Questions: Deductive Reasoning

Question 1

Consider: 'All mammals are warm-blooded. Whales are mammals. Therefore, whales are warm-blooded.' Which description best fits this argument?

• A. Valid and sound
• B. Valid but unsound
• C. Invalid and unsound
• D. Invalid but with a true conclusion

Answer: (A)

The argument is valid because the conclusion follows necessarily from the premises — there is no possible world in which both premises are true and the conclusion is false. It is also sound because both premises are in fact true. Valid + true premises = sound.

Question 2

A valid deductive argument guarantees that its conclusion is true.

• T. True
• F. False

Answer: False

Validity only guarantees that IF the premises are true, the conclusion must be true. A valid argument can have false premises and a false conclusion — for example, 'All birds can fly; penguins are birds; therefore penguins can fly' is valid but unsound because the first premise is false. Truth of the conclusion requires both validity and true premises, which is the definition of soundness.

Question 3

What distinguishes a valid argument from a sound argument?

Model answer: A valid argument is one where the conclusion follows necessarily from the premises — it is impossible for the premises to be true and the conclusion false. A sound argument is valid AND has premises that are actually true. Validity is a structural property; soundness adds a factual requirement.

The distinction matters because you can assess validity by inspecting logical form alone, without knowing whether the premises are true. Soundness requires both the right structure and accurate premises. Many philosophical arguments are valid but disputed on grounds of soundness — the premises are contested.