Question

Use what you know about compound statements to determine if "A piece of paper is an object that can be drawn on " would be considered a good definition. Explain.

Answer 1

Short answer: No — it’s not a good definition.

Why (using compound-statement / logical reasoning):
- Let P(x) mean “x is a piece of paper” and D(x) mean “x is an object that can be drawn on.” The proposed definition asserts P(x) ↔ D(x) (P iff D).
- For a good definition both directions should hold:
- Necessity: P(x) → D(x). “If x is paper then x can be drawn on.” This is not always true (e.g. some papers are waxed, laminated, or coated photo paper that resist ordinary drawing). So the implication can fail.
- Sufficiency: D(x) → P(x). “If x can be drawn on then x is paper.” This is false (whiteboards, walls, cloth, glass, canvas, cardboard, etc. can be drawn on but are not pieces of paper).

Other problems: the terms are vague — “object” is overly broad, and “can be drawn on” is ambiguous (what kinds of marks, with what tools?). As a compound statement it’s only a conjunction (“object” AND “can be drawn on”), which is too weak and too broad to uniquely pick out paper.

Better form: use genus and differentia. For example: “A piece of paper is a thin, flat sheet made from cellulose pulp or fibers, commonly used for writing, printing, or packaging.” This gives clear, necessary, and (mostly) sufficient conditions.