The Objectivist Theory of Concepts

The Objectivist theory of concepts is the only valid theory of concept-formation, here I will be explicating what it entails about the specifics of how a given concept is formed.

The very first stage of awareness involved in the formation of concepts is that of sensation. To move from this stage onto the level of perception one must differentiate different qualia and separate them out of the chaotic mess that is directly provided by the senses. These separated stimuli are then automatically integrated into distinct entities---we get not just "brownness," "smoothness," "woodenness," etc. as distinct information, but the specific entity that is a table (note: on this level the concept "table" does not yet exist---its just a thing, I highlight what it is that I am speaking about only such that the reader can understand what entity it is that is being integrated here).

Then, still on the perceptual level, it is possible for some higher animals to differentiate certain individual entities---this thing as against that thing. A dog can recognise his owner out of a crowd of people (and non-people, again, the dog has no concept "man" yet), because he has learned the specific attributes that his owner has as against those other entities with which he has become acquainted.

These key processes of differentiation and integration are necessary also for the move from perceptual to conceptual:

We begin the formation of a concept by isolating a group of concretes. We do this on the basis of observed similarities that distinguish these concretes from the rest of our perceptual field. The similarities that make possible our first differentiations, let me repeat, are observed; they are available to our senses without the need of conceptual knowledge. At a higher stage of development, concepts are often necessary to identify similarities—e.g., between two philosophies or two political systems. But the early similarities are perceptually given, both to (certain) animals and to men.^[1]

What makes man unique in this process of observing similarities between different entities is his power of abstraction---his ability to mentally separate out those relevant aspects of what he perceives from whatever other aspects are there. Man is capable of selectively focusing only on the attributes shared by all tables, and ignoring those that are not---man can ignore that different tables differ in their dimensions, their colour, their specific texture, etc., and focus only on what is essential to tableness. Animals are not capable of this process---the animal (at best) gains only the observed similarities embedded within an entire entity that cannot be cognitively ignored.

Once a man has separated these aspects out from a number of particulars and grouped them together, his cognitive task is not yet complete. In order to form a concept he must integrate this group---"blending all the relevant [attributes] into an inseparable whole."^[2] This "mental entity"^[3] is then able to stand in for an infinite number of possible permutations that might be found^[4] in concrete examples in the future---we can now, when we see a new table immediately grasp it not as its own entirely unique particular, but as a unit of the concept "table."

So, to summarise, the formation of a concept goes as follows:

1. differentiation of qualia (e.g. the individual sensations of brown, smooth, cold, etc.) within the constant noise on the sensational level---perceptual;
2. integration of differentiated qualia into entities (a complete object that is brown, smooth, and cold)---perceptual;
3. differentiation of entities (this thing as against that thing)---perceptual;
4. abstraction of differentiated entities (having a certain number of legs, having this certain pattern, having a flat top)---conceptual, and;
5. integration of abstracted aspects into concepts ("table")---conceptual.

The final piece of this puzzle is found in Ayn Rand's recognition that concept-formation is fundamentally a mathematical process. On the level of abstraction (4), man differentiates the certain groups of entities by reference to their commensurable characteristics---i.e. those aspects that can be reduced down to the same unit of measurement. Then on the level of integration (5), we can only integrate into a unit those concretes whose differences are differences in measurement only---we cannot arbitrarily form whatever concepts we want, the thing that is the "same" between different concretes which are of the same concept is that they share attributes but not the measurements of those attributes. "No aspect of the process is capricious. In both its parts, concept-formation depends on our mind's recognition of objective, mathematical relationships."^[5]