Sufficient vs. Necessary Conditions

[Gbonoma]

Hello All,

Can someone please use an outside the box or more unconventional method to help explain sufficient vs. necessary conditions? I am particularly having difficulty with these as they relate to the logical reasoning section.

For example, if a question asks to identify the assumption required by the argument. I understand that the assumption should connect the evidence and conclusion but I am having trouble with what to look for, any techniques or ideas for what to consider when tackling these questions is appreciated.

Thank you!

Grace

[Clay Cooper]

Hi Grace,

Thanks for your question, and welcome to the forum! I think it will be a great resource for you.

I am glad that this question fell to me - I think it is one on which I may be able to help you. The first thing I would suggest is going back to review the parts of whichever books you are working from that cover assumption questions and, especially, conditional reasoning. This is really important: even when what the book teaches us is difficult or we have a hard time with it, it is still important to look back and review what the book has to say, and keep practicing; doing so will improve your understanding and make you better at both concepts.

That said, there are several different ways to think about conditional reasoning that I have encountered, some of which are more helpful in certain situations than others. Here are a couple of examples:

-proof ---> proved
This one is most helpful to me in justify and principle questions; I think about what's on the left side of my arrow (sufficient condition) as the proof, and what's on the right side of my arrow (necessary condition) as what is proved by that proof. For example, if firing a rocket into the ocean proves that you're capable of nuclear warfare, here's what we have:
fired rocket capable of nuclear warfare

-if ---> then
Similarly, anytime I can translate a conditional statement into an if, then statement, I can diagram it easily; the if goes on the left (except when it is 'only if'; see lesson 2) and the then goes on the right. For instance, if I said that if you can't get a fair trial, you should stay in Russia, that looks like this:
~can get a fair trial should stay in Russia.

Note that the if, then construct applies even to rules that aren't originally expressed as explicit if, then statements. For instance, this statement can be translated to an if, then statement, and that's how I would attack it: Only ducks walk like ducks. I can translate that to: if it walks like a duck, then it is a duck.

At that point, the diagram (walks like a duck is a duck) is easy.

I hope that helps! Keep working hard and don't get discouraged - conditional reasoning and assumption questions are two of the hardest concepts in LR.