, perché indica la via da est a ovest che porta al luogo della supposta sepoltura dell’apostolo Giacomo (Iago in spagnolo, da cui Sant’Iago). In una sorta di inversione, il Cammino di Santiago si chiama a sua volta Via Lattea, per sottolineare la sua natura di via “sotto le stelle”. La Via Lattea è anche il titolo di un film di Luis Buñuel del 1969 che narra le avventure di due pellegrini in cammino verso la tomba di San Giacomo, e i metaforici duelli sulle questioni dottrinali che li accompagnano per tutto il percorso, fino alla meta. In spirito programmaticamente buñueliano, il matematico ateo Piergiorgio Odifreddi e il giornalista credente Sergio Valzania (e per un tratto lo storico cattolico Franco Cardini) hanno affrontato il Cammino di Santiago de Compostela tra il 24 aprile e il 26 maggio 2008, dando vita a continue e quotidiane schermaglie verbali su Radio3. Le ripercorrono ora in questo libro: schermaglie che, partendo dalla contrapposizione fra la natura e Dio, si allargano a toccare non solo la scienza e la religione, ma anche l’etica, la filosofia, la storia e l’arte, per approdare infine a una meditazione sulla vita tutta.

ODIFREDDI, Piergiorgio, Un matematico eclettico e stravagante. Conferenza su Alan Turing, Casagrande, 2012, pp. 48 (collana Alfabeti). Cf.: http://www.ibs.it/code/9788877136381/odifreddi-piergiorgio/matematico-eclettico-e- stravagante.html “Turing è entrato come una meteora nella storia della scienza nel 1936. E non c’è bisogno di essere matematici per capire che se era nato, nel 1912, nel 1936 aveva ventiquattro, anni. Ebbene, a ventiquattro anni Turing ha scritto una tesi, noi diremmo una tesi di laurea, che ha rivoluzionato il nostro mondo... ”. Con la sua inconfondibile verve, Odifreddi racconta qui una delle avventure intellettuali più affascinanti, e drammatiche del Novecento, offrendoci di fatto una sintetica introduzione al vero padre dell’informatica.

ODIFREDDI, Piergiorgio, Che cos’è la logica? CD Audio. Con libro, Luca Sossella Editore, 2012, pp. 12 (collana Auditorium). http://www.ibs.it/code/9788889829196/odifreddi-piergiorgio/che-cos-e-la-logica.html La logica è lo studio della ragione, e la logica matematica è lo studio matematico della ragione matematica. Di questo e altro si parla in questa introduzione alla logica, figlia del paradosso e madre della ragione.

ODIFREDDI, Piergiorgio, Idee per diventare matematico. Strumenti razionale per la comprensione del mondo. Con aggiornamento on line, Zanichelli, 2012, pp AEL*(collana I mestieri de la scienza). Cf.: http://www.ibs.it/code/9788808193933/odifreddi-piergiorgio/idee-per-diventare- matematico.html Cosa significa essere un matematico? Come lo si diventa? Dove inizia e dove finisce la ricerca? Quali sono i limiti di essa? Quali sono le emozioni di uno scienziato? Cerca di rispondere a queste domande Piergiorgio Odifreddi, professore di Logica all’Università di Torino e presso la Cornell University di New York, nonché giornalista e divulgatore scientifico. Intellettuale eclettico e arguto, Odifreddi racconta la matematica in modo semplice e intuitivo, "immergendola" nel resto della cultura e mostrandone le attinenze con la filosofia, la musica, la pittura, la letteratura, le scienze della vita e la teologia.

ODDIFREDDI, Piergiorgio, Una via di fuga. Il grande racconto della geometria moderna, Mondadori, 2012 [2011], pp. 254 (collana Oscar grandi bestsellers). Cf.: http://www.ibs.it/code/9788804622796/odifreddi-piergiorgio/via-di-fuga-il.html Una via di fuga. Da cosa? E perché? Non certo dalla geometria, di cui “C’è spazio per tutti” aveva raccontato in maniera brillante la storia del periodo classico, esibendone i legami non 37

solo con la scienza e la natura, ma anche con l’arte e l’architettura. E di cui Piergiorgio Odifreddi continua qui a raccontare, allo stesso modo, la complementare storia del periodo moderno. Il riferimento alla fuga è anzitutto musicale, perché questo libro si presenta come una composizione a più voci, che si intrecciano e si inseguono fra loro per arrivare a una stretta finale: l’abbattimento dell’ordinario paradigma euclideo, al quale in genere ci si limita nelle scuole, e la scoperta di straordinarie geometrie alternative, che permeano la scienza e l’arte delle età moderna e contemporanea. Ma il riferimento alla fuga è anche pittorico, perché una di queste geometrie alternative è quella proiettiva, ispirata e stimolata dall’invenzione della prospettiva. Far convergere le rette parallele in un punto, non a caso chiamato “di fuga”, ha scardinato, oltre all’arte del Rinascimento, la matematica nei secoli successivi, e richiesto un ripensamento della percezione e della concezione dello spazio. Il riferimento del titolo, infine, è storico. Perché, in un certo senso, di una letterale fuga si tratta e si narra. Non dalla geometria stessa, come dicevamo, ma dal vecchio Euclide e dai suoi vecchi Elementi, verso nuovi geometri e nuove geometrie.

ODIFREDDI, Piergiorgio, C’é spazio per tutti. Il grande racconto della geometria, Mondadori, 2011 [2010], pp. 266 (collana Oscar bestsellers). Cf.: http://www.ibs.it/code/9788804612483/odifreddi-piergiorgio/c-e-spazio-per-tutti.html Come tutte le scienze, anche la geometria affonda le sue radici nella notte dei tempi. Ricostruirne la storia significa ripercorrere il cammino stesso della civiltà umana, e individuare le tracce lasciate da questa disciplina nelle opere d’arte di tutte le epoche e di tutti i popoli. A cominciare per esempio dalle piramidi, che ci rivelano le conoscenze degli Egizi nel campo dei poligoni e dei solidi. O dallo Sri Yantra, un antico e misterioso oggetto di culto indiano che nasce da una complessa intersezione di triangoli. Fino all’arte contemporanea, dove scopriamo la struttura nascosta nei singolari dipinti di Salvador Dalì, o ci soffermiamo sull’arte astratta di Kandinsky e Mondrian, le cui opere sembrano essere state pensate appositamente per illustrare un testo di geometria. Con il suo consueto stile, sempre leggero e divertente, Piergiorgio Odifreddi trasforma quello che è stato e continua a essere uno dei peggiori incubi scolastici per gli studenti di ogni generazione in un viaggio attraente, ricco di sorprese e di curiosità. Una straordinaria occasione per riscoprire in una nuova luce vecchie conoscenze come Pitagora, Euclide e Archimede, per abbandonare timori e stereotipi, e partire con entusiasmo alla conquista dello spazio geometrico.

ODIFREDDI, Piergiorgio, Hai vinto, GALILEO! La vita, il pensiero, il dibbatito su scienza e fede, Arnoldo Mondadori Editore, 2012, pp. 133 (collana Oscar bestsellers). Cf.: http://www.amazon.com/Hai-vinto-Galileo-Saggi-Italian- ebook/dp/B008CM4SDS/ref=sr_1_11?s=books&ie=UTF8&qid=1453843504&sr= 1-11&refinements=p_27%3APiergiorgio+Odifreddi#reader_B008CM4SDS Nell’autunno del 1609, esattamente quattrocento anni fa, Galileo Galilei puntò in aria il cannocchiale e... apriti cielo! L’attonito scienziato scoprì che la Luna ha monti e valli, Venere fasi simili a quelle lunari, Giove quattro grandi satelliti che gli girano attorno, Saturno strane anomalie (i famosi anelli), che il Sole ruota su se stesso, e le costellazioni e la Via Lattea sono composte di innumerevoli stelle. Queste rivelazioni cambiarono radicalmente la sua vita e la nostra storia, inaugurando la nuova e acuta astronomia degli scienziati e scatenando le vecchie e ottuse reazioni dei teologi. Per due volte, nel 1616 e nel 1633, il Sant’Uffizio alzò la voce e Galileo abbassò la testa, dannandosi la memoria per aver salva la pelle. Ma poiché, come notava Oscar Wilde, chi dice la verità prima o poi viene scoperto, di fronte ai progressi e alle conquiste della scienza oggi possiamo felicemente affermare: “Hai vinto, Galileo!”. Per evitare di cadere nello stesso errore dei denigratori, di condannare senza conoscere o conoscere senza capire, questo libro ripercorre la strada che ha portato alla vittoria dell’eliocentrismo: l’antica formulazione proposta da Aristarco e quella moderna riproposta da Copernico, la coraggiosa e tragica protodifesa intrapresa da Giordano Bruno, il sistematico

