Bernard Bolzano

English summary: In this comprehensive diary from 1820-1821 Bolzano deals with the concept of a consistency of a function and with questions pertaining to differential calculus, for example commutativity theorems of differentiation with functions of several variables. In mechanics, he attempts to determine the mean force of two forces acting in the same direction by means of functional equations which are accounted for by mechanical considerations. He does a detailed calculation of ovals composed of arcs which come closest to an ellipse. German description: In diesem reichhaltigen Heft aus den Jahren 1820-1821 beschaftigt Bolzano sich eingehend mit dem Begriff der Stetigkeit einer Funktion und mit Fragen aus der Differentialrechnung, z. B. mit dem Satz von der Vertauschbarkeit der Differentiation bei Funktionen von mehreren Veranderlichen. In der Mechanik sucht er die mittlere Kraft von zwei in dieselbe Richtung wirkenden Kraften mittels aus mechanischen Grunden motivierter Funktionalgleichungen zu bestimmen. Ausfuhrlich berechnet er aus Kreisbogen zusammengesetzte Ovale, welche einer Ellipse am nachsten kommen.

English summary: The lectures which Bernard Bolzano held from 1805 up to his dismissal in January of 1820 as a professor for Catholic religious education at the University of Prague in the context of the philosophical studies were published anonymously in 1834 in a four-volume edition with which Bolzano was very unhappy. As part of the collected works of Bolzano there is now for the first time a new critical edition of this work which includes the corrections and variants of a master copy authorized by Bolzano. The textbook is divided into three parts: In the first part Bolzano explains the concept of religion and other terms which are essential for his philosophy of religion and presents the most important theories of natural religion and rational religion, divided into "natural dogmatics" and "natural morality." In the second part, Bolzano studies the miracles which serve as a confirmation of Catholic Christianity. In the third part, he describes the individual individual articles of faith of "Old Catholic dogmatics" and those of "Old Catholic morality." German description: Im dritten Teil des Lehrbuchs des Religionswissenschaft (=Bande 8,1-8,4) behandelt Bolzano systematisch die Lehren des Katholizismus, wie er sie in den Jahren 1806-1819 der philosophischen Fakultat der Karl-Ferdinandeischen Universitat in Prag vorgetragen hat. Die ganze Dogmatik gliedert er in katholische Theologie oder die Lehre von Gott und katholische Kosmologie oder die Lehre von der Schopfung.

English summary: The 248 paragraphs of the manuscript Zur Physik II (On Physics II), written between 1841 and 1847, constitute an autonomous treatise on natural philosophy. Bolzanos opinion is based on the assumption that the entire universe had a nuclear particle structure. Certain atoms are distinguished by the fact that they are isolated in a continuum of ether atoms. Each of these atoms is surrounded by ether which provides a causal relationship to other atoms also of the same type. Thus for Bolzano there is no actio in distans in the sense of classical physics. In accordance with a conformal physical field theory, Bolzano provides an alternative description of long-range forces. German description: Die 248 Paragraphen des Manuskripts Zur Physik II aus den Jahren 1841 bis 1847 bilden eine eigenstandige Abhandlung zur Naturphilosophie. Bolzanos Anschauung basiert auf der Annahme, dass das ganze Weltall eine atomare Teilchenstruktur hat. Gewisse Atome sind dadurch ausgezeichnet, dass sie in einem Kontinuum von Atheratomen isoliert stehen. Jedes ausgezeichnete Atom besitzt eine Atherumgebung, welche die Kausalbeziehung zu anderen ausgezeichneten Atomen vermittelt. Fur Bolzano gibt es somit keine 'actio in distans' im Sinne der klassischen Physik. In Ubereinstimmung mit einer physikalischen Feldtheorie gibt Bolzano eine alternative Beschreibung fernwirkender Krafte.

English summary: In Bolzanos correspondence with the Royal Bohemian Society of Sciences there are, among other things, a long experts report on the problem of solving algebraic equations higher than those of the fourth degree und several reports on Christian Doppler's work in physics. In the last two essays, Bolzano puts Euclidean geometry on a topological foundation. His remarks culminate in a particular case, Jordan's famous curve theorem, for which there are various ideas for proof in Bolzano's manuscripts. German description: Im Schriftwechsel Bolzanos mit der Koniglich Bohmischen Gesellschaft der Wissenschaften finden sich u.a. ein langes Gutachten uber das Problem, algebraische Gleichungen hoheren Grades als der des vierten zu losen, und mehrere Gutachten uber physikalische Arbeiten von Christian Doppler. In den beiden letzten Abhandlungen stellt Bolzano die Euklidische Geometrie auf eine topologische Grundlage. Seine Ausfuhrungen gipfeln in einem Sonderfall von Jordans beruhmtem Kurvensatz, fur den es in Bolzanos Manuskripten verschiedene Beweisideen gibt.

