Beginning Conditionals II: Necessary and Sufficient

Among the tasks we're charged with on the LSAT are recognizing and avoiding confusion with necessity vs. sufficiency. On the arguments section, mixups about necessary and sufficient circumstances constitute a good number of the flaws we deal with. On games, mistaking a necessary condition for a sufficient one (or vise versa) will typically cost you two or more answers.

In most cases, the idea of necessary and sufficient can be expressed conditionally in the form:

sufficient --> necessary

On the LSAT, if an event or condition is sufficient to bring about a result (or to know information about something else), it always brings about that result (or reveals that information). For instance, spending too long in sunlight is sufficient to cause sunburn. Too long in the sun goes on the left side (the sufficient side) of our conditional.

TLS --> SB

Much of this is counter-intuitive because in the real world we have things like sunscreen. In LSAT Land, however, when I tell you spending too long in sunlight causes sunburn, it causes sunburn no matter what SPF you're wearing.

Where things begin to get confusing is when we start to think about the necessary side of our conditional. From my original premise, we can infer that a sunburn is necessary to spend too long in the sun. What? That's right. Now in the real world, again, this is silly. How can basking too long in the sun lead to sunburn if sunburn is a requirement for basking too long in the sun? By my original statement, you haven't actually been in the sun too long until you've at least gotten a sunburn. I know this because of the contrapositive (the other thing I know to be true).

TLS --> SB
~SB --> ~TLS

If you don't have a sunburn, you haven't spent too long in the sun. SB was a necessary condition (on the right side of my conditional) for TLS. If I remove the necessary condition (~SB) then I necessary remove what was sufficient to cause it (~TLS).

Notice what's happened here. My necessary condition, when negated, became a sufficient condition for something else. Likewise, my sufficient condition, negated, became necessary for my negated necessary condition. (Confused yet?) Look at these statements again.

TLS --> SB
~SB --> ~TLS

Spending too long in the sun is sufficient to get a sunburn. Getting sunburned necessarily follows spending too long in the sun (and is, in fact, requisite for doing so).

Not getting sunburned, then, is sufficient to tell you that you haven't spent too long in the sun. Not spending too long in the sun is necessary to avoid sunburn.

Another familiar example to think about is your car. Gas is necessary for your car to run. Putting gas on the necessary side of my conditional yields:

R --> G

If your car runs, then it's got gas. The contrapositive says:

~G --> ~R

Without gas, the car doesn't run. Why? Gas is necessary for it to run. Removing a necessary condition is sufficient to tell you the other side of your conditional won't happen. Not having gas is sufficient to prevent the car from running.

The LSAT writers confuse these ideas quite a bit and it's your job to notice. An argument might say "In order to run, a car must have gas. Joe's car won't run, so he must be out of gas." This isn't necessarily true, however, as many things can stop your car--bad fuel pump, no oil, brick wall, etc.

The argument could also have been written "In order to run, a car must have gas. Joe's car has gas, so it will run." Having gas is great, but the fact that vandals stole the engine is going to be a slight obstacle to operating Joe's vehicle.

The lesson here is that necessary conditions aren't necessarily sufficient, and sufficient conditions aren't necessarily necessary. Gas (necessary to run the car) isn't sufficient to run it--you need oil and spark plugs and stuff. Being out of gas (sufficient to stop the car) isn't necessary to stop it--other problems can do the job just fine. Running the car (sufficient to let you know you've got gas) isn't necessary to let you know--there are other ways. The car not running (a necessary result of being out of gas) is not sufficient to tell you you're out of gas--you might have mechanical problems.

In the first Beginning Conditionals post, I gave an example about eating peas. The mistake I made as a four-year-old was between necessary and sufficient. Eating all my peas was necessary for me to be allowed outside, but it was not sufficient.

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