id: 05995441
dt: j
an: 2012c.00402
au: Epple, Moritz
ti: Between timelessness and historiality: On the dynamics of the epistemic
objects of mathematics.
so: ISIS 102, No. 3, 481-493 (2011).
py: 2011
pu: University of Chicago Press, Chicago, IL
la: EN
cc: E20
ut: mathematical definitions; epistemic objects; dynamics; timelessness
ci:
li: doi:10.1086/661622
ab: The author discusses the temporal structure of mathematical research
through the analysis of four definitions related to a mathematical
object, known nowadays as knot, from different times and places. Using
for the analysis a letter of the Italian mathematician Enrico Betti
(1863), an unpublished manuscript of the Scottish natural philosopher
James Clerk Maxwell (1868), and the monographs by Kurt Reidemeister
(1932) and Dale Rolfsen (1976), he concludes the following. “1. None
of these definitions makes sense in mathematical practice without a
technical framework. This framework is referred to but not explained in
the definitions. 2. The dynamics of the epistemic objects of
mathematical research (knots) are secondary to the dynamics of the
epistemic configurations as a whole. To understand the former it is
necessary to understand the latter. 3. The dynamics of epistemic
configurations of mathematical research does not follow law-like
processes. Very different types of change may happen (and did happen in
the present case), and some of them link the dynamics of epistemic
configurations with events and developments beyond the bounds of the
research field in question.”
rv: Yuri V. Rogovchenko (Umeå)