"Necessary if Sufficient" !?

January 19, 2022 10:01 PM

Is the phrase "necessary if sufficient" a term of art in logic or philosophy? If so, what does it mean?

I finished a Coursera philosophy class and the quizzes were basically reading-comprehension multiple choice.

One question style would ask "In this passage, the what can be said about the relationship of fairness to justice?" or some such, and then the answers would be:

A) It is necessary and sufficient
B) It is necessary but not sufficient
C) It is sufficient but not necessary
D) It is sufficient if necessary
E) It is necessary if sufficient

I'm familiar with the the formulations in A, B and C. Furthermore I feel like they are self-explanatory.

But D and E are new to me and, quite frankly, I can't parse them. It's possible they were just decoys to fill up space but if they mean something, can you please explain? Maybe with a simple example?

posted by mark k to Religion & Philosophy (9 answers total)

Best answer: Decoys. Those are nonsensical, meaningless formulations as far as I can tell.
posted by Alterscape at 10:16 PM on January 19, 2022 [23 favorites]

Best answer: They're multiple-choice fluff. They formally have meanings but they're not useful.

"A is necessary for B": A => B
"sufficient if necessary": (A => B) => (B => A)

The only way to have the top-level implication false is (B => A) false. So B true, A false. And (A => B) true, which allows that.

So "sufficient if necessary" <=> "sufficient".
posted by away for regrooving at 11:46 PM on January 19, 2022

Best answer: "A is necessary for B" would actually be B => A, while "A is sufficient for B" would be A => B.
posted by augustimagination at 12:03 AM on January 20, 2022 [4 favorites]

Best answer: (agreed on the multiple-choice fluff! truth-table-wise, "sufficient if necessary" is equivalent to "necessary", and "necessary if sufficient" is equivalent to "sufficient". so you can think of D as just "necessary" and E as just "sufficient" and answer accordingly. as far as philosophical examples, I have no idea as my logic background lies entirely within math)
posted by augustimagination at 12:09 AM on January 20, 2022 [4 favorites]

Best answer: The 2 terms have no relationship; you could say they're orthogonal. Odd phrasing, but I would parse it extremely literally.
posted by theora55 at 6:26 AM on January 20, 2022

Best answer: The only way this is not multiple choice fluff is if there are other conditions. For example if for any X (A & X=> B) => ( B & X => A) gives you option E. There may be cases where X is not met and there is no marginal relationship between A and B.
posted by a robot made out of meat at 7:03 AM on January 20, 2022

Best answer: It depends on what the paragraph says.

Let's consider two cases:
and) Both fairness and truth are necessary for justice
or) Either fairness or truth on their own are sufficient for justice

D) It is sufficient if necessary
and) FALSE Both fairness and truth are necessary but neither sufficient on their own
or) NONE Since neither is necessary on its own, this statement doesn't apply.

E) It is necessary if sufficient
and) NONE. Since neither is sufficient, this statement doesn't apply
or) FALSE Both truth and fairness are sufficient, but neither is necessary
posted by Tell Me No Lies at 7:36 AM on January 20, 2022

Best answer: The basic answer that these are decoy phrases and "not a thing" in philosophy is right. However, in the context of an actual philosophy class you may want to keep in mind that the classical logic take on "necessary"/"sufficient" represented in answers so far as not the only one. To get a better handle on why I say this, it may be useful to have a look at the SEP entry on necessary and sufficient (where the "standard theory" is more or less what answers here have been articulated). Outside the "standard theory" I think there would be various ways of actually making useful sense of those phrases, if one wanted. (For fun, I might suggest going to office hours if this course has that and see what if anything the instructor had in mind...)
posted by advil at 8:47 AM on January 20, 2022

Response by poster: OK thanks all! Best answers all around. After digesting them I can now imagine a question where that phrasing makes sense but am also pretty confident I didn't miss anything subtle in the class itself; they were just filler.

For fun, I might suggest going to office hours if this course has that and see what if anything the instructor had in mind

I did a little Coursera when it first started but not since. Back then there were TA's and active forums; this class felt like sitting in an deserted lecture hall on an abandoned campus and listening to a recording. Made 10 years ago. Office hours would be downright Kafkaesque.

But the lectures and reading were quite good and I got it for free, so shouldn't really complain.
posted by mark k at 11:09 AM on January 20, 2022