Kent Worthington on Similarity and Difference

How Ideas Work Review Series: Part II

G. Stolyarov II

A Journal for Western Man-- Issue XLIV-- December 19, 2005

            Note: This is the second of five articles discussing Kent Worthington’s innovative book, How Ideas Work. The first article is “Kent Worthington on Consistency and Contradiction.

            Mr. Worthington opens the second chapter of How Ideas Work—“Similarity and Difference”—discussing concept formation in small children and how this process greatly broadens the children’s ability to refer to the world around them. If a child merely points at a book, for example, he can only refer to a present book immediately in front of him. However, by using the word, “book,” he is able to refer to any book—past or present, directly accessible or not, existent or not. Any book that has the potential to be written is encompassed by the concept, “book.”

            Pointing does not suffice to achieve the same breadth as conceptual knowledge, because it is impossible to point to an entity’s characteristics—those attributes which cannot exist except as incorporated into the entity. An entity’s shape, color, and spatial dimensions are among such characteristics. One cannot identify “the color red” by moving one’s finger in its direction. One can only point to a red book, but this is insufficient for analyzing color qua characteristic. One can only isolate the characteristic mentally, for the purpose of analysis, without actually altering the material properties of the entities being analyzed. This is the purpose concepts serve: to arrange and rearrange entities in a plethora of mental “piles” on the basis of essential common characteristics.

            A single entity can be organized into a multitude of mental piles depending on its characteristics. A given book—for example—can be put into the pile of “novels” on the basis of its content and the pile of “paperbacks” on the basis of its cover’s material. Both a novel and a newspaper can be put into the larger pile of “printed material.”  The process of abstraction allows the mind to overcome a significant perceptual limitation: the fact that “[a] perceptual entity cannot be in two places (two piles) at the same time” (36). By using words and concepts, one can leave the perceptual entity where it was originally and yet place it into as many mental piles as is warranted by the entity’s actual characteristics.

            Two considerations are required to form a concept: similarity and difference. One must ask both how the entities classified under a specific concept are similar to each other and how they differ from all others not included in the concept (37). Many concepts identifying perceptual entities, such as “dog,” “tree,” or “man” are first based on the essential characteristic of shape: the shape of a tree is required for an entity to be classified as a tree. Concepts for nouns identifying perceptual entities are typically formed with shape as the organizing characteristic.  Essential characteristics on which concepts for adjectives are formed may include size, color, and texture: the corresponding concepts might be “big and small, black and blue, hard and soft” (37).

            Mr. Worthington draws an explicit connection between his theory of concepts and Ayn Rand’s comparison of a concept to a “file folder” which contains all the entities with the essential characteristic defining the concept. The “file folder” is open to including any and all entities that share this characteristic—whether or not these particular entities are presently known.

            The process of abstraction, “of mentally isolating a characteristic from its entities and focusing on it, as opposed to the entities themselves” (39), can enable one to form higher-level concepts—identifying entities on the basis of characteristics that exist in reality, but whose evidence is more complex and less directly perceptible. “Property” is such an abstract concept—and it requires considerable discernment to determine which entities fit into the mental pile, “Joe’s property.” It is not enough to look at Joe and all the entities in his vicinity, because some of those might not belong to Joe, and Joe might have other more remote entities that do belong to him. Property must be examined in an interspatial, intertemporal context: it is the result of the individual applying his mind to reality in order to either transform entities from their original “state of nature” or to obtain through consensual trade entities that have already been thus transformed. Only an extensive hierarchy of abstract concepts, including “labor,” “mind,” “state of nature,” “consent,” and “trade” will enable one to arrive at the idea of “property.”

            There are two levels at which concepts are formed. The primary level of abstraction is based on directly evident perceptual characteristics, such as shape. The shape of a book enables one to categorize it under the concept, “book.” Higher-level concepts, however, are formed on the basis of characteristics of which man is not automatically aware. A “novel” is such a concept, whose essential characteristic is not shape, but rather a book’s content. Higher-level concepts are dependent on primary ones—and must be in order to maintain their tie to reality—just as the concept, “novel,” is dependent on the concept, “book.”

            Essential characteristics and relationships enable one to form higher-level concepts. An essential “refers to a relationship where something does not occur without something else” (42). Without a given essential characteristic, Entity X would cease to be Entity X; for example, without a thumb, a given man would continue to be a man. Without a brain, however, he will not be able to function as a man—nor as anything else, for that matter. Having a brain is an essential characteristic of man, whereas having a thumb—while useful—is not (42).

Mr. Worthington examines essential relationships through the designations of “broader” and “narrower.” “[T]he broader concept is essential to the entities of the narrower one” (44), and all the entities of the narrower concept are encompassed by the broader concept. For example, “book” is the broader concept whereas “novel” is the narrower one. The concept, “book,” is essential to the concept, “novel,” and all novels are also books.

