Bernard Bolzano

Bernard (Bernhard) Placidus Johann Nepomuk Bolzano (October 5, 1781 – December 18, 1848) was a Bohemian mathematician, theologian, philosopher, logician and antimilitarist of German mother tongue. He was born in Prague. Download high resolution version (599x689, 112 KB)In the public domain by age This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... Download high resolution version (599x689, 112 KB)In the public domain by age This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... is the 278th day of the year (279th in leap years) in the Gregorian calendar. ... 1781 was a common year starting on Monday (see link for calendar). ... is the 352nd day of the year (353rd in leap years) in the Gregorian calendar. ... Year 1848 (MDCCCXLVIII) was a leap year starting on Saturday (link will display the full calendar) of the Gregorian Calendar (or a leap year starting on Monday of the 12-day slower Julian calendar). ... Flag of Bohemia Bohemia (Czech: ; German: ) is a historical region in central Europe, occupying the western and middle thirds of the Czech Republic. ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... Theology finds its scholars pursuing the understanding of and providing reasoned discourse of religion, spirituality and God or the gods. ... A philosopher is a person who thinks deeply regarding people, society, the world, and/or the universe. ... Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration. ... Nickname: Motto: Praga Caput Rei publicae Location within the Czech Republic Coordinates: , Country Czech Republic Region Capital City of Prague Founded 9th century Government  - Mayor Pavel Bém Area  - City 496 km²  (191. ...

Family

Bolzano was the son of two pious Catholics. His father, Bernard Pompeius Bolzano, was born in northern Italy and moved to Prague, where he married Maria Cecelia Maurer, the (German-speaking) daughter of a Prague merchant. Only two of their twelve children lived to adulthood.

Career

Bolzano entered the University of Prague in 1796 and studied mathematics, philosophy and physics. Starting in 1800, he also began studying theology, becoming a Catholic priest in 1804. He was appointed to the then newly created chair of philosophy of religion in 1805. He proved to be a popular lecturer not just in religion but also philosophy, and was elected head of the philosophy department in 1818. Bolzano alienated many faculty and church leaders with his teachings of the social waste of militarism and the needlessness of war. He urged a total reform of the educational, social, and economic systems that would direct the nation's interests toward peace rather than toward armed conflict between nations. Upon his refusal to recant his beliefs, Bolzano was dismissed from the university in 1819. His political convictions (which he was inclined to share with others with some frequency) eventually proved to be too liberal for the Austrian authorities. He exiled to the countryside and at that point devoted his energies to his writings on social, religious, philosophical, and mathematical matters. Although forbidden to publish in mainstream journals as a condition of his exile, Bolzano continued to develop his ideas and publish them either on his own or in obscure Eastern European journals. In 1842 he moved back to Prague, where he died in 1848. The Charles University of Prague (also simply University of Prague; Czech: Univerzita Karlova; Latin: Universitas Carolina) is the oldest and most prestigious Czech university and among the oldest universities in Europe, being founded in 1340s (for the exact year, see below). ... Year 1796 (MDCCXCVI) was a leap year starting on Friday (link will display the full calendar) of the Gregorian calendar (or a leap year starting on Monday of the 11-day slower Julian calendar). ... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... The philosopher Socrates about to take poison hemlock as ordered by the court. ... This article needs additional references or sources for verification. ... // ON MAY 5 1853 MR.FADER HAD SEX WITH A MAN NAME MR WIEN THEN THEY HAD SON NAMEDMRS COTURE AND MR MANOOGIAN WENT INTO MRS HASKELLS OFFICE NAKED AND DANCED AROUND AND MASTERBATED ON HER CHEST AND SHE LICKED IT OFF THEN THEY HAD ORAL SEEX WITH NAPLOEAN OF... Theology finds its scholars pursuing the understanding of and providing reasoned discourse of religion, spirituality and God or the gods. ... This article does not cite any references or sources. ... Philosophy of religion is the rational study of the meaning and justification ( or rebuttal) of fundamental religious claims, particularly about the nature and existence of God (or gods, or the divine). ... 1805 was a common year starting on Tuesday (see link for calendar). ... 1818 (MDCCCXVIII) is a common year starting on Thursday of the Gregorian calendar or a common year starting on Saturday of the 12-day slower Julian calendar. ... 1819 common year starting on Friday (see link for calendar). ... Liberalism is an ideology, philosophical view, and political tradition which holds that liberty is the primary political value. ... Exile (band) may refer to: Exile - The American country music band Exile - The Japanese pop music band Category: ... Rural areas are sparsely settled places away from the influence of large cities and towns. ... Publishing is the activity of putting information in the public arena. ... Look up mainstream in Wiktionary, the free dictionary. ... A journal (through French from late Latin diurnalis, daily) is a daily record of events or business. ... Pre-1989 division between the West (grey) and Eastern Bloc (orange) superimposed on current national boundaries: Russia (dark orange), other countries of the former USSR (medium orange),members of the Warsaw pact (light orange), and other former Communist regimes not aligned with Moscow (lightest orange). ... 1842 was a common year starting on Saturday (see link for calendar). ... Year 1848 (MDCCCXLVIII) was a leap year starting on Saturday (link will display the full calendar) of the Gregorian Calendar (or a leap year starting on Monday of the 12-day slower Julian calendar). ...

