For example, the conceptual chain is:
Man -> Animal -> Organism -> Entity
All of these are things that you can point to and say: "There's a Man/Animal/Organism".
The fact that Man is a type of Animal, does that mean that Man is a first level concept and Animal is a second level one?
asked Feb 28 at 17:32
The formulation, "what you can point to and perceive directly," is a close approximation to Ayn Rand's own formulations. The best reference that I know of is Ayn Rand's book, Introduction to Objectivist Epistemology, the chapter titled "Abstraction from Abstractions." A key excerpt from that chapter can be found in The Ayn Rand Lexicon, topic of "Hierarchy of Knowledge":
Starting from the base of conceptual development—from the concepts that identify perceptual concretes—the process of cognition moves in two interacting directions: toward more extensive and more intensive knowledge, toward wider integrations and more precise differentiations. Following the process and in accordance with cognitive evidence, earlier-formed concepts are integrated into wider ones or subdivided into narrower ones.
The "level of abstraction" is the number of antecedent concepts (or conceptual steps) one needs to know before one can grasp the concept in question. This can include integrating lower level (less abstract) concepts into higher level (more abstract) ones, or subdividing less abstract concepts into narrower but nevertheless more abstract ones.
The example, "Man : animal : organism : entity," is a hierarchy in terms of the genus-differentia relation. But a wider genus isn't necessarily a higher level of abstraction if the concept in question involved subdividing less abstract, antecedent concepts. Consider the relation between "animal" and "primate," for instance. My understanding is that "primate" is a more abstract (more specialized) classification even though it is a narrower classification than animal. Likewise for "car" versus "sedan."
Update: Definition of Primate
In the comments, the questioner asks for elaboration of the "level of abstraction" of "primate" (vs. "animal") based on a definition of primate (as a biological category).
Ayn Rand regarded "primate" (in biological usage) as a specialized scientific term, although a lay person can form a rough idea of "primate" by example, e.g., monkeys, chimps, gorillas, humans, etc. To gain a clearer idea of just how technical the term "primate" really is in biology, refer to the Wikipedia article on "Primate." For example, that article lists the following classification structure:
A fairly concise dictionary definition of "primate" (in biological usage) can be found on-line: http://www.merriam-webster.com/dictionary/primate. In basic terms, that definition lists the essential distinguishing characteristics of "primate" as forward-looking eyes, hands that grasp, and brain size relative to body size (vs. other animals). The broad conceptual genus ("Kingdom") is "animal." (Objectivism points out that proper definitions of most concepts need to specify the genus and the differentia. Axiomatic concepts and concepts denoting sensations are exceptions to this principle.)
"Primate" (in biological usage) is formed by subdividing "animal" according to additional characteristics possessed by some animals (the primates) but not by other animals. Ayn Rand offers further discussion of subdividing concepts into narrower concepts in her article, "Abstraction from Abstractions," in ITOE, Chapter 3.
The issue of scientific terminology versus ordinary terms is discussed by Ayn Rand in the Appendix of Introduction to Objectivist Epistemology: Expanded Second Edition (ITOE2), Chapter on "Definitions" (p. 230 hc), subsection on "Philosophical vs. Specialized Definitions" (pp. 233-235 hc). She is specifically asked if it would be valid to define "man" as a "rational primate." She explains that this is not valid because "primate" is a technical scientific term (p. 235 hc):
Philosophical problems have to be solved on a level of knowledge available to a normal adult at any period of human development; so that philosophical concepts are really not dependent on the development of individual sciences. And "primate" or "mammal" would be a very specialized subdivision of a concept according to a particular science.
More broadly, the level of abstraction of a concept rests on how much prior knowledge is needed to grasp the concept. "Animal" can be grasped fairly easily from everyday experience, but a precise understanding of "primate" requires considerable additional knowledge on a more detailed level, within the broad domain of animals in general.
The questioner's comment also briefly mentions the idea of a "set" and its members. It should be emphasized that concepts, in the Objectivist view, are not arbitrary groupings of whatever man finds convenient to group together for some particular purpose. There are specific rules of concept-formation identified by Objectivism as essential for proper conceptual understanding and usability of man's concepts. One such rule is "Rand's Razor," for which explanatory excerpts can be found under that topic in The Ayn Rand Lexicon. The basic principle is:
. . . concepts are not to be multiplied beyond necessity -- the corollary of which is: nor are they to be integrated in disregard of necessity.
The Lexicon excerpts provide additional explanation of what this principle means and how to apply it. ("Necessity" here refers to cognitive necessity.)
Another point important to remember about the Objectivist view of concepts is that a concept is not synonymous with, or created by, its definition. One cannot look only at the definition of a concept to understand the full range and variety of units subsumed by the concept. Refer to the Lexicon topic of "Definitions" for further explanation of the nature and role of definitions.