Our Wonderfully and Confusingly Flexible Language
There are many ways to express logical implication in English, including 'if A then B', 'A only if B', and 'B is necessary for A'. A real-world example illustrates how ambiguous phrasing can lead to serious misunderstandings.
THE IDEA
Our Wonderfully and Confusingly Flexible Language
Several English expressions can represent the same logical implication:
A → B
including phrases putting A first and partner phrases putting B first:
• A implies B. B is implied by A.
• If A then B. B if A.
• A is a sufficient condition for B. B is a necessary condition for A.
• A is true only if B is true. Only if B is true is A true.
I think it is hard to be convinced that all eight of these statements mean the same thing, and I expect some people will write to me telling me I’ve got it wrong (so I’m checking rather carefully that I don’t have any typos). I think the last is the most confusing. Here is a tragic example.
Cheng reports an incident in Cobb County, Georgia, in which a policeman was recorded reassuring a panicky white woman that “we only shoot black people”. This is logically equivalent to saying
We shoot you only if you are black.
which is in turn equivalent to
Only if you are black do we shoot you.
or in arrows
we shoot you → you are black
or in words
If we shoot you then you must be black.
This gives the logical direction of the policeman’s claim. It does not establish that the claim accurately describes police behavior or provide a probability for an actual traffic stop.
When to use it
In legal contracts, precise language for conditions is crucial to avoid misinterpretation.
In public statements by authorities, ambiguous phrasing can lead to dangerous misunderstandings (e.g., police policies).
In mathematics and computer science, logical implications are used with strict definitions for correctness.
In everyday arguments, clarifying whether a condition is necessary or sufficient helps avoid logical fallacies and miscommunication.
FROM THEORY TO EVERYDAY LIFE
In practice
Policeman's Statement
The reported statement 'we only shoot black people' makes being black a necessary condition for being shot, if interpreted literally. It does not say that everyone who is black will be shot. Formalizing the claim clarifies its meaning without establishing that it is true.
A MOMENT TO REFLECT
Put it to work.
Think of a statement you often hear that uses 'only if'. Could it be misinterpreted? How would you rephrase it to avoid ambiguity?
Why is it important to be precise when using logical implications in legal or policy language?
How does the phrase 'A is sufficient for B' differ from 'A is necessary for B'? Give an example from everyday life.
CONTINUE THE CONVERSATION
Source texts
- The Art of Logic How to Make Sense in a World that Doesn’t (Eugenia Cheng)