The Problem of Universals consists of the question: To what do people refer when we use terms that can be applied to different particular things? For example the term “man” is applied not just to one entity, but to many entities that are each called a “man.” Another example is “spherical.” Many different things can be said to be “spherical.” An answer to the Problem of Universals will explain how this use of single terms for multiple different objects works.
In Introduction to Objectivist Epistemology, (ITOE) Rand claims to have solved the ancient Problem of Universals. She describes in detail the process by which man forms generally applicable concepts from his perceptions of particulars in reality. Critics sometimes charge that Rand is giving us an epistemological theory when a solution to the Problem of Universals calls for an ontological theory. (Ontology, properly conceived, is the branch of metaphysics that deals with the most fundamental classification of existents; it is the study of “what there is,” metaphysically.)
But considering the Problem of Universals purely ontological, and thus considering Rand’s theory of concept formation irrelevant to it, improperly privileges variants of “Realism” (about universals) by treating the rejection of such abstract objects as sufficient to define a single theory (variously referred to as “Nominalism” or “Anti-Realism.”) The rejection of universals in external reality does not specify a positive theory of what universals are and how they are related to external reality. Much more explanation is required to do this, as evidenced by the various subcategories of Nominalism/Anti-Realism. In ITOE, Ayn Rand presents an alternative theory on the level of the variants of Anti-Realism in the Internet Encyclopedia of Philosophy. (i.e. Predicate Nominalism, Resemblance Nominalism, Trope Nominalism and Conceptualism.)
While I think Rand gives the reader enough to decide on her ontological views in ITOE, she does not emphasize the specifically ontological basis of her theory in the main text of the book, as I recall. (Note that the appendix of ITOE contains a lot of material worth reading.) Her focus is mainly methodological and developmental.
The comments below were made by me on reddit in this thread. In them, I am explaining my understanding of the ontological basis of Rand’s theory of concepts. I mostly confine myself to describing the position, rather than arguing at length for it and against other theories. (Though I do give some demonstrative examples.) My reddit username is Sword_of_Apollo:
Sword_of_Apollo: I think a good deal of confusion about the status of universals is generated by the fact that, in order to describe anything in discussion, we have to use concepts. In discussions like this, we have to clearly and carefully distinguish the wordless percept from any concept used to describe it.
So what do we actually perceive? We perceive this entity with its own inseparable properties/actions. We perceive another entity with its own inseparable properties/actions. We perceive a third entity with yet another set of inseparable properties/actions. The external things we perceive by extrospection are sheer particulars. In themselves, the entities do not partake in external universals of any kind: not common essences and not common properties.
Ayn Rand says that we form basic concepts of entities by differentiating and integrating perceived entities on the basis of differences and relative similarities, omitting measurements of the isolated entities to complete the integration.
“Very well,” a Rand critic might say, “I see how we can form concepts of entities without positing entity essences, such as ‘horseness’ or ‘manness.’ But what about universal properties? Don’t entities have to metaphysically partake in universal property existents, such as ‘whiteness’ and ‘sphericality’ in order for us to have commensurable things to measure (and omit the measurements from) in the formation of concepts of entities and concepts of properties?”
No. What we are measuring and omitting the measurements from are the discreet, perceived entities, with their integral properties and actions, not disembodied property universals. When our senses measure and our minds omit measurements, they are using relationships among particular entities. (1)
Relationships are a separate class of existents. They are “metaphysically dependent” existents, like properties and actions, and unlike entities themselves. (They are actions, properties and relationships “of something.”) But they are not entities and are not properties; they are irreducible existents, not to be “explained by” (mischaracterized as) abstract objects or metaphysically shared properties. Like other aspects of entities, (actions, etc.) some relationships are directly perceived as aspects of reality and are epistemologically primary, [e.g. “above,” “behind,” “faster than,” “more blue-looking than.”]
So when we describe something as “blue,” we are referring not to an abstract object, but to a perceived relationship between how the object looks to us and how other “blue” objects look to us, as against “red” objects. The relationship between the “blue” objects is closer than the relationship between either of them and the “red” object, as determined along the wordless perceptual dimension that we conceptually describe as “color.”
