A term does two jobs at once. It points to things, and it carries an idea of what those things are like. Traditional logic gives each job a name.
Key idea
The extension of a term is the set of things it applies to. Its comprehension (also called intension) is the set of features it implies. Add a feature, and the comprehension grows while the extension shrinks or stays the same.
Why it works
Every feature you add is one more test a thing must pass. "Dog" applies to every dog. "Black dog" applies only to the dogs that also pass the "black" test, so fewer things fit. "Small black dog" adds a third test, and fewer still pass. The tests pile up (comprehension grows) as the crowd that passes them thins out (extension shrinks). If every member already had the feature, the crowd stays the same size, which is why we say "shrinks or stays the same".
| Term | Comprehension (features) | Extension (things) |
|---|---|---|
| animals | living, able to move and sense | every animal |
| mammals | + hair, nurses its young | every mammal |
| dogs | + the features of a dog | every dog |
| sheepdogs | + bred to herd sheep | only the sheepdogs |
Worked examples
Worked example: Ordering terms
Which has the greatest extension, and which the greatest comprehension: "lemons", "fruits", "citrus fruits"?
- Line them up from wide to narrow: fruits → citrus fruits → lemons. Every lemon is a citrus fruit, and every citrus fruit is a fruit.
- The widest term applies to the most things: "fruits" has the greatest extension.
- The narrowest term carries the most features (fruit, citrus, and lemon): "lemons" has the greatest comprehension.
Answer: extension: fruits; comprehension: lemons
Worked example: Thing or feature?
For the term "planet", is "Mars" part of the extension or the comprehension? What about "orbits a star"?
- Mars is one of the things the word "planet" applies to: extension.
- "Orbits a star" is a feature every planet has: comprehension.
Answer: Mars: extension; orbits a star: comprehension
Common mistake
Expecting both to grow together. A richer idea is a narrower idea: as comprehension grows (dog, black dog, small black dog), extension shrinks or stays the same. Check with a picture: each new feature is a smaller circle drawn inside the last one.