  I develop a new view of the structure of space--called infinitesimal
atomism--as a reply to Zeno's paradox of measure. According to this view, space
is composed of ultimate parts with infinitesimal size, where infinitesimals are
understood within the framework of Robinson's nonstandard analysis. Notably,
this view satisfies a version of additivity: for every region that has a size,
its size is the sum of the sizes of its disjoint parts. In particular, the size
of a finite region is the sum of the sizes of its infinitesimal parts. Although
this view is a coherent approach to Zeno's paradox and is preferable to
Skyrms's (1983) infinitesimal approach, it faces both the main problem for the
standard view (the problem of unmeasurable regions) and the main problem for
finite atomism (Weyl's tile argument), leaving it with no clear advantage over
these familiar alternatives.
