Diagramming “Unless” Conditional Statements

The word ‘unless’ indicates the presence of a conditional relationship, but diagramming such statements into our more familiar if A, then B visual form (e.g. A➝ B) can be more precarious than usual. The best way to avoid mistakes is to consistently apply a formulaic approach.

The Unless Formula works as follows:

⎯ 1. Isolate what follows the indicator word unless.
⎯ 2. Treat it as the necessary condition.
⎯ 3. Negate the remaining element.
⎯ 4. Use it as the sufficient condition.

Let’s try to apply the formula from above—one step at a time—using the following example:

Unless you take the LSAT, you cannot apply to law school.

1. Isolate what follows the indicator word unless.
   “…take the LSAT”
2. Treat it as the necessary condition.
   [_] ➝ Take the LSAT
3. Negate the remaining element.
   “…you cannot apply to law school” becomes “you can** apply to law school”
4. Use it as the sufficient condition.
   Apply to Law School (AL) ➝ Take the LSAT (LSAT)

** Keep in mind that two negatives make a positive.

This gives us the following diagram:

AL ➝ LSAT

What that diagram means is that if you applied/apply to law school, then you must have taken the LSAT. That makes sense! Unless you take the LSAT, you cannot apply to law school, so…if you applied…you must have taken it!

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Keep in mind that the words…

⎯ unless
⎯ until
⎯ without, and
⎯ except

…all mean the same thing in the context of a conditional statement and should be treated as equivalents. The Unless Formula should be applied to them as well.

In the following examples, consider what is required — i.e. what must occur — in order for another thing to occur:

1. We cannot take off until the pilot gets here.

Takeoff ➝ Pilot

2. A lawyer cannot make big decisions without the client’s informed consent.

Big Decisions ➝ Informed Consent

3. The kids cannot play outside unless it is sunny out.

Outside ➝ Sunny

4. People at my law school are friendly except during final exams.

NOT Friendly ➝ Final Exams

In this last example, the diagram says that if people at the law school are NOT friendly (remember: we negate the sufficient condition), that means final exams are happening.