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Bolzano Bernhard:     more detail

Paradoxin des Unendlichen by Bernhard Bolzanos, 2006-11-30 PRECURSORS OF MODERN LOGIC: BOLZANO: An entry from Gale's <i>Encyclopedia of Philosophy</i> by Yehoshua Bar-Hillel, 2006 BOLZANO, BERNARD(17811848): An entry from Gale's <i>Encyclopedia of Philosophy</i> by Yehoshua Bar-Hillel, 2006 Journal of the History of Philosophy: Vol. 45, No. 4, October 2007.(PHILOSOPHICAL ABSTRACTS): An article from: The Review of Metaphysics by Gale Reference Team, 2007-09-01

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1. CATHOLIC ENCYCLOPEDIA: Bernhard Bolzano
   (Catholic Encyclopedia)Category Society Religion and Spirituality BBernhard Bolzano. Austrian mathematician and philosopher, b. at Prague,5 October, 1781; d. 18 December, 1848. As a student he devoted  
   http://www.newadvent.org/cathen/02643c.htm
   
   Extractions: Home Encyclopedia Summa Fathers ... B > Bernhard Bolzano A B C D ... Z Austrian mathematician and philosopher, b. at Prague, 5 October, 1781; d. 18 December, 1848. As a student he devoted himself chiefly to mathematics with marked success. Against the wish of his father, he entered the ecclesiastical state and was ordained in 1805. In the same year he was appointed professor of the philosophy of religion in the University of Prague. His lectures and discourses were strongly tinged with rationalism , and it was not long before he was denounced to the ecclesiastical authorities. Through the personal intervention of the Prince-Archbishop Salm-Salm of Prague, he retained his professorship until 1820, when the long-threatened dismissal was suddenly put into effect in consequence of disorders that occurred in the seminary of Leitmeritz then under the direction of Dr. Fessl, who, as a disciple and friend of Bolzano, was strongly imbued with the latter's rationalizing spirit. Bolzano spent the remainder of his life in studious retirement, first on the estate of his friend Johann Hoffmann, at Techobuz, near Prague, and later in the house of his brother at Prague. A small pension, and the generosity of Count Leo Thun, relieved him of all monetary care. Bolzano was always a loyal son of the Catholic Church. There is, however, a strong rationalizing tendency in his writings on doctrinal subjects, and his refusal to retract several propositions taken from his printed works justified his dismissal from the University of Prague. Bolzano's contributions to the science of mathematics are of the highest order. In 1804 he published a theory of parallel lines which anticipated Legendre's well-known theory. He shares with

2. Bernhard Bolzano
   Bernhard Bolzano PADRE REFUGIASE NA MATEMÁTICA Bernhard Bolzano nasceu e morreu em Praga, Tchecoslováquia, e embora fosse padre tinha idéias contrárias às da Igreja. Suas descobertas matemáticas foram muito pouco reconhecidas por seus  
   http://www.leonardodavi.hpg.ig.com.br/bernhard_bolzano.htm
   
   Extractions: Bernhard Bolzano PADRE REFUGIA-SE NA MATEMÁTICA Bernhard Bolzano nasceu e morreu em Praga, Tchecoslováquia, e embora fosse padre tinha idéias contrárias às da Igreja. Suas descobertas matemáticas foram muito pouco reconhecidas por seus contemporâneos. Em 1817 publicou o livro "Rein Analytisches Beweis" (Prova puramente analítica ) , provando através de métodos aritméticos o teorema de locação em Álgebra, exigindo para isso um conceito não geométrico de continuidade de uma curva ou função. Bolzano, a essa época, já havia percebido tão bem a necessidade de rigor em Análise, que Klein o chamou "pai da aritmetização", embora tivesse menos , influência que Cauchy com sua análise baseada em conceitos geométricos mas embora os dois nunca tivessem se encontrado, suas definições de limite, derivada, continuidade e convergência eram bem semelhantes. Em uma obra póstuma de 1850, Bolzano chegou a enunciar propriedades importantes dos conjuntos finitos e, apoiando-se nas teorias de Galileu, mostrou que existem tantos números reais entre e 1, quanto entre e 2, ou tantos em um segmento de reta de um centímetro quanto em um segmento de reta de dois centímetros. Parece ter percebido que a infinidade de números reais é de tipo diferente da infinidade de números inteiros, sendo não enumeráveis, estando mais próximo da Matemática moderna do que qualquer um de seus contemporâneos.

