Necessary and sufficient

kristymoawad

I understand that this is probably a dumb question but I keep having difficulties with flaw questions that have answers that "confuse necessary and sufficient conditions."

This is what I understand so far:
If I eat an apple, I will be healthy.

So eating an apple is a sufficient condition to being healthy since I can be healthy through other ways as well. It doesn't have to necessarily be by eating an apple.
I just know that if I eat an apple, I will definitely be healthy. To reiterate, being healthy doesn't necessarily have to do anything with eating an apple.

So if I say:
1. if I eat an apple, I will be healthy
2. I am healthy
3. I ate an apple

Is that confusing necessary for sufficient? Which flaw is this?

Can I have an example of both types of confusions (confusing necessary for sufficient / sufficient for necessary)?

Thank you!

fishtwentyfive

If you do this:

1. A > B
2. B
Conclusion: A

then you have confused the necessary condition (B) as a sufficient condition for acquiring A, which is not supported by the premises.

If you do this (where ~ means 'not'):
1. A > B
2. ~ A
Conclusion: ~B

then you have confused the sufficient condition (A) as being necessary for the existence of B. You have essentially claimed not B simply because A is not present. B might be around for some other reason; it might have some other sufficient condition.

kristymoawad

Okay. I had more trouble with confusing sufficient for necessary.


This problem came up for me when I was working on PT 73 section 4, question 25:

I > T
L > T
L
Conclusion: I

For my answer I incorrectly put, "taking a necessary condition for L to be a sufficient condition"

The answer is "taking a necessary condition for I to be a sufficient condition"

So is this flawed argument assuming that:
I > T
L > T
L
T (assumption)
T > I (illogical)
I (conclusion)

Am I doing this right?

fishtwentyfive

The flawed argument works in this manner, like you've illustrated:

1. I > T
2. L > T
3. L
4. T
5. T > I
Conclusion: I

But note that arriving at T (4.) is actually not an assumption; it's derived validly from premises 2 and 3. But yes the 'illogical' move is thinking that you can derive (T > I). This is where the confusion lies, namely confusing the necessary condition for I as the sufficient condition for I.