To emphasize the lack of abstract objects, I’ll take a few examples and show how we can conceptualize metaphysically different properties under one “universal.”
Imagine two sheets of paper we would call “white” and indistinguishable in color. They must have the “whiteness” universal in common, right? Well imagine that you look at them with an ultraviolet-sensitive camera and find that one of them has much greater reflectivity in the UV. These papers both look white to us, but if we only saw UV light, would we be tempted to say that they both share a “universal color property” in common? I don’t think so.
Look at the center of a peacock’s tail feather; it’s blue. Find a piece of paper that matches that shade of blue. Do they share an abstract property object? Well, we know that the physical basis for the blue color of the paper is the absorption of the other colors of light. The peacock feather, on the other hand, gets its blue from the scattering and interference of white light, rather than absorption of a large part of the visible spectrum. A different set of properties generates the same “color” relationship with our eyes and other objects.
A cannonball and an inflatable rubber ball are described as having the same shape: spherical. Yet one gets its outward shape by being a solid chunk of lead, whereas the other gets its shape from being pressurized with air. The inflatable ball can easily lose its shape by being punctured with an ice pick. The cannon ball is not so susceptible. A different set of properties has given rise to what we describe as a “common shape” (a relationship of similarity along the wordlessly perceived dimension of “shape,” as against cubical things, etc.)
So if one strictly defines “nominalism” as the rejection of abstract objects in extrospective reality, then Objectivism is nominalist. According to Objectivism, universals are real only qua aspects of consciousness. Also, contrary to the mainstream nominalism that I’m aware of, Objectivism holds that concepts have an objective basis in the reality of entities and their integral properties, actions and relationships. They have, overall, an epistemologically mandatory structure and objectively proper definitions at each level of knowledge. They are not mere conventional conveniences based on vague, subjective “similarities.”
Sword_of_Apollo: On reading a bit of ITOE, I came across Rand’s definition of a concept:
A concept is a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted.
Given that this definition mentions units having the same distinguishing characteristics, one might wonder if the charge of /u/respighi that “realism [about universals] is smuggled in through the back door” is accurate; that Ayn Rand assumes that particular entities participate in universal objects called “characteristics.”
But my explanation is this: Rand does not mean that there is any thing literally the same in different entities. Remember that we are describing wordlessly perceived objects by means of concepts. We describe and relate entities in terms of the abstraction, “characteristics.” We have already gone through the process by which we can regard different objects as “the same” in certain respects, even though they are not literally, perceptually identical in any way.
A way to describe the relationships of commensurability among entities we perceive, by means of concepts, is to say that the objects have “the same characteristics, but different measurements.”
But in perceived reality, the particular “measurements of a characteristic” cannot be separated from the entity.
One might fault Rand here from a metaphysical/ontological perspective for not making this more explicit and clear, but I don’t think it’s a fundamental flaw in the content of her theory. It’s also possible, in my current view, that the definition of concepts should be reformulated in terms of relationships to eliminate the seeming implication of literal sameness in different entities. But to really say for sure, I’d have to do some deeper thinking about it.
So the ontological basis of Ayn Rand’s theory of concepts lies in all ontological categories, including particular entities, integral properties of particulars, integral actions of particulars, and, especially relevant to the Objectivist theory as against others, relationships among particulars. This recognition of the role of relationships pervades the Objectivist philosophy throughout. It has very important consequences for epistemology and for moral theory.
Both the main text and the appendix of Introduction to Objectivist Epistemology is highly recommended.
(1) Some evidence of Ayn Rand’s concern with the importance of relationships as part of the metaphysical basis for measurement (and hence, for concept formation) from ITOE: “Measurement is the identification of a relationship–a quantitative relationship established by means of a standard that serves as a unit.” p. 9 [emphasis mine]
“Measurement is the identification of a relationship in numerical terms–and the complexity of the science of measurement indicates the complexity of the relationships which exist in the universe and which man has barely begun to investigate.” p. 39 [emphasis mine]