sviluppo compiuto da Keplero e Galileo, le feroci persecuzioni intentate dal cardinal Bellarmino e da papa Urbano VIII, la definitiva sistemazione raggiunta da Isaac Newton, la verifica sperimentale ottenuta con il pendolo di Foucault, e la subdola riscrittura della storia attentata da Giovanni Paolo II e Benedetto XVI. E, soprattutto, ci sollecita a leggere (o rileggere) le grandi opere di Galileo (il Sidereus Nuncius, le Lettere copernicane, il Saggiatore, il Dialogo sopra i due massimi sistemi e i Discorsi sopra due nuove scienze), per scoprire che non si tratta solo di scienza. Perché, come disse Italo Calvino, che se ne intendeva, Galileo è stato “il più grande scrittore della letteratura italiana di ogni secolo”. ODIFREDDI, Piergiorgio, Matematico e impertinente. Varietà differenziale. Con DVD. Mondadori, pp. 96 (collana Piccola biblioteca oscar). Cf. http://www.ibs.it/code/9788804583295/odifreddi-piergiorgio/matematico-e- impertinente-variet-a.html In un mondo in cui la corsa impazzita verso l’iperspecializzazione sta creando delle distanze incolmabili e inconciliabili tra cultura scientifica e cultura umanistica, Piergiorgio Odifreddi, noto e illustre studioso di logica matematica, offre in quest’opera –uno spettacolo teatrale su DVD e il testo riscritto in un libro– un esempio di sincretismo tra pensiero, immagini, suoni che svela al lettore-spettatore l’infinita bellezza del mondo e dei numeri, della musica e dei colori, passando dal racconto di Achille pié veloce battuto da una tartaruga al processo a Galileo, dai misteri dello zero e dell’infinito ai mille paradossi della finzione teatrale. ODIFREDDI, Piergiorgio, The Mathematical Century: The 30 Greatest Problems of the Last 100 Years, Princeton: Princeton University Press, 2006, pp. 226. Cf.: http://www.casadellibro.com/libros-ebooks/piergiorgio-odifreddi/20083447 The twentieth century was a time of unprecedented development in mathematics, as well as in all sciences: more theorems were proved and results found in a hundred years than in all of previous history. In The Mathematical Century, Piergiorgio Odifreddi distills this unwieldy mass of knowledge into a fascinating and authoritative overview of the subject. He concentrates on thirty highlights of pure and applied mathematics. Each tells the story of an exciting problem, from its historical origins to its modern solution, in lively prose free of technical details. Odifreddi opens by discussing the four main philosophical foundations of mathematics of the nineteenth century and ends by describing the four most important open mathematical problems of the twenty-first century. In presenting the thirty problems at the heart of the book he devotes equal attention to pure and applied mathematics, with applications ranging from physics and computer science to biology and economics. Special attention is dedicated to the famous “23 problems” outlined by David Hilbert in his address to the International Congress of Mathematicians in 1900 as a research program for the new century, and to the work of the winners of the Fields Medal, the equivalent of a Nobel prize in mathematics. This eminently readable book will be treasured not only by students and their teachers but also by all those who seek to make sense of the elusive macrocosm of twentieth- century mathematics. ODIFREDDI, Piergiorgio, Érase una vez una paradoja, Barcelona: RBA Libros, 2013, pp. 304. Cf.: http://www.casadellibro.com/libro-erase-una-vez-una- paradoja/9788490069936/2177571 En este original libro se cuentan un buen puñado de historias muy diferentes entre sí, pero con un nexo que las une: todas ellas encierran paradojas. Aparentemente contrarias a toda lógica, las paradojas en manos de Piergiorgio Odifreddi se convierten en mecanismos efectivos, y al mismo tiempo demoledores, para analizar el mundo que nos rodea y replantearse desde la base muchas de las convicciones que en teoría creíamos inamovibles. ODIFREDDI, Piergiorgio, Blog Repubblica.it. Cf.: http://odifreddi.blogautore.repubblica.it/

ODIFREDDI, Piergiorgio, YouTube. Cf.: https://www.youtube.com/user/podifreddi ODIFREDDI, Piergiorgio, Che cosa è la verità?”, YouTube. Festa di Scienza e Filosofia, quinta edizione. Foligno, Auditorium San Domenico, sabato 12 aprile 2015, 2:00:52. Cf.: §♦♦♦♦♦§ https://www.youtube.com/watch?v=xtVmYofEjvI

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BUNGE, Mario, Matter and Mind. A Philosophical Inquiry, Dordrecht-Heidelberg- London-New York: Springer, 2010, pp. 319 (Boston Studies in the Philosophy of Science, Volume 287). Cf.: http://www.rosenfels.org/Mario_Bunge_-_Matter_and_Mind_- _A_Philosophical_Inquiry_(Springer,_2010).pdf In general, all the so-called Big Questions call for comprehensive and systematic philosophies, rather than a few clever aphorisms and thought experiments, such as imagining how people would behave in a dry twin of our planet. Particularity, fragmentation and unchecked fantasy are marks of philosophical improvisation. But of course breadth and system are not enough: We also want rigor, depth, and the promise of truth in tackling significant problems. In other words, we want to use the best extant knowledge to help solve important problems by placing them in a broad context and in relation to other knowledge items, even other disciplines if necessary, and handling them rigorously and in depth. I believe that a philosophy is spineless without ontology, confused without semantics, acephalous without epistemology, deaf without ethics, paralytic without social philosophy, and obsolete without scientific support – and no philosophy at all with neither. All those branches of philosophy are treated in the nine tomes of my Treatise (1974–1989). The present book has a far narrower scope: it focuses on the modern conceptions of matter and mind. Incidentally, its comprehension does not require any specialized knowledge. Only the two appendices make use of some formal tools. My Dictionary of Philosophy (2003) may help elucidate some philosophical terms. (“Preface”, M.B., p. XI). BUNGE, Mario, Materia y mente. Una investigación filosófica, Pamplona (Navarra, España): Laetoli, 2015, pp. 528 (Colección Biblioteca Bunge n.º 7 ). Traducción del inglés de Rafael González del Solar. Unas páginas de este libro en El País (Madrid, España), “La relación entre pseudociencia y política”, 24 de octubre de 2015. http://elpais.com/elpais/2015/10/20/ciencia/1445356175_841379.html Este libro, publicado en inglés en 2010 y traducido ahora al español, aborda dos de los problemas más antiguos y difíciles de la filosofía de la ciencia: ¿qué es la materia? y ¿qué es la mente? Materia y mente es una obra extraordinaria que en sus más de 500 páginas compendia las principales ideas sostenidas por Mario Bunge a lo largo de su carrera. Algunas de las principales tareas propuestas en este libro –escribe el autor– consisten en dilucidar los conceptos generales de materia y mente a la luz de la ciencia contemporánea. BUNGE, Mario, “Moderate Mathematical Fictionism”, in AGAZZI, Evandro and György DARVAS (eds.), Philosophy of Mathematics Today, Dordrecht-Boston- London: Kluwer Academic Publishers, 1997, pp. 51-72 (Episteme 22). Cf.: http://www.lesacademies.org/en/iaps/publications/aips-tables-of- contents?showall=&start=1

BUNGE, Mario Works by, philpapers. [184 titles]. Cf.: http://philpapers.cdp.uwo.ca/s/Mario%20Bunge

BUNGE, Mario, “Bibliographic items”, [57 articles], Geomar, Helmholtz Centre for Ocean Research Kiel. Cf.: http://geomar- search.kobv.de/authorSearch.do;jsessionid=EF318081B270ECD2D71C8F07C202 3CFD?query=Bunge%2C+Mario&plv=2

