Objects, real objects, good old objects such as this pencil, the Empire State Building, Joseph Stalin, or your kid brother, are believed, by most of us, to be fully determinate, that is, ontologically complete, objects. Surely, we say, if something is an honest-to-goodness object out there in the world, then with respect to every property F, either it has it, or it does not have it; tertium non datur. Of course we may not know, with respect to some properties, whether a given object has them or not: but this is beside the point. This metaphysical tenet leads to another, logical, tenet which also seems to be plainly, even inevitably, true: that identity must be a symmetrical relationship; i.e. that if a is identical with b, then b is identical with a. We take an object, a, to be identical with an object, b, if every property of a is a property of b. Now if we adopt the thesis of the total ontological determinacy of all objects, i.e., that with repsect to every pair of complementary properties F and not-F, every object x must either be F or else be not-F, then it does follow that if b has all of a's properties, then a has all b's properties, for all objects are determinate with respect to the same (i.e., the total) set of properties. Thus if a is identical to b then b is identical to a, and identity must be a symmetrical relationship. The basic claim of the present article is that the thesis of total ontological determinacy of all objects is incorrect. I do not deny that ontologically complete objects exist, and that the concept of absolute, Leibnizian identity applies to them. But I shall argue that the overwhelming majority of the objects actually referred to, objects such as Jimmy Carter, this shirt, the man on my right, etc., are not ontologically complete. The concept of identity which applies to them is not absolute identity, but a modified version of Geach's relative identity.'