Beyond “Unless”: Advanced Conditional Reasoning

It’s fair to say that conditional reasoning is either the bane of your test prep, or a welcome escape from the uncertainty that plagues causal reasoning.  In the first few months of test prep, you will likely see conditional reasoning everywhere: understanding conditional reasoning can easily turn into an obsession, prompting you to diagram whenever you come across any of the indicators of conditionality. The costs of this approach ultimately outweigh the benefits. As you progress through your studies, you will hopefully develop a more careful, judicious approach to diagramming. As we’ve said in the past, you should diagram only when you think it will help you better understand what the author is saying.

Now, look at the last sentence in the previous paragraph. Conditional reasoning is front and center in that sentence, thanks to the fairly uncommon necessary condition indicator only when. In recent years, test makers have made a concerted effort to convey conditionality using relatively unexpected phrasing, in part because they know that most test-takers have learned the basic approach to the more common conditional constructions. Here’s how you want to handle the less common ones:

Not Until 

Not until is primarily a temporal preposition, which literally means “not before a stated time or event.” Not every sentence using this construction will convey conditional dependence. When it does, the grammatical structure of these sentences is shown in the diagram below:

Not until [1st clause: subject + auxiliary verb] [2nd clause: auxiliary verb + subject]

The conditional relationship between the two clauses is as follows:

S                                 N

2nd clause    →    1st clause

For example:

Not until the car came to a complete stop did we see the damage to the front bumper.

S                                 N

See damage    →    Complete stop

Not until the stars aligned did I win the lottery

S                                 N

Win lottery   →    Stars aligned

Not until I got into Yale did I stop worrying about my future

S                                 N

Stop worrying   →    Got into Yale

In all of these examples, the clause that follows immediately after the preposition not until is the necessary condition. The remainder of the sentence functions as a sufficient condition. The same would be true with not unless and only when. All of these are necessary condition indicators.

None But, None Except, No… Except

The language immediately following these indicators is the necessary condition; the remainder is the sufficient. Think of all three of these indicators as synonymous with the word only – a classic necessary condition indicator. Let’s take a look at a few examples:

None but the brave die young.

S                                 N

Die young    →    Brave

None of the students finished the test, except for those who had prepared for it.

S                                 N

Finish test   →    Prepared

No cars except SUV’s  can safely travel this road.

S                                 N

Safely travel   →    SUV

Only vs. The Only

The difference between only and the only is small, but critical. Whereas only is a classic necessary condition indicator, the language immediately following the phrase the only is actually the sufficient condition. For instance, the following pairs of statements are identical in meaning, even though the first statement uses the word only, whereas the second uses the phrase the only:

Invitations were extended only to wealthy donors

Wealthy donors are the only ones who were invited

S                                 N

    Invite    →  Wealthy donors

Only sports cars can drive this fast

The only cars that can drive this fast are sports cars

S                                 N

Drive fast  →    Sports cars

All Except, All But

Unlike none except and none but, which are synonymous with only and function as simple necessary condition indicators, all except and all but are a bit more complicated: they must be translated not as single conditional statements, but as pairs of conjoined conditional statements. Such statements are also known as exceptive propositions. Let’s take a look at an example:

All but 1st year associates received a raise.

The sentence above contains a pair of conditional relationships: 1) no 1st year associate received a raise; and 2) everyone who is not a 1st year associate did:

S                                 N

1) 1st year associate   →    Receive a raise

2) 1st year associate   →   Receive a raise

Now, let’s consider the contrapositives of each conditional relationship:

S                                 N

1) Receive a raise   →    1st year associate

2) Receive a raise   →   1st year associate

When each of the two original relationships is combined with the contrapositive of the other, the two resulting propositions amount to the following bi-conditional relationship:

S                                 N

1st year associate    ←→    Receive a raise

Contrapositive:        Receive a raise    ←→   1st year associate

In other words, only one of two outcomes are possible: either you are a 1st year associate who didn’t receive a raise, or else you are not a 1st year associate who did receive a raise.

Keep in mind the above is not an exhaustive list of sufficient and necessary condition indicators: the more common ones have been discussed extensively on our Forum, Blog, and, of course, the Logical Reasoning Bible and LSAT course materials. If your goal is a top-1% score (and why would you want anything less?), it is important to prepare for each and every eventuality. As you’ve probably heard, curve balls on the LSAT are the new normal.