DEGIOVANNI, Marco, Roberto LUCCHETTI, Alfredo MARZOCCHI e Maurizio PAOLINI, Matematica per la vita, anche dove non te l’aspetti, Milano: Fondazione Achille e Giulia Boroli, 2009, pp. 200. Cf.: http://www.fondazioneaegboroli.it/fondazione/collana_XVI.html Fin dall’antichità la matematica ha rappresentato la prima espressione di conoscenze strutturate e cumulative: a titolo di esempio, il fatto, dimostrato da Euclide, che esistano infiniti numeri primi si intende acquisito per sempre. La concezione galileiana della scienza ha trasformato la matematica nel linguaggio in cui una teoria deve esprimersi per essere considerata scientifica. Come conseguenza, le scienze della natura, dalla fisica alla chimica e alla biologia, hanno adottato il processo di matematizzazione, che si è esteso anche ad alcuni aspetti delle scienze umane. Dal canto suo, la matematica ha risposto, soprattutto nel ’900, con una formidabile moltiplicazione delle strutture matematiche messe a disposizione degli studiosi delle varie discipline. Si giunge così ai giorni nostri, in cui le più disparate valutazioni vengono spesso ricondotte a parametri numerici, ritenuti più “oggettivi” non sempre a proposito. In realtà la costruzione di un’interpretazione matematica calzante è impresa quanto mai impegnativa. Può impressionare il fatto che sappiamo prevedere le prossime eclissi di Sole per molti anni, mentre le previsioni del tempo non arrivano a sette giorni. Il fatto è che i moderni strumenti di misura consentono di acquisire miriadi di dati, che però spesso rimangono “muti”, perché manca la chiave interpretativa. Questa constatazione dovrebbe anche indurre a ridimensionare la visione scolastica di matematica “tutta correttezza procedurale”. Fatta salva la necessaria competenza tecnica, ciò che si richiede nel progresso della scienza, matematica compresa, è sempre un contributo di idee. Di cosa parla questo libro Il volume Matematica per la vita ci introduce in maniera originale nel mondo della matematica e ci fa scoprire che tanti aspetti della nostra quotidianità possono essere interpretati e spiegati alla luce dei numeri. Nei sette capitoli del libro (Alcune strutture, Modelli e previsioni, La gestione razionale del caso, Computer e soluzioni approssimate, La matematica nell’arte, Giochi e applicazioni, La matematica nelle scienze umane e nella vita), i quattro Autori spiegano alcune nozioni fondamentali della matematica per poi mostrare che i numeri si trovano in molti “luoghi” e possono aiutarci a modellizzare molti eventi. Spesso diamo per scontate le cose che facciamo, senza renderci conto che i numeri fanno da sfondo ai nostri pensieri, alle nostre azioni e alle nostre attività quotidiane. Acquisire una competenza matematica significa diventare più critici e capaci di interpretare correttamente gli eventi. Perché è stato scritto L’apprendimento della matematica di norma viene associato a un’attività noiosa e, per tante persone, alle difficoltà incontrate a scuola. Inoltre spesso facciamo corrispondere la matematica a qualcosa di astratto, in fondo poco importante: e ciò che conta nella vita è saper fare qualche somma o moltiplicazione quando serve. Gli autori di Matematica per la vita sanno quanto più profondo sia il nostro rapporto con essa, e hanno scritto questo volume per rendere i lettori più consapevoli e capaci di cogliere delle sfumature della nostra quotidianità che altrimenti ci sfuggirebbero. Grazie a Matematica per la vita una materia di studio spesso considerata “fredda” diventa carica di significati ed emozioni.

DEHAENE, Stanislas, Le Code de la conscience, Paris: Odile Jacob, 2014, pp. 432. Cf.:

http://www.odilejacob.fr/catalogue/sciences/neurosciences/code-de-la- conscience_9782738131058.php http://www.amazon.fr/gp/product/2738131050?ie=UTF8&isInIframe=1&n=3010 61&redirect=true&ref_=dp_proddesc_0&s=books&showDetailProductDesc=1#r eader_B00O9CQ1WQ

D’où viennent nos perceptions, nos sentiments, nos illusions et nos rêves ? Où s’arrête le traitement mécanique de l’information et où commence la prise de conscience ? L’esprit humain est-il suffisamment ingénieux pour comprendre sa propre existence ? La prochaine étape sera-t-elle une machine consciente de ses propres limites ? Depuis plus de vingt ans, Stanislas Dehaene analyse les mécanismes de la pensée humaine. Dans ce livre, il invite le lecteur dans son laboratoire où d’ingénieuses expériences visualisent l’inconscient et démontent les bases biologiques de la conscience. Grâce à l’imagerie cérébrale et même à des électrodes introduites dans la profondeur du cortex, nous commençons enfin à comprendre les algorithmes qui nous font penser. Détecter la présence de la conscience, décoder à quoi pense un individu, un bébé ou même un animal, sortir les patients du coma, doter les machines d’un début de conscience… Le Code de la conscience ouvre d’extraordinaires perspectives pratiques et intellectuelles, en accordant une importance égale aux implications technologiques, philosophiques, personnelles et éthiques de la résolution du dernier des mystères.

Stanislas Dehaene est professeur au Collège de France, titulaire de la chaire de psychologie cognitive expérimentale et membre de l’Académie des sciences. Il a publié Les Neurones de la lecture et La Bosse des maths, qui ont rencontré un très grand succès.

DEHAENE, Stanislas, Consciousness and the Brain. Deciphering How the Brain Codes Our Thoughts, New York: Viking Adult, 2014, pp. 352. ISBN-13: 978-0670025435 (Hardcover). Cf.: http://www.amazon.com/Consciousness-Brain-Deciphering-Codes- Thoughts/dp/0670025437 http://www.amazon.com/Consciousness-Brain-Deciphering-Codes- Thoughts/dp/0670025437#reader_0670025437 Stanislas Dehaene is a French psychologist and cognitive neuroscientist. He is currently heading the Cognitive NeuroImaging Unit within the NeuroSpin building of the Commissariat A l’Energie Atomique in Saclay near Paris, France’s most advanced brain imaging center. He is also a professor at College de France in Paris, where he holds the newly created chair of Experimental Cognitive Psychology. In 2005, he was elected as the youngest member of the French Academy of Sciences. Stanislas Dehaene’s interests concern the brain mechanisms of specifically human cognitive functions such as language, calculation, and conscious reasoning. His research relies on a variety of experimental methods, including mental chronometry in normal subjects, cognitive analyses of brain-lesioned patients, and brain-imaging studies with positron emission tomography, functional magnetic resonance imaging, and high-density recordings of event- related potentials. Formal models of minimal neuronal networks are also devised and simulated in an attempt to throw some links between molecular, physiological, imaging, and behavioral data. Stanislas Dehaene is the author of over 190 scientific publications in major international journals. He has received several international prizes including the McDonnell Centennial Fellowship, the Louis D prize of the French Academy of Sciences (with D. Lebihan), and the Heineken prize in Cognitive Science from the Royal Academy of the Netherlands. He has

published an acclaimed book The Number Sense, which has been translated in eight languages, and Reading in the Brain, that appeared in November 2009. He has also edited three books on brain imaging, consciousness, and brain evolution, and has authored two general-audience documentaries on the human brain. “Brilliant… Dehaene’s special contribution is his global-workspace theory, the first step in a complete account of why some neural processes lead to conscious experience…. Dehaene’s account is the most sophisticated story about the neural basis of consciousness so far. It is essential reading for those who want to experience the excitement of the search for the mind in the brain.” –Chris Frith, Nature “Stanislas Dehaene’s remarkable book is the best modern treatment of consciousness I have read to date. Dehaene, a world-class scientist, has pioneered the development of a set of experiments for studying consciousness that have revolutionized the field and given us the first direct approach to its biology. Simply stated this book is a tour de force. It opens up a whole new world of intellectual exploration for the general reader.” –Eric Kandel, author of In Search of Memory and The Age of Insight, and winner of the Nobel Prize in Physiology or Medicine KALAT, James W. [James W. Kalat], Review: “Consciousness and the Brain: Deciphering How the Brain Codes our Thoughts, by Stanislas Dehaene”, Journal of Undergraduate Neuroscience Education (JUNE), Spring 2014, vol. 12, n.º 2. Cf.: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3971003/

“Consciousness and the Brain…”, Wikipedia. Last modified: 17 November 2015. Cf.: https://en.wikipedia.org/wiki/Consciousness_and_the_Brain

DEHAENE, Stanislas, Site, Collège de France, Psychologie cognitive expérimentale. Cf. : http://www.college-de-france.fr/site/stanislas-dehaene/Bibliographie.htm

DEHAENE, Stanislas, “Selected Publications”, Unicog.org. Cf.: http://www.unicog.org/biblio/Author/DEHAENE-S.html

DEHAENE, Stanislas, La Bosse des maths: Quinze ans après, Paris: Odile Jacob, 2010, édition revue et augmentée, pp. 380 (Collection Sciences). Cf.: http://www.amazon.fr/Bosse-maths-Quinze-ans- apr%C3%A8s/dp/2738125247/ref=asap_bc?ie=UTF8 http://www.amazon.fr/Bosse-maths-Quinze-ans- apr%C3%A8s/dp/2738125247/ref=asap_bc?ie=UTF8#reader_B00CDAJCVI Oui, la bosse des maths existe ! Enfants ou adultes, calculateurs prodiges ou simples mortels, nous venons tous au monde avec une intuition des nombres. Peut-on localiser des zones spécifiques du cerveau ? L’imagerie cérébrale permet-elle d’identifier les neurones dédiés aux mathématiques ? Et comment aider l’enfant qui rencontre des difficultés à calculer ? Pour comprendre pourquoi vous n’arrivez pas à retenir 7 x 8, comment une lésion cérébrale peut vous faire oublier 3 – 1 ou comment apprendre à extraire la racine cinquième de 759 375, suivez l’auteur dans les circonvolutions cérébrales de La Bosse des maths ! « Le livre de Stanislas Dehaene allie qualité scientifique et richesse des références historiques. Une lecture passionnante qui conduit des animaux mathématiciens aux bébés qui comptent et aux calculateurs prodiges. Une très belle illustration des sciences cognitives. » La Recherche. Stanislas Dehaene est professeur au Collège de France, titulaire de la chaire de psychologie cognitive expérimentale et membre de l’Académie des sciences. Il a publié Les Neurones de la lecture, qui a rencontré un très grand succès.

