The Counterexample Method

“One well-built exception can defeat a universal claim.”

01 / PLAINLY

What it means, plainly

A counterexample is a case that contradicts a universal claim. It can also expose invalid reasoning by keeping the premises true while making the conclusion false.

02 / CONTEXT

A little more

To refute All X are Y, find an X that is not Y. To show an inference is invalid, construct a case with true premises and a false conclusion.

03 / WHY IT MATTERS

Why it matters

It tests an overbroad rule with a decisive case instead of leaving the disagreement at the level of impressions.

04 / EXAMPLE

A familiar example

The claim all prime numbers are odd falls to 2, which is both prime and even.

05 / LIMIT

What it does not mean

An anecdote does not refute a probabilistic trend; the target must actually be universal.

06 / NOTICE

Notice it in your day

Take a sentence containing ‘all’ or ‘never.’ Look for a real or imagined case that meets its condition but not its claimed result.

FINAL NOTE

The idea worth keeping

Match the force of the counterexample to the exact force of the claim.

QUESTIONS / 02

Questions people still have

How many counterexamples can defeat a universal claim?

One, if it genuinely meets the condition and contradicts the universal result.

Does one anecdote disprove a trend?

No. A probabilistic trend can allow exceptions.