# Bernard Bolzano's manuscripts

Bernard Bolzano died in 1848. He had worked for many years on

Zimmermann received the collection of Bolzano's manuscripts, having been left them in Bolzano's will. Had his interests been more inclined towards mathematics, it is indeed possible that he would have found such gems within the manuscripts that he would have devoted much of his life to them. However, Zimmermann's interests were more in the area of philosophy and indeed he was appointed to the chair of philosophy in Prague in 1852, only four years after Bolzano's death. One of Bolzano's collaborators, Franz Prihonsky, had ensured that not all of Bolzano's mathematical work lay unpublished in Zimmermann's possession, for he published Bolzano's

Martin Jasek was a secondary school teacher of mathematics in Pilsen. He worked with the Bolzano manuscripts in the National Library in Vienna, and became fascinated with the discoveries he made. He published four papers published between 1920 and 1923 and gave three lectures to the Union of Czech Mathematicians and Physicists on 3 December 1921, 14 January 1922, and 4 December 1922. Jasek had discovered that the unpublished

The task which the Committee set itself proved far more difficult than they had first anticipated. Financial support for the project was initially quite strong but, as publication was delayed, it became harder to persuade sponsors to put up further finance.

The Czechoslovak Academy of Sciences began a new push to publish Bolzano's manuscripts in the early 1960s. Before the first volume in the series appeared in 1969 there were a number of related publications. Kazimír Vecerka published Bolzano's

*Grössenlehre*Ⓣ which was intended to be an introduction to mathematics covering many different areas of mathematics such as numbers, elementary geometry, geometry in general, function theory, methodology, and the ideas of quantity and space. Specific parts such as*Functionenlehre*Ⓣ, and*Zahlenlehre*Ⓣ were written, much was in a less complete form with workings and reworkings of parts of his ambitious project. Towards the end of his life Bolzano realised that he would never complete the work, and he tried to find someone who would be able to understand what he had written and also be able to continue developing parts which were unfinished. He chose Robert Zimmermann who was 24 years old at the time of Bolzano's death.Zimmermann received the collection of Bolzano's manuscripts, having been left them in Bolzano's will. Had his interests been more inclined towards mathematics, it is indeed possible that he would have found such gems within the manuscripts that he would have devoted much of his life to them. However, Zimmermann's interests were more in the area of philosophy and indeed he was appointed to the chair of philosophy in Prague in 1852, only four years after Bolzano's death. One of Bolzano's collaborators, Franz Prihonsky, had ensured that not all of Bolzano's mathematical work lay unpublished in Zimmermann's possession, for he published Bolzano's

*Paradoxien des Unendlichen*Ⓣ, in 1851. It may be considered as the first book on set theory, and certainly Cantor praises the work highly in his own, much more developed, contributions to the topic. In 1909 Charles Peirce wrote that Bolzano's*Paradoxien des Unendlichen*Ⓣ conferred:-... a singular benefit upon humanity.Except for this noteworthy publication, after Bolzano's death the remaining manuscripts were in Zimmermann's possession until 1882 when he gifted them to the Austrian Academy of Sciences (Kaiserliche Akademie der Wissenschaften in Wien). Ten years later the Austrian Academy of Sciences gifted the Bolzano manuscripts to the manuscript section of the Austrian National Library. That no complete works of Bolzano had been published during this period was not due to lack of interest. Several attempts had been made but the size of the task, and the difficulty of tracing various improvements that Bolzano had continued to make, meant that every attempt had failed.

Martin Jasek was a secondary school teacher of mathematics in Pilsen. He worked with the Bolzano manuscripts in the National Library in Vienna, and became fascinated with the discoveries he made. He published four papers published between 1920 and 1923 and gave three lectures to the Union of Czech Mathematicians and Physicists on 3 December 1921, 14 January 1922, and 4 December 1922. Jasek had discovered that the unpublished

*Functionenlehre*Ⓣ contained some important results in analysis showing that Bolzano had made certain discoveries in that topic well before similar results had been discovered by others. Jasek's lectures interested other Czech mathematicians, particularly Karel Petr and Karel Rychlik, and on 5 March 1924 the Czech Academy of Sciences set up the Bolzano Committee to:-... acquire, unify, and publish Bolzano's manuscripts.The chairman of the committee was Karel Petr, the secretary was Martin Jasek, while Karel Rychlik was one of eight other members. Some manuscripts were in Prague but the main collection was in the Austrian National Library in Vienna. The Czech Academy of Sciences paid for Jasek to spend about eighteen months working with the manuscripts in Vienna where he made photocopies (in an early form which produced white writing on a black background), bringing the copies back to Prague where the main task of preparing the work for publication was to take place. The Committee set itself the task of publishing the first volume of Bolzano's manuscripts, which they intended to be

*Functionenlehre*Ⓣ, in 1925 and then the remaining material over the following five years.The task which the Committee set itself proved far more difficult than they had first anticipated. Financial support for the project was initially quite strong but, as publication was delayed, it became harder to persuade sponsors to put up further finance.