DEHAENE, Stanislas, The Number Sense: How the Mind Creates Mathematics. Revised and Updated edition, 2011, New York: Oxford University Press, pp. 352. Cf.: http://www.amazon.com/The-Number-Sense-Creates- Mathematics/dp/0199753873/ref=pd_cp_14_4?ie=UTF8&refRID=131CTHEB3XSMQEJ M262H http://www.amazon.com/The-Number-Sense-Creates- Mathematics/dp/0199753873/ref=pd_cp_14_4?ie=UTF8&refRID=131CTHEB3XSMQEJ M262H#reader_0199753873 Our understanding of how the human brain performs mathematical calculations is far from complete, but in recent years there have been many exciting breakthroughs by scientists all over the world. Now, in The Number Sense, Stanislas Dehaene offers a fascinating look at this recent research, in an enlightening exploration of the mathematical mind. Dehaene begins with the eye-opening discovery that animals –including rats, pigeons, raccoons, and chimpanzees– can perform simple mathematical calculations, and that human infants also have a rudimentary number sense. Dehaene suggests that this rudimentary number sense is as basic to the way the brain understands the world as our perception of color or of objects in space, and, like these other abilities, our number sense is wired into the brain. These are but a few of the wealth of fascinating observations contained here. We also discover, for example, that because Chinese names for numbers are so short, Chinese people can remember up to nine or ten digits at a time--English-speaking people can only remember seven. The book also explores the unique abilities of idiot savants and mathematical geniuses, and we meet people whose minute brain lesions render their mathematical ability useless. This new and completely updated edition includes all of the most recent scientific data on how numbers are encoded by single neurons, and which brain areas activate when we perform calculations. Perhaps most important, The Number Sense reaches many provocative conclusions that will intrigue anyone interested in learning, mathematics, or the mind. “Is number sense innate or learnt? A bit of both? How do our brains do math, anyway? And where did the ability come from? Stanislas Dehaene, a mathematician who became a neuroscientist, is uniquely qualified to answer such questions, and The Number Sense is a delight.” –Ian Stewart, New Scientist “Whether he is explaining how this neural machinery begins its numerical magic early in infancy, how it attains the sophistication required for complex calculations, or how it misfires when the brain suffers certain types of injuries, Dehaene weaves the latest technical research into a remarkably lucid and engrossing investigation. Even readers normally indifferent to mathematics will find themselves marveling at the wonder of minds making numbers.” – Booklist “In this lively and readable book, Dehaene integrates the latest scientific evidence on how numbers are represented in the brains of animals and humans, then relates this knowledge to the challenges of early mathematics education. Dehaene is masterful in his ability to explain complex scientific findings in a manner that will be accessible to any audience. His writing is clear, and his examples are fascinating, taking us through the worlds of animal mathematicians, idiot savants, newborn infants, and split-brain patients, all as a means of understanding our innate sense of number.” –Jim Stigler, Professor of Psychology, University of California, Los Angeles “It is now possible to see the human brain as it listens, reads, communicates and calculates. The Number Sense describes recent exciting findings on how the brain calculates. In a clear and exciting way it provides the needed background to understand both the innate endowment of numeracy and what may be necessary to acquire the skills of mathematics. For psychologists, neuroscientists, educators and all who work with number, this book is of basic importance.” –Mike Posner, Professor of Psychology, Department of Cognitive and Decision Sciences, University of Oregon

DEHAENE, Stanislas and Elizabeth BRANNON (Edited by), Space, Time and Number in the Brain. Searching for the Foundations of Mathematical Thought, London: Academic Press, 2011, pp. 374. Cf.: http://www.sciencedirect.com/science/book/9780123859488 The study of mathematical cognition and the ways in which the ideas of space, time and number are encoded in brain circuitry has become a fundamental issue for neuroscience. How such encoding differs across cultures and educational level is of further interest in education and neuropsychology. This rapidly expanding field of research is overdue for an interdisciplinary volume such as this, which deals with the neurological and psychological foundations of human numeric capacity. A uniquely integrative work, this volume provides a much needed compilation of primary source material to researchers from basic neuroscience, psychology, developmental science, neuroimaging, neuropsychology and theoretical biology. * The first comprehensive and authoritative volume dealing with neurological and psychological foundations of mathematical cognition * Uniquely integrative volume at the frontier of a rapidly expanding interdisciplinary field * Features outstanding and truly international scholarship, with chapters written by leading experts in a variety of fields

MONTEMAYOR, Carlos and Rasmus GRØFELDT WINTHER, “Review: Space, Time and Number in the Brain: Searching for the Foundations of Mathematical Thought edited by Stanislas Dehaene and Elizabeth Brannon”, The Mathematical Intelligence, Volume 37, Issue 2, June 2015, pp. 93-98. Cf.: http://link.springer.com/article/10.1007%2Fs00283-014-9515-8

DEHAENE, Stanislas, Les neurones de la lecture, Paris : Odile Jacob, 2007, pp. 478 (Collection Sciences). Cf.: http://www.amazon.fr/Les-Neurones-lecture-Jean-Pierre- Changeux/dp/2738119743 http://www.amazon.fr/Les-Neurones-lecture-Jean-Pierre- Changeux/dp/2738119743#reader_B00F2TF9J6 Les Neurones de la lecture s’ouvre sur une énigme : comment notre cerveau de primate apprend-il à lire ? Comment cette invention culturelle, trop récente pour avoir influencé notre évolution, trouve-t-elle sa place dans notre cortex ? Voici qu’émerge une nouvelle science de la lecture. Tandis que l’imagerie cérébrale en révèle les circuits corticaux, la psychologie en dissèque les mécanismes. Ces résultats inédits conduisent à une hypothèse scientifique nouvelle. Au cours de l’acquisition de la lecture, nos circuits neuronaux, conçus pour la reconnaissance des objets, doivent se recycler pour déchiffrer l’écriture –une reconversion lente, partielle, difficile, qui explique les échecs des enfants et suggère de nouvelles pistes pédagogiques. Qu’est-ce que la dyslexie ? Certaines méthodes d’enseignement de la lecture sont-elles meilleures que d’autres ? Pourquoi la méthode globale est-elle incompatible avec l’architecture de notre cerveau ? Utilise-t-on les mêmes aires cérébrales pour lire le français, le chinois ou l’hébreu ? La lecture subliminale existe-t-elle ? Autant de questions auxquelles Stanislas Dehaene, spécialiste de la psychologie et de l’imagerie cérébrale, apporte l’éclairage des avancées les plus récentes des neurosciences. Stanislas Dehaene est professeur au Collège de France, titulaire de la chaire de psychologie cognitive expérimentale et membre de l’Académie des sciences. Il est l’auteur de La Bosse des maths.

DEHAENE, Stanislas, Reading in the Brain: The New Science of How We Read, New York: Penguin Books (reprint edition), 2010, pp. 400. ISBN 13: 978-0143118053 (paperback edition). http://www.amazon.com/Reading-Brain-New-Science- Read/dp/0143118056/ref=la_B000APVWYI_1_2?s=books&ie=UTF8&qid=1454082046& sr=1-2&refinements=p_82%3AB000APVWYI http://www.amazon.com/Reading-Brain-New-Science- Read/dp/0143118056/ref=la_B000APVWYI_1_2?s=books&ie=UTF8&qid=1454082046& sr=1-2&refinements=p_82%3AB000APVWYI#reader_B002SR2Q2I The transparent and automatic feat of reading comprehension disguises an intricate biological effort, ably analyzed in this fascinating study. Drawing on scads of brain-imaging studies, case histories of stroke victims and ingenious cognitive psychology experiments, cognitive neuroscientist Dehaene (The Number Sense) diagrams the neural machinery that translates marks on paper into language, sound and meaning. It’s a complex and surprising circuitry, both specific, in that it is housed in parts of the cortex that perform specific processing tasks, and puzzlingly abstract. (The brain, Dehaene hypothesizes, registers words mainly as collections of pairs of letters.) The author proposes reading as an example of neuronal recycling—the recruitment of previously evolved neural circuits to accomplish cultural innovations—and uses this idea to explore how ancient scribes shaped writing systems around the brain’s potential and limitations. (He likewise attacks modern whole language reading pedagogy as an unnatural imposition on a brain attuned to learning by phonics.) This lively, lucid treatise proves once again that Dehaene is one of our most gifted expositors of science; he makes the workings of the mind less mysterious, but no less miraculous. – (From Publishers Weekly)

EINSTEIN, Albert, “Mathematics… a product of human thought”, Today in Science History. CF.: http://todayinsci.com/E/Einstein_Albert/EinsteinAlbert- MathematicsHumanQuote500px.htm

