The Paradigm Shift in the 19th-century Polish Philosophy of Mathematics

Abstract

The Polish philosophy of mathematics in the 19th century had its origins in the Romantic period under the influence of the then-predominant idealist philosophies. The decline of Romantic philosophy precipitated changes in general philosophy, but what is less well known is how it triggered changes in the philosophy of mathematics. In this paper, we discuss how the Polish philosophy of mathematics evolved from the metaphysical approach that had been formed during the Romantic era to the more modern positivistic paradigm. These evolutionary changes are attributed to the philosophers Henryk Struve, Antoni Molicki and Julian Ochorowicz, and mathematicians Karol Hertz and Samuel Dickstein. We also show how implicit ideas (i.e., those not declared openly) from the area between the philosophy of science and general philosophy played a crucial role in the paradigm shift in the Polish philosophy of mathematics.

Keywords

• Polish philosophy
• philosophy of mathematics
• Romantic philosophy
• Positivism
• Samuel Dickstein
• Karol Hertz