The Art of Logic · Part 4 · Words and terms · B2
Extension and Intension: How Much a Term Covers
Part 4 of The Art of Logic: every term has two sides: the things it covers, and what it says about them. Add a quality and you cover fewer things. The comparative correlative (the more…, the fewer…) and words of quantity (more, fewer, less), with Philo, Sophia, Marcos and Demetria.
Tonight, two words that sound alike and mean opposite things: extension and intension.
With an s. Extension is how many things a term covers. Intension is how much it tells you about them.
Like the two pans of a scale. When one goes up, the other goes down.
The extension of a term is the set of things it applies to. The extension of “animal” is every animal that exists. Logicians also call it the term’s denotation.
The intension of a term is the set of qualities it implies: “animal” implies a living, sensing body. Logicians also call it the term’s connotation. Careful: in everyday English, connotation usually means the feelings a word carries, as when “cheap” has a negative connotation and “inexpensive” does not. Logic uses the word in its older, stricter sense.
Sister Miriam Joseph states the rule simply: as the intension of a term increases, its extension decreases. “Animal” covers millions of creatures; “dog” says more and covers fewer; “sheepdog” says still more and covers fewer still.
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