Beowulf Essay, Research Paper

Bernard Bolzano

(1784-1848)

Bernard Bolzano was a philosopher and mathematician whose contributions were not truly recognized until long after his death. He is especially important in the fields of logic geometry and the theory or real numbers.

Bernardus Placidus Johann Nepomuk Bolzano was born in Prague, Bohemia, (which is now part of the Czech Republic), on October 5, 1781 as the fourth child out of twelve children. His mother was a German-speaking native of Prague, his father a dealer in small wares from Northern Italy who had immigrated to Bohemia early in life. 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 Christian Church and the Priest?s way of life.

He entered the University of Prague in 1796, where he studied philosophy, mathematic and physics. He entered even though it was against his father?s wishes. 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. During that time Emperor Francis of Austria Established special chairs of religion in all universities and higher schools throughout the Empire.

These were intended to teach people to become ?good Christians and responsible citizens? and counteract ideas emanating from the French Revolution.

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 movement 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.

For the next Fourteen years, Bolzano taught at the university, lecturing mainly on ethics, social questions and the links between mathematics and philosophy. He was very popular with both the student body, which appreciated his straightforward expression of his beliefs, and his fellow professors, who recognized his intelligence. In 1818, he became Dean of the philosophy department. However, the Austro Hungarian authorities became displeased with his liberal views. In 1819, he published important works on geometry and the foundations of mathematical analysis. His sermons, preached also on public holidays, were meticulously prepared and highly popular, not least because despite

the Emperor?s intentions they put forward a liberal, tolerant and enlightened point of view. This progressive stance and Bolzan?s blunt criticisms of the prescribed theology textbook brought him to the unwelcome notice of conservatives in church and state, and after several investigations, he was removed from office. This removal came during the period of the strongest conservative reaction to ligeralism im Metternichian Austria. Bolzano was forbidden for the rest of his life to teach or preach exhortations. He was not allowed to publish, his post opened and censored. Later the ban on publication was relaxed to allow the publication of works without political or religious content. Bolzano was also subject to the4 indignity of a prolonged (1821-5) ?trial? within the church. Bolzano defended his views and their compatibility Catholic doctrine throughout, but he was thereafter forbidden to hear confession, though allowed to continue celebrating mass.

Bolzano?s removal from office had the positive effect of giving him the leisure and energy to pursue research, which as a highly conscientious teacher with poor health he would otherwise have been unable to do. From 1823-1830 Bolzano went to live every summer in Techobuz at the estate of Josef and Anna Hoffmann, wintering at the house of his brother Johann Bozano, a merchant. Anna Hoffmann cared especially for Bolzano and took pains to maintain his health. From 1830-1841 Bolzano lived permanently with the Hoffmans in Techobuz. IN this period he produced his most important works, the Legrbuch der Religionswissenschaft (1834) and the Wissenschaftslefre ( 1837), each in four volumes. Bolzano also met with his former students Johann Mechail Fesl and Franz Prihonsky, and through his students many of his works were published anonymously or under their names abroad.

Being a philosopher, Bolzano attacked his mathematics philosophically. He believed that first clear concepts could only be obtained by using logic on basic principles and definitions. By finding the foundations, the use was guaranteed proof. Sometimes, this system gave him discoveries that were amazing. At other times, especially in mathematics, it gave wrong answers.

Bolzano did contribute much to mathematics. His work attacked mainly three subjects: geometry, the theory of real numbers and logic. In geometry, he attempted to handle the problem of Euclid?s parallel postulate. He found several problems in Euclid?s reasoning but was unable to solve them because he lacked the proper mathematical tool of topology, which had not yet been invented. He did establish definitions for basic geometric concepts and was the first person to state the Jordan curve theorem, that a simple closed curve divides a plane into two parts. In the theory of real numbers, he tried to find its foundation and reconcile infinite quantities, a concept that had stumped previous mathematicians. Although he did not succeed, he did come up with some important discoveries including the Bozano Weierstrass theorem, a modern difinition of a continuous function and the non-differentiable Bolzano function. In addition, he recognized some of the paradoxical qualities of infinite sets, a breakthrough, which he did not pursue and would be later, stated by Cantor. In logic, his ideas were generally ignored until the modern day. Not just trying to place mathematics on a logical foundation, he went a step further and tried to place all the sciences and human thinking under its scope.

In his works, he tackles basic ideas like abstract truth, human judgment and rules of science. Today, his in now considered one of the precurusors to modern logic.

Bibliography

?20th WCP: Bernard Bolzano-Pedagoue.? October 12, 2000. http://www.bu.edu/wcp/papers/teac/teaclore.htm

Abbott, David PhD. Ed. ?Bolzano, Bernardus Placidus Johann Nepomuk.? The Biographical Dictionary of Sciences: Mathematics. New York: peter Bedrick Books, 1985.

?The Bernard Bolzano Pages.? October 12, 2000. http://sbg.ac.at/fph/bolzano/bolzano=life.html

?Bolzano.? October 12, 2000. http://www-groups.dcs.st-and.ac.uk/~history/mathematicians/bolzano.html

Rootselaar, B. Van. :Bolzano, Bernard.? Dictionary of Scientific Biography, New York: Charles Scribner?s Sons, 1970. vol. 1, pg. 273-279.

Bolzano, Bernard

(1781-1848)

?20th WCP: Bernard Bolzano-Pedagoue.? October 12, 2000. http://www.bu.edu/wcp/papers/teac/teaclore.htm

Abbott, David PhD. Ed. ?Bolzano, Bernardus Placidus Johann Nepomuk.? The Biographical Dictionary of Sciences: Mathematics. New York: peter Bedrick Books, 1985.

?The Bernard Bolzano Pages.? October 12, 2000. http://sbg.ac.at/fph/bolzano/bolzano=life.html

?Bolzano.? October 12, 2000. http://www-groups.dcs.st-and.ac.uk/~history/mathematicians/bolzano.html

Rootselaar, B. Van. :Bolzano, Bernard.? Dictionary of Scientific Biography, New York: Charles Scribner?s Sons, 1970. vol. 1, pg. 273-279.

Bibliography

?20th WCP: Bernard Bolzano-Pedagoue.? October 12, 2000. http://www.bu.edu/wcp/papers/teac/teaclore.htm

Abbott, David PhD. Ed. ?Bolzano, Bernardus Placidus Johann Nepomuk.? The Biographical Dictionary of Sciences: Mathematics. New York: peter Bedrick Books, 1985.

?The Bernard Bolzano Pages.? October 12, 2000. http://sbg.ac.at/fph/bolzano/bolzano=life.html

?Bolzano.? October 12, 2000. http://www-groups.dcs.st-and.ac.uk/~history/mathematicians/bolzano.html

Rootselaar, B. Van. :Bolzano, Bernard.? Dictionary of Scientific Biography, New York: Charles Scribner?s Sons, 1970. vol. 1, pg. 273-279.