3. Bolzano Bernhard Theory Of Science
   bolzano bernhard Theory of Science. Author BolzanoBernhard. Title Theory of Science Subject  
   http://www.books-city.com/Bolzano-Bernhard-Theory-of-Science-0520017870.html

4. Famous People
   Bethe Hans Binnig Gerd Biot Jean Baptiste Blackett Patrick Bloch Felix BloembergenNicolaas Bohr Aage Bohr Niels Boltzmann Ludwig bolzano bernhard Born Max  
   http://www.aldebaran.cz/famous/list_abc.html

5. Bolzano
   Translate this page bolzano bernhard tchèque, 1781-1848 La conception rationaliste dece prètre philosophe, d'origine italienne, le conduit à la  
   http://www.sciences-en-ligne.com/momo/chronomath/chrono1/Bolzano.html

6. New Links For Continental Philosophy
   2000; Wilhelm Dilthey (Britannica Online); Bolzano The Bolzano Pages;bolzano bernhard Bolzano (Paul Golba, Seton Hall Univ.); Bolzano  
   http://www.baylor.edu/~Scott_Moore/new_cont.html
   
   Extractions: for Contemporary Continental Philosophy What's New in The Notebook Return to the Notebook November 2002 August 2002 September 2001 July 2001 Derrida: Traces of God: The Faith of Jacques Derrida by Bruce Ellis Benson [Books and Culture, September/October 2000] Schmitt: Down on Law: The complicated legacy of the authoritarian jurist Carl Schmitt by William E. Scheuerman [Boston Review, April/May 2001] Eagleton: The centre cannot hold by Terry Eagleton [The Guardian, June 23, 2001]

7. Www.iper1.com - Bernhard Bolzano
   Translate this page Cerca la rima. Bernhard Bolzano. Agazzano Albuzzano Arenzano ArizzanoArzano Avezzano Bazzano Bianzano bolzano bernhard Bolzano Borgo  
   http://www.iper1.com/rime/index-asp--cerca-llll-Bernhard Bolzano.htm

8. Bernhard Bolzano - Acapedia - Free Knowledge, For All
   acapedia.org home acapedia feedback. Friends of Acapedia Bernhard Bolzano. FromWikipedia, the free encyclopedia. (There is currently no text in this page).  
   http://acapedia.org/aca/Bernhard_Bolzano

9. Einige Der Bedeutenden Mathematiker
   Translate this page Bieberbach Ludwig, 1886-1982. Birkhoff Georg David, 1884-1944. Bolyai János, 1802-1860.bolzano bernhard, 1781-1848. Boole George, 1815-1864. Borel Emile, 1871-1956.  
   http://www.zahlenjagd.at/mathematiker.html
   
   Extractions: Einige der bedeutenden Mathematiker Abel Niels Hendrik Appolonius von Perga ~230 v.Chr. Archimedes von Syrakus 287-212 v.Chr. Babbage Charles Banach Stefan Bayes Thomas Bernoulli Daniel Bernoulli Jakob Bernoulli Johann Bernoulli Nicolaus Bessel Friedrich Wilhelm Bieberbach Ludwig Birkhoff Georg David Bolyai János Bolzano Bernhard Boole George Borel Emile Briggs Henry Brouwer L.E.J. Cantor Georg Ferdinand Carroll Lewis Cassini Giovanni Domenico Cardano Girolamo Cauchy Augustin Louis Cayley Arthur Ceulen, Ludolph van Chomsky Noel Chwarismi Muhammed Ibn Musa Al Church Alonzo Cohen Paul Joseph Conway John Horton Courant Richard D'Alembert Jean Le Rond De Morgan Augustus Dedekind Julius Wilhelm Richard Descartes René Dieudonné Jean Diophantos von Alexandria ~250 v. Chr. Dirac Paul Adrien Maurice Dirichlet Peter Gustav Lejeune Eratosthenes von Kyrene 276-194 v.Chr. Euklid von Alexandria ~300 v.Chr. Euler Leonhard Fatou Pierre Fermat Pierre de Fischer Ronald A Sir Fourier Jean-Baptiste-Joseph Fraenkel Adolf Frege Gottlob Frobenius Ferdinand Georg Galois Evariste Galton Francis Sir Gauß Carl Friedrich Germain Marie-Sophie Gödel Kurt Goldbach Christian Hadamard Jacques Hamilton William Rowan Hausdorff Felix Hermite Charles Heawood Percy Heron von Alexandrien ~60 n.Chr.