English summary: On more than two thousand closely written folios, Bolzanos Mathematical Diaries provide a complete account of his scientific development between 1799 and 1844. Using this authentic account, it is possible to date Bolzanos most significant discoveries in mathematics and logic and to reveal his sources which were often almost inaccessible. Furthermore, these records contain supplements to those works already published and to his completed unpublished works. German description: Bolzanos Mathematische Tagebucher geben auf uber zweitausend eng beschriebenen Folioseiten einen luckenlosen Bericht uber seine wissenschaftliche Entwicklung von 1799 bis 1844. Anhand dieses authentischen Berichts konnen Bolzanos wichtigste mathematische und logische Entdeckungen datiert und seine oft schwer zuganglichen Quellen erschlossen werden. Daruber hinaus enthalten diese Aufzeichnungen Erganzungen zu seinen veroffentlichten und abgeschlossenen nachgelassenen Werken.

English summary: This critical edition of Bolzano's main philosophical work incorporates his own corrections, among other things. It originated as Bolzano's attempt to refute skepticism. In order to do so, he had to analyze the concept of the truth in itself to begin with, and this analysis led him to the concept of the proposition in itself. In this context he developed his theory of the reduction of sentences to a basic form which all have in common. All of these analyses and identifications of terms culminate in a theory of logical truth and of logical consequence. This is an outstanding achievement in the history of occidental thought. German description: Diese kritische Edition des philosophischen Hauptwerks Bolzanos berucksichtigt u.a. seine eigenen Verbesserungen. Den Ausgangspunkt des Werkes bildet Bolzanos Versuch, den Skeptizismus zu widerlegen. Daher musste er zunachst den Begriff der Wahrheit an sich analysieren; diese Analyse fuhrte ihn zum Begriff des Satzes an sich. Im Zusammenhang damit entwickelte er seine Theorie der Reduktion sprachlicher Satze auf eine allen gemeinsame Grundform. Alle diese Begriffsanalysen und Begriffsbestimmungen gipfeln in einer Theorie der logischen Wahrheit und der logischen Folge. Sie ist eine herausragende Leistung in der Geschichte des abendlandischen Denkens.

English summary: On more than two thousand closely written folios, Bolzanos Mathematical Diaries provide a complete account of his scientific development between 1799 and 1844. Using this authentic account, it is possible to date Bolzanos most significant discoveries in mathematics and logic and to reveal his sources which were often almost inaccessible. Furthermore, these records contain supplements to those works already published and to his completed unpublished works. German description: Bolzanos Mathematische Tagebucher geben auf uber zweitausend eng beschriebenen Folioseiten einen luckenlosen Bericht uber seine wissenschaftliche Entwicklung von 1799 bis 1844. Anhand dieses authentischen Berichts konnen Bolzanos wichtigste mathematische und logische Entdeckungen datiert und seine oft schwer zuganglichen Quellen erschlossen werden. Daruber hinaus enthalten diese Aufzeichnungen Erganzungen zu seinen veroffentlichten und abgeschlossenen nachgelassenen Werken.

English summary: This critical edition of Bolzano's main philosophical work incorporates his own corrections, among other things. It originated as Bolzano's attempt to refute skepticism. In order to do so, he had to analyze the concept of the truth in itself to begin with, and this analysis led him to the concept of the proposition in itself. In this context he developed his theory of the reduction of sentences to a basic form which all have in common. All of these analyses and identifications of terms culminate in a theory of logical truth and of logical consequence. This is an outstanding achievement in the history of occidental thought. German description: Diese kritische Edition des philosophischen Hauptwerks Bolzanos berucksichtigt u.a. seine eigenen Verbesserungen. Den Ausgangspunkt des Werkes bildet Bolzanos Versuch, den Skeptizismus zu widerlegen. Daher musste er zunachst den Begriff der Wahrheit an sich analysieren; diese Analyse fuhrte ihn zum Begriff des Satzes an sich. Im Zusammenhang damit entwickelte er seine Theorie der Reduktion sprachlicher Satze auf eine allen gemeinsame Grundform. Alle diese Begriffsanalysen und Begriffsbestimmungen gipfeln in einer Theorie der logischen Wahrheit und der logischen Folge. Sie ist eine herausragende Leistung in der Geschichte des abendlandischen Denkens.

