Questions: Validity and Soundness

Question 1

Consider this argument: 'All fish can fly. Salmon are fish. Therefore salmon can fly.' Which assessment is correct?

• A. Invalid and unsound — the conclusion is false, so the logical structure fails
• B. Valid but unsound — the logical form is correct, but a premise is false
• C. Invalid but sound — the premises are clearly wrong, which breaks the validity
• D. Valid and sound — if you accept the premises, the conclusion follows

Answer: (B)

The argument is valid: IF all fish can fly and IF salmon are fish, THEN it necessarily follows that salmon can fly. The logical form is impeccable — the conclusion cannot be false while both premises are true. But the first premise is false (fish cannot fly), which makes the argument unsound. The key insight is that validity is purely about the relationship between premises and conclusion, entirely independent of whether the premises are actually true. A false conclusion signals a false premise, not an invalid structure.

Question 2

An argument has the following structure: 'All even numbers are divisible by 3. Six is an even number. Therefore six is divisible by 3.' The argument is valid, and the conclusion happens to be true. Is the argument sound?

• A. Yes — the conclusion is true, so the argument must be sound
• B. Yes — the argument is valid, and since the conclusion is true, the premises must be true
• C. No — soundness requires both valid form AND all premises to be true, and premise one is false
• D. No — an argument with a false premise cannot be valid

Answer: (C)

Soundness requires (1) a valid argument AND (2) all premises actually true. Here, premise one ('all even numbers are divisible by 3') is false — consider 4 or 8. Even though the conclusion is true and the form is valid, the argument is unsound because a premise is false. This illustrates that you can have a valid argument with a false premise that arrives at a coincidentally true conclusion. Truth of the conclusion alone does not establish soundness.

Question 3

If a valid argument has a true conclusion, then most its premises is expected to also be true.

• T. True
• F. False

Answer: False

A valid argument with a false premise can still yield a true conclusion by coincidence. Example: 'All mammals are mortal. Socrates is a tree. Therefore Socrates is mortal.' The second premise is false, but the conclusion is true. Validity only guarantees that IF all premises are true THEN the conclusion is true — it says nothing about what happens when premises are false. Only soundness guarantees a true conclusion through logical necessity (valid form + true premises).

Question 4

A sound argument guarantees a true conclusion.

• T. True
• F. False

Answer: True

A sound argument is by definition (1) valid — the conclusion cannot be false if all premises are true — and (2) has all true premises. These two conditions together guarantee the conclusion is true: the premises are true (by condition 2), so the conclusion must be true (by condition 1, which says a valid argument with all true premises cannot have a false conclusion). Soundness is the gold standard precisely because it provides this guarantee.

Question 5

Why is validity a structural property of an argument rather than a factual one? What exactly is being evaluated when we ask whether an argument is valid?

Model answer: Validity evaluates the logical relationship between premises and conclusion — specifically, whether it is possible for all premises to be true while the conclusion is false. If no such possibility exists, the argument is valid. This assessment is entirely independent of whether the premises are actually true. We are asking about the argument's form, not its content. A valid argument could have wildly false premises about fantasy creatures; what matters is that IF those premises were true, the conclusion would necessarily follow.

The structural/factual distinction is the heart of this topic. Validity is about necessity given the premises — it asks 'if the premises held, could the conclusion fail?' Factual assessment asks 'do the premises actually hold?' Conflating these leads to the common error of calling an argument invalid because its premises are false, or calling an argument sound because its conclusion sounds right. Keeping the questions separate is what enables formal logic to be a rigorous discipline.