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In ordinary English (also natural language) "necessary" and "sufficient" indicate relations between conditions or states of affairs, not statements. For example, being a man is a necessary condition for being a brother, but it is not sufficient—while being a man sibling is a necessary and sufficient condition for being a brother.
The absence these conditions guarantees the outcome cannot occur, and no other condition can overcome the lack of this condition. Further, necessary conditions are not always sufficient. For example, AIDS necessitates HIV, but HIV does not always cause AIDS. In such instances, the condition demonstrates its necessity but lacks sufficiency.
Tests of sufficiency in biology are used to determine if the presence of an element permits the biological phenomenon to occur. In other words, if sufficient conditions are met, the targeted event is able to take place. However, this does not mean that the absence of a sufficient biological element inhibits the biological event from occurring.
Cause-in-fact is determined by the "but for" test: But for the action, the result would not have happened. [1] (For example, but for running the red light, the collision would not have occurred.) The action is a necessary condition, but may not be a sufficient condition, for the resulting injury.
Wherever logic is applied, especially in mathematical discussions, it has the same meaning as above: it is an abbreviation for if and only if, indicating that one statement is both necessary and sufficient for the other. This is an example of mathematical jargon (although, as noted above, if is more often used than iff in statements of definition).
Example 1. One way to demonstrate the invalidity of this argument form is with a counterexample with true premises but an obviously false conclusion. For example: If someone lives in San Diego, then they live in California. Joe lives in California. Therefore, Joe lives in San Diego. There are many places to live in California other than San Diego.
However, in logic, the technical use of the word "implies" means "is a sufficient condition for." [3] That is the meaning intended by statisticians when they say causation is not certain. Indeed, p implies q has the technical meaning of the material conditional: if p then q symbolized as p → q. That is, "if circumstance p is true, then q ...
Consider lung cancer as an example. Smoking is a major component cause of lung cancer, but not everyone who smokes develops lung cancer. Other component causes might include genetic predisposition, other environmental factors, etc. Only when all necessary component causes are present does the sufficient cause of lung cancer come into play.