10. Www.olschki.it/ANALITIC.TXT
    Translate this page Massimo Boi Francesco Boiardo Matteo Maria Boiardo Matteo Maria - Opere Boito ArrigoBologna Bolzano Bolzano - Toponomastica bolzano bernhard Bonaventura da  
    http://www.olschki.it/ANALITIC.TXT

11. Mat
    Matemaatikkojen henkilökuvia Matemaatikkoja aakkosjärjestyksessä Great MathematiciansArchimedes bolzano bernhard Placidus Einstein Albert de Fermat Pierre  
    http://kotisivu.mtv3.fi/elot/mat.htm

12. BOLZANO, BERNHARD
    founded in 1641, had Robert Ainsworth, the Latin lexicographer, and John Lemprihre, author of the classical dictionary, among its masters  
    http://86.1911encyclopedia.org/B/BO/BOLZANO_BERNHARD.htm
    
    Extractions: The earliest form of the name is Bodleton or BotFieltun, and the most important of the later forms are Bodeltown, Botheltunle-Moors, Bowelton, Boltune, Bolton-super-Moras, Bolton-in-yeMoors, Bolton-le-Moors. The manor was granted by William I. to Roger de Poictou, and passed through the families of Ferrcrs and Pilkington to the Harringtons of Hornby Castle, who lost it with their other estates for their adherence to Richard III. In 1485 Henry VII. granted it to the first earl of Derby. The manor is now held by different lords, but the earls of Derby still have a fourth part. The manor of Little Bolton seems to have been, at least from Henry III.’s reign, distinct from that of Great Bolton, and was held till the 17th century by the Botheltons or Boltons. During the Civil War Bolton sided with the parliament, and in February 1643 and March 1644 the royalist forces assaulted the town, but were on both occasions repulsed. On the 28th of May 1644, however, it was attacked by Prince Rupert and Lord Derby, and stormed with great slaughter. On. the 15th of October 1651 Lord Derby, who had been taken prisoner after the battle of Worcester, was brought here and executed the same day. Up to the beginning of the ~9th century the market day was Monday, but the customary Saturday market gradually superseded this old chartered market. In 1251 William de Ferrers

13. Bolzano, Bernhard.
    Translate this page bolzano, bernhard. bernhard bolzano, nacido en Oct. 5, 1781, muertoen Dic. 18, 1848, fue un filósofo checo, matemático, y teólogo  
    http://euler.ciens.ucv.ve/matematicos/bolzano.html
    
    Extractions: Bolzano, Bernhard. Bernhard Bolzano, nacido en Oct. 5, 1781, muerto en Dic. 18, 1848, fue un filósofo checo, matemático, y teólogo quien hizo contribuciones significantes tanto en la matemática como en la teoría del conocimiento. Un sacerdote del catolicismo, fue puesto (1805) como máximo exponente de la filosofía y la religión en Praga. Sin embargo en 1819 fue Bolzano suspendido de su posición a causa de presión del gobierno austríaco, los cuales se oponían a su pacifismo y su expresión de la justicia económica. Aunque algunos de sus libros tenían que ser publicados fuera de Austria a causa de la censura del gobierno, continuó escribiendo y jugó un papel importante en la vida intelectual de su país. Entre los trabajos importantes de Bolzano están Rein Analytischer Beweis (Una Prueba Pura Analítica, 1817), que contiene un esfuerzo exitoso de librar al cálculo del concepto del infinitesimal; Wissenschaftslehre (1837), un esfuerzo de completar la teoría de la ciencia y el conocimiento; y el póstumo Paradoxien des Unendlichen (1851; Ingl. Paradojas del infinito,1950).La Teoría Matemática Infinita de Bolzano anticipa a la Teoría de los Conjuntos Infinitos de Cantor. Su distinción entre psicología y lógica influyeron en Edmund Husserl y los propuestos más adelante de PHENOMENOLOGY. Autor: Pete A. Y. Gunter.

