Extension, Comprehension, and Generalizations

In logic, terms become the smallest building blocks of arguments. A term is any word or phrase that denotes a commonly known concept. Now by connecting two terms in a proper declarative sentence, one can form a proposition – and through the assertion of two or more true propositions, one can reason their way to a logical conclusion.

Obviously terms should be used clearly and unambiguously – but they should also be understood in themselves in two ways: by their extension and their comprehension (or intension). The chief difference between the two is that extension is quantitative while comprehension (or intension) is qualitative. Extension thus means the ability to count out all the objects in the world that are denoted by the term. For example, the extension of the term “All United States citizens” refers to all the 300+ million people who are members of the U.S. Now the comprehension (or intension) is qualitative because it forms the logical definition of the term, including the term's attributes, features, or qualities. In other words, extension is concrete while intension is abstract.

This logical dichotomy, which originates with the ancient Greeks, is one helpful way of sorting out the problem of political correctness when it comes to matters of gender. In his logic textbook, Socratic Logic, Dr. Peter Kreeft states:

…so many people today… immediately and thoughtlessly reject all “generalizations” like “men are more aggressive than women” as “stereotypes.” They are confusing comprehension and extension. They are misinterpreting a statement about comprehension as if as if it were one about extension, and that is why they think that the fact that Mrs. X is more aggressive than Mr. X disproves the statement that “men are more aggressive than women.” They cannot or will not rise to the original statement’s level of abstraction and argue with it on its own level. The statement is not about all the individuals that have the nature of male and the nature of female, but about those natures in abstraction from the individuals that have them. Those who reject all rationalizations because they can find some exceptions to them are thinking only on the concrete sense level of extension, not on the abstract conceptual level of comprehension; they are operating like cameras (sense experience) plus computers (calculating the quantities of extension), but not like human minds (understanding essences, natures, “whats”).

Nominalism – which is commonly found in our colleges and drilled into the minds of the politically correct – denies any reality of essences or natures and thus it declares that there are only individuals, only particulars; no universals. Accordingly there is no male and female nature, nor any human nature – only equal individuals with equal rights. Nominalism is thus a key source of radical egalitarianism and individualism.

But on the side of common sense Aristotelian reason, it is precisely because we can know essences or natures that we can say that (for example) effeminacy in males is a vice, not a virtue, nor an amoral reality, because it is contrary to the masculine nature. Cameras and computers, to use Kreeft’s analogy, cannot know natures because they are not minds – but we do have God-given minds, so let’s use them instead of speeding up a process of devolution in the name of rights and political correctness.

G.K. Chesterton would say that it is the exception that proves the rule. This is precisely because he knew the difference between extension and intension. Natures or essences are unchanging – but our society is bent on trying to “disprove the rule” (i.e. the nature) through the promotion of the unnatural. This is all the more reason for Catholics (both lay and clergy) to faithfully live out a rich sacramental and liturgical life. In the world we are bombarded with self-defeating nominalism, but in the liturgy we can find the truth and reality of male and female expressed tangibly.