Works

Bolzano's early work Paradoxien des Unendlichen (The Paradoxes of the Infinite) was greatly admired by many of the eminent logicians who came after him, including Charles Peirce, Georg Cantor, and Richard Dedekind. Bolzano's main claim to fame, however, is his 1837 Wissenschaftslehre (Theory of Science), a work in four volumes that covered not only philosophy of science in the modern sense but also logic, epistemology and scientific pedagogy. The logical theory that Bolzano developed in this work has come to be acknowledged as ground-breaking. Other works are a four-volume Lehrbuch der Religionswissenschaft (Textbook of the study of religion) and the metaphysical work Athanasia, a defense of the immortality of the soul. Bolzano also did valuable work in mathematics, which remained virtually unknown until Otto Stolz rediscovered many of his lost journal articles and republished them in 1881. A logician is a philosopher, mathematician, or other whose topic of scholarly study is logic. ... Charles Sanders Peirce (IPA: /pɝs/), (September 10, 1839 – April 19, 1914) was an American polymath, physicist, and philosopher, born in Cambridge, Massachusetts. ... Georg Ferdinand Ludwig Philipp Cantor (March 3, 1845, St. ... Richard Dedekind Julius Wilhelm Richard Dedekind (October 6, 1831 – February 12, 1916) was a German mathematician who did important work in abstract algebra and the foundations of the real numbers. ... Queen Victoria, Queen of the United Kingdom (1837 - 1901) 1837 (MDCCCXXXVII) was a common year starting on Sunday (see link for calendar). ... Otto Stolz (1842–1905) was an Austrian mathematician noted for his work on mathematical analysis and infinitesimals. ... Year 1881 (MDCCCLXXXI) was a common year starting on Saturday (link will display the full calendar). ...

Wissenschaftslehre (Theory of science)

In his 1837 Wissenschaftslehre Bolzano attempted to provide logical foundations for all sciences, building on abstractions like part-relation, abstract objects, attributes, sentence-shapes, ideas and propositions in themselves, sums and sets, collections, substances, adherences, subjective ideas, judgments, and sentence-occurrences. These attempts were basically an extension of his earlier thoughts in the philosophy of mathematics, for example his 1810 Beiträge where he emphasized the distinction between the objective relationship between logical consequences and our subjective recognition of these connections. For Bolzano, it was not enough that we merely have confirmation of natural or mathematical truths, but rather it was the proper role of the sciences (both pure and applied) to seek out justification in terms of the fundamental truths that may or may not appear to be obvious to our intuitions. Queen Victoria, Queen of the United Kingdom (1837 - 1901) 1837 (MDCCCXXXVII) was a common year starting on Sunday (see link for calendar). ... As used in philosophy, in general, an object is something that can have properties and relations. ... Mereology is a collection of axiomatic formal systems dealing with parts and their respective wholes. ... In mathematics, a set can be thought of as any collection of distinct objects considered as a whole. ... 1810 was a common year starting on Monday (see link for calendar). ... Theory of justification is a part of epistemology that attempts to understand the justification of statements and beliefs. ...

Metaphysics

Bolzano's metaphysical system, as he describes it in the Wissenschaftslehre, is composed of four realms:

(1) The realm of language, consisting in words and sentences. (2) The realm of thought, consisting in subjective ideas and judgments. (3) The realm of logic, consisting in objective ideas and propositions in themselves. (4) The realm of all objects, which also contains the other three realms and divides into attributes and pure objects. In philosophy, an object is a thing, an entity, or a being. ...

