No discussion of conditional statements would be complete without a thorough review of sufficient conditions. Luckily, and entirely coincidentally, that’s the topic of today’s post in our ongoing review of diagramming LR questions.
Simply put, the sufficient guarantees the necessary. As long as the sufficient condition is satisfied, the necessary must follow. For example:
“If you study hard, then you’ll do well on the LSAT.”
To illustrate this relationship, we’ll want to diagram the above with the sufficient condition leading to the necessary condition, in the form of:
Suff. —> Necc.
Thus, for this particular conditional statement, we would diagram:
SH —> DW (Study Hard —> Do Well)
So what happens if we satisfy the sufficient? Well, if it is in fact the case that we studied hard, then we know based on the conditional above that we’ve triggered the necessary, and that it is also the case that we will do well on the LSAT.
This particular sentence employs our favorite indicator word for sufficient conditions: “if.” “If” is a great tip-off that we’re looking at the sufficient condition. Its counterpart, “then,” indicates the necessary. The order in which “if” and “then” (or their equivalents) appear is not important; what matters is the Suff. —> Necc. structure. For instance:
“I’m not going out with you if you wear that fedora.”
This sentence actually has the sufficient condition following the necessary, unlike in the last example. But we wouldn’t diagram the statement in that order, because the sufficient is still triggering the necessary, not the other way around. Thus, recognizing that the “if” is giving us the sufficient condition, we diagram:
GOWY (Wear Fedora —> not Going Out With You)
Keeping the right order is essential. Reversing the sufficient and necessary conditions leads to a conclusion known by logic geeks the world over as the “Converse Fallacy,” which A) is invalid, B) produces a non-representative diagram, and C) is typically frightfully absurd.
“If you’re a dog, then you’ve got a tail.”
The above should be diagrammed:
D —> T (Dog —> Tail)
The converse fallacy would then be T —> D, which reads “If you have a tail, then you’re a dog.” But I can’t play fetch with my iguana, and there are numerous odd Youtube videos displaying human caudal appendages, so this is clearly not true.
Accurate identification of the sufficient and necessary statements is absolutely key for diagramming, but it doesn’t have to be too difficult. Even in the absence of familiar indicator words, reframing the statement as an “if-then” conditional will be sufficient to guarantee your success.