Here's a breakdown:
* Idea: A thought or suggestion about something. It's a concept, a plan, or a possibility.
* Ideal: A standard of perfection or excellence. It's a vision of how something should be.
Relationship:
* An idea can be an ideal: For example, "the idea of world peace" could be considered an ideal.
* An ideal can inspire an idea: An ideal of a better society might spark an idea for a new social program.
Contradiction:
* While an idea can be an ideal, not all ideas are ideals. Many ideas are simply practical or mundane.
* An idea may not be achievable or even desirable, while an ideal usually represents a positive aspiration.
In summary:
"Idea" and "ideal" are connected but distinct. An idea can be an ideal, and an ideal can inspire ideas, but they are not synonymous.