Bolzano devotes a great part of the Wissenschaftslehre to an explanation of these four realms and their relations. Two distinctions play a prominent role in his system. Firstly, each realm divides into parts and wholes. Words are parts of sentences, subjective ideas are parts of judgments, objective ideas are parts of propositions in themselves, and attributes are parts of pure objects. Secondly, all objects divide into those that exist, and those that are in themselves. Bolzano's original claim is that the logical realm is populated by objects of the latter kind. Mereology is a collection of axiomatic formal systems dealing with parts and their respective wholes. ... There is no universally accepted theory of what the word existence means. ...

Satz an Sich (Proposition in itself)

Satz an Sich is a basic notion in Bolzano's Wissenschaftslehre. It is introduced at the very beginning, in section 19. Before giving a definition, Bolzano first introduces the notions of proposition (spoken or written or otherwise) and idea. "The grass is green" is a proposition (Satz): in this connection of words, something is said or asserted. "Green grass", however, is only an idea (Vorstellung). Something is represented by it, but it does not say or assert anything. Bolzano's notion of proposition is fairly broad: "A rectangle is round" counts a proposition, even though it is false by virtue of self-contradiction, because it is composed in an intelligible manner out of intelligible parts. A Satz an Sich is what is thought when one thinks about a proposition and can still ask oneself whether or not this proposition has been said or thought by someone or not. Hence a Satz an Sich states that something is or isn't, with no condition on it being true or not or on it being spoken, thought etc. or not. Bolzano's use of the term an sich differs greatly from that of Kant; for his use of the term see an sich. This article is about the word proposition as it is used in logic, philosophy, and linguistics. ... IDEA may refer to: Electronic Directory of the European Institutions IDEA League Improvement and Development Agency Individuals with Disabilities Education Act Indian Distance Education Association Integrated Data Environments Australia Intelligent Database Environment for Advanced Applications IntelliJ IDEA - a Java IDE Interactive Database for Energy-efficient Architecture International IDEA (International Institute... Broadly speaking, a contradiction is an incompatibility between two or more statements, ideas, or actions. ... Immanuel Kant Immanuel Kant (April 22, 1724 – February 12, 1804) was a Prussian philosopher, generally regarded as one of Europes most influential thinkers and the last major philosopher of the Enlightenment. ... The noumenon (plural: noumena) classically refers to an object of human inquiry, understanding or cognition. ...

Logic

According to Bolzano, all propositions are composed out of three (simple or complex) elements: a subject, a predicate and a copula. Instead of the more traditional copulative term 'is', Bolzano prefers 'has'. The reason for this is that 'has', unlike 'is', can connect a concrete term, such as 'Socrates', to an abstract term such as 'baldness'. "Socrates has baldness" is, according to Bolzano, preferable to "Socrates is bald" because the latter form is less basic: 'bald' is itself composed of the elements 'something', 'that', 'has' and 'baldness'. Bolzano also reduces existential propositions to this form: "Socrates exists" would would simply become "Socrates has existence (Dasein)". This article or section does not cite its references or sources. ...

A starring role in Bolzano’s logical theory is played by the notion of variations: various logical relations are defined in terms of the changes in truth value that propositions incur when their non-logical parts are replaced by others. Logically analytical propositions, for instance, are those in which all the non-logical parts can be replaced without change of truth value. Two propositions are 'compatible' (vertraglich) with respect to one of their component parts x if there is at least one term that can be inserted that would make both true. A proposition Q is 'deducible' (ableitbar) from a proposition P, with respect to certain of their non-logical parts, if any replacement of those parts that makes P true also makes Q true. If a proposition is deducible from another with respect to all its non-logical parts, it is said to be 'logically deducible'. Besides the relation of deducibility, Bolzano also has a stricter relation of 'consequentiality' (Abfolge). This is an asymmetric relation that obtains between true propositions, when one of the propositions is not only deducible from, but also explained by the other. In logic and mathematics, a logical value, also called a truth value, is a value indicating to what extent a proposition is true. ... In mathematics, a binary relation R on a set X is antisymmetric if it holds for all a and b in X that if a is related to b and b is related to a then a = b. ... An explanation is a statement which points to causes, context, and consequences of some object, process, state of affairs, etc. ...

