Bernard Bolzano


This page is intended to report on any meetings on Bolzano’s mathematics. For now it includes a brief description of the events that have taken place in Prague since 2010, as well as a list of some previous events.

Bolzano Symposium in Prague 2019

Organised by Steve Russ, the symposium Bolzano’s Mathematics and the General Methodology of the Sciences was held on the 8th of August as part of the 16th Congress on Logic, Methodology and Philosophy of Science and Technology. The symposium consisted of 10 talks which were divided into 4 sessions:
Chair: Steve Russ
Michael Otte: Bolzano, Kant and the evolution of the concept of concept (abstract and paper)
Annapaola Ginammi and Arianna Betti: Bolzano’s theory of ground and consequence and the traditional theory of concepts (abstract)
Paola Cantù: Bolzano’s requirement of a correct ordering of concepts and its inheritance in modern axiomatics (abstract)
Chair: Arianna Betti
Johan Blok: Did Bolzano Solve the Eighteenth Century Problem of Problematic Mathematical Entities? (abstract and discussion in absentia)
Kateřina Trlifajová: Bolzano and the part-whole principle for infinite collections (abstract and slides)
Elías Fuentes Guillén: On Bolzano’s early rejection of infinitesimals (abstract and slides)
Chair: Peter Simons
Davide Crippa and Elías Fuentes Guillén, with Jan Makovský: Bernard Bolzano’s 1804 examination: mathematics and mathematical teaching in early 19th century Bohemia (abstract and slides)
Jan Šebestík: Looking at Bolzano’s mathematical manuscripts (abstract)
Chair: Steve Russ
Anna Bellomo: Bolzano’s measurable numbers: sets or sums? (abstract and slides)
Peter Simons: On the several kinds of number in Bolzano (abstract and slides)

An additional talk on Bolzano’s mathematics, entitled “On continuity in Bolzano’s 1817 Rein analytischer Beweis…”, was presented by Marlena Fila at the Symposium of the Association for the Philosophy of Mathematical Practice. Her abstract can be found here.
Two reports of the symposium were elaborated: one for the Newsletter of the International Bernard Bolzano Gesellschaft, which can be found here, and one for the Proceedings of the 16th CLMPST, to be published by College Publications. In addition, two posters (posterA and posterB) were produced using a detail from a famous oil painting by Heinrich Hollpein and a lithograph based on it. The photographs by Dagmar Landová in Bildnisse Bolzanos are the sources.
Steve Russ was able to make a short research visit in December 2018 to an archive in Prague thanks to a grant from the British Society for the History of Mathematics, which led to the Bolzano Symposium at the 16th CLMPST. A report about this visit can be found here.

Bolzano in Prague 2017

The meeting Bolzano in Prague 2017 was held from the 27th to the 29th of November. Organised by Steve Russ and Davide Crippa, this was a small research-oriented meeting celebrating the 200th anniversary of some major achievements of Bolzano to be found in his two mathematical works of 1817. The discussions focused mainly on the recently defended PhD theses of Johan Blok and Elías Fuentes Guillén, although other works were also discussed. Each session discussion was introduced and chaired by one of the participants:
Stefan Roski: “Simplicity and Economy in Bolzano’s Theory of Grounding” and “Simplicity, Generality, and Economy: Philosophical Background of the RAB” (3rd paper)
Johan Blok: “Bolzano’s Early Quest for A Priori Synthetic Principles
Skype session with Jan Šebestík, Paul Rusnock and Elías Fuentes Guillén
Johan Blok: “Bolzano’s Early Quest for A Priori Synthetic Principles” (slides)
Davide Crippa: “The Germanic Development of the Pre-Modern Notion of Number” (long summary)
Summary of progress and Skype session with Jan Šebestík, Paul Rusnock and Elías Fuentes Guillén
Kateřina Trlifajová: “Bolzano’s measurable numbers: are they real?
Steve Russ and Kateřina Trlifajová: “Bolzano’s Infinite Quantities” (abstract)
Final discussion and preparation of some output Report on the meeting.

The Google group “Bolzano in Prague 2017”, which still persists, was created to discuss matters that arose from the texts. If you would like to join the group, please send an email to Steve Russ ( Research questions for discussion (from Steve Russ) can be found here.
A short paper by Steve Russ on the 200th anniversary of some mathematical achievements of Bernard Bolzano, entitled “Bolzano in Bohemia”, was published in Mathematics Today (Vol. 53, No. 6, pp. 278-281). Copies for personal use can be obtained on request to the author.
Participants: Steve Russ, Davide Crippa, Kateřina Trlifajová, Alena Vencovská, Magdalena Hykšová, Marta Vlasáková, Johan Blok, Stefan Roski, Ansten Klev, Ladislav Kvasz, Joan Bertran San-Millán (in person). Jan Šebestík, Paul Rusnock and Elías Fuentes Guillén (by Skype).
The venue was hosted by the Kabinet pro studium vědy, techniky a společnosti and the Centrum pro teoretická studia.

Bolzano in Prague 2014

The meeting Bolzano in Prague 2014 was held from the 16th to the 19th of July. Organised by Arianna Betti and Steve Russ, it addressed several aspects of Bolzano’s thought, including topics in ethics, politics, aesthetics, theology, mathematics, logic, methodology and philosophy of science. More information can be found here.

Photo by Elías Fuentes Guillén

Bolzano in Prague 2010

The meeting Philosophy and Mathematics in the Work of Bernard Bolzano was held in Prague (and Těchobuz) from the 15th to the 18th of April. It was organised to celebrate the 200th anniversary of the publication of Bolzano’s Beyträge zu einer begründeteren Darstellung der Mathematik. More information can be found here.

Previous meetings

1981: Impact of Bolzano’s Epoch on the Development of Science, Prague.
1981: Bernard Bolzano, Konference českých matematiků, Prague.
1981: Bernard Bolzano 1781-1848, Prague.
1973: Bolzano als Logiker, Vienna.