A little room to wonder

Concepts & Definitions

A definition makes a term usable within a stated context. Test its criteria against examples instead of relying on a familiar-looking picture.

What must something satisfy before your chosen label applies?

A wooden tangram set with coloured pieces arranged inside a square frame.
Tangram pieces can be grouped by stated properties. The photograph does not determine the fictional blue-tile rule; that rule is supplied in the worked example.Nevit Dilmen · Source · CC BY-SA 3.0

Give the word a job

A label can group things without explaining the grouping rule. A definition supplies criteria for how a term is being used. In a paper game, the author can introduce a new term and state its rule. In another context, an established term may already have a convention that needs to be checked.

A description need not be a definition. Saying that a tile is blue describes one feature; it does not settle whether every blue object is that kind of tile. Ask which features the proposed rule requires and which merely happen to appear in the example.

Worked example: define an invented tile category

An invented game defines a sun tile as a blue, four-sided tile. Card A is a blue triangle, B a blue quadrilateral, C a yellow quadrilateral and D a blue circle. Only B satisfies both stated conditions. A and D meet the colour condition; C meets the side-count condition. One condition alone is insufficient.

Change the definition to a blue tile or a four-sided tile. Now all four qualify. The cards have not changed; the connective has. Record the revised wording rather than claiming that the earlier sorting was mistaken under its original rule.

Check both boundaries

A useful test includes a clear example and a near miss. If an intended example is excluded, the definition may be too narrow for the purpose. If an unintended case qualifies, it may be too broad. Those judgements require a stated purpose, not just a preference for one result.

Mathematical categories can be nested. Under the usual definition of a rectangle by four right angles, a square remains a rectangle. Extra properties can identify a special case without removing it from the broader category. A typical sketch is not the category boundary.

Keep the rule and observation separate

Inventing a label does not establish a fact about nature. The game author may define sun tile, but deciding whether a real drawing has four straight sides still involves examining it. If an edge is hidden, the honest answer can be not enough information.

Use a short rule, test cases and a revision note. This keeps clarification manageable: another reader can identify whether they dispute the definition, a recorded feature or the result of applying the rule. No personal labels are needed.

Only if you feel like trying

Test a definition

  1. Write the original sun-tile rule and draw or label the four supplied cards.
  2. Sort them using and, then repeat using or. Keep both rules visible.
  3. Add one uncertain card with a hidden edge. State which observation would settle its classification.

Optional paper or spoken reasoning with supplied fictional examples. No personal beliefs, experiences, accounts, purchases or public sharing are required.