The question of necessary and sufficient conditions for something relates to how we evaluate arguments. A necessary condition for an event is something which is absolutely required to exist or happen if the event is to occur. An example of this would be the existence of oxygen for human life - without oxygen, we could not live. Therefore, the existence of oxygen is a necessary conditon for human life.
A sufficient condition for an event, on the other hand, does not have to exist for the event to occur, but if it exists, then the event will occur. To continue with our above example, the absence of oxygen is a sufficient condition for human death. Human death can happen without the absence of oxygen and does not require the absence of oxygen. However, if oxygen disappears, then people die. Thus, an absence of oxygen is a sufficient condition for human death.
A more formal way for saying that one thing, p, is a sufficient condition for some other thing, q, would be to say "if p then q," which is a standard hypothical proposition. Confusing necessary and sufficient conditions is one way to understand how some of the rules of inference with hypothetical propositions can be violated. The fallacy of affirming the consequent, for example, makes the assumption that a sufficient condition is also a necessary condition.
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