Realists claim that where objects are similar or agree in attribute, there is some one thing that they share or have in common. Nominalists deny this. Realists call these shared entities universals.
Universals - are entities that can be simultaneously exemplified by several different objects. And they claim that universals encompass the properties things possess, the relations into which they enter, and the kinds to which they belong.
We can categorize things in a variety of ways; color, shape (square, round), kind (elephant, tree). This is an important part of our experience. We group things. Most concede that we classify objects that reflect our interest, goals and values. Plato said that things instantiate, exhibit, or exemplify a single property, quality or attribute. This schema has been known as metaphysical realism. Those that are critics are nominalists.
Nominalists argue that there are deep conceptual problems with the metaphysical machinery implied by the Platonic Schema.
The debate between realists and nominalists is one of the oldest debates in metaphysics.
Metaphysical realists insist that attribute agreement presupposes a distinction between types of categories/objects: particulars & universals.
Particulars - a regular person would refer to this as “things” - familiar concrete objects like human beings, animals, plants, inanimate material bodies, etc.
A particular occupies a single space at a given time.
Universals - Contrasting particulars, repeatable entities. At any given time numerically one and the same universals can be exhibited. For example, people with the same virtue, cars with the same shape, houses with the same color.
There are more than one type of universal.
Monadic Universals - they are universals that exemplify individually or one by one. All the examples above apply to this. There are also relation universals, like being a mile apart or being next to.
These examples are symmetrical relations because they go both ways. Ie: A is related to B, so B shares the same relationship to A.
Asymmetrical is a relationship in a certain order. Ie: A being the father of B, doesn’t mean B is the father of A. This example is a dyadic relation or two place, but there is many chains to the n-place relation. These are known as polyadic universals.
Relations are polyadic universals, but colors, virtues, and shapes are all monadic.
Aristotelian can be broken down further to kinds and properties.
Kinds - are things like the various biological species and genera.
Properties - objects exemplify properties.
A simple summation is objects exemplify properties by possessing them, things exemplify kinds by belonging to them. Kinds constitute particulars that exemplify them as what they are, properties merely characterize particulars. This viewpoint in practice becomes quite complex. A cat and a dog can be kind mammal, but two dogs are closer related than that of the dog and cat. Then there are relationship universals that each one brings more universals to each, becoming a never ending chain.
Despite this complexity, realists insist this helps with explaining a wide range of phenomena.
The most basic form of discourse is the subject-predicate sentence.
Essentially we have a particular and we say something about it. If (1) is true, it depends on what (1) says as a composition and that it is relevant to the world. So a linguistic and a nonlinguistic structure.
Predicates express or connote properties, kinds, and relations; and where we have a true subject-predicate sentence, the universal expressed by the predicate is exemplified by the referent of the sentence’s subject term. A realist views that Socrates is courageous is also the same as Socrates exemplifies courageousness or better put a exemplifies F-ness.
The most obvious appearance for this is in abstract singular terms, which are expressions like triangular, wisdom, mankind and courage. They are all singular terms, but they also pair with expressions that can play the predicate role (general terms) - triangularity/triangular, wisdom/wise, mankind/man, courage/courageous, and red(noun)/red(adjective). The moral realist insists that the pairs are related in a distinct way: abstract singular term are for picking out a certain property/kind and the general term appears to be an expression of objects that exemplify that property/kind.
Realists insist that the abstract singular term is referring to the universal as they’re functioning as referential roles.
Triangularity is a shape - triangularity is the kind, but the universal is triangle.
A view among realists is that you can’t have a completely unrestricted view of the subject-predicate sentence discussed above. This type of unrestricted view causes problems. There is a paradox with a particular example. Let’s say does not exemplify itself. For A to not exemplify itself is exemplifying this. The point being that there shouldn’t be an unrestricted/unlimited choices when it comes to universals precisely because of this paradox.
Another issue is with a regress of explaining subject-predicate truth.
(1) a is F, how is this explained? Well (2) a exemplifies F-ness. The problem here is that the answer to (1) is (2), but (2) is another subject-predicate. How do we explain (2)? Well, (3) a exemplifies the exemplification of F-ness - another subject-predicate. This is a regress that goes on infinitely because (1) is validated by (2), but for (2) to be validated, (3) needs to be validated and on and on.
Realists have argued that relations bind objects together only by the link of exemplification. Exemplification links objects into relational facts without any further links.
Another issue that comes up is the predicate of “bachelor”. What universal would this be? Being a bachelor. The problem is that this universal is a property of being a male, human and unmarried. Wouldn’t there be no need for such the universal of bachelor as it can be broken down into three universals? This led to some realists calling for restrictions on predication.
This is where the distinction between undefined and defined predicates emerged. Simply put, thee are predicates that are not defined in terms of other predicates - also known as primitive predicates (undefined). Defined predicates can be explained by reference to the universals correlated with the primitive predicates which they are defined.
This is a good explanation, but it brings problems. The central one is the difficulty in neatly dividing primitive and defined.
The predicate “game” illustrates this point. What does game break down into? Competition, but some games are literally throwing a ball against a wall by oneself. Sport, but are card games, or board games sports?
This particular section has a pretty good discussion regarding the differences between Aristotle and Plato’s view of exemplifying.
The Platonist view is that there are properties, kinds and relations that are not exemplified - never have and never will. The Aristotelian view is one that universals are ones that we can perceive being exemplified in spatiotemporal objects (existing in space and time).
The Platonist’s are embracing “two worlds” ontology where universals are independent of the concrete world of space and time. They arrive at this view as universals are things that presuppose the exemplification. One must know of the universal square prior to seeing an object exemplify squareness.