Deductive Validity Lab

Find the counterexample, not the winning opinion

This lab examines deductive validity in a small and fully specified system: classical propositional logic with two propositions, P and Q. A logical form is valid when there is no assignment of truth values that makes every premise true while its conclusion is false.

Choose an argument pattern. The table will show four possible assignments to P and Q, evaluate the premises and conclusion in each row, and highlight any counterexample. A counterexample is a case where the premises all hold but the conclusion fails. One such row is enough to establish invalidity for this formal pattern.

How to read the result

If an argument is valid, this does not tell us whether P or Q represents a true statement about the world. If it is invalid, the conclusion could accidentally be true anyway. These two points distinguish logical structure from evidence.

Try comparing modus ponens, affirming the consequent, modus tollens and denying the antecedent. Think of an ordinary example for each and ask what facts would be required to justify its premises.

Where the model stops

This is not a natural-language argument evaluator, a test of personal intelligence, or a complete logic textbook. Real arguments can be ambiguous and can depend on probability, evidence or meaning beyond a two-variable formal model.

The Stanford Encyclopedia of Philosophy sources linked below explain deduction, validity and forms of argument in greater depth.