TY - JOUR
AU - Mazurkiewicz, Stany
PY - 2020/07/31
Y2 - 2024/05/23
TI - At the origins of contemporary philosophy of mathematics: Kant, Hegel, Bolzano
JF - Characteristica Universalis Journal
JA - CUJournal
VL - 1
IS - 1
SE - Articles
DO - 10.5281/zenodo.4294177
UR - https://cujournal.com.ar/index.php/home/article/view/8
SP - 105-134
AB - <p>In this article we will study the philosophical logic of Kant (1724-1804), Hegel (1770-1831) and Bolzano (1781-1848) in relation to mathematical questions. We will try to show that their three philosophies are strongly influenced by their different definitions of mathematical rationality. We will show that the history of mathematics has undergone a real epistemological break between the generations of Kant and those of Hegel and Bolzano, and can therefore help us to understand the meaning and scope of Kant's criticism of his two successors. Indeed, mathematics seems to break itself from the criteria of intuitive construction and spatial representation which were crucial for Kant. The new possibilities offered by mathematics, functioning from then on - as Kantlui himself suggests in a passage in his work - in a synthetic but not intuitive way, call for a renewal of logic and, more generally, of philosophical discursivity as a whole. Logic no longer has to limit itself to the criterion of the (empirical) validity of transcendental logic, nor does it have to wait for the verification of the meaning of its categories by an intuition that is never reduced. However, Hegel and Bolzano set up completely different logics, thus opening up two philosophical traditions, dialectical and analytical, which have been in opposition to each other ever since. Returning to the origin of such a divergence seems to us to shed light on the possible points of encounter between the two paradigms. It is in the notion of subject that we locate the crux of the polemic.</p>
ER -