When most people think of something as "nominal," they think of a thing that exists in name only. For example, some countries might have an official state religion and citizens are thus "nominal" members of that religion—they are members in name only. Another example could be that a certain economic factor is nominal; a figure exists as something of a placeholder until it is vetted or reconciled with another figure (such as inflation). In these cases, the idea of something being nominal is uncontroversial. But there is a very interesting arena where nominalism is not so easily taken for granted, and that is within the realm of philosophy.
Philosophy has long grappled with the problem of "the one and the many." If we look at two apples sitting next to each other on a table, how is it that each one is an apple while occupying distinct space and being comprised of distinct matter? Most people take it for granted that a red apple and a green apple are both apples, but how are they both an "apple"? A common answer is that they have the same basic physical traits, chemical composition, and so forth. But this does not really answer the question of why they are called the same thing. Furthermore, a detailed micro-analysis would determine that each apple is really 100 percent unique from any other thing. Are they called the same because there is something non-physical uniting them? Or do we say they are the same merely as a convenient way to speak about physical objects?
This brief example should hopefully show that the question of how things can be "one" and "many" is not always a straightforward thing. At least, it is not straightforward for those interested in such inquiry. Historically, philosophers have tried to solve this problem by putting forth different metaphysical arguments. Metaphysics is the philosophical discipline that deals with reality, causation, and related topics. Over time there has been a great deal of back-and-forth between the metaphysical positions of nominalism and realism.
Nominalism is best understood against the view it starkly opposes, which is Platonic realism (hereafter used interchangeably with realism). Realism generally holds that universals, essences ("what-ness"), and abstract objects exist in some way. Platonic realism, named after the ancient Greek philosopher Plato, argues that such things exist in their own right, within their own realm which is completely independent of the physical world. For example, in realism there is such a thing as Blueness or the color Blue. The realist says that the water is blue because its color is somehow representative of (or participates in) the universal idea of Blue. Anything that is blue is so called because of its relation to the ultimate Blue. The universal Blue exists in an immaterial and entirely abstract way, but it exists nonetheless. We can say that Socrates is a man because he participates in Man. Particulars like Socrates are always instances of the Universal (Man). These examples merely aim to show some very basic ideas surrounding Platonic realism. Contemporary variations of realism are more complex and nuanced, and they also tend to integrate things like numbers, sets, propositions, and much more.
At first glance, Platonic realism seems bizarre. To ask "where" these things exist is to misunderstand what they are. We come to know about them only by thinking very deeply about various things, such as humanity, justice, beauty, colors, and so on. The conclusion at the end of a long reasoning chain is that the only way such things can make sense to talk about is if they exist in an absolute sense.
Platonic realism seems to resolve certain issues. For example, the question of how there are two apples is resolved by holding that each of them resembles or is an exemplification of the universal Apple. Yet, this type of realism has been hotly contested since it was first advanced.
Opponents of Platonic realism, such as nominalists, point out many problems with this view. A major one is that realism only shifts the problem of the one and the many into the realm of universals. If we take Platonic realism seriously, we end up with an infinite regress of universals/ideas. Against the realists, nominalists argue that realism about universals and abstract objects is untenable or incoherent.
Nominalism is a type of metaphysical anti-realism. It holds that things like universals, essences, and abstract objects do not exist at all. Instead, these things "exist" simply as names given to physical (concrete) particulars. As mentioned above, an example of an essence or universal would be "Man" or "Blue." For the nominalist, "Man" and "Blue" are simply naming conventions given to physical things. In nominalism, there is no such thing as the color blue or mankind. When he says that "the water is blue," the nominalist does not think that "blue" is anything real. If the nominalist says that "mankind" is depraved, "mankind" will not attach to or signify anything real. As an anti-realist view, nominalism is related to conceptualism. Conceptualism holds that universals exist as mental abstractions, but do not have extramental existence. There is no realm where "Blue" or "Man" exist. The conceptualist will hold that "blue" exists in his mind as an abstraction from water, whereas the nominalist will affirm only linguistic convention.
Realism and nominalism have gone back and forth for millennia. Fruitful advances have been made in helping those interested to better explicate their own understanding of reality. As alluded to above, there are other problems that realism tries to address. An important one is the nature of change over time. For example, what makes the Amazon River the same river today as it was 500 years ago? Specifically, is it correct to call it the same river? If so, why? Again, it certainly seems as though the physical constituents of the thing cannot provide adequate explanation. By positing the universal "River," the realist can offer a potential solution. Against the realist, the nominalist raises objections such as that universals are unnecessary, are outside of our understanding, or that they create more problems than they solve.
In the Christian worldview, both realism and nominalism are difficult to reconcile with the Bible. The realist typically conceives of universals as uncreated and self-existent. Yet, the Bible tells us only God exists in this way (Exodus 3:14; John 1:1–3; Colossians 1:16–17; Hebrews 1:3). On the other hand, the Bible does speak in such way that numbers, as well as terms like sin and humanity are real. The Bible does not intimate that when God speaks to us about things He is merely using an arbitrary naming convention.
A promising solution to the problem addressed by realism and nominalism was originally advanced by Aristotle and subsequently refined into Christian thought by medieval churchmen like Thomas Aquinas. This view, called "moderate realism," holds that universals do not exist in their own realm, but that they nonetheless exist in the form of the object itself and within the mind of the knowing subject. Further explication of this view is beyond the scope of this article, but there are many reasons for Christians to consider it. A Christian moderate realism can place God as metaphysically ultimate while providing a framework for addressing universals and particulars. In contradistinction, nominalism seems to render many passages in Scripture without objective meaning, and therefore faces a tall order to obtain Christian acceptance.