“El número de Dios”, Medium.com, 23 de octubre de 2015. Cf.: https://medium.com/@veronicanunezriv/el-número-de-dios- b827e86b73e0#.ufzk3r7p1

FRENKEL, Edward, Love and Math: The Heart of Hidden Reality, New York: Basic Books, 2014 [2013], pp. 304. ISBN: 978-0-465-06495-3 (paperback). Cf.: http://www.amazon.com/Love-Math-Heart-Hidden- Reality/dp/0465064957/ref=pd_rhf_dp_s_cp_3?ie=UTF8&dpID=619L4%2Bxmo ZL&dpSrc=sims&preST=_SL500_SR87%2C135_&refRID=11620DACWWQCA 00479SF#reader_0465064957 U.C. Berkley mathematician Frenkel reveals the joy of pure intellectual discovery in this autobiographical story of determination, passion, and the Langlands program—a sort of Grand Unified Field Theory of mathematics. As a teenager Frenkel was converted from math hater to eager theorist by a mathematical friend of the family, enough to pursue it despite his struggles against an unapologetically anti-Semitic Soviet educational system. Frenkel writes casually of climbing over the fence to sit in on advanced classes at Moscow State University, a top school that didn&’t accept Jews. With the help of mentors, he worked hard and eventually found his way to Harvard and the freedom to focus on his research. Frenkel balances autobiographical narrative with enthusiastic discussions of his own work on the Langlands program, a web of algebraic conjectures named after a Canadian mathematician that is noted for its usefulness in organizing seemingly chaotic data into regular patterns full of symmetry and harmony, and its applications to quantum theory. While the math can be heavy going, Frenkel&’s gusto will

draw readers into his own quest, pursuing the deepest realities of mathematics as if it were a giant jigsaw puzzle, in which no one knows what the final image is going to look like. B&w illus. (Oct.) ♦♦♦♦♦ What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren’t even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry. In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we’ve never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space. Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man’s journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century’s leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat’s last theorem, that had seemed intractable before. At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics. ♦♦♦♦♦

Edward Frenkel mounts a passionate case against math’s reputation as an arcane and boring field [and] argues for math’s beauty and relevance”. –Page-Turner blog, The New Yorker

GONZÁLEZ SANTOS, Alberto, Ciencia y fe de la mano, pp. 43. Cf.: http://www.ebenezer-es.org/otros_temas/otros_autores/cienciayfe.pdf

GOYA DIZ, Ana y Cristina PATIÑO EIRÍN (edición a cargo de), El tapiz humanista. Actas del I Curso de Primavera. IV Centenario del Quijote. Lugo 9-12 de mayo de 2005, Santiago de Compostela: Universidade, Servizo de Publications e Intercambio Científico, pp. 356, pp. Cf.: https://books.google.es/books?id=JEy2eXR3R4MC&pg=PA190#v=onepage&q&f =false

HERSCH, Reuben [Department of Mathematics and Statistics, University of New Mexico, USA], Experiencing Mathematics: What do we do? when we do mathematics?, American Mathematical Society, 2014, pp. xviii + 293. Cf.: http://bookstore.ams.org/MBK-83/ https://books.google.fr/books?id=8YkCAQAAQBAJ&hl=fr&source=gbs_similar books https://books.google.fr/books?id=8YkCAQAAQBAJ&printsec=frontcover&hl=fr &source=gbs_ge_summary_r&cad=0#v=onepage&q&f=falsev

HERSCH, Reuben, and Vera JOHN-STEINER, Loving + Hating Mathematics, Princeton: Princeton University Press, 2011, pp. 432. Cf.:

https://books.google.fr/books?id=gvsHAnAuIp4C&dq=how%20is%20it%20possi ble%20that%20mathematics%20a%20product%20of%20human%20thought& hl=fr&source=gbs_similarbooks Mathematics is often thought of as the coldest expression of pure reason. But few subjects provoke hotter emotions –and inspire more love and hatred– than mathematics. And although math is frequently idealized as floating above the messiness of human life, its story is nothing if not human; often, it is all too human. Loving and Hating Mathematics is about the hidden human, emotional, and social forces that shape mathematics and affect the experiences of students and mathematicians. Written in a lively, accessible style, and filled with gripping stories and anecdotes, Loving and Hating Mathematics brings home the intense pleasures and pains of mathematical life. These stories challenge many myths, including the notions that mathematics is a solitary pursuit and a “young man’s game,” the belief that mathematicians are emotionally different from other people, and even the idea that to be a great mathematician it helps to be a little bit crazy. Reuben Hersh and Vera John-Steiner tell stories of lives in math from their very beginnings through old age, including accounts of teaching and mentoring, friendships and rivalries, love affairs and marriages, and the experiences of women and minorities in a field that has traditionally been unfriendly to both. Included here are also stories of people for whom mathematics has been an immense solace during times of crisis, war, and even imprisonment--as well as of those rare individuals driven to insanity and even murder by an obsession with math. This is a book for anyone who wants to understand why the most rational of human endeavors is at the same time one of the most emotional. Introduction (pp. 1-8) http://press.princeton.edu/chapters/i9283.pdf

HERSCH, Reuben (Editor), 18 Unconventional Essays on the Nature of Mathematics, New York: Springer Science and Business Media, 2006, pp. 326. Cf.: https://books.google.fr/books?id=rx3oUTzjh8sC&pg=PA292&lpg=PA292&dq=h ow+is+it+possible+that+mathematics+a+product+of+human+thought&source=bl &ots=7h4UHs1TUD&sig=ahyPnEk- dbSqzZ9FigHcKlaUZCg&hl=fr&sa=X&ved=0ahUKEwjVi86kk8XKAhWK2xoK HUR7Cfc4FBDoAQgfMAA#v=onepage&q=how%20is%20it%20possible%20tha t%20mathematics%20a%20product%20of%20human%20thought&f=false https://books.google.fr/books?id=rx3oUTzjh8sC&dq=how+is+it+possible+that+ mathematics+a+product+of+human+thought&hl=fr&source=gbs_navlinks_s REUBEN HERSH is professor emeritus at the University of New Mexico, Albuquerque. He is the recipient (with Martin Davis) of the Chauvenet Prize and (with Edgar Lorch) the Ford Prize. Hersh is the author (with Philip J. Davis) of The Mathematical Experience and Descartes’ Dream, which won the National Book Award in l983, and What is Mathematics, Really?

HERSCH, Reuben, What is Mathematics, Really?, New York-Oxford: Oxford University Press, 1997, pp. 368. Cf.: https://books.google.fr/books?id=cocpm4oBKqwC&dq=how%20is%20it%20pos sible%20that%20mathematics%20a%20product%20of%20human%20thought &hl=fr&source=gbs_similarbooks https://books.google.fr/books?id=cocpm4oBKqwC&printsec=frontcover&hl=fr& source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false

DAVIS, Philip [Division of Applied Mathematics, Brown University] Reuben HERSCH, and Elena Anne MARCHISOTTO [Department of Mathematics, California State University], The Companion Guide to the Mathematical Experience: Study edition, Boston: Birklhäuser, 2013, pp. 120. Cf.: https://books.google.fr/books?id=ZQXVBwAAQBAJ&dq=how%20is%20it%20p ossible%20that%20mathematics%20a%20product%20of%20human%20though t&hl=fr&source=gbs_book_other_versions

DAVIS, Philip, Reuben HERSCH, and Elena Anne MARCHISOTTO, The Mathematical Experience, Study Edition, Boston: Birkhäuser, 2011 [Reprint of 1995 edition. Updapted with Epilogues by the Authors], pp. 500 (Modern Birkhäuser Classics). Cf.: https://books.google.fr/books?id=KcafKzslE_AC&printsec=frontcover&hl=fr&s ource=gbs_ge_summary_r&cad=0#v=onepage&q&f=false Winner of the 1983 National Book Award! “[...] a perfectly marvelous book about the Queen of Sciences, from which one will get a real feeling for what mathematicians do and who they are. The exposition is clear and full of wit and humor [...]” – The New Yorker (1983 National Book Award edition) Mathematics has been a human activity for thousands of years. Yet only a few people from the vast population of users are professional mathematicians, who create, teach, foster, and apply it in a variety of situations. The authors of this book believe that it should be possible for these professional mathematicians to explain to non-professionals what they do, what they say they are doing, and why the world should support them at it. They also believe that mathematics should be taught to non-mathematics majors in such a way as to instill an appreciation of the power and beauty of mathematics. Many people from around the world have told the authors that they have done precisely that with the first edition and they have encouraged publication of this revised edition complete with exercises for helping students to demonstrate their understanding. This edition of the book should find a new generation of general readers and students who would like to know what mathematics is all about. It will prove invaluable as a course text for a general mathematics appreciation course, one in which the student can combine an appreciation for the esthetics with some satisfying and revealing applications. The text is ideal for 1) a GE course for Liberal Arts students 2) a Capstone course for perspective teachers 3) a writing course for mathematics teachers. A wealth of customizable online course materials for the book can be obtained from Elena Anne Marchisotto ([email protected]) upon request.

