Conditional Reasoning Diagramming Drill #4

[Morgan O'Donnell]

My question is from the drill #4 :

T dances sixth only if P dances third... the posted solution is T6 ---> P3 but why is the solution P3 ----> T6 ? in this instance P must dance third for T to dance 6?

thanks anyone...

Jerry

[Dave Killoran]

Hey Jerry,

I had your messaged reposted after it was accidentally deleted. That was my fault entirely. Sorry!!

that aside, let's look at the question you ask. The key is to examine the conditional sentence:

T dances sixth only if P dances third

In this sentence, the conditional indicator "only if" appears. While "if" alone is a sufficient indicator, "only if" is a necessary indicator, and thus P3 is the necessary condition T6 is thus the sufficient condition, resulting in the following diagram:

T6 P3

Please let me know if that makes sense. Thanks!

[Jerry.C]

Dave, sorry about the posting area.. and thanks for the response, that one is still fuzzy but your answer helps. Thanks.

[Dave Killoran]

No worries--the mistake was on our part!

Think of "only" as a very dominant word. "Only" by itself introduces a necessary condition. So, when you see a sentence with "only" in it, whatever it modifies becomes the necessary condition.

The confusion here comes because "if" is a sufficient condition indicator, and typically when you see "if," that is modifying the sufficient condition.

So what happens when the two are combined and we see "only if" ? That's when it gets confusing. But, the rule is that "only" is dominant, so "only if" is actually a necessary condition indicator, and whatever it modifies is automatically the necessary condition. In this case, "only if" modifies P3, so that's our necessary condition. It's great because I don't have to think through the situation, I can just respond to the indicators and know what the diagram is automatically.

Does that help explain it a little better?