English summary: On more than two thousand closely written folios, Bolzanos Mathematical Diaries provide a complete account of his scientific development between 1799 and 1844. Using this authentic account, it is possible to date Bolzanos most significant discoveries in mathematics and logic and to reveal his sources which were often almost inaccessible. Furthermore, these records contain supplements to those works already published and to his completed unpublished works. German description: Bolzanos Mathematische Tagebucher geben auf uber zweitausend eng beschriebenen Folioseiten einen luckenlosen Bericht uber seine wissenschaftliche Entwicklung von 1799 bis 1844. Anhand dieses authentischen Berichts konnen Bolzanos wichtigste mathematische und logische Entdeckungen datiert und seine oft schwer zuganglichen Quellen erschlossen werden. Daruber hinaus enthalten diese Aufzeichnungen Erganzungen zu seinen veroffentlichten und abgeschlossenen nachgelassenen Werken.

English summary: The Bolzano biography written by Gregor Zeithammer (1800-1881) has up to now only been cited in excerpts. The text-critical, annotated edition of the manuscript from Zeithammers literary estate, which is preserved at the literary archives in Prague, makes this important source for research on Bolzano completely accessible. German description: Die Bolzano-Biographie von Gregor Zeithammer (1800-1881) wurde bisher nur in Auszugen zitiert. Die textkritische, kommentierte Edition des Manuskripts aus dem Zeithammer-Nachlass des Literaturarchivs in Prag macht diese wichtige Quelle der Bolzano-Forschung nun vollstandig zuganglich.

English summary: On more than two thousand closely written folios, Bolzanos Mathematical Diaries provide a complete account of his scientific development between 1799 and 1844. Using this authentic account, it is possible to date Bolzanos most significant discoveries in mathematics and logic and to reveal his sources which were often almost inaccessible. Furthermore, these records contain supplements to those works already published and to his completed unpublished works. German description: Bolzanos Mathematische Tagebucher geben auf uber zweitausend eng beschriebenen Folioseiten einen luckenlosen Bericht uber seine wissenschaftliche Entwicklung von 1799 bis 1844. Anhand dieses authentischen Berichts konnen Bolzanos wichtigste mathematische und logische Entdeckungen datiert und seine oft schwer zuganglichen Quellen erschlossen werden. Daruber hinaus enthalten diese Aufzeichnungen Erganzungen zu seinen veroffentlichten und abgeschlossenen nachgelassenen Werken.

English summary: The lectures which Bernard Bolzano held from 1805 up to his dismissal in January of 1820 as a professor for Catholic religious education at the University of Prague in the context of the philosophical studies were published anonymously in 1834 in a four-volume edition with which Bolzano was very unhappy. As part of the collected works of Bolzano there is now for the first time a new critical edition of this work which includes the corrections and variants of a master copy authorized by Bolzano. The textbook is divided into three parts: In the first part Bolzano explains the concept of religion and other terms which are essential for his philosophy of religion and presents the most important theories of natural religion and rational religion, divided into "natural dogmatics" and "natural morality." In the second part, Bolzano studies the miracles which serve as a confirmation of Catholic Christianity. In the third part, he describes the individual individual articles of faith of "Old Catholic dogmatics" and those of "Old Catholic morality." German description: Bolzano untersucht die Wunder der christlichen Tradition auf der Grundlage seiner Definition des Wunders als eines ungewohnlichen (nicht ubernaturlichen) Ereignisses, das eine sittliche Wahrheit glaubhaft machen soll.

English summary: On more than two thousand closely written folios, Bolzanos Mathematical Diaries provide a complete account of his scientific development between 1799 and 1844. Using this authentic account, it is possible to date Bolzanos most significant discoveries in mathematics and logic and to reveal his sources which were often almost inaccessible. Furthermore, these records contain supplements to those works already published and to his completed unpublished works. German description: Bolzanos Mathematische Tagebucher geben auf uber zweitausend eng beschriebenen Folioseiten einen luckenlosen Bericht uber seine wissenschaftliche Entwicklung von 1799 bis 1844. Anhand dieses authentischen Berichts konnen Bolzanos wichtigste mathematische und logische Entdeckungen datiert und seine oft schwer zuganglichen Quellen erschlossen werden. Daruber hinaus enthalten diese Aufzeichnungen Erganzungen zu seinen veroffentlichten und abgeschlossenen nachgelassenen Werken.

