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Can you help me wrap my head around conditional reasoning?

Asked by drdoombot (8145points) November 6th, 2009

I understand how conditional reasoning works symbolically, with arrows and contrapositives and the like. However, I don’t get it. It sort of doesn’t make sense in my mind. Specifically, I don’t get sufficient and necessary conditions, other than the order in which they are supposed to appear. Here’s how one of my study books describes sufficient conditions:

A sufficient condition can be defined as an event or circumstance whose occurrence indicates that a necessary condition must also occur.

And here’s necessary conditions:

A necessary condition can be defined as an event or circumstance whose occurrence is required in order for a sufficient condition to occur.

Huh? They sound almost exactly the same! A sufficient condition makes a necessary condition occur, and a necessary condition is required for a sufficient condition to occur. This almost makes them sound interchangeable when I know they definitely are not. Reading those definitions makes me feel like I’m going in a circle. Like saying “Apples come from apple trees because apple trees make apples.”

Maybe I’m thinking to hard about the meanings of the words “sufficient,” and “necessary,” or maybe I’m tired, but something isn’t clicking for me…

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