As Fine would say, There is the following view. In addition to individual objects, there are arbitrary objects. But for how long has this view been held? If we look close enough, we find talk about arbitrary objects, disguised in different terminologies, when Locke talks about general ideas, or even when Plato talks about Ideas. Yet, many have cast aside the possibility of such sort of objects, claiming them to be dispensable, or even outright contradictory. This is due to their characteristic feature: a certain arbitrary P must have the properties common to all individual P's, and only those properties. This feature, however, is remarkably close to the one presented by another important concept, essence. In fact, for Locke, at least in one understanding of essence (nominal essence), an arbitrary P and the essence of P are the same thing. Zalta's theory of objects also implies a similar reduction. This suggests a close connection between arbitrary objects and essence.
In this talk, we shall analyze the general form of arguments for and against the existence of arbitrary objects, and see how these arguments have been presented by different authors throughout the history of Philosophy. We, then, present different theories of arbitrary objects and of essence put forward by some of these authors, and see how the two concepts are connected in each of them. At last, we analyze the formal aspects of these theories, and how a same logical framework, with different interpretations, may be used to explain how essence and arbitrariness work.