English summary: The lectures which Bernard Bolzano held from 1805 up to his dismissal in January of 1820 as a professor for Catholic religious education at the University of Prague in the context of the philosophical studies were published anonymously in 1834 in a four-volume edition with which Bolzano was very unhappy. As part of the collected works of Bolzano there is now for the first time a new critical edition of this work which includes the corrections and variants of a master copy authorized by Bolzano. The textbook is divided into three parts: In the first part Bolzano explains the concept of religion and other terms which are essential for his philosophy of religion and presents the most important theories of natural religion and rational religion, divided into "natural dogmatics" and "natural morality." In the second part, Bolzano studies the miracles which serve as a confirmation of Catholic Christianity. In the third part, he describes the individual individual articles of faith of "Old Catholic dogmatics" and those of "Old Catholic morality." German description: Als entscheidendes Kriterium fur die Wurdigung der verschiedenen Religionen bestimmt Bolzano ihre sittliche Zutraglichkeit. Daraus ergibt sich fur ihn die vorrangige Stellung der christlichen Religion.

English summary: The manuscript Zur Physik (On Physics), which is part of Bolzanos literary estate kept in Prague, deals mainly with problems of natural philosophy. These include questions from the field of general physics, acoustics, optics, electricity, magnetism and gravitation, thermodynamics, biology, the history of the earth as well as new achievements in the area of technical-scientific instruments. Bolzano comments on the achievements of his contemporaries such as Ampere, Avogadro, Berzelius, Carnot, Faraday, Fries, Herbart, Herschel, Osann, Poisson or Wilhelm Eduard Weber. This manuscript shows that Bolzano was on the way to developing his own natural philosophy. German description: Das im Prager Nachlass Bolzanos aufbewahrte Manuskript Zur Physik behandelt vorwiegend Probleme der Naturphilosophie: der allgemeinen Physik, der Akustik, der Optik, der Elektrizitat, des Magnetismus und der Gravitation, der Warmelehre, der Biologie, der Erdgeschichte, sowie neue Errungenschaften auf dem Gebiet der technisch-wissenschaftlichen Instrumente. Dabei referiert und kommentiert Bolzano Ausfuhrungen von Zeitgenossen wie Ampere, Avogadro, Berzelius, Carnot, Faraday, Fries, Herbart, Herschel, Osann, Poisson oder Wilhelm Eduard Weber. Mit diesem Manuskript, das zum Teil Erganzungen zu den 1851 postum erschienenen Paradoxien des Unendlichen enthalt, war Bolzano unterwegs zu einer eigenen Naturphilosophie.

English summary: On more than two thousand closely written folios, Bolzanos Mathematical Diaries provide a complete account of his scientific development between 1799 and 1844. Using this authentic account, it is possible to date Bolzanos most significant discoveries in mathematics and logic and to reveal his sources which were often almost inaccessible. Furthermore, these records contain supplements to those works already published and to his completed unpublished works. German description: Bolzanos Mathematische Tagebucher geben auf uber zweitausend eng beschriebenen Folioseiten einen luckenlosen Bericht uber seine wissenschaftliche Entwicklung von 1799 bis 1844. Anhand dieses authentischen Berichts konnen Bolzanos wichtigste mathematische und logische Entdeckungen datiert und seine oft schwer zuganglichen Quellen erschlossen werden. Daruber hinaus enthalten diese Aufzeichnungen Erganzungen zu seinen veroffentlichten und abgeschlossenen nachgelassenen Werken.

