Conditions - Am I Understanding This?

rdyoung12

-so if you fail a sufficient condition, the rule "goes away" ?
-but if you satisfy a necessary condition, the rule also "goes away" ?
-you would not want to rely on a contrapositive of any of these rules in these two situations above?

Matt Sorr

To address your bullets in numbered order:

1. Correct
2. Correct
3. No, you don't need to consider contrapositives in these situations

Think about it like this: if the sufficient has been failed, it doesn't matter if the necessary is failed, because failing the necessary would lead to you taking the contrapositive and negating the sufficient (which has already happened since the sufficient was failed).

If you satisfy the necessary, it doesn't matter if the sufficient condition is confirmed or failed, because confirming the sufficient would just lead to the necessary being satisfied, which has already happened, and failing the sufficient, as mentioned above, always means the rule disappears.

I hope this helps some! When I first started heeding JY's advice to quickly disregard a rule if the sufficient was failed or the necessary was satisfied, it felt super unnatural to me. I second guessed myself a bunch and felt flustered. Once you get in the routine of doing it, though, it'll start to feel natural and you'll save a bunch of time by quickly moving through the rules.

rdyoung12

EDIT/UPDATE: this 7Sage lesson explains it: https://7sage.com/lesson/conditional-rules-trigger-v-irrelevant/

Yes, that does help and I'm grateful for your reply. But I'm still stuck in a bit of a mental rabbit hole. I guess I'm wondering about inferences we can make about the other element not found to be false.

@"Matt Sorr" said: Think about it like this: if the sufficient has been failed, it doesn't matter if the necessary is failed, because failing the necessary would lead to you taking the contrapositive and negating the sufficient (which has already happened since the sufficient was failed).

So, in the case of a sufficient being failed, must the necessary be false or is the status of the necessary simply unknown here? If the sufficient is failed, is the contrapositive true? or is it only a maybe could be true? we just don't 100% know what happens to the necessary in this case without more info.

@"Matt Sorr" said: If you satisfy the necessary, it doesn't matter if the sufficient condition is confirmed or failed, because confirming the sufficient would just lead to the necessary being satisfied, which has already happened, and failing the sufficient, as mentioned above, always means the rule disappears.

In the case of a necessary being true then the sufficient must also be true? That makes sense assuming that is correct.
Or in this case the sufficient could be true?

Matt Sorr

@rdyoung12 Apologies for the late reply. Been away from my account for a bit.

So, in the case of a sufficient being failed, must the necessary be false or is the status of the necessary simply unknown here? If the sufficient is failed, is the contrapositive true? or is it only a maybe could be true? we just don't 100% know what happens to the necessary in this case without more info.

If a sufficient is failed, the status of the necessary is unknown. Here's an example:

Every time it rains, Bob plays video games. So the logical relationship would be (raining) --> (Bob plays video games). The sufficient condition is it raining and the necessary condition is Bob playing video games. If I then tell you that it's not raining, we'd negate the sufficient. So we know it's not raining, but does that mean Bob won't play video games? We have no idea. Maybe Bob also plays video games on some days when it doesn't rain. Maybe he doesn't. We've just got no clue, so the necessary is unknown.

In the case of a necessary being true then the sufficient must also be true? That makes sense assuming that is correct.
Or in this case the sufficient could be true?

If the necessary is true, we know nothing about the sufficient. That means it's not the case that the sufficient must be true but rather that it could be true. I'll use the same example from above to illustrate this:

(raining) --> (Bob plays video games). If I tell you Bob is playing video games, it confirms the necessary condition. Therefore, it's possible that it's raining, but it's also possible that it's not. This is because if it's raining, Bob has to play video games, and we already know that Bob is playing video games, so it's totally possible that it's raining. If it's not raining, that doesn't affect the fact that Bob is playing video games. Sure, every time it rains Bob plays video games, but that doesn't mean Bob only plays video games when it rains. Maybe he also busts out the Xbox every time he gets happy, or every time his dog barks, or every time he eats, etc.

Sorry if this still doesn't clear it up!