Conditional Reasoning Language

[PB410]

Hi,

I'm kind of confused at times in identifying the sufficient and necessary conditions when I encounter certain wording. An example is from the LRB when covering if and only if:

Anna will attend if and only if Basil attends.

Which comes out to
1. A and B both attend
2. Neither A nor B attend

I am more interested in the language when you break down the original premise:
1. A if B
and
2. A only if B

A if B confuses me, because it reads as B A,
while A only if B is structurally reversed A B

The term if is usually used to introduce a sufficient, so I am confused why B would be the sufficient = B A

[Dave Killoran]

Hi PB,

Thanks for the question! The short answer is that in "A if B," the "if" modifies B, and thus B is the sufficient condition and A is the necessary condition, resulting in a B A diagram. In the second diagram, "only if" introduces a necessary condition, and thus the diagram is reversed. Thus, in short:

"If" introduces a sufficient condition.
"Only if" introduces a necessary condition.

I know that is tricky, but it's a great example of how small differences in language can result in a huge difference in meaning!

The long answer is something I've talked about previously, and this thread contains a complete explanation of the relationship, and then a set of links to related articles and discussions: lsat/viewtopic.php?t=13591&p=33075

Please take a look at that and let me know if it helps. Thanks!