14. Bolzano, Bernhard.
    bolzano, bernhard. bernhard bolzano, b. Oct. 5, 1781, d. Dec. 18, 1848,was a Czech philosopher, mathematician, and theologian who  
    http://euler.ciens.ucv.ve/English/mathematics/bolzano.html
    
    Extractions: Bolzano, Bernhard. Bernhard Bolzano, b. Oct. 5, 1781, d. Dec. 18, 1848, was a Czech philosopher, mathematician, and theologian who made significant contributions to both mathematics and the theory of knowledge. A Roman Catholic priest, he was appointed (1805) to the chair of philosophy and religion at Prague. In 1819, however, Bolzano was suspended from his position because of pressure from the Austrian government, which opposed his pacifism and his expressed concerns with economic justice. Although some of his books had to be published outside Austria because of government censorship, he continued to write and to play an important role in the intellectual life of his country. Among Bolzano's important works are Rein analytischer Beweis (Pure Analytical Proof, 1817), which contains an effort to free calculus successfully from the concept of the infinitesimal; Wissenschaftslehre (1837; Eng. trans. and abridgment, Theory of Science, 1972), an attempt at a complete theory of science and knowledge; and the posthumous Paradoxien des Unendlichen (1851; Eng. trans., Paradoxes of the Infinite, 1950). Bolzano's theories of mathematical infinity anticipated Georg CANTOR's theory of infinite sets (see SET THEORY). His distinction between psychology and logic influenced Edmund HUSSERL and later proponents of PHENOMENOLOGY. Author: Pete A. Y. Gunter

15. Bernhard Bolzano
    bernhard bolzano nasceu e morreu em Praga, Tchecoslováquia, e embora fosse padre tinha idéias contrárias às da  
    http://www.brasil.terravista.pt/magoito/1866/Historia/bolzano.htm

16. Bolzano
    Visit the New Advent website for the Summa Theologica, Church Fathers, Catholic Encyclopedia and more. Home Catholic Encyclopedia B bernhard bolzano  
    http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Bolzano.html
    
    Extractions: Bernard Bolzano was a Czech philosopher, mathematician, and theologian who made significant contributions to both mathematics and the theory of knowledge. Bolzano entered the Philosophy Faculty of the University of Prague in 1796, studying philosophy and mathematics. Bolzano wrote My special pleasure in mathematics rested therefore particularly on its purely speculative parts, in other words I prized only that part of mathematics which was at the same time philosophy. In the autumn of 1800 he began 3 years of theological study. While pursuing his theological studies he prepared a doctoral thesis on geometry. He received his doctorate in 1804 writing a thesis giving his view of mathematics, and what constitutes a correct mathematical proof. In the preface he wrote:- I could not be satisfied with a completely strict proof if it were not derived from concepts which the thesis to be proved contained, but rather made use of some fortuitous, alien, intermediate concept, which is always an erroneous transition to another kind.

17. References For Bolzano
    Biography in Encyclopaedia Britannica. Books J Berg, bolzano's Logic (Stockholm,1962). H Fels, bernhard bolzano, sein Leben und sein Werk (Leipzig, 1929).  
    http://www-gap.dcs.st-and.ac.uk/~history/References/Bolzano.html
    
    Extractions: J Berg, Bolzano's Logic (Stockholm, 1962). H Fels, Bernhard Bolzano, sein Leben und sein Werk (Leipzig, 1929). V Jarnik, Bolzano and the foundations of mathematical analysis (Prague, 1981). L Novy, Bolzano, in H Wussing and W Arnold, Biographien bedeutender Mathematiker (Berlin, 1983). J Sebestik, (Paris, 1992). Articles: Y Bar-Hillel, Bolzano's propositional logic, Arch. Math. Logik Grundlagenforsch. J Berg, Bolzano and situation semantics: variations on a theme of variation, Bolzano - Studien. Philos. Natur. J Berg, Bolzano on induction, Bolzano - Studien. Philos. Natur. J Berg, Is Russell's antinomy derivable in Bolzano's logic?, Bolzano - Studien. Philos. Natur. Bolzano - Studien. Philos. Natur. J Berg, A requirement for the logical basis of scientific theories implied by Bolzano's logic of variation, in Impact of Bolzano's epoch on the development of science (Prague, 1982), 415-425.