*Functionenlehre*Ⓣ appeared in 1930, five years behind schedule and at the time when the Committee had expected the whole project to be completed. Progress for a while was at least steady with*Zahlentheorie*Ⓣ being published in 1931, and*Von dem besten Staate*Ⓣ in 1932. There was a delay until 1935 before the next volume*Der Briefwechsel B Bolzano's mit F Exner*Ⓣ was published. This contained letters between Bolzano and the philosopher Franz Exner (1802-1853). The fifth and final publication by the Committee was*Memoires géométriques*Ⓣ which did not appear until 1948. However, in 1948, Communists took control of the country and in 1952 the Czech Academy of Sciences was disbanded and at the same time the Bolzano Committee was also disbanded. The Czechoslovak Academy of Sciences was founded in 1952 but the Bolzano Committee was not at this stage re-established under the new academy. This did happen in 1958 but three years later the new Committee was disbanded with no further volumes of Bolzano's manuscripts being published during these three years.The Czechoslovak Academy of Sciences began a new push to publish Bolzano's manuscripts in the early 1960s. Before the first volume in the series appeared in 1969 there were a number of related publications. Kazimír Vecerka published Bolzano's

*Anti-Euclid*in 1967. It contained Bolzano's ideas concerning the reform and improvement of Euclidean geometry. Bob van Rootselaar published Bolzano's corrections to his*Functionenlehre*Ⓣ in 1969. It is, perhaps one of, Bolzano's attempts to correct certain errors in*Functionenlehre*Ⓣ. The first volume in the new series*Bernard Bolzano-Gesamtausgabe*Ⓣ published by*Friedrich Frommann Verlag*and edited by Eduard Winter, Jan Berg, Friedrich Kambartel, Jaromir Louzil, and Bob van Rootselaar, contains a biography of Bolzano together with details of the topics on which he worked: mathematics, logic, theology, philosophy and aesthetics. The second volume, which set the scene for the whole series, appeared in 1972. Jan Berg describes its contents:-This is a detailed catalogue of that part of Bolzano's manuscripts which was donated in 1892 to the then existing Court Library in Vienna by his former disciple Robert Zimmermann (1824-1898). Moreover, in the supplement, 19 letters from Bolzano to the philosopher Franz Exner (1802-1853), dealing inter alia with questions of logical semantics, are described. ... The bibliography lists (1) in chronological order all works of Bolzano published in any language until March 1971 and (2) literature on Bolzano in alphabetic order ... The section on the division of the Bernard Bolzano-Gesamtaus-gabe does not correspond to the present conception of the editors. In particular, the plan for part II (the posthumous works of Bolzano) has been extensively revised during the last decade. For example, [the] subsection ... containing Bolzano's scientific diaries is now scheduled to embrace 20 volumes in about 35 instalments.Further details of this series of volumes is given at THIS LINK

