The Paradox of Infinite Limits: A Realist Response
Dr Patricia Palacios, University of Salzburg
In this talk, we distinguish between different uses of mathematical limits in physics, and we determine the conditions under which an infinite limit should be understood as giving rise to an “infinite idealization”, intended as a misrepresentation of the target system by way of introducing an infinite system. We point out that when infinite limits are used as infinite idealizations they can lead one to the Paradox of Infinite Limits, which allegedly poses a threat to scientific realism. In particular, this depends on whether the idealization is essential for the explanation of the physical phenomenon under investigation. Instead, other uses of infinite limits such as approximations and abstractions do not raise any substantial problem for scientific realism. We also argue that, even in the case of “essential idealizations”, there are ways of coping with the alleged incompatibility between infinite idealizations and scientific realism, which ultimately rely on empirical considerations.