Following, Not Being True
An argument is a set of premises offered in support of a conclusion. Logic studies one relation only, whether the conclusion follows, and it is remarkably indifferent to whether anything said is true.
An argument is valid when it is impossible for all the premises to be true and the conclusion false. Notice what this does not say. It says nothing about whether the premises are actually true. Validity is about the form of the inference, not its content:
All fish are mammals. All mammals are green. Therefore all fish are green.
Every sentence here is false, and the argument is perfectly valid. Meanwhile:
Paris is in France. Therefore 2 + 2 = 4.
Both sentences are true, and the argument is invalid, the conclusion does not follow from the premise, it merely happens to be true alongside it.
Soundness is the stricter notion: an argument is sound when it is valid and all its premises are actually true. A sound argument therefore guarantees a true conclusion, which is why soundness is what we usually want and validity is what logic can check.
The reason logic studies form is that validity travels. Any argument of the shape
is valid whatever and are, this is modus ponens. Two forms and their near-miss counterparts are worth memorising:
| Form | Pattern | Valid? |
|---|---|---|
| Modus ponens | If P then Q; P; so Q | Yes |
| Modus tollens | If P then Q; not Q; so not P | Yes |
| Affirming the consequent | If P then Q; Q; so P | No |
| Denying the antecedent | If P then Q; not P; so not Q | No |
The last two are formal fallacies, and they are the commonest reasoning errors in ordinary argument precisely because they look so like the valid pair.
Logic in this narrow sense is deductive: the conclusion is already contained in the premises, and a valid deduction adds no information. Inductive arguments, generalising from cases, can be strong or weak but never valid, since their conclusions genuinely go beyond their premises.
Common pitfall: calling an argument "valid" because you agree with it, or "invalid" because a premise is false. A false premise makes an argument unsound, never invalid. Validity is a property of the inference alone, and an argument made entirely of falsehoods can be impeccably valid.