A valid form can never take true premises to a false conclusion. That gives us a test: to prove a form invalid, find one argument of that form that does exactly that.
Key idea
The counterexample method: build an argument with the same form, whose premises are plainly true and whose conclusion is plainly false. One such argument proves the form invalid.
Why it works
A valid form guarantees "true premises, true conclusion" for every argument of that form. So a single argument of the form with true premises and a false conclusion shows the guarantee fails, and the form is invalid. Every argument that shares the form shares the flaw.
Worked example: Breaking a form
Show that this form is invalid: "All C are B. All A are B. So all A are C."
- Choose words for A, B and C that make both premises plainly true: C = dogs, B = mammals, A = cats.
- Premises: "All dogs are mammals" (true). "All cats are mammals" (true).
- Conclusion: "All cats are dogs" (plainly false).
- Same form, true premises, false conclusion.
Answer: The form is invalid.
Worked example: A failed attempt
Does "All dogs are animals. All mammals are animals. So all dogs are mammals." show the same form is invalid?
- It has the same form (C = mammals, B = animals, A = dogs).
- But its conclusion, "All dogs are mammals", is true.
- True premises with a true conclusion prove nothing about the form.
Answer: No. The conclusion must be false.
Common mistake
Changing the form while building the counterexample (for example, turning "All A are B" into "Some A are B"), or using premises that are not clearly true. Then the counterexample proves nothing. Check three things, in order: same form? premises plainly true? conclusion plainly false?