Rand summarizes and critiques four traditional answers to those epistemological and metaphysical questions: extreme realism, moderate realism, nominalism, and conceptualism. The two realist schools regard concepts and universals as intrinsic, “as special existents unrelated to man’s consciousness—to be perceived by man directly,” though not by sensory means (53). The nominalist and conceptualist schools regard concepts and universals as subjective, “as products of man’s consciousness, unrelated to the facts of reality” (53).
            In Rand’s theory, concepts are regarded as objective, “as produced by man’s consciousness in accordance with the facts of reality, as mental integrations of factual data computed by man—as products of a cognitive method of classification whose processes must by performed by man, but whose content is dictated by reality” (54).[i]
            David Armstrong’s celebrated treatise on universals appeared in 1978. This watershed work classified all the traditional and contemporary schools (save Rand’s) under a great divide: realism and nominalism. Realism is divided into extreme and moderate realism, where these now include modern varieties, not only ancient and medieval varieties. The realist holds that in mind-independent reality, there are not only particulars, but universals. Nominalism is divided into predicate, concept, class, and resemblance nominalism. The nominalist holds that there is nothing in mind-independent reality besides particulars and that each particular is a single undifferentiated whole.[ii]
           Under Armstrong’s characterization of realism and nominalism, we should say that Rand’s theory is neither. Rand holds that everything in mind-independent reality is a concrete particular. That includes recurring properties and relations. It includes the similarity relation (1, 10, 13–15). Unlike epistemologists in the moderate realist tradition, which includes Armstrong himself, Rand does not take for universals the multiple identical or similar entities, attributes, and actions that exist in mind-independent reality. The constitution of a universal requires also the membership relation and measurement relations in Rand’s view. These are not in mind-independent reality, though their bases are in mind-independent reality.[iii]
           Rand’s theory is not realist, neither is it nominalist. In her view, the properties and relations on which universals and concepts are based—properties and relations such as identity, similarity, and having measurable dimensions—are concrete circumstances that occur independently of whether we grasp them and compose our concepts with them.
           Armstrong’s division of the schools and his arguments concerning their virtues and failings is the main currency with which subsequent academically successful work on universals has been transacted. What Rand had called nominalism would now be called predicate nominalism. What she had called conceptualism would now be called concept nominalism.[iv]
            Predicate nominalism proposes that a particular object is a stone just in case “is a stone” applies to it. To say that the object is an instance of a stone is only to contend that the word stone correctly means such objects as this one. There is nothing more to the universal stone than the meaningful word stone. The universal is merely the shadow of the word.
            One objection to predicate nominalism is that stones are the kind stones before the predicate “is a stone” comes about. How could correctly saying of something that it is a stone be logically prior to the existence of the kind stones? It could not. Authentic predication is identification of identities (Boydstun 1991, 44–45). If identifying any and all concretes were logically prior to the existence of those concretes, then identifications of any and all concretes could be made before any such concretes existed. Like some monotheists, we might imagine such identifications prior to all concrete existence as residing in the divine understanding. This is not logically possible under Rand’s conception of logic. A wholly nonconcrete identifier has no identity and cannot exist (Rand 1957, 1016, 1035–37; 1966–67, 39, 79–82; 1974, 24–31). The existence and identity of some concretes is logically presupposed for authentic identifications. Most stones are among those preexisting concretes. Moreover, identification of stones designed by humans are not logically prior to the identities of these possible concretes. Identification in predication is not logically prior to identity.
           Being specifically a stone is more than having “is a stone” said of it. Predicate nominalism ignores the metaphysical objectivity of universals. The universal said in the general term stone is an aspect of particular existents held in a certain way by conceptual consciousness. 
           Concept nominalism proposes that a particular object is a stone just in case it falls under the concept stone in the mind. But, surely, many particulars were stones before one obtained the concept stone subsuming those particulars. The argument just given against predicate nominalism goes through against concept nominalism.[v]
            Predicate nominalism and concept nominalism do not countenance the circumstance that predicates and concepts are actions of consciousness holding as their object those aspects of existence that are under their correlate universals. They do not countenance universals. That is, they do not countenance the circumstance that the objects of predicates and concepts are aspects of existence held in a certain way by consciousness. These theories neglect universals and so neglect the sound anchorage of predicates and concepts to the world.
            Extreme realism about universals, as Rand remarked, proposes that universals are mind-independent existents that are the archetypes in terms of which concretes may be characterized. The archetypes are to be “perceived by man directly, like any other kind of concrete existents, but perceived by some nonsensory or extrasensory means” (53). A nice modern example of this sort of view is Kurt Gödel’s favored view of the epistemology and ontology of sets, in the theoretical sense of the term sets.

            Any collection of seventeen items is an instance of a certain single self-same finite set, which we may call S₁₇. Gödel thought that just as we perceive by the senses some collection of concrete items that are seventeen in number, so the mind perceives purely intellectually the universal S₁₇ of which that particular concrete collection is a member.

            In Rand’s view, all consciousness is a specific sort of action on a content, and this action is made possible by a specific means. That would be so for a direct intellectual perception no less than for a direct sensory perception (78–82). It is so for direct sensory perception. A sensory perception is an action of consciousness having a content that is some aspect of concrete particular existents.

            Gödel agreed that direct intellectual perception would require some definite means. He conjectured that there was some such means, so far unknown to us, but that it was independent of our sensory means of comprehending existence. To this day, the means of purely intellectual perception that Gödel envisioned remains undetected, not located, and unnecessary to suppose. We have available far less extravagant accounts of the objectivity of sets and our knowledge of them. These accounts invoke means that are at root sensory, and Rand’s is such an account.

            Rand would have us analyze the concept length as an attribute of many kinds of objects (and of the spaces between them). The attribute and its objects are given in perception. We can mentally isolate the attribute and consider it apart from the particular objects in which it has been perceived. Our concept of seventeen inches is a particular magnitude of length applicable to innumerable different objects and regions of space (6–8, 10–11). The concept number and the concept set are demonstrably implicit in the concept seventeen inches, seventeen pears, or seventeen anything. Abstract entities like numbers and sets are traceable to sensory perception. They are ontologically and cognitively objective. There is no need to take them to be intrinsic, no need to take them to be mind-independent archetypes accessed by mysterious means. We can account for them more realistically than is done by extreme realism.
 
[I'll hold off on discussing the relation of Rand's theory to modern moderate realism. There is plenty of thought to absorb from this tablet thus far.]

It seems that under objectivism concepts come in two varieties; true and not-true (false). A true concept would be one which describes some aspect of reality while a false concept describes an illusion.

Historically there have been prominent examples of an alliance between nominalism and Platonism. Abelard and John of Salisbury, the only two defenders of nominalism at the time of the great controversy whose works remain to us, are both Platonists; and Roscellin, the famous author of the sententia de flatu vocis, the first man in the Middle Ages who carried attention to nominalism, is said and believed (all his writings are lost ) to have been a follower of Scotus Erigena, the great Platonist of the ninth century. The reason of this odd conjunction of doctrines may perhaps be guessed at. The nominalist, by isolating his reality so entirely from mental influence as he has done, has made it something which the mind cannot conceive; he has created the so often talked of “improportion beween the mind and the thing in itself.” And it is to overcome the various difficulties to which this gives rise, that he supposes this noumenon, which, being totally unknown the imagination can play about as it pleases, to be the emanation of archetypal ideas. The reality thus receives an intelligible nature again, and the peculiar inconveniences of nominalism are to some degree avoided. (134–35, in Peirce on Signs, J. Hoopes, editor)