Forming the higher-level concept, “novel,” enables one to narrow one’s mental focus, whereas other uses of abstraction on the basis of essentials enable one to broaden that focus. One can begin with “narrower” perceptual concepts, such as “dog” and “cat” and discover a characteristic the two concepts have in common—locomotion. On the basis of this essential characteristic—without which dogs and cats would cease to be dogs and cats—one can place both dogs and cats in the category of “animals,” a higher-level concept than the ones leading to its formation. All the particulars unique to dogs or cats are omitted in forming this concept, because they are not essential to animals qua animals. An animal can have pointy ears or round ones and still possess the essential characteristic of locomotion.

As one forms concepts of ever higher levels, one needs to continuously ascertain their relevance to reality. Definitions are indispensable to this task—as they make clear precisely what actual entities a given concept refers to. A proper definition for a concept includes a genus, “a concept, broader than the one being defined, which distinguishes the entities of the defined concept from all other entities that lie outside the genus” (53). The definition also requires a differentia, “the characteristic (often a set of characteristics) that distinguishes the entities of the defined concept from all other entities that lie inside the genus” (53). The sum of the genus and differentia forms the definition. Applying this insight to today’s cultural and intellectual “mainstream” will expose numerous blatant fallacies, including the idea of the “trade deficit.”

Mr. Worthington analyzes the proper definition of a deficit: “a measurement of spending  (genus) that exceeds funds available (differentia)” (55). When one country has a “trade deficit” with another, however, no party spends more than the funds available to it; every individual and firm involved pay for the goods they receive with money they actually possess. The nations are not doing the spending, either; the private parties who trade goods and services are. Thus, the concept of the “trade deficit” fails to meet the definition of “deficit” in both its genus and its differentia. It is a pseudo-concept, smuggled into the “deficit” file by opponents of free trade, who use the connotation of deficits as dangerous and undesirable to thereby unjustifiably portray free trade with other countries as dangerous and undesirable.

What enabled the enemies of free trade to attack it by creating pseudo-concepts was the lack of clear definitions for abstract concepts in most people’s minds. Another prevalent method of the “mainstream” assault on man’s conceptual faculty comes in the form of “package deals.” The term “extremist” has been used with ever-increasing frequency to denounce someone as dangerous or undesirable. Yet Mr. Worthington asks:

Is the relationship an essential one? What about carrying honesty or integrity to extremes? Should a judge carry justice to extremes in his courtroom? Should a chef carry culinary excellence to extremes in his kitchen? Should a child carry to extremes the requirement of looking both ways before he crosses the street? Obviously, extremism with regard to many actions is most desirable and certainly not dangerous (58). 

By claiming that “Islamist fanatics are dangerous because they are extreme,” mainstream ideology seeks to instill in its followers the presupposition that anything extreme is dangerous—that only the average, the mediocre, the moderate, the blurry, the approximate, and the perpetually doubt-ridden is appropriate for a “safe” society. In fact, however, Islamist fanatics are dangerous because they are Islamist and fanatical. Dangerousness is not essential to extremism. One will be dangerous if one carries a bad idea to extremes, but bad ideas in moderation are dangerous as well—in some respects more so, because their influence then becomes more subtle and insidious. Good ideas in extremes can only bring about extreme good—and are desperately needed in today’s society, which will otherwise “moderate” itself to death.  

               How does one escape fallacies like those of “trade deficits” and “extremism”? One learns to define concepts on the basis of essentials; one always makes sure that one’s definitions are clear, precise, and linked inextricably to reality. Mr. Worthington’s system helps individuals learn to think for themselves and access the real world, freed from dangerous popular misconceptions.

You can order How Ideas Work at

G. Stolyarov II is a science fiction novelist, independent filosofical essayist, poet, amateur mathematician and composer, contributor to organizations such as Le Quebecois Libre, Enter Stage Right, and the Autonomist.  Mr. Stolyarov is the Editor-in-Chief of The Rational Argumentator and a Senior Writer for the Liberal Institute ( He can be contacted at

This TRA feature has been edited in accordance with TRA's Statement of Policy.

Click here to return to TRA's Issue XLIV Index.

Learn about Mr. Stolyarov's novel, Eden against the Colossus, here.

Read Mr. Stolyarov's comprehensive treatise, A Rational Cosmology, explicating such terms as the universe, matter, space, time, sound, light, life, consciousness, and volition, here.

Read Mr. Stolyarov's four-act play, Implied Consent, a futuristic intellectual drama on the sanctity of human life, here.

Visit TRA's Principal Index, a convenient way of navigating throughout the issues of the magazine. Click here.