IRVINE, Andrew D. (edited by) [University of British Columbia, Vancouver, Canada], Philosophy of Mathematics, Burlington, MA; Oxford, UK and Amsterdam (The Netherlands): Elsevier, 2009, pp. 733. Cf.: https://books.google.fr/books?id=mbn35b2ghgkC&printsec=frontcover&hl=fr&s ource=gbs_ge_summary_r&cad=0#v=onepage&q&f=false

KARPINSKY, Jakug, Causality in Sociological Research, Dordrecht-Boston-London: Kluwer Academic Publishers, 1990, pp. 192 (Synthese Library Volume 212). Cf.: https://books.google.fr/books?id=i3KhBQAAQBAJ&pg=PA184&lpg=PA184&dq=agazzi +probability+in+the+sciences&source=bl&ots=RYgC1P42P_&sig=C8-aQYbIR0M7Ld- OYwCynKkl5qU&hl=fr&sa=X&ved=0ahUKEwiqluP1_fXKAhWiQZoKHcr7AXg4ChD oAQg0MAQ#v=onepage&q=agazzi%20probability%20in%20the%20sciences&f=false The general treatment of problems connected with the causal conditioning of phenomena has traditionally been the domain of philosophy, but when one examines the relationships taking place in the various fields, the study of such conditionings belongs to the empirical sciences.

Sociology is no exception in that respect. In that discipline we note a certain paradox. Many problems connected with the causal conditioning of phenomena have been raised in sociology in relatively recent times, and that process marked its empirical or even so-called empiricist trend. That trend, labelled positivist, seems in this case to be in contradiction with a certain type of positivism. Those authors who describe positivism usually include the Humean tradition in its genealogy and, remembering Hume’s criticism of the concept of cause, speak about positivism as about a trend which is inclined to treat lightly the study of causes and confines itself to the statements on co-occurrence of phenomena. https://books.google.fr/books?id=i3KhBQAAQBAJ&dq=agazzi%20probability%20in% 20the%20sciences&hl=fr&source=gbs_book_other_versions

KLINE, Morris, Mathematics for Nonmathematician, New York: Dover, 1985, pp. 672. Cf.: [This Dover edition, first published in 1985, is an unabridged republication of the work first published by Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, in 1967, under the title Mathematics for Liberal Arts] http://store.doverpublications.com/0486248232.html http://www.amazon.com/Mathematics-Nonmathematician-Dover- Books/dp/0486248232#reader_0486248232 Practical, scientific, philosophical, and artistic problems have caused men to investigate mathematics. But there is one other motive which is as strong as any of these –the search for beauty. “Mathematics is an art, and as such affords the pleasures which all the arts afford.” In this erudite, entertaining college-level text, Morris Kline, Professor Emeritus of Mathematics at New York University, provides the liberal arts student with a detailed treatment of mathematics in a cultural and historical context. The book can also act as a self-study vehicle for advanced high school students and laymen. Professor Kline begins with an overview, tracing the development of mathematics to the ancient Greeks, and following its evolution through the Middle Ages and the Renaissance to the present day. Subsequent chapters focus on specific subject areas, such as “Logic and Mathematics,” “Number: The Fundamental Concept,” “Parametric Equations and Curvilinear Motion,” “The Differential Calculus,” and “The Theory of Probability.” Each of these sections offers a step-by-step explanation of concepts and then tests the student’s understanding with exercises and problems. At the same time, these concepts are linked to pure and applied science, engineering, philosophy, the social sciences or even the arts. In one section, Professor Kline discusses non-Euclidean geometry, ranking it with evolution as one of the “two concepts which have most profoundly revolutionized our intellectual development since the nineteenth century.” His lucid treatment of this difficult subject starts in the 1800s with the pioneering work of Gauss, Lobachevsky, Bolyai and Riemann, and moves forward to the theory of relativity, explaining the mathematical, scientific and philosophical aspects of this pivotal breakthrough. Mathematics for the Nonmathematician exemplifies Morris Kline's rare ability to simplify complex subjects for the non-specialist. ***** Morris Kline (1908–1992) had a strong and forceful personality which he brought both to his position as Professor at New York University from 1952 until his retirement in 1975, and to his role as the driving force behind Dover's mathematics reprint program for even longer, from the 1950s until just a few years before his death. Professor Kline was the main reviewer of books in mathematics during those years, filling many file drawers with incisive, perceptive, and always handwritten comments and recommendations, pro or con. It was inevitable that he would imbue the Dover math program ― which he did so much to launch ― with his personal point of view that what mattered most was the quality of the books that were selected for reprinting and the point of view that stressed the importance of applications and the usefulness of mathematics. He urged that books should concentrate on demonstrating how mathematics could be used to solve problems in the real world, not solely for the creation of intellectual 50

structures of theoretical interest to mathematicians only. Morris Kline was the author or editor of more than a dozen books, including Mathematics in Western Culture (Oxford, 1953), Mathematics: The Loss of Certainty (Oxford, 1980), and Mathematics and the Search for Knowledge (Oxford, 1985). His Calculus, An Intuitive and Physical Approach, first published in 1967 and reprinted by Dover in 1998, remains a widely used text, especially by readers interested in taking on the sometimes daunting task of studying the subject on their own. His 1985 Dover book, Mathematics for the Nonmathematician could reasonably be regarded as the ultimate math for liberal arts text and may have reached more readers over its long life than any other similarly directed text. In the Author's Own Words:"Mathematics is the key to understanding and mastering our physical, social and biological worlds." "Logic is the art of going wrong with confidence." "Statistics: the mathematical theory of ignorance." "A proof tells us where to concentrate our doubts." ― Morris Kline - See more at: http://store.doverpublications.com/0486248232.html#sthash.zqBOUseN.dpuf LENG, Mary [Lecturer in Philsophy, University of Liverpool], Mathematics and Reality, New York: Oxford University Press, 2010, pp. x + 278. ISBN: 978-0-19-928079-7 (Hardback). Cf.: http://www.amazon.com/Mathematics-Reality-Mary- Leng/dp/0199280797#reader_0199280797

BURGESS, John P. [Department of Philsophy, Princeton University], Review: “Mary Leng. Mathematics and Reality…”, Philosophia Mathematica (Oxford Journals), Vol. 18, Issue 3, 2010, pp. 337-344. Cf.: http://philmat.oxfordjournals.org/content/18/3/337.extract

LAVERS, Gregory [Concordia University], Review: “Mary Leng, Mathematics and Reality”, Notre Dame Philosophical Reviews (Notre Dame, Indiana), September 11, 2010. Cf.: http://ndpr.nd.edu/news/24486-mathematics-and-reality/ TROBOK, Majda [University of Rijeka], Review: “Mary Leng, 2010, Mathematics and Reality, Oxford University Press”, s.d., pp. 5. Cf.: https://bib.irb.hr/datoteka/558085.Trobok_Review_on_Leng.pdf

LIZARZABURU, Alfonso y Gustavo ZAPATA (Comps.), Pluriculturalidad y aprendizaje de la matemática en América Latina. Experiencias y desafíos., Madrid: Ediciones Morata-PROEIB ANDES [Programa de Formación en Educación Intercultural Bilingüe para los Países Andinos] y la Deutsche Stiftung für Inernationale Entwicklung (DSE), 2001, pp. .272. Cf.: https://books.google.es/books?id=dNOosCbbLn4C&printsec=frontcover&hl=fr& source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false http://www.edmorata.es/libros/pluriculturalidad-y-aprendizaje-de-la- matematica-en-america-latina Este libro es el fruto de una iniciativa impulsada desde hace varios años por muy diversos actores con el fin de efectuar un balance de la situación educativa de los pueblos indígenas de América latina y encontrar salidas conceptuales y pedagógicas con los propios sujetos de los programas educativos desarrollados en áreas indígenas y zonas populares de América latina, entre los cuales se encuentran también investigadores y especialistas en la materia. Después de dos actividades centradas en el tema del aprendizaje y el desarrollo de las lenguas indígenas y el castellano como segunda lengua, en 1997 se realizó en el Cuzco (Perú) el seminario sobre “El aprendizaje de la matemática en los pueblos indígenas de América Latina”, en el cual participantes provenientes de todo el continente presentaron estudios de caso, así como resultados de sus investigaciones.

