Questions: Introduction to Deductive Validity

Question 1

Consider the argument: 'All cats are reptiles. Fluffy is a cat. Therefore, Fluffy is a reptile.' Is this argument valid?

• A. No — the premises are false, so the argument cannot be valid
• B. No — a valid argument must have a true conclusion
• C. Yes — if the premises were true, the conclusion would necessarily follow
• D. Yes — but only because Fluffy happens not to be a cat in reality

Answer: (C)

Validity concerns logical structure, not truth content. The question is: if the premises were true, would the conclusion have to be true? Here, if all cats really were reptiles and Fluffy really were a cat, then Fluffy would necessarily be a reptile. The argument is valid. The fact that the premises are actually false is irrelevant to validity — it only means the argument is not sound. This is the central distinction students must internalize: validity is about the conditional relationship between premises and conclusion, not about whether those premises are true.

Question 2

What does it mean for an argument to be sound?

• A. The argument is persuasive and its conclusion is widely accepted
• B. The argument is valid and all its premises are actually true
• C. The argument has a true conclusion, regardless of how the premises relate to it
• D. The argument cannot be logically refuted by any counterexample

Answer: (B)

Soundness adds factual truth to logical structure. A sound argument is (1) valid — the conclusion must follow from the premises — and (2) actually has true premises. Only a sound argument gives you a genuine reason to believe its conclusion, because it guarantees the conclusion is true. A valid argument with false premises tells you nothing about the world — it only tells you that if those premises were true, the conclusion would be too. Soundness is the combination that earns real epistemic force.

Question 3

To prove that an argument is invalid, it suffices to construct one possible scenario in which all premises are true but the conclusion is false.

• T. True
• F. False

Answer: True

This is the counterexample method for disproving validity. Validity requires that NO possible scenario makes the premises true and the conclusion false. So finding even one such scenario — one possible world, one assignment of truth values, one concrete case — is enough to show the argument is invalid. By contrast, proving validity is harder: you must show that no such scenario exists, which typically requires a proof rather than a single example.

Question 4

A valid argument with true premises might still have a false conclusion.

• T. True
• F. False

Answer: False

This is exactly what validity means: if an argument is valid, it is impossible for the premises to be true while the conclusion is false. So if you also know the premises are actually true (making the argument sound), the conclusion is guaranteed to be true. A valid argument with true premises and a false conclusion would be a logical contradiction — it would violate the definition of validity itself.

Question 5

Explain why a valid argument can give you no genuine reason to believe its conclusion.

Model answer: Validity only guarantees a conditional: if the premises were true, the conclusion would be true. But if the premises are actually false, the argument tells you nothing about the real world. A valid argument with false premises can have a false conclusion, a true conclusion, or any conclusion at all — validity alone doesn't determine it. Only when you also know the premises are true (i.e., the argument is sound) do you have genuine reason to accept the conclusion.

This is why evaluating arguments requires two separate checks: (1) Is it valid — does the conclusion follow from the premises? (2) Are the premises true? Both must be confirmed. A structurally impeccable argument built on false premises is no better than a bad argument for the purpose of establishing truth. This is also why being persuaded by a valid-seeming argument should prompt you to scrutinize the premises, not just admire the logical form.