<email@example.com> wrote in message news:firstname.lastname@example.org... > Matheology § 285 > > In this article, I argue that it is impossible to complete infinitely many > tasks in a finite time. A key premise in my argument is that the only > way to get to 0 tasks remaining is from 1 task remaining, when tasks > are done 1-by-1. I suggest that the only way to deny this premise is > by begging the question, that is, by assuming that supertasks are > possible. <snip>
Supertasks are mathematical constructs, and, unless shown that there is something intrinsically incongruent in these constructions, they are certainly "possible", and since after Zeno in use to model real-world problems. Time is also irrelevant, it is impossible to complete infinitely many tasks *effectively*: but we are using limits, i.e. where the constructions allow limits to exist, we are not pretending that the process is completed one step at a time, we are rather leveraging the structural features that can be legitimately extended.
> JEREMY GWIAZDA > Article first published online: 4 MAR 2012 > Pacific Philosophical Quarterly > Volume 93, Issue 1, pages 1?7, March 2012 > <http://onlinelibrary.wiley.com/doi/10.1111/j.1468-0114.2011.01412.x/full> > > Therefore it is not possible to enumerate all rational numbers > (always infinitely many remain) by all natural numbers (always > infinitely many remain) or to traverse the lines of a Cantor list (always > infinitely many remain).