Este seminario forma parte de una serie de seminarios sobre la Educación Intercultural Bilingüe cuyos resultados se presentan en la colección “Educación, culturas y lenguas en América Latina” que se inició con el libro Sobre las huellas de la voz. Sociolingüística de la oralidad y la escritura en su relación con la educación, publicado en 1998. Estas actividades de reflexión sobre la Educación Intercultural Bilingüe en América latina son auspiciadas y organizadas por la Fundación Alemana para el Desarrollo Internacional (DSE) y la Deutsche Gesellschaft für Technische Zusamrnenarbeit (GTZ), por intermedio del PROPEIB Andes, en cooperación con la Oficina Regional de la UNESCO para América latina y el Caribe (OREALC). Alfonso Lizarzaburu y Gustavo Zapata, editores de esta publicación, recopilan algunas de las ponencias presentadas en el seminario de Cuzco, así como artículos de autores especializados en el tema. Los títulos y autores de los diferentes capítulos son: * Matemática y lenguajes. ¿Cómo seguir siendo amerindio y aprender la matemática de la que se tiene y se tendrá necesidad en la vida? (André Cauty). * La matemática en América Central y del Sur: Una visión panorámica (Ubiratan D’Ambrosio). * Nuevos enfoques en la enseñanza de la matemática y la formación de profesores indígenas (Kleber Gesteira e Matos). * Matemática andina: Abordaje psicogenético (Ruperto Romero y Gustavo Gottret). * La enseñanza de la matemática a educandos quechuas en el marco de la reforma educativa (Adán Pari Rodríguez). * El aprendizaje de las matemáticas en el Proyecto Experimental de Educación Bilingüe de Puno y en el Proyecto de Educación Bilingüe Intercultural del Ecuador: Reflexiones sobre la práctica y experiencias relacionadas (Martha Villavicencio). * Hacia una didáctica intercultural de las matemáticas (Joachim Schroeder). * Aportaciones a la discusión sobre la enseñanza de las matemáticas a partir de la didáctica y la etnomatemática (Isabel Soto Cornejo). * La matemática en la vida y en la escuela: Dos décadas de investigación (Terezinha Nunes). * Algunas consideraciones fundamentales sobre los procesos de enseñanza y aprendizaje de la matemática en relación con los pueblos indígenas de América Latina (Alfonso E. Lizarzaburu). [Reseña aparecida en la revista SUMA, n.º 39, Febrero de 2002] http://divulgamat2.ehu.es/divulgamat15/index.php?option=com_content&view=article&i d=9227:pluriculturalidad-y-aprendizaje-de-la-matemca-en-amca-latina-experiencia-y- desaf&catid=53:libros-de-divulgaciatemca&directory=67 La “Introducción” (pp. 19-47) presenta la problemática abordada en el seminario desde una perspectiva regional e internacional, así como una síntesis sistemática de los aportes de los participantes y los desafíos pendientes. *AEL MANNING, Philip, “The magical marriage of math and science”, The News Observer, June 7, 2009. Cf.: http://www.newsobserver.com/living/article10351544.html

(M)APHORISMS, Old and New Quotes. Cf.: §♦♦♦♦♦§ http://www.math.ku.dk/~olsson/links/maforisms.html

MARCISZEWSKI, Witold (editor), Dictionary of Logic as Applied in the Study of Language: Concepts/Methods/Theories, Dordrecht: Springer Science + Business Media, 2014 [1981], pp. 456. Cf.: https://books.google.fr/books?id=hrjnCAAAQBAJ&printsec=frontcover&hl=fr &source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false 1. STRUCTURE AND REFERENCES 1.1. The main part of the dictionary consists of alphabetically arranged articles concerned with basic logical theories and some other selected topics. Within each article a set of concepts is defined in their mutual relations. This way of defining concepts in the context of a theory provides better understanding of ideas than that provided by isolated short definitions. A disadvantage of this method is that it takes more time to look something up inside an extensive article. To reduce this disadvantage the following measures have been adopted. Each article is divided into numbered sections, the numbers, in boldface type, being addresses to which we refer. Those sections of larger articles which are divided at the first level, i.e. numbered with single numerals, have titles. Main sections are further subdivided, the subsections being numbered by numerals added to the main section number, e.g. I, 1.1, 1.2, ... , 1.1.1, 1.1.2, and so on. A comprehensive subject index is supplied together with a glossary. The aim of the latter is to provide, if possible, short definitions which sometimes may prove sufficient. As to the use of the glossary, see the comment preceding it.

MARQUIS, Jean-Pierre [Département de Philosophie, Université de Montréal], “Mario Bunge’s Philosophy of Mathematics: An Appraisal”, Science & Education, (Springer, Netherlands), Volume 21, Issue 10, October 2012, pp. 1567-1594. Cf.: http://link.springer.com/article/10.1007/s11191-011-9409-5 In this paper, I present and discuss critically the main elements of Mario Bunge’s philosophy of mathematics. In particular, I explore how mathematical knowledge is accounted for in Bunge’s systemic emergent materialism.

MATTHEWS, Michael R. [School of Education, University of New South Wales, Sydney, Australia], “Mario Bunge: Systematic Philosophy and Science Education: An Introduction, Science & Education, Vol. 21, n.º 10, October 2012, pp. 1393-1403. Cf.: https://www.researchgate.net/publication/257662525_Mario_Bunge_Systematic_ Philosophy_and_Science_Education_An_Introduction

MATTHEWS, Michael R. [School of Education, University of New South Wales, Sydney, Australia], “Mario Bunge: Physicist, philosopher and defender of Science”, Revista Electrónica de Investigación en Educación en Ciencias (REIEC), n.º 4, n.º Especial 1, 2009, pp. 1-9. Cf.: http://www.google.fr/url?sa=t&rct=j&q=&esrc=s&source=web&cd=26&cad=rja &uact=8&ved=0CE0QFjAFOBRqFQoTCIvCo9LBnMcCFUi3FAodGLAEkw&u rl=http%3A%2F%2Fdialnet.unirioja.es%2Fdescarga%2Farticulo%2F2882614. pdf&ei=JozHVYuXKMjuUpjgkpgJ&usg=AFQjCNEJW7y0HXqtiDEXqWneiQF lVCDnFA&sig2=5hYcnvrUtCvCw_fwONeyyg

MATTHEWS, Michael R. [School of Education, University of New South Wales, Sydney, Australia], “The Nature of Science and Science Teaching”, in FRASER, B.J., and K.G. TOBIN (Eds.), International Handbook of Science Education, Great Britain: Kluwer Academic Publishers, 1998, pp. 981-999. Cf.: http://faculty.education.illinois.edu/m-osbor/507SE06/matthews.pdf

MATTHEWS, Michael R. [School of Education, University of New South Wales, Sydney, Australia], “Un lugar para la historia y la filosofía de la enseñanza de las ciencias”, Comunicación, Lenguaje y Educación, n.º 11-12, 1991, 141-155. Cf.: https://www.researchgate.net/publication/28269228_Un_lugar_para_la_historia_ y_la_filosofia_en_la_ensenanza_de_las_ciencias

McCRIGHT, Aaron M., An Abridged Reading List in the Sociologies of Science and Technology, Lyman Briggs College, Department of Sociology, Michigan State University, July 9, 2014, pp. 23. Cf.: http://nebula.wsimg.com/aad45d00e7eb880f23b2165accb402ca?AccessKeyId=D4 B121E926A26559DD2A&disposition=0&alloworigin=1

RODRÍGUEZ del RÍO, Roberto y Enrique ZUAZUA IRIONDO, “Enseñar y aprender matemáticas: del Instituto a la Universidad”, en Actas de las Jornadas Territoriales de Matemáticas: “Del Bachillerato a la Universidad: ¿una discontinuidad evitable?”, Leganés (Madrid, España), noviembre de 2004. Madrid: Consejería de Educación de la Universidad de Madrid, Dirección General de Ordenación Académica, 2005, pp. 81-107. Versión revisada y actualizada del artículo “Enseñar y aprender Matemáticas” de los mismos autores, publicado en la Revista de Educación del MEC, nº 329, 2002, pp. 239-256. Cf.: http://eprints.ucm.es/9538/1/enseniaryaprender.pdf http://www.mat.ucm.es/~rrdelrio/publica/publicaciones.html

SALVADOR, Adela [Universidad Politécnica de Madrid], “Recursos para el aula. El número de oro”, s.d., Cf.: http://www2.caminos.upm.es/Departamentos/matematicas/grupomaic/conferenci as/11.Numero%20de%20oro.pdf

SINCLAIR, Robert, Where is Mathematics? (Point of View) [Mathematical Biology Unit, Okinawa Institute of Science and Technology Graduate University, Japan], Proceedings of the IEEE, vol. 102, nº 1, January 2014, pp. 4. Cf.: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6685881

SKORDEV, Dimiter G. (Edited by) [Sophia University, Bulgaria], Mathematical Logic and Its Applications, New York and London: Plenum Press, 1987, pp. 371. Cf.: https://books.google.fr/books?id=82XdBwAAQBAJ&printsec=frontcover&hl=fr &source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false

