According to Ariel Meirav, the root of some of our most noteworthy
difficulties in the metaphysics of concrete entities has been the
traditional tendency to focus on the horizontal dimension of wholes
(i.e. relations between the parts of a whole), and to neglect the
vertical dimension (i.e. relations between the whole itself and its
parts). In Wholes, Sums and Unities, Meirav formulates a critique of
widely accepted mereological assumptions, presents a new conception of
wholes as `Unities', and demonstrates the advantages of this new
conception in treating a variety of metaphysical puzzles (such as that
of Tibbles the cat). More generally he suggests that conceiving wholes
as Unities offers us a new way of understanding the world in
non-reductive terms.