Thinking in Definitions

From the time I first read Ayn Rand’s theory of concepts, almost sixty years ago, I have thought of myself as someone who thinks in definitions.
 
Why? All our knowledge, with the exception of proper nouns, consists of concepts. Combinations of concepts that make important connections to each other are called principles. When concepts and principles are well crafted, they become extremely illuminating, to myself, of course, but also to others when I write and teach. In simple terms, thinking in definitions means I know what I am thinking and talking about and, I would hope, others, my students and readers, also understand what I am saying.
 
Unfortunately, definitions today, if any attempt at a definition is made, fall into the “kinda, sorta, maybe, let’s assume” category, or are the positivists’ nonobjective arbitrary constructs, useful only in pushing words around in rationalistic discussions or writing. Textbooks, in particular, provide definitions that are too long and wordy, nonessential, and violate most of the rules of good definition.
 
What is a good definition? One that identifies genus and differentia of the referents being defined, that is, the general category within which the referents are distinguished and their essential distinguishing characteristic, which as Ayn Rand states, is the one that explains and causes most or all of the other distinguishing characteristics.
 
Human beings, for example, are animals that possess the capacity to reason. “Animal” is the genus and “capacity to reason” is the differentia, the characteristic that explains and causes all or most of the others that humans share, such as the ability to speak a language or to build skyscrapers. The definition is concise and, as Rand says, summarizes and condenses all our knowledge of humans in the “file folder,” to use Rand’s metaphor, stored in our minds.
 
Note that we all have our own file folders of humans that can be thin (for a child), thick (for most adults), or fat (for, say, a biologist or psychologist). The definition is written, to continue the metaphor, on the outside of the folder with the word that denotes the concept written on the tab.
 
The rules of a good definition are straightforward—identify genus and differentia but also ensure that the definition is truly essential and is not too broad or narrow, circular, vague, obscure, metaphorical, or, if possible, negative. It does require practice to become competent at the skill.
 
Thinking in definitions can also be thought of as thinking in ranges of measurement. Ayn Rand identifies abstraction as measurement omission, but that does not mean we forget about the measurements. It means that in the process of identifying the differentia of a concept we must be aware of the “stopping points” or boundaries of those measurements that are omitted. In this process, we limit the concept to a certain range. 
 
Tables, for example, are not a mile long, nor are they only one inch long. Bridges are flat with supports and hold objects called automobiles, but bridges are not tables. A toy table may be flat with supports and hold tiny teacups and saucers, but it is not the type of table adults eat dinner on.
 
The concept “human” is based on the range of measurements that describes our distinctive type of mental processing and distinguishes it from that of the higher mammals, the lower end of the continuum being the point at which we observe humans using reason to form and apply concepts, but not the higher mammals.
 
When the boundaries of cholera, to use three examples from McCaskey’s article “Induction in the Socratic Tradition,” were narrowed to an illness involving an “organic poison,” after dismissing season of year and foul water as competing causes, Robert Koch further narrowed the range of measurements, the cause and differentia, to the bacterium he called the comma bacillus. When Charles Wells, after many experiments, narrowed the boundaries of dew to droplets created in accordance with the laws of heat, particularly liquefaction, he recognized that condensation from vapor in the air was the cause and differentia. In both cases, the range of measurements of the respective differentia, comma bacillus and water condensation, were sufficiently limited to establish the concepts as universal.
 
Lord Kelvin concluded, after two hundred years of imprecise and often inaccurate tidal measurements, that Newton had been right, namely that tides are ocean movements that result from gravitational pull of the sun and moon, measurements omitted.
 
There are options in the formation process, as Ayn Rand points out, because different concepts may use different “stopping points” in the continuum. Hence, the English word “man” can be a synonym of human being or, using the range of measurements describing male and female anatomy, can mean a male person. The Yiddish word “mensch,” now an accepted part of the English language, means a rational, volitional human being who acts with integrity and honor. 
 
Options in concept formation are what make translation from one language to another challenging, because the range of measurements used in the concept’s formation differ from language to language. Keeping in mind the continuums that constitute our concepts enables us to maintain contact with reality, the reality of the different-but-similar referents we are discussing.
 
Thinking in well-constructed definitions especially enables us quickly to bring to mind the meaning of broad abstractions—abstractions from abstractions, and concepts of consciousness. Thinking in not-so-well-constructed definitions leaves us with the “kinda, sorta, maybe, let’s assume” category that even academics are guilty of, rationalists and positivists in particular.
 
The favorite vehicle of argumentation of these rationalists and positivists is to make grossly unrealistic assumptions and then announce, “Let’s assume, by definition, that dogs can fly or that humans are “brains in a vat,” and see where that takes us. If, by definition, they mean, and they usually do, arbitrary, disconnected floating abstractions and flimsily constructed tautologies, which violate all the rules of good definition, knowledge can be anything they want it to be, which is where we are today as consequence of Immanuel Kant’s inability to find reality and his positivist followers who restricted awareness of reality to the level of perceived concretes.
 
Flying dogs (and maybe brains in a vat) may make interesting fiction, but they do not make good science. In economics, the doctrine of pure and perfect competition does not even make good fiction—“perfect” information, that is, omniscience, just being one of its absurd assumptions. (See Kirkpatrick, In Defense of Advertising, 118–21.)
 
Concepts, to emphasize, are not “true by definition.” A concept, and its definition, is “true by reality,” that is, true by our having correctly identified the referents in reality and having summarized and condensed the file folder’s content for ease of use. They are open-ended in the sense that they apply to all referents of the same kind, past, present, and future—because they are classifications and cross-classifications (in our minds) of reality.
 
Concepts and their definitions are cognitive necessities, and they are constructed to meet cognitive needs. They are not “out there,” embedded in the concretes of the world. As Rand states, concepts and essences are epistemological, not metaphysical.