18. 10.4. Bolzano, Bernhard (1781-1848)
    a topic from HistoriaMatematica Discussion Group HM Bernard or bernhard bolzano? post a message on this topic post a message on a new topic 29 Jul 2001 HM Bernard or bernhard bolzano?, by "Robert  
    http://www.shu.edu/html/teaching/math/reals/history/bolzano.html
    
    Extractions: 10.4. Bolzano, Bernhard (1781-1848) IRA Bernard Bolzano was a philosopher and mathematician whose contributions were not fully recognized until long after his death. He is especially important in the fields of logic, geometry and the theory of real numbers. Bernardus Placidus Johann Nepomuk Bolzano was born in Prague, Bohemia (now part of the Czech Republic), on October 5, 1781. His father was an art dealer and both parents were very pious Christians. Coming from such a religious household, Bernard grew up with a high moral code and a belief in holding to his principles. It was this background that attracted him to the Church and the priestly life. Bolzano entered the University of Prague in 1796, where he studied philosophy, mathematics and physics. After graduation, he joined the theology department at the university and was ordained a Catholic priest in 1804. Despite his dedication to the Church, he did not give up his mathematical interests and was at one time recommended for the chair of the mathematics department. The year 1805 started a struggle that would dominate the rest of his life. In a political move, the Austrian-Hungarian Empire set up a chair in the philosophy of religion at each university. The empire was comprised of many different ethic groups that were prone to nationalistic movements for independence. Spurred by the "free thinking" of the recent French Revolution, these movements were becoming a serious problem to holding the empire together. The creation of the chair was part of a greater plan to support the Catholic Church. The authorities considered the Church to be conservative and hoped it would control the liberal thinking of the time. Bolzano was appointed to the position at the University of Prague. As far as the authorities were concerned, this was a bad idea. Bolzano, though a priest, was a "free thinker" himself and was not afraid to express his beliefs in Czech nationalism.

19. 10.4. Bolzano, Bernhard (1781-1848)
    10.4. bolzano, bernhard (17811848). IRA. Bernard bolzano was a philosopherand mathematician whose contributions were not fully recognized  
    http://www.shu.edu/projects/reals/history/bolzano.html
    
    Extractions: 10.4. Bolzano, Bernhard (1781-1848) IRA Bernard Bolzano was a philosopher and mathematician whose contributions were not fully recognized until long after his death. He is especially important in the fields of logic, geometry and the theory of real numbers. Bernardus Placidus Johann Nepomuk Bolzano was born in Prague, Bohemia (now part of the Czech Republic), on October 5, 1781. His father was an art dealer and both parents were very pious Christians. Coming from such a religious household, Bernard grew up with a high moral code and a belief in holding to his principles. It was this background that attracted him to the Church and the priestly life. Bolzano entered the University of Prague in 1796, where he studied philosophy, mathematics and physics. After graduation, he joined the theology department at the university and was ordained a Catholic priest in 1804. Despite his dedication to the Church, he did not give up his mathematical interests and was at one time recommended for the chair of the mathematics department. The year 1805 started a struggle that would dominate the rest of his life. In a political move, the Austrian-Hungarian Empire set up a chair in the philosophy of religion at each university. The empire was comprised of many different ethic groups that were prone to nationalistic movements for independence. Spurred by the "free thinking" of the recent French Revolution, these movements were becoming a serious problem to holding the empire together. The creation of the chair was part of a greater plan to support the Catholic Church. The authorities considered the Church to be conservative and hoped it would control the liberal thinking of the time. Bolzano was appointed to the position at the University of Prague. As far as the authorities were concerned, this was a bad idea. Bolzano, though a priest, was a "free thinker" himself and was not afraid to express his beliefs in Czech nationalism.

20. Re: [HM] Bernard Or Bernhard Bolzano? By Julio Gonzalez Cabillon
    Re HM Bernard or bernhard bolzano? by Julio Gonzalez Cabillon Subject Re HM Bernard or bernhard bolzano?  
    http://mathforum.com/epigone/historia_matematica/smixroiqua/5.1.0.14.2.200107311

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