Quadruple distribution of Existences. 1. The Infinite. 2. The Finient 3. Product of the two former. 4. Combining Cause or Agency.
But such promise is not realised. The dialogue takes a different turn, and recurs to the general distinction already brought to view between the Finient (Determinans) and the Infinite (Indeterminatum). We have it laid down that all existences in the universe are divided into four Genera: 1. The Infinite or Indeterminate. 2. The Finient or the Determinans. 3. The product of these two, mixed or compounded together Determinatum. 4. The Cause or Agency whereby they become mixed together. — Of these four, the first is a Genus, or is both One and Many, having numerous varieties, all agreeing in the possession of a perpetual More and Less (without any limit or positive quantity): that which is perpetually increasing or diminishing, more or less hot, cold, moist, great, &c., than any given positive standard. The second, or the Determinans, is also a Genus, or One and Many: including equal, double, triple, and all fixed ratios.[23]
[23] Plato, Philêbus, pp. 24-25.
The third Genus is laid down by Plato as generated by a mixture or combination of these two first — the Infinite and the Determinans. The varieties of this third or compound Genus comprise all that is good and desirable in nature — health, strength, beauty, virtue, fine weather, good temperature:[24] all agreeing, each in its respective sphere, in presenting a right measure or proportion as opposed to excess or deficiency.
[24] Plato, Philêbus, p. 26 A-B.
Fourthly, Plato assumes a distinct element of causal agency which operates such mixture of the Determinans with the Infinite, or banishment and supersession of the latter by the former.
Pleasure and Pain belong to the first of these four Classes — Cognition or Intelligence belongs to the fourth.
We now approach the application of these generalities to the question in hand — the comparative estimate of pleasure and intelligence in reference to Good. It has been granted that neither of them separately is sufficient, and that both must be combined to compose the result Good: but the question remains, which of the two elements is the most important in the compound? To which of the four above-mentioned Genera (says Sokrates) does Pleasure belong? It belongs to the Infinite or Indeterminate: so also does Pain. To which of the four does Intelligence or Cognition belong? It belongs to the fourth, or to the nature of Cause, the productive agency whereby definite combinations are brought about.[25]
[25] Plato, Philêbus, pp. 27-28, p. 31 A.