A deductive argument promises that its conclusion must follow. When it keeps that promise, logicians call it valid.
Key idea
An argument is valid when it is impossible for all its premises to be true and its conclusion false. Validity is about the link between premises and conclusion, not about whether they are actually true.
Why it works
Validity comes from the form of an argument. "All B are C; all A are B; so all A are C" is valid whatever A, B and C are: if every A is inside B and every B is inside C, every A is inside C. Put in any words and the link holds.
Worked example: Valid, with a false premise
"All penguins can fly. Pip is a penguin. So Pip can fly."
- The first premise is false: penguins cannot fly.
- But imagine both premises were true. Then Pip would have to fly.
- There is no way for the premises to be true and the conclusion false.
Answer: Valid (but, as we will see, not sound).
Worked example: Invalid, though every statement is true
"All squares are rectangles. All squares are shapes. So all rectangles are shapes."
- Every statement here is true.
- The form is: all A are B; all A are C; so all B are C.
- Put other words in the same form: "All dogs are mammals. All dogs are pets. So all mammals are pets." The premises are true and the conclusion is false (wild bears are not pets).
- So the form can fail, and the argument is invalid.
Answer: Invalid, even though everything in it is true.
Common mistake
Calling an argument invalid because a premise is false, or valid because you agree with the conclusion. Validity ignores the facts. Test: pretend the premises are true. If the conclusion could still be false, the argument is invalid.