Philosophy · Make

A definition that needs revising

When does an invented category become too broad or too narrow?

Invent a precise category for five supplied shape cards, including a boundary case. Your definition must tell another reader what to do.

15–25 minutes, or one comparison for a first try. More time is optional.

A irregular quad and B square each have one inside dot. C triangle has one, D rectangle has two, E rectangle has a dot on its boundary.
A definition is a usable membership rule. Open full-size diagram ↗

Start here

Call the target category “one-dot quad”. Card A is an irregular quadrilateral with one dot inside; B is a square with one dot inside. These are your intended examples.

Use your idea or the example below. Talk, write, draw, point or listen first. You can stop after one step.

Try it your way.

  1. Add three near-misses

    C is a triangle with one inside dot. D is a rectangle with two inside dots. E is a rectangle with one dot centred on its top edge. These are deliberately different cases.

  2. Test a broad definition

    “A shape with a dot” wrongly includes C, D and E. It does not state side count, exact dot count or whether an edge counts as inside.

  3. Test a narrow definition

    “A square with one inside dot” keeps B but wrongly excludes intended example A. A definition can exclude something you meant to include as well as include too much.

  4. Write the working definition

    For this game use: “A closed four-sided shape with exactly one dot strictly inside.” Apply it again: A and B pass; C, D and E do not. “Strictly inside” excludes the boundary.

One possible version

A definition is a usable membership rule

All five cards and the category name are invented for this activity.

  • A and B are intended members even though their side lengths and angles differ.
  • The final rule requires four sides, exactly one dot and an interior position. Each requirement removes a different near-miss.
  • C fails side count; D fails exact dot count; E fails the strictly-inside condition.

This is a locally invented category, not a new official geometry term. Agreeing a rule is different from proving that a word has always meant it.

A different way.

Compare only A, B and C first. Cards may be described aloud, enlarged or marked by a scribe; drawing neatness is irrelevant.

If you want more.

Add a four-sided outline with a curved side and decide whether your use of “side” needs clarification. State any revised convention before sorting it.

Something to keep?

Which single word in my definition changed a card’s membership?

You can keep a question, a sketch or a change of mind. A finished product is optional.

This opens an editable starter in your project tools. It asks before replacing open work. Choosing it does not save or share your work automatically.

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