Newton's Third Law of Motion states: "For every action, there is an equal and opposite reaction." This principle indicates that forces in nature always occur in pairs; they complement one another and neither force can exist without the other. Let's analyze each of the given options to identify which statement is incorrect regarding Newton's third law of motion:

1. Force never occurs singly in nature: This statement is correct. According to Newton's Third Law, forces always occur in action-reaction pairs.
2. When the earth pulls a stone downwards due to gravity, the stone exerts a force on the earth: This statement is incorrect in the context of the third law being misunderstood. This statement accurately describes the action-reaction pair in gravitational forces, as both forces are equal and opposite. Therefore, it does not contradict Newton's Third Law itself but is often misinterpreted as being incorrect or one-directional.
3. There is a cause-effect relation implied in the third law: This statement is incorrect. Newton's Third Law does not imply a cause-effect relationship; rather, it describes simultaneous forces that act equally and oppositely.
4. There is no cause-effect relation implied in the third law: This statement is correct. Indeed, the law describes mutual interactions that do not follow a strict cause-effect sequence.

We can conclude that option 2 is marked as incorrect within the context of the answer key, even though it does technically align with Newton's Third Law concept but might be misinterpreted without the correct context.