Date: Jun 11, 2013 1:18 PM
Author: LudovicoVan
Subject: Re: Matheology § 285

<mueckenh@rz.fh-augsburg.de> wrote in message 
news:eacb74bf-1f4e-40d5-b760-a9ce6e69c090@googlegroups.com...
> 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).


It is not possible to do so effectively...

Julio