Relations and Infinite Regress in Plato

Extract

In a recent paper on “The Theory of Forms, Relations and Infiinite Regress” (Dialogue, Vol. 8 [1969–70], 116 ff.), T. G. Smith claims to have trapped Plato's theory of Forms in a vicious regress. According to Smith, the regress is “the consequence of 1) Plato's view that there are Forms for relations; 2) The view that the exemplifications of Forms are derivative and owe their lesser degree of reality to their relationship to their Form; 3) the consequence that each relation between a set of particulars and their Form must be intelligibly distinct and different from the relation holding between all other sets of particulars and their respective forms [Forms ?]” (p. 121). I have no particular quarrel with (1) and (2), but I cannot agree with (3). In what follows I hope to show that (3) not only cannot be extracted from Plato but it is patently false. In section I I shall outline Smith's argument. I shall then present in section II my case against it. I shall make some general remarks in section III.