SOKAL, Alan [professor of physics at New York University], and Jean Bricmont [professor of theoretical physics at the Université de Louvain in Belgium], Fashionable Nonsense: Postmodern Intellectuals’ Abuse of Science, New York: Picador, 1998. Cf.: http://emilkirkegaard.dk/en/wp-content/uploads/Fashionable-Nonsense- Postmodern-Intellectuals-Abuse-of-Science-Alan-Sokal-Jean-Bricmont.pdf In 1996, Alan Sokal published an essay in the hip intellectual magazine Social Text parodying the scientific but impenetrable lingo of contemporary theorists. On the heels of the fierce academic debate that followed the hoax, Sokal teams up with Jean Bricmont to expose the abuse of scientific concepts in the writings of today’s most fashionable postmodern thinkers. From Jacques Lacan and Julia Kristeva to Luce Irigaray and Jean Baudrillard, the authors document the errors made by some postmodernists using science to bolster their arguments

and theories. Witty and closely reasoned, Fashionable Nonsense dispels the notion that scientific theories are mere “narratives” or social constructions, and explores the abilities and the limits of science to describe the conditions of existence. “The modem sciences are among the most remarkable of human achievements and cultural treasures. Like others, they merit –and reward– respectful and scrupulous engagement. Sokal and Bricmont show how easily such truisms can recede from view, and how harmful the consequences can be for intellectual life and human affairs. They also provide a thoughtful and constructive critical analysis of fundamental issues of empirical inquiry. It is a timely and substantial contribution.” –Noam Chomsky “An excellent discussion...The present book is a plea for a sensible understanding of science and a welcome antidote to irrationality.” –Simon Moss, Houston Chronicle “Sokal and Bricmont’s book should have an impact at least on the next generation of students… Although Sokal and Bricmont focus on the abuse and misrepresentation of science by a dozen French intellectuals, their book broaches a much larger topic — the uneasy place of science and the understanding of scientific rationality in contemporary culture.” Thomas Nagel, The New Republic “Sheer chutzpah and cleverness... The book is a sobering catalog of idiocies by some of those claimed to be the best thinkers of our times… I recommend this book.” –Russell Jacoby, Los Angeles Weekly “[An] important and well-documented book... Every passage is followed by the authors’ often humorous debunking of the writers’ garbled science and obscure language. It’s good reading.” –Raleigh News-Observer

TEGMARK, Max [MIT physics professor (1967-)], Out Mathematical Universe. My Quest for the Ultimate Nature of Reality, New York: Alfred A. Knopf, 2014, IX + 432. Cf.: http://www.amazon.com/Our-Mathematical-Universe-Ultimate- Reality/dp/0307599809 Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians.

“Galileo famously said that the universe is written in the language of mathematics. Now Max Tegmark says that the universe IS mathematics. You don’t have to necessarily agree, to enjoy this fascinating journey into the nature of reality.” Prof. Mario Livio, author of Brilliant Blunders and Is God a Mathematician?

TYMOCZKO, Thomas [Professor of Philosophy at Smith College], New Directions in the Philosophy of Mathematics: An Anthology, Revised and Expanded Edition, Princeton, New Jersey: Princeton University Press, 1998, pp. 436. Cf.: https://books.google.fr/books?id=HFa03eq- 9LQC&printsec=frontcover&hl=fr&source=gbs_ge_summary_r&cad=0#v=onep age&q&f=false The traditional debate among philosophers of mathematics is whether there is an external mathematical reality, something out there to be discovered, or whether mathematics is the product of the human mind. This provocative book, now available in a revised and expanded 55

paperback edition, goes beyond foundationalist questions to offer what has been called a “postmodern” assessment of the philosophy of mathematics--one that addresses issues of theoretical importance in terms of mathematical experience. By bringing together essays of leading philosophers, mathematicians, logicians, and computer scientists, Thomas Tymoczko reveals an evolving effort to account for the nature of mathematics in relation to other human activities. These accounts include such topics as the history of mathematics as a field of study, predictions about how computers will influence the future organization of mathematics, and what processes a proof undergoes before it reaches publishable form. This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work.

WIGNER, Eugene, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”, Communications in Pure and Applied Mathematics (New York, John Wiley and Sons), vol. XIII, n.º 1, February 1960. Richard Courant Lecture in Mathematical Sciences delivered at New York University, May 11, 1959. Cf.: http://math.northwestern.edu/~theojf/FreshmanSeminar2014/Wigner1960.pdf GRATTAN-GUINNESS, Ivor, “Solving Wigner’s Mystery: The Reasonable (Though Perhaps Limited) Effectiveness of Mathematics in the Natural Sciences, The Mathematical Intelliger, vol. 30, n.º 3, 2008, pp. 7-17. Cf.: http://www.sfu.ca/~rpyke/cafe/reasonable.pdf ABBOT, Derek [School of Electrical and Electronic Engineering, The University of Adelaide, Australia], “The Reasonable Ineffectiveness of Mathematics”, Proceedings of the IEEE, vol. 101, n.º 10, October 2013, pp. 2147-2153. Cf.: https://www.researchgate.net/publication/256838918_The_Reasonable_Ineffectiv eness_of_Mathematics_Point_of_View WOLENSKI, Jan (Edited by), Philosophical Logic in Poland, Dordrecht: Springer Science + Business Media, 2013 [1994], pp. viii + 367. Translated from the Polish. Cf.: https://books.google.fr/books?id=HEHsCAAAQBAJ&printsec=frontcover&hl=fr &source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false Poland has played an enormous role in the development of mathematical logic. Leading Polish logicians, like Lesniewski, Lukasiewicz and Tarski, produced several works related to philosophical logic, a field covering different topics relevant to philosophical foundations of logic itself, as well as various individual sciences. This collection presents contemporary Polish work in philosophical logic which in many respects continue the Polish way of doing philosophical logic. This book will be of interest to logicians, mathematicians, philosophers, and linguists.

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París, 6 de marzo de 2016 Queridos amigos y colegas: El viernes 15 de enero de 2016 tuve la gran suerte y el placer de descubrir el programa “Le grand mystère des mathématiques” [Título original: The Great Math Mystery] presentado por el Canal 7 Arte de TV (Francia). Fueron 53’ de un encantador viaje por los caminos de la matemática –“La matemática es la lengua con la que Dios ha escrito el universo” (Galileo Galilei, 1564-1642)2– a lo largo de la historia guiado por el renombrado astrofísico y escritor Mario Livio. Para los que aman la matemática será un verdadero gozo hacer este recorrido orientados por Mario Livio y otros matemáticos, astrofísicos e ingenieros. Como dice la presentación del programa en francés: Une enquête captivante, formidablement illustrée d’exemples, en même temps qu’un voyage visuel vertigineux. Entre construction neuronale et ordre cosmique, à la frontière de l’invention et de la découverte, les mathématiques, extraordinaire énigme, n’ont pas fini de révéler, d’anticiper et de surprendre. [Una encuesta cautivante, formidablemente ilustrada de ejemplos, al mismo tiempo que un viaje visual vertiginoso. Entre construcción neuronal y orden cósmico, en la frontera de la invención y el descubrimiento, la matemática, extraordinario enigma, no ha cesado de revelar, anticipar y sorprender”]. Para quienes se sitúan en el polo opuesto –a quienes tal vez se podría aplicar lo que digo en la “Introducción” al libro Pluriculturalidad y aprendizaje de la matemática en América Latina, parodiando a Joseph Paul Goebbles (ministro de propaganda e información de Hitler: Cada vez que escucho la palabra cultura… saco mi pistola’. Solo hay que reemplazar la palabra ‘cultura’ por ‘matemática’.3 este video podría tal vez suscitarles menos horror o menosprecio por la matemática, e incluso interés por ella, porque nos incita creativamente a descubrir y valorar este “lenguaje” absolutamente necesario, si bien no suficiente. Lindo fin de semana y mis mejores deseos para ustedes y sus seres queridos. Alfonso o Sísifo sonriente P.S.: Les agradeceré que me confirmen la recepción de este mensaje y el fichero adjunto. Grazie e tanti auguri.

------Alfonso E. Lizarzaburu UNESCO International Consultant on Education Honorary Professor of the Ricardo Palma University (Peru) Adviser to the Presidency of the UNESCO Club Valencia (Spain) Member of the Executive Board and of the Governing Council of the World Committee for Lifelong Learning (France) 7, rue Carrière Mainguet 75011 Paris France Telephone: (1) 43.79.31.03 E-mail: [email protected]

2 Galileo Galilei, El ensayador, Buenos Aires: Ediciones Aguilar, 1981, p. 63. Se trata del trabajo final y más importante de la polémica sobre las características de los cometas en la que participó Galileo, científico y matemático italiano. Fue publicado en italiano en octubre de 1623 por la Academia Linceana en Roma con el título Il sagiattore. Fue dedicado al Papa Urbano VIII. 3 Lizarzaburu, Alfonso y Gustavo Zapata (coordinadores), Pluriculturalidad y aprendizaje de la matemática en América Latina, Madrid: Editorial Morata, 2001, p. 25]. 57