BY JONATHAN DOLHENTY, PH.D.
THE PROBLEM OF KNOWLEDGE
A Brief Introduction to Epistemology
The Comprehension of an Idea
The Extension of an Idea
The Relation between Comprehension and Extension
Comparison of Comprehension and Extension
The Nature of Ideas: The Comprehension of an Idea, The Extension of an Idea, The Relation between Comprehension and Extension
The Comprehension of the Idea
The comprehension of an idea is the sum total of all the attributes or thought-elements which constitute the idea in its representation of a thing. Sometimes this is also referred to as the connotation of an idea. The comprehension or connotation of an idea gives the content of the idea.
Let’s take our idea of “human being” for an example. What elements are important? Human beings are a substance with a material body that is living, sentient, and rational. The elements&emdash;substance, material body, living, sentient, rational&emdash;form the comprehension of the idea of “human being.” This tells us what a “human being” is. A plant is a living material substance. This is its comprehension. An animal is a sentient living material substance. This is its comprehension.
The Extension of the Idea
The extension of an idea is the application of this content to the individuals and groups in which it is found. It is the sum total of all the individuals and groups to which can idea can be applied. For the idea of “human being,” the extension will include each and every individual which is a human being, from the first human being to the future human being. For the idea of “dog,” the extension will include each and every dog that ever existed and will exist in the future. Sometimes the extension of an idea is called its denotation.
A couple of things need to be said at this point so there’s no confusion. First of all, an idea can refer to something which has no actual existence other than in your mind. We can have ideas of dragons and unicorns, for example. The extension of these ideas would include all the dragons and unicorns that were ever thought or described. Secondly, some ideas may have an extension which includes only a single individual. The idea of “the tallest building” can have no more than one member in its extension. The same holds true for such ideas as “the highest mountain,” “the strongest man,” and “the last state to join the United States.”
We must also be careful sometimes about how we apply the extension of an idea. Language and custom may cause confusion. We may use an idea which ordinarily signifies an entire class of individuals but which we may not mean for it to do so. We may make a statement in which we really mean to include only a limited portion of the extension of an idea. When I was growing up in a Dutch community, it was not uncommon to hear Irish neighbors say “The Dutchman is a stubborn person.” I don’t think they intended to convey the idea that each and every Dutchman was stubborn, but that many of them were. This is a use of language which must be watched in the course of an argument. It has to be realized that the extension of the idea of “Dutchman” is being limited in this case. Logicians call this limitation of the extension of an idea the universe of discourse. It has no value for logicians since it is arbitrary and subject to mere convention.
The Relation Between Comprehension and Extension
Usually logicians say that the comprehension of an idea can be neither increased nor decreased without changing the idea itself. This is especially true when we consider class-ideas where the comprehension is clear and fixed. The comprehension simply contains the essential elements of the class. If an essential element is taken away, it would certainly change the whole idea of the thing.
Consider again the idea of “human being.” The essential elements are substance, material body, living, sentient, and rational. Take out any one or more of these essential elements and what happens? Well, we don’t have the same idea of “human being” anymore, do we? The idea of “human being” is clear and fixed and if its comprehension is increased (by adding an additional element) or decreased (by taking an element away), the idea is not the same as it was before.
Unfortunately, we don’t always have a clear and fixed comprehension of every idea. Take, for instance, the idea of “virus.” We simply don’t know at this time whether a virus is a plant-form or an animal-form. A virus exhibits characteristics which cause some confusion. Botanists and zoologists both claim it for their study. So the idea of “virus” is not so clear and fixed at this time.
The comprehension of the idea of “whale” used to include that of “fish.” This was once considered an essential element of the idea. (Remember how the biblical story of Jonah was first presented to you?) But science came along and proved that the whale is really a mammal. So the element of “fish” had to go and the essential element of “mammal” entered into the comprehension of “whale.”
It seems that the farther we go from the broad classes in nature and the closer we come to particular individuals, the more difficulty we experience in uncovering the really essential elements which distinguish one from the other. Our ideas in these cases may not be fixed and clear and exact. We are making new discoveries all the time and that shouldn’t bother us at all.
Regardless of what has been said above, the general rule of comprehension still holds. The comprehension of an idea can be neither increased nor decreased without changing the idea itself.
There is a similar rule about the extension of an idea. This rule says that an idea can be increased or decreased without destroying the idea. This simply means that the comprehension of an idea can be applied to more or fewer individuals without any change in the idea as such. The idea of “human being” will remain the same whether it includes one individual or millions of individuals. The idea of “dog” will remain the same whether it includes all dogs or just my Lhasa Apso, Ming. Trees and weeds die, but the ideas of “tree” and “weed” continue on without change.
There are two general rules in considering comprehension and extension, or connotation and denotation. The first rule says: The comprehension of an idea always remains the same, while the extension of the idea may change continually.
The second rule says: As the comprehension of an idea increases, the extension of the idea decreases; and as the extension of the idea increases, the comprehension of the idea decreases.
The chart below may help you understand these general rules.
|Living material substance|
|Sentient living material substance|
|Rational sentient living material substance|
Dr. Jonathan Dolhenty was the Founder and President of The Center for Applied Philosophy and the Radical Academy, and is Honorary Philosophy Editor at Self-Educated American. Self-Educated American has adopted these projects beginning with a republishing and preserving of all of Dr. Dolhenty’s work.