English summary: The lectures which Bernard Bolzano held from 1805 up to his dismissal in January of 1820 as a professor for Catholic religious education at the University of Prague in the context of the philosophical studies were published anonymously in 1834 in a four-volume edition with which Bolzano was very unhappy. As part of the collected works of Bolzano there is now for the first time a new critical edition of this work which includes the corrections and variants of a master copy authorized by Bolzano. The textbook is divided into three parts: In the first part Bolzano explains the concept of religion and other terms which are essential for his philosophy of religion and presents the most important theories of natural religion and rational religion, divided into "natural dogmatics" and "natural morality." In the second part, Bolzano studies the miracles which serve as a confirmation of Catholic Christianity. In the third part, he describes the individual individual articles of faith of "Old Catholic dogmatics" and those of "Old Catholic morality." German description: Als den wertvollsten Bestandteil der naturlichen Religion schatzt Bolzano die naturliche Moral ein; besondere Aufmerksamkeit widmet er dem obersten Sittengesetz, das auch fur Gott verbindlich sei. Die naturliche Religion muss durch die auf Wundern grundende Offenbarung erganzt werden. Wunder seien Winke Gottes, gewisse sittlich zutragliche Lehren glaubig anzunehmen. Eine Auseinandersetzung mit abweichenden Theorien der Offenbarung und der Wunder beschliesst den Band.

English summary: On more than two thousand closely written folios, Bolzanos Mathematical Diaries provide a complete account of his scientific development between 1799 and 1844. Using this authentic account, it is possible to date Bolzanos most significant discoveries in mathematics and logic and to reveal his sources which were often almost inaccessible. Furthermore, these records contain supplements to those works already published and to his completed unpublished works. German description: Bolzanos Mathematische Tagebucher geben auf uber zweitausend eng beschriebenen Folioseiten einen luckenlosen Bericht uber seine wissenschaftliche Entwicklung von 1799 bis 1844. Anhand dieses authentischen Berichts konnen Bolzanos wichtigste mathematische und logische Entdeckungen datiert und seine oft schwer zuganglichen Quellen erschlossen werden. Daruber hinaus enthalten diese Aufzeichnungen Erganzungen zu seinen veroffentlichten und abgeschlossenen nachgelassenen Werken.

English summary: This critical edition of Bolzano's main philosophical work incorporates his own corrections, among other things. It originated as Bolzano's attempt to refute skepticism. In order to do so, he had to analyze the concept of the truth in itself to begin with, and this analysis led him to the concept of the proposition in itself. In this context he developed his theory of the reduction of sentences to a basic form which all have in common. All of these analyses and identifications of terms culminate in a theory of logical truth and of logical consequence. This is an outstanding achievement in the history of occidental thought. 201001411 - BOLZANO: GES. AUSG. I/14,1 This critical edition of Bolzano's main philosophical work incorporates his own corrections, among other things. It originated as Bolzano's attempt to refute skepticism. In order to do so, he had to analyze the concept of the truth in itself to begin with, and this analysis led him to the concept of the proposition in itself. In this context he developed his theory of the reduction of sentences to a basic form which all have in common. All of these analyses and identifications of terms culminate in a theory of logical truth and of logical consequence. This is an outstanding achievement in the history of occidental thought. German description: Diese kritische Edition des philosophischen Hauptwerks Bolzanos berucksichtigt u.a. seine eigenen Verbesserungen. Den Ausgangspunkt des Werkes bildet Bolzanos Versuch, den Skeptizismus zu widerlegen. Daher musste er zunachst den Begriff der Wahrheit an sich analysieren; diese Analyse fuhrte ihn zum Begriff des Satzes an sich. Im Zusammenhang damit entwickelte er seine Theorie der Reduktion sprachlicher Satze auf eine allen gemeinsame Grundform. Alle diese Begriffsanalysen und Begriffsbestimmungen gipfeln in einer Theorie der logischen Wahrheit und der logischen Folge. Sie ist eine herausragende Leistung in der Geschichte des abendlandischen Denkens.

English summary: On more than two thousand closely written folios, Bolzanos Mathematical Diaries provide a complete account of his scientific development between 1799 and 1844. Using this authentic account, it is possible to date Bolzanos most significant discoveries in mathematics and logic and to reveal his sources which were often almost inaccessible. Furthermore, these records contain supplements to those works already published and to his completed unpublished works. German description: Bolzanos Mathematische Tagebucher geben auf uber zweitausend eng beschriebenen Folioseiten einen luckenlosen Bericht uber seine wissenschaftliche Entwicklung von 1799 bis 1844. Anhand dieses authentischen Berichts konnen Bolzanos wichtigste mathematische und logische Entdeckungen datiert und seine oft schwer zuganglichen Quellen erschlossen werden. Daruber hinaus enthalten diese Aufzeichnungen Erganzungen zu seinen veroffentlichten und abgeschlossenen nachgelassenen Werken.