Assuming that string theory does not rule out point-like particles such as quarks, how can a group of one-dimensional objects be seen as having no dimensions at all?
Strings are much smaller than the particles we currently observe, so for all (practical) matters and purposes they are 0-dimensional - except compared to other strings.
Strings are 1-dimensional, so 0-dimensional objects are "ruled out". However, in M-Theory objects of all sorts of dimensions (0, 1, 2, ..., N) are supposed to exist.