### References (show)

- Biography in
*Dictionary of Scientific Biography*(New York 1970-1990). - Biography in
*Encyclopaedia Britannica.* - 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). - S Russ,
*The mathematical works of Bernard Bolzano*(Oxford University Press, Oxford, 2004). - J Sebestik,
*Logique et mathématique chez Bernard Bolzano*(Librairie Philosophique J Vrin, Paris, 1992). - Y Bar-Hillel, Bolzano's propositional logic,
*Arch. Math. Logik Grundlagenforsch.***1**(1952), 65-98. - Y Bar-Hillel, Bernard Bolzano, in P Edwards (ed.),
*The Encyclopedia of Philosophy***1**(Collier Macmillan, London, 1967), 337-338 - J Berg, Bolzano and situation semantics: variations on a theme of variation,
*Bolzano - Studien. Philos. Natur.***24**(4) (1987), 373-377. - J Berg, Bolzano on induction,
*Bolzano - Studien. Philos. Natur.***24**(4) (1987), 442-446. - J Berg, Is Russell's antinomy derivable in Bolzano's logic?,
*Bolzano - Studien. Philos. Natur.***24**(4) (1987), 406-413. - J Berg, H Ganthaler and E Morscher, Bolzanos Biographie in tabellarischer übersicht,
*Bolzano - Studien. Philos. Natur.***24**(4) (1987), 353-372. - 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. - K Berka, Bolzano's philosophy of science, in
*Impact of Bolzano's epoch on the development of science*(Prague, 1982), 427-442. - K Berka, Bernard Bolzano - historian of logic (Czech),
*DVT---Dejiny Ved Tech.***31**(3) (1998), 121-130. - P Bussotti, The problem of the foundations of mathematics at the beginning of the nineteenth century : Two lines of thought: Bolzano and Gauss (Italian),
*Teoria (N.S.)***20**(1) (2000), 83-95. - A Canada and S Villegas, Bolzano's theorem in several variables? (Spanish),
*Gac. R. Soc. Mat. Esp.***7**(1) (2004), 101-121. - C Chihara, Frege's and Bolzano's rationalist conceptions of arithmetic,
*Rev. Histoire Sci.***52**(3-4) (1999), 343-361. - A Coffa, Kant, Bolzano and the emergence of logicism,
*J. Philos.***74**(1982), 679-689. - A Coffa, Kant, Bolzano and the emergence of logicism, in
*Frege's philosophy of mathematics*(Harvard Univ. Press, Cambridge, MA, 1995), 29-40. - A Coffa, Bolzano and the birth of semantics, in The Semantic Tradition from Kant to Carnap (Cambridge University Press, Cambridge, 1991), 22-40.
- L J Cohen, Bolzano's theory of induction, in
*Impact of Bolzano's epoch on the development of science*(Prague, 1982), 443-457. - G J W Dorn, Zu Bolzanos Wahrscheinlichkeitslehre,
*Bolzano - Studien. Philos. Natur.***24**(4) (1987), 423-441. - B I B Fedorov, Bolzano's ideas on the methodological analysis of science (Russian),
*Methodological analysis of the foundations of mathematics 'Nauka'*(Moscow, 1988), 36-46. - B I Fedorov, B Bolzano as a precursor of constructivism, II (Russian),
*Logical investigations*(Russian) No. 8 (Moscow, 2001), 210-216, - W Felscher, Bolzano, Cauchy, epsilon, delta,
*Amer. Math. Monthly***107**(9) (2000), 844-862. - R George, Bolzano on time,
*Bolzano - Studien. Philos. Natur.***24**(4) (1987), 452-468. - R George, Bolzano's concept of consequence,
*J. Philos.***83**(10) (1986), 558-564. - R George, Bolzano's consequence, relevance, and enthymemes,
*J. Philos. Logic***12**(3) (1983), 299-318. - J Hafner, Bolzano's criticism of indirect proofs,
*Rev. Histoire Sci.***52**(3-4) (1999), 385-398. - M Hyksova, Bolzano's inheritance research in Bohemia, Mathematics throughout the ages, Holbaek, 1999/Brno, 2000 (Prometheus, Prague, 2001), 67-91,
- D M Johnson, Prelude to dimension theory : The geometrical investigations of Bernhard Bolzano,
*Archive for History of Exact Science***17**(1976), 275-296. - P Kitcher, Bolzano's ideal of algebraic analysis,
*Studies in Hist. and Philos. Sci.***6**(3) (1975), 229-269. - W Kunne, Bernard Bolzano, in
*Routledge Encyclopedia of Philosophy***1**(London, New York, 1998), 824-828. - D Laugwitz, Bolzano's infinitesimal numbers,
*Czechoslovak Math. J.***32**(1982), 667-670. - D Laugwitz, Bemerkungen zu Bolzanos Grössenlehre,
*Arch. History Exact Sci.***2**(1964/1965), 398-409. - P Lingua, La teoria dei numeri reali in un manoscritto di B. Bolzano,
*Period. Mat.*(4)**42**(1964), 209-214. - K Macak, Bernard Bolzano and the calculus of probabilities (Czech),