Mathematics

Bolzano made several original contributions to mathematics. In Parallelogram area theory he demonstrated that for similar rhombi, the ratio of the area of rhombus A to the area of rhombus B is equal to the square of the ratio of the width of A to the width of B. To the foundations of mathematical analysis he contributed the introduction of a fully rigorous ε-δ definition of a mathematical limit and the first purely analytic proof of the Intermediate Value Theorem (also known as Bolzano's theorem). Today he is mostly remembered for the Bolzano-Weierstrass theorem, which Karl Weierstrass developed independently and published years after Bolzano's first proof and which was initially called the Weierstrass theorem until Bolzano's earlier work was rediscovered. A parallelogram. ... Analysis has its beginnings in the rigorous formulation of calculus. ... For the medical term see rigor (medicine) Rigour (American English: rigor) has a number of meanings in relation to intellectual life and discourse. ... In mathematics, a continuous function is a function in which arbitrarily small changes in the input produce arbitrarily small changes in the output. ... In mathematics, the concept of a limit is used to describe the behavior of a function, as its argument gets close to either some point, or infinity; or the behavior of a sequences elements, as their index approaches infinity. ... Analytic may refer to Analytic proposition or analytic philosophy, in philosophy Analytic geometry, analytic function, analytic continuation, analytic set in mathematics. ... In mathematics, a proof is a demonstration that, assuming certain axioms, some statement is necessarily true. ... In analysis, the intermediate value theorem is either of two theorems of which an account is given below. ... In calculus, the intermediate value theorem is either of two theorems of which an account is given below. ... The Bolzano-Weierstrass theorem in real analysis states that every bounded sequence of real numbers contains a convergent subsequence. ... Karl Theodor Wilhelm Weierstrass (Weierstraß) (October 31, 1815 – February 19, 1897) was a German mathematician who is often cited as the father of modern analysis. // Karl Weierstrass was born in Ostenfelde, Westphalia (today Germany). ...

Philosophical legacy

Due to the fact that Bolzano's most important work, the Wissenschaftslehre, could not be published during his lifetime, the impact of his thought on philosophy initially seemed destined to be slight. His work was rediscovered, however, by Edmund Husserl and Kazimierz Twardowski, both students of Franz Brentano. Through them, and through Gottlob Frege, also an admirer, Bolzano became a formative influence on both phenomenology and analytic philosophy. Edmund Gustav Albrecht Husserl (April 8, 1859, Prostějov – April 26, 1938, Freiburg) was a German philosopher, known as the father of phenomenology. ... Kazimierz Jerzy Skrzypna-Twardowski, Ritter von Ogończyk (October 20, 1866, Vienna, Austria – February 11, 1938, Lwów, Poland) was a Polish philosopher and logician. ... · Franz Brentano Franz Clemens Honoratus Hermann Brentano (January 16, 1838 Marienberg am Rhein (near Boppard) - March 17, 1917 Zürich) was an influential figure in both philosophy and psychology. ... Friedrich Ludwig Gottlob Frege (8 November 1848, Wismar – 26 July 1925, IPA: ) was a German mathematician who became a logician and philosopher. ... This article is about the philosophical movement. ... Analytic philosophy is a generic term for a style of philosophy that came to prominence during the 20th Century. ...

Writings in English

• Theory of science, attempt at a detailed and in the main novel exposition of logic with constant attention to earlier authors. (Edited and translated by Rolf George University of California Press, Berkeley and Los Angeles 1972)
• Theory of science (Edited, with an introduction, by Jan Berg. Translated from the German by Burnham Terrell - D. Reidel Publishing Company, Dordrecht and Boston 1973)
• Ewald, William B., ed., From Kant to Hilbert: A Source Book in the Foundations of Mathematics, 2 vols. Oxford University Press, 1996 contains the three following essays:
• 1810. Contributions to a better grounded presentation of mathematics, 174-224.
• 1817. Purely analytic proof of the theorem that between any two values which give results of opposite sign, there lies at least one real root of the equation, 225-48.
• 1851. Paradoxes of the Infinite, 249-92 (excerpt).
• Paradoxes of the infinite - Translated from the German of the posthumous edition by Fr. Prihonský and furnished with a historical introduction by Donald A. Steele - Routledge & Kegan Paul, 1950.
• On the mathematical method and correspondence with Exner - Translated by Paul Rusnock and Rolf George - Amsterdam, Rodopi, 2004.
• The mathematical works of Bernard Bolzano - Edited by Steve Russ - Oxford, Oxford University Press, 2004.
• Selected Writings on Ethics and Politics - Translated by Paul Rusnock and Rolf George - Amsterdam, Rodopi, 2007.

External links

Wikimedia Commons has media related to:

Bernard Bolzano

• O'Connor, John J; Edmund F. Robertson "Bernard Bolzano". MacTutor History of Mathematics archive.  
• Biography of Bernard Bolzano
• Bernard Bolzano's Theory of Science

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References

Künne, Wolfgang. (1998). "Bolzano, Bernard". Routledge Encyclopedia of Philosophy 1: 823-827. London: Routledge. Retrieved on 2007-03-05