Asked by cj
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.
Answers
Answered by
GPT-5 mini
No — it is not a good definition.
Why: In logic-terminology the sentence
P: "x is a piece of paper"
Q: "x is an object that can be drawn on"
asserts P → Q (if something is a piece of paper then it can be drawn on). A good definition needs an equivalence (a biconditional): P ↔ (definition condition). That is, the defining condition must be both necessary and sufficient. The given sentence only gives a necessary condition (pieces of paper can be drawn on) but not a sufficient one, because many things that can be drawn on (canvas, whiteboard, wall, fabric, etc.) are not pieces of paper.
Additional problems: the phrase "object that can be drawn on" is vague (what counts as “can be drawn on”? any surface at all?) and does not use genus-and-differentia form (a clear general class plus specific distinguishing features).
A better definition would be specific and biconditional, e.g.:
"An object is a piece of paper iff it is a thin, flat sheet made from processed cellulose fibers (pulp) typically used for writing, printing, or drawing." This gives both necessity and sufficiency and is more precise.
Why: In logic-terminology the sentence
P: "x is a piece of paper"
Q: "x is an object that can be drawn on"
asserts P → Q (if something is a piece of paper then it can be drawn on). A good definition needs an equivalence (a biconditional): P ↔ (definition condition). That is, the defining condition must be both necessary and sufficient. The given sentence only gives a necessary condition (pieces of paper can be drawn on) but not a sufficient one, because many things that can be drawn on (canvas, whiteboard, wall, fabric, etc.) are not pieces of paper.
Additional problems: the phrase "object that can be drawn on" is vague (what counts as “can be drawn on”? any surface at all?) and does not use genus-and-differentia form (a clear general class plus specific distinguishing features).
A better definition would be specific and biconditional, e.g.:
"An object is a piece of paper iff it is a thin, flat sheet made from processed cellulose fibers (pulp) typically used for writing, printing, or drawing." This gives both necessity and sufficiency and is more precise.
There are no human answers yet. A form for humans to post answers is coming very soon!