The art of thinking · Concepts, categories and definition
Intension and extension
Also known as: Intension, Extension (logic), Comprehension and extension, Sense and reference
German: Intension und Extension
In logic and semantics, the intension of a term is its meaning — the properties something must have to fall under it — and its extension is the set of things it actually applies to.
- Thinking models
- Philosophy
- Logic
In one sentence
A term’s intension is its meaning or defining properties; its extension is the set of things it actually applies to.
Example
The intension of “safety-relevant parameter” is a definition; its extension is the list of 37 parameters in a given machine. Changing the definition can change the list — so the list needs the definition next to it.
How it applies
- History: The Logic of Port-Royal (1662) distinguished the comprehension of an idea from its extension. Frege’s distinction of sense (Sinn) and reference (Bedeutung, 1892) and Carnap’s intension and extension (1947) refined it: “the morning star” and “the evening star” have the same extension, Venus, but different intensions.
- Inverse relation: Adding features to an intension usually narrows the extension — the more specific the definition, the fewer things fall under it.
- Definitions of both kinds: An intensional definition states properties (genus and differentia); an extensional definition lists the members.
- Technical documentation and metadata: A metadata value has an intension (what the value means) and an extension (the items tagged with it). Classification schemes stay usable when the intension of each value is written down, so that new items can be tagged consistently.
Intension vs. extension in variant lists
“Applies to all variants with option B” is intensional and stays correct when variants are added; a list of variant numbers is extensional and has to be updated. Both are valid — the documentation should know which one it uses.
How to read this pool
Entries, context cards and transitional topics
The art of thinking explains ways of thinking — where a method comes from, what it asks of you and how it was adapted later. You meet four kinds of content here, each with its own job:
- Glossary entry
- Defines one concept or method of thinking: its origin, an example and how it relates to neighboring ideas. “X vs. Y” sections set two methods side by side.
- Context card of the art of thinking
- A short, self-contained answer to one question about a way of thinking — its lineage, its steps, its limits. These cards are listed on The art of thinking only.
- Transitional topicBridges both pools
- A context card that bridges both pools: it shows how a way of thinking was adapted into documentation, analysis or quality practice. It sits with the reference context cards and is marked as transitional wherever it appears.
- Reference entry or context card
- Belongs to the Glossary & Norms Space on regulation, norms and engineering. Entries here link to one only where a method is also an established tool of documentation or quality work, such as the five whys or a user’s mental model.