An extra talk on Bolzano’s mathematics is being presented at the APMP Symposium held on the Tuesday before our Symposium. It is in Session 9C (APMP 5) at 17.15 on Tuesday 6th August:

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

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

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

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

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

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

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