Problem of universals

Philosophy is contemplating puzzles about existence. An example is the problem of universals.

It appears that certain properties are shared among multiple objects or events, e.g. redness or injustice. It is difficult to imagine a property-less object (a ball with no colour, shape, size, etc.) or an object-less property (redness with no underlying object that is itself red), so what is the nature of these common properties, how do they combine with, or form, objects? And when one of two red objects is destroyed, what happens to redness?

There are many philosophical positions regarding universals. Plato’s extreme realism is at one end of the spectrum, where universals are the causal and teleological explanation of the way things are in the world. Beauty is a property that exists in some ideal form totally independent of anyone thinking about beauty or of beautiful things existing, and it is responsible for the beauty that we see in particular things in the world. On a realist account, universal do not exist in space and time in the same way that particular instantiations of the universal exist in space and time, but are fundamental to our ability to describe and know anything about particulars. Russell talks about universals subsisting in contrast to particulars existing; and for Russell we need one from each category, combined in the right way, in order to describe and to know anything about the world.

At the other end of the spectrum, we might consider beauty to be a mental construction formed by observing patterns and commonality, and we might think that it exists only so far as beautiful things exist and people think about them and spot the similarity, or that there is nothing more than commonality.

Someone who is sceptical about universals might refer to the third man argument, which calls into question the role that universals play: If I ask ‘what makes an apple red?’ and answer ‘a universal, redness’, then it appears that I am claiming there is a relationship between the red thing and the universal redness that explains the thing being red. If this universal-particular relationship causes the colour in the apple because the colour resides in the universal, then how do we explain the universal itself being red? Is there another universal to explain the redness or the original? Do we need an infinite supply and are we thus left infinitely far from an explanation as to how the quality may be present in the original? If the universal is not itself red, then how is it responsible for redness in other things?

Resemblance nominalists would suggest that, rather than creating many millions of complex entities which are extremely strange and difficult to explain, we could simply group particulars together by virtue of their resemblances. What we call a universal, such as redness, could be reclassified as the resemblance of a group such as the set of red things. This seems much simpler.

However, we then need to define ‘resemblance’. We cannot simply say that for two things to resemble one another they must share certain likenesses, since defining likeness is our original purpose. Set-construction is difficult for the resemblance nominalist. When trying to define the set of red things we might proceed as follows: a red chair, a red apple, a green apple… so the set of red things defines ‘being red’ with reference to a green object. One cannot argue that the wrong resemblance is being used here, and that the problem will subside if the set is constructed with reference to the correct resemblance, because ‘being red’ is just what we are trying to define so ‘being red’ cannot be used as a guide to the set’s construction. (Russell instead suggests that ‘resemblance’ is a universal itself.)

We might at this point ask why we are trying to construct these sets or to define properties, the existence of which we are not committed to.

The problem of universals, when expanded to understand its full implications, and when we consider the full scope of universals, appears to threaten our ability to do things that we want to do. Roger Penrose contends that mathematics cannot be properly understood without the Platonic view that "mathematical truth is absolute, external and eternal, and not based on man-made criteria ... mathematical objects have a timeless existence of their own..." (1989: 151).

A realm of eternal abstract objects that exemplify perfection and allow us to generalise and free us from the constraints of space and time are key in the formulation of a priori statements. Russell tries to prove that all a priori knowledge deals exclusively with the relations of universals. He goes on to argue that universals allow us to formulate a priori statements which can be shown to be true without a single specific instance. For example, we can say that “all products of two integers, which have never been and will never be thought of by any human being, are over 100”.

Universals are yet to be explained but they are vital for allowing us knowledge of things that we are not acquainted with: identity, sameness, equality, property-less points, the infinite, and the foundations of mathematics.