An extra talk on Bolzano’s mathematics was presented at the APMP Symposium held on the Tuesday before our Symposium: 

Marlena Fila,  On continuity in Bolzano’s 1817 Rein analytischer Beweis … Abstract

Bolzano’s Mathematics and the General Methodology of the Sciences (BMMS)


Thursday 8th August in Sessions 17B, 18B, 19B, and 20B

09.00 – 10.30   Session 17B     Concepts and methodology 

Chair:  Steve Russ

1. Michael Otte:  Bolzano, Kant and the evolution of the concept of concept. Abstract     Paper

2. Annapaola Ginammi, Arianna Betti:  Bolzano’s theory of ground and consequence and the traditional theory of concepts.  Abstract

3. Paola Cantù:  Bolzano’s requirement of a correct ordering of concepts and its inheritance in modern axiomatics. Abstract

11.00 – 12.30    Session 18B    The mathematical infinite and other problems

Chair:  Arianna Betti

4. Johan Blok:  Did Bolzano Solve the Eighteenth Century Problem of Problematic Mathematical Entities?   Abstract .   Discussion in absentia

5. Kateřina Trlifajova:  Bolzano and the part-whole principle for infinite collections.  Abstract   Slides

6. Elías Fuentes Guillén:  On Bolzano’s early rejection of infinitesimals.    Abstract  Slides

14.00 – 15.00     Session 19B     Mathematical manuscripts

Chair:  Peter Simons

7. Davide Crippa, Elías Fuentes Guillén, Jan Makovsky:  Bernard Bolzano’s 1804 examination: mathematics and mathematical teaching in early 19th century Bohemia.  Abstract. Slides

8. Jan Sebestik:  Looking at Bolzano’s mathematical manuscripts. Abstract

15.15 – 16.15     Session 20B     Kinds of Numbers

Chair:  Steve Russ

9. Anna Bellomo:  Bolzano’s measurable numbers: sets or sums? Abstract    Slides

10. Peter Simons:  On the several kinds of number in Bolzano.  Abstract   Slides