Comprehension: This refers to the *meaning* or *intension* of a concept – the defining properties or characteristics that determine whether something belongs to that concept. It answers the question: "What makes something a member of this category?"
Extension: This refers to the *set of things* to which the concept applies – all the individual instances or members that satisfy the definition. It answers the question: "What things are members of this category?"
Here are some examples to illustrate the difference:
Example 1: "Even numbers"
* Comprehension: An even number is an integer that is divisible by 2 without any remainder. This is the defining characteristic.
* Extension: {..., -4, -2, 0, 2, 4, 6, 8, ...} This is the infinite set of all even numbers.
Example 2: "Red objects"
* Comprehension: A red object is an object that reflects light predominantly in the wavelengths corresponding to the color red. This is a more complex definition involving physics.
* Extension: This is a vast and ever-changing set including apples, fire engines, stop signs, certain birds, etc. The exact extension is practically impossible to list completely.
Example 3: "Prime numbers less than 10"
* Comprehension: A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. "Less than 10" further restricts the set.
* Extension: {2, 3, 5, 7} This is a finite and easily listable set.
Example 4: "Shakespearean tragedies"
* Comprehension: This is a subjective concept involving literary analysis. It usually implies a play written by Shakespeare that features a protagonist's downfall due to a tragic flaw, often resulting in death.
* Extension: {Hamlet, Macbeth, King Lear, Othello, Romeo and Juliet, ...} While there's generally agreement on core members, some plays might be debated (e.g., is *Measure for Measure* a tragedy?).
Key Differences Summarized:
* Comprehension is about the *meaning* or *defining properties*. It's intensional.
* Extension is about the *set of things* that fit the meaning. It's extensional.
The comprehension of a concept may remain the same, but its extension can change based on new discoveries or changes in understanding. For example, our understanding of "planet" (comprehension) changed, leading to a change in its extension (Pluto was removed from the list).