The aim of this thesis is to introduce and elaborate a new conception of the
relation between wholes and parts. Wholes, I propose, can be conceived of as
'Unities', in contrast to their currently familiar conception as 'sums'. Following a
clue given in the distinction which Plato draws in the Theaetetus (203c-205e)
between two conceptions of a complex entity, I argue that a similar distinction can
be coherently developed in modern terms.
Part I is preoccupied with general conceptual and historical background. Some
theoretical constraints on any theory of wholes and parts are challenged and found
to be merely apparent.
In Part II the conception of wholes as sums is presented, and it is extensively
argued that modern discussions of wholes generally presuppose this conception.
This presupposition is shared not only by authors who subscribe to the 'classical'
mereological theories of Lesniewski, and Goodman, but also by theorists of holistic
sympathies (making use, for example, of the notion of an organic whole, or of a
Gestalt) who rely on 'neoclassical' theories. It is urged that this conception suffers
from serious, fundamental difficulties and drawbacks.
In Part III the conception of wholes as Unities is introduced. A theory of
Unities is laid down in systematic, formal detail, and the points of divergence from
presuppositions of traditional theories are discussed. It is shown how in conceiving
of concrete entities (of certain types) as Unities one is free from many difficulties
which beset their conception as sums. Finally, it is shown how the theory of Unities
provides a powerful tool for resolving some central metaphysical puzzles
concerning concrete entities, especially puzzles associated with preservation of
identity in the face of loss or gain of parts.