From the Beginning to Plato

344 PLATO: METAPHYSICS AND EPISTEMOLOGY
of Forms is the same relation as his earlier notion of participation—in the sense
that for a Form S to participate in a Form F is for S to possess F as a property,
just as for an individual S to participate in a Form F is for it to have F as a
property. 46 Consequently, self-predication is a feature of the Sophist’s Kinds 47
since the ontological analysis of the fact that the Triangle is a figure is: the Kind
Triangularity participates in the Kind Figure, and hence is a figure in the same
way as particular triangles are. Given that the Kinds are also ‘divine’ (254b),
they must be the same Forms which we find in the middle period dialogues.
Divinity also characterizes the ‘Henads’ of the Philebus (62a), a very late
dialogue mainly concerned with ethical problems but containing important and
notoriously obscure passages on metaphysics with Pythagorean overtones absent
from earlier works. The obscurity is probably due, in part, to the metaphysics of
the Philebus being grounded in Plato’s ‘unwritten doctrines,’ 48 about which our
knowledge is very thin.
Plato divides ‘all beings’ into the categories of (1) Limit, (2) the Unlimited,
(3) the mixture of Limit and the Unlimited, (4) the cause of this mixture. (4) is
relatively clear, being identified with intellect, but the rest of the scheme resists
interpretation because of the shifting usage of the notions of Limit and Unlimited,
and the bizarre diversity of examples from the mixed class.
The Limit-Unlimited contrast is associated with the contrast between one
‘Henad’ with a specific number of species, and its indefinitely large range of
generable and destructible instances (16c-d). But Limit is later explained in
terms of the notion of a numerical ratio or measure (2 5 a), and still later
connected to the ideas of moderation and a balanced and good proportion (26a).
Correspondingly, the Unlimited is not only associated with the idea of an
indefinite range of particular instances but is explained in terms of scales of
qualities referred to with pairs of comparative adjectives: hotter-colder, higherlower,
etc., which are generally characterized as admitting the more and the less,
and as in themselves admitting no definite quantity. Further, the Unlimited also
includes pleasure and the life of pleasure. The difficulties are further
compounded by Plato’s identification of these different notions of Limit and
Unlimited (23c) and by the disparate nature of the examples from the mixed
class: it includes a moderate amount of pleasure, the life which combines
pleasure and intellect, the art of music, fair weather, health and virtue of character.
As these last examples show, Plato’s scheme cannot be interpreted in terms of
Aristotle’s notions of form (Limit), matter (Unlimited) and composite (mixture).
Nevertheless, it appears that Plato is analysing entities into what can be loosely
called ‘formal’ and ‘material’ elements.
How do the Forms fit into this classification? If the One of the One-Many
problem raised at 13e–15c corresponds to a (perhaps ‘mathematicized’) Form
from earlier dialogues, then since the One-Many problem arises for all items in
classes (1)–(3) (23e, 24e, 26d), Forms do not fall under any one of these classes
but rather there are Forms for all the beings in (1)–(3). So, for instance, the