*Mathematics in the 19th century (Czech), Vyskov, 1994*(Prometheus, Prague, 1996), 39-55. - P Mancosu, Bolzano and Cournot on mathematical explanation,
*Rev. Histoire Sci.***52**(3-4) (1999), 429-455. - P Maritz, The Bolzano house in Prague,
*Austral. Math. Soc. Gaz.***28**(4) (2001), 177-183. - H Metzler, Bernard Bolzanos Beitrag zum Gestaltwandel der Logik, in
*Impact of Bolzano's epoch on the development of science*(Prague, 1982), 479-489. - J Meurers, Bolzanos Paradoxien des Unendlichen und die von Seeliger-Charlierschen Sätze über ein unendliches Universum,
*Philos. Natur.***15**(1974/75), 176-190. - E Morscher, Bolzanos Syllogistik,
*Bolzano - Studien. Philos. Natur.***24**(4) (1987), 447-451. - M Nemcova, Frantisek Josef Studnicka and Bernard Bolzano (Czech),
*Mathematics in the 19th century (Czech), Vyskov, 1994*(Prometheus, Prague, 1996), 115-119. - L Novy, Les mathématiciens sous l'absolutisme autrichien : Bernard Bolzano et Franz Xaver Moth,
*Boll. Storia Sci. Mat.***15**(1) (1995), 49-59. - L Novy, Bolzano's contribution to science and society, in
*Impact of Bolzano's epoch on the development of science*(Prague, 1982), 9-23. - J Proust, Bolzano's theory of representation,
*Rev. Histoire Sci.***52**(3-4) (1999), 363-383. - P Rusnock, Philosophy of mathematics: Bolzano's responses to Kant and Lagrange,
*Rev. Histoire Sci.***52**(3-4) (1999), 399-427. - S Russ, Bolzano's analytic programme,
*The Mathematical intelligencer***14**(3) (1992), 45-53. - S Russ, Bolzano's analytic programme (Czech),
*Pokroky Mat. Fyz. Astronom.***38**(5) (1993), 249-259. - S Russ, Influence of Bolzano's methodology on the development of his mathematics, in
*Impact of Bolzano's epoch on the development of science*(Prague, 1982), 335-337. - S B Russ, A translation of Bolzano's paper on the intermediate value theorem,
*Historia Math.***7**(2) (1980), 156-185. - G Schubring, Bernard Bolzano - Not as Unknown to His Contemporaries as is Commonly Believed?,
*Historia Mathematica***20**(1993), 45-53. - J Sebestik, The mathematical system of Bernard Bolzano (Spanish),
*Mathesis***6**(4) (1990), 393-417. - J Sebestik, Bernard Bolzano et son mémoire sur le théorème fondamental de l'analyse,
*Rev. Histoire Sci. Appl.***17**(1964), 129-164. - J Sebestik, Forme, variation et déductibilité dans la logique de Bolzano,
*Rev. Histoire Sci.***52**(3-4) (1999), 479-506. - P Simons, Bolzano, Tarski, and the limits of logic,
*Bolzano - Studien. Philos. Natur.***24**(4) (1987), 378-405. - H Sinaceur, Cauchy et Bolzano,
*Rev. Histoire Sci. Appl.***26**(2) (1973), 97-112. - H Sinaceur, Réalisme mathématique, réalisme logique chez Bolzano,
*Rev. Histoire Sci.***52**(3-4) (1999), 457-477. - H Sinaceur, Bolzano et les mathématiques, in
*Les philosophes et les mathématiques*(Ellipses, Paris, 1996), 150-173. - D D Spalt, Bolzanos Lehre von den messbaren Zahlen 1830-1989,
*Arch. Hist. Exact Sci.***42**(1) (1991), 15-70. - D D Spalt, Die mathematischen und philosophischen Grundlagen des Weierstrass schen Zahlbegriffs zwischen Bolzano und Cantor,
*Arch. Hist. Exact Sci.***41**(4) (1991), 311-362. - W Stelzner, Compatibility and relevance: Bolzano and Orlov, in The Third German-Polish Workshop on Logic & Logical Philosophy, Dresden, 2001,
*Logic Log. Philos.*No. 10, (2002), 137-171. - P Thompson, Bolzano's deducibility and Tarski's logical consequence,
*Hist. Philos. Logic***2**(1981), 11-20. - J van Benthem, The variety of consequence, according to Bolzano,
*Studia Logica***44**(4) (1985), 389-403. - B van Rootselaar, Bolzano's corrections to his Functionenlehre,
*Janus***56**(1969), 1-21. - B van Rootselaar, Bolzano's theory of real numbers,
*Arch. History Exact Sci.***2**(1964/1965), 168-180. - A Vogt, On the relationship between philosophy and mathematics in the work of B Bolzano and B Riemann, in
*Impact of Bolzano's epoch on the development of science*(Prague, 1982), 365-366. - R V'yborn'y, Bolzano's anniversary,
*Austral. Math. Soc. Gaz.***28**(4) (2001), 177-183. - H Wussing, Bernard Bolzano und die Grundlegung der Analysis,
*Mitt. Math. Ges. DDR*(2-4) (1981), 128-152.

### Additional Resources (show)

Other pages about Bolzano's manuscripts:

Written by J J O'Connor and E F Robertson

Last Update October 2005

Last Update October 2005