The Great Math Mystery Mario Livio

Transcription

“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
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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-ScientistsUnderstanding/dp/1439192367/ref=mt_hardcover?_encoding=UTF8&me=
http://www.amazon.com/Brilliant-Blunders-Einstein-ScientistsUnderstanding/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.
3
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/MarioLivio/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-unmatematico/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.
4
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/MarioLivio/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-SolvedMathematical/dp/0743258215/ref=asap_bc?ie=UTF8
http://www.amazon.com/Equation-That-Couldnt-SolvedMathematical/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
5
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-WorldsAstonishing/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-WorldsAstonishing/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
6
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-ExpansionCosmological/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-ExpansionCosmological/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 everaccelerating 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.).
§♦♦♦♦♦§
7
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/
8
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=googhydr0a821&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-porjustus.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-sistematolemaico-urbano-VIII-orazio-grassi-9419.html
HERNÁNDEZ GONZÁLEZ, Francisco Javier y Sebastián SALGADO GONZÁLEZ,
“El Renacimiento y la nueva ciencia”, Duererías. Cuadernos de Filosofía, 20102011, 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-ilsaggiatore-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
§♦♦♦♦♦§
10
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-ofcontents?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
11
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=0-102-24-00&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.
12
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.
13
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-ofcontents?showall=1&limitstart
http://www.ebay.it/itm/8891709247-SCIENCE-METAPHYSICS-RELIGIONEVANDRO-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
14
religion. This is the attitude of "scientism" that has produced as a reaction an attitude of antiscience.
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
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 whyquestion. 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 whyquestion. 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.
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.
15
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-theSciences/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
Introduction. Observability and Scientific Realism
16
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=id9IxdcBi&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 storicoconcettuali 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
17
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
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
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 languagedependency 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
18
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
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.:
19
http://mimesisedizioni.it/libri/filosofia/centro-internazionaleinsubrico/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 (JeanMarie 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.
20
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. 239314.
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-Conocimientocientifico-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-deoccidente/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.:
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-ycosmologia/9789681661793/1708021
21
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 1721 October 2003. Cf.:
https://books.google.fr/books?id=RWysXQC_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
22
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 TechnoScientific 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
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
23
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”
24
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
25
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
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.:
26
http://www.amazon.es/Ciencia-Logica-Mundos-PosiblesHochschulschriften/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
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-lacienciaepistemologia-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
27
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-mondoantico-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.:
28
http://www.booklooker.de/B%C3%BCcher/E-Agazzi+Storia-delle-Scienze-dalsecolo-XIX-al-mondo-contemporaneo-Volumesecondo/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/wpcontent/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”,
29
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=S1870879X2010000100011&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
30
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).
31
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-HeildelbergNew York-Hong Kong-London-Milan-Paris-Tokyo, 2004, pp. 367. Cf.:
http://www.lesacademies.org/en/iaps/publications/aips-tables-ofcontents?showall=&start=1
“Evandro Agazzi Filosofo della scienza”, Il Protagora (Mimesis Edizioni), Anno XXXVII, lugliodicembre, 2010, sesta serie, n.º 14, 2010, pp. 535. Cf.:
http://mimesisedizioni.it/riviste/il-protagora/vol-14-evandro-agazzi-filosofo-dellascienza.html#yt_tab_products1
§♦♦♦♦♦§
32
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-mondoin.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.
33
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-numerida.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
34
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-ilgrande.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-lavventura.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/matematicoimpertinente.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
35
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/matematicoimpenitente.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/matematicoimpenitente.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-eradarwin.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.:
36
http://www.ibs.it/code/9788850232994/odifreddi-piergiorgio-valzania-sergio/vialattea.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-estravagante.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-diventarematematico.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-Italianebook/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
38
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-eimpertinente-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 twentiethcentury mathematics.
ODIFREDDI, Piergiorgio, Érase una vez una paradoja, Barcelona: RBA Libros, 2013,
pp. 304. Cf.:
http://www.casadellibro.com/libro-erase-una-vez-unaparadoja/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/
39
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
§♦♦♦♦♦§
BUNGE, Mario, Matter and Mind. A Philosophical Inquiry, Dordrecht-HeidelbergLondon-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-BostonLondon: Kluwer Academic Publishers, 1997, pp. 51-72 (Episteme 22). Cf.:
http://www.lesacademies.org/en/iaps/publications/aips-tables-ofcontents?showall=&start=1
BUNGE, Mario Works by, philpapers. [184 titles]. Cf.:
http://philpapers.cdp.uwo.ca/s/Mario%20Bunge
40
BUNGE, Mario, “Bibliographic items”, [57 articles], Geomar, Helmholtz Centre for
Ocean Research Kiel. Cf.:
http://geomarsearch.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.:
41
http://www.odilejacob.fr/catalogue/sciences/neurosciences/code-de-laconscience_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-CodesThoughts/dp/0670025437
http://www.amazon.com/Consciousness-Brain-Deciphering-CodesThoughts/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 eventrelated 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
42
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-ansapr%C3%A8s/dp/2738125247/ref=asap_bc?ie=UTF8
http://www.amazon.fr/Bosse-maths-Quinze-ansapr%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.
cognitive expérimentale et membre de l’Académie des sciences. Il a publié Les Neurones de
la lecture, qui a rencontré un très grand succès.
43
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-CreatesMathematics/dp/0199753873/ref=pd_cp_14_4?ie=UTF8&refRID=131CTHEB3XSMQEJ
M262H
http://www.amazon.com/The-Number-Sense-CreatesMathematics/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
44
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-PierreChangeux/dp/2738119743
http://www.amazon.fr/Les-Neurones-lecture-Jean-PierreChangeux/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.
cognitive expérimentale et membre de l’Académie des sciences. Il est l’auteur de La Bosse des
maths.
45
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-ScienceRead/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-ScienceRead/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/EinsteinAlbertMathematicsHumanQuote500px.htm
“El número de Dios”, Medium.com, 23 de octubre de 2015. Cf.:
https://medium.com/@veronicanunezriv/el-número-de-diosb827e86b73e0#.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-HiddenReality/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
46
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.:
47
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=ahyPnEkdbSqzZ9FigHcKlaUZCg&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
48
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
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
(elena.marchisotto@csun.edu) 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
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-aQYbIR0M7LdOYwCynKkl5qU&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.
49
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-DoverBooks/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-MaryLeng/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-lamatematica-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.
51
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-ydesaf&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
52
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
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
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
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
53
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
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-NonsensePostmodern-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
54
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-UltimateReality/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=HFa03eq9LQC&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
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.
§♦♦♦♦♦§
56
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.
P.S.:
Alfonso o Sísifo sonriente
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: alfonso.lizarzaburu@gmail.com
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

The Great Math Mystery Mario Livio

Transcription

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