According to Platonic realism, universals exist in a "realm" (often so called) that is separate from space and time; one might say that universals have a sort of ghostly or heavenly mode of existence, but, at least in more modern versions of Platonism, such a description is probably more misleading than helpful. It will make the theory seem less mysterious if we say, instead, that it is meaningless (or a category mistake) to apply the categories of space and time to universals. In any event, we never see or otherwise come into sensory contact with Platonic universals, and they definitely do not exist at any distance, in either space or time, from our bodies. Obviously they do not exist in the way that ordinary physical objects exist. Nonetheless these universals do, according to Plato and other Platonic realists, exist in the broadest sense. Most modern Platonists avoid the possible ambiguity by never claiming that universals exist, but "merely" that they are.
Plato's theory of universals is also called 'Platonism', or 'Platonic realism', or just 'realism' for short. This sort of realism must not be confused with other doctrines called 'realism' in philosophy or in other fields. The word 'realism' is extremely ambiguous; it has a dozens of different senses in philosophy and also outside of philosophy. 'Platonic realism' is probably most precise.
The theory is expounded in The Republic. And elsewhere: notably in the Phaedo, the Phaedrus, the Meno and the Parmenides.
These sorts of universals are called, after Plato, forms or ideas, but Plato's universals certainly are not ideas in the mind. They are not mental entities at all, unless, as on some theories, they are ideas in God's mind. Due to the potential confusion, 'form', 'Platonic form', or simply 'universal' are terms more usually used by philosophers. (See The Forms.)
To flesh out Plato's view, we might say, first, that the forms are archetypes, meaning original models, of which particular objects, properties, and relations are copies. So this apple is a copy of the form of applehood, this particular redness here is a copy of the form of redness, and so forth. Particulars are then supposed to be "copies" of the forms — whatever "copy" is supposed to mean here. That, anyway, is one way that, on Plato's view, the forms might be related to particular instances of objects and properties and so on. Another way they might be related, for Plato, is that particulars are said to participate in the forms, and the forms are said to inhere in the particulars. This talk of "participation" and "inherence" is admittedly rather mysterious. What does it mean to say this apple participates in applehood? What does it mean to say applehood inheres in this apple? We do not get very enlightening answers from Plato, as we will see shortly.
To further flesh out Platonic realism, it is useful to consider how the theory satisfies the three constraints on theories of universals listed on problem of universals.
- On Plato's view, there are some forms that are not instantiated at all, but that does not by itself mean that the forms could not be instantiated. Forms can have lots of copies; or, they can inhere in lots of things. Either way, the forms are capable of being instantiated by many different things. But it is just not clear what either account of instantiation, in terms of "copies" or in terms of "inherence," amounts to. For example, what does it mean to say that this particular apple is a copy of the form of applehood? Does it mean the apple is the same shape as the form? Probably not; the form, after all, is not supposed to have a shape because it is not spatial. What would it mean to say that apple participates in applehood? Is that like membership in a club, somehow? It is not clear. There is, in any event, is a basic problem for Plato's theory that Platonic realists generally are concerned to solve: exactly how are we supposed to spell out how particulars instantiate the forms?
There are some typical Platonist solutions to this problem. Firstly the Platonist typically claims that it would not be contradictory to say that a form has itself no concrete (spatial) location and yet has in abstracto spatial qualities, if it is the form of something spatial. Then the apple would indeed have the same shape as its form. Secondly the Platonist typically claims that the relationship between a particular and the form it is an instance of, is really very intelligible and that we tend to grasp this concept easily, unproblematically applying it in every day life ((wo)man is a born Platonist, so to say) - and that the mystery is only created by the artificial demand to somehow explain our normal understanding of it as if it were highly problematical; which of course we cannot do (as it isn't), confusing ourselves with the mere illusion of a problem, a method that can be abused to render suspect any concept in philosophy.
- On Plato's view, universals are definitely abstract. Moreover, if we can conceive of universals, then we have to be able to conceive of these abstract forms. When one thinks of redness in general, then according to Plato, one is thinking of the form of redness. That might be possible somehow, but it raises another problem: how did we get the concept of something, a form, that exists neither in space nor in time? The forms are supposed to exist in a special realm of the universe, apart from space and time. How could we have any concept of them, then? We did not get the concept via sense-perception. We can see the apple and its redness, but those things merely participate in the forms, or they are just copies of the forms; to conceive of this apple and this redness is not to conceive of applehood or redness-in-general. So how did we come by the concept at all? So Plato, famously, solves the problem by saying that our souls are born with the concepts of the forms, and we just have to be reminded of those concepts from back before we were born, back when our souls were in close contact with the forms in the Platonic heaven. This is known as the doctrine of recollection. For this reason Plato is known as one of the very first rationalists, believing as he did that we are born with a fund of a priori concepts, to which we have access through a process of Reason or intellection — a process that critics find to be rather mysterious.
The modern Platonist's solution to this would typically be to claim that, as we can only experience an object by means of general concepts, the universality of its qualities is an unavoidable given; that the critic of Platonism already shows a remarkable grasp of the special relation between the abstract and the concrete and that he only has to stop deluding himself in thinking that it somehow implies a contradiction. Of a spatial object it would be absurd to say that it was and was not in the same place; but an abstract object is real in its instantiation - and thus knowable by it, so that Platonism is reconcilable with empiricism - and still as such abstract and thus not real. It is simply the natural way of the abstract. This is not inconceivable: the critic has, after all, understood it perfectly; he has merely to abandon his prejudice and accept it.
- Platonic realism is probably strongest in satisfying the third constraint, that is, as a theory of what general terms refer to. Forms seem to be just the perfect referents for our general terms. Indeed, probably the most popular argument for Platonic realism says that universals explain best the meaning general terms have; on this argument, when we speak of 'applehood' or 'redness', the best way to understand what such terms mean is to say that they refer to Platonic forms. It is said that Platonism gets most of its plausibility because, when we talk about redness, for example, we seem to be referring to something that is apart from space and time, but which has lots of specific instances.
Problems such what participation is, and how we can have any concept of the forms, would appear to be very difficult, no matter what the modern Platonist says. Nonetheless, realism does still have its strong defenders. Its popularity through the ages is cyclic.