Consider the following argument and pick the correct answer: All four-legged…
2024
Consider the following argument and pick the correct answer:
All four-legged creatures have wings.
All spiders have exactly four legs.
Therefore, all spiders have wings.
Answer: B. Valid argument; false premises, false conclusion — Concept — in logic, validity is a property of the form, not of the facts An argument is valid when its structure alone guarantees that the conclusion cannot…
- A.
Valid argument; true premises, true conclusion
- B.
Valid argument; false premises, false conclusion
- C.
Invalid argument; true premises; true conclusion
- D.
Invalid argument; true premises; false conclusion
Show answer & explanation
Correct answer: B
Concept — in logic, validity is a property of the form, not of the facts
An argument is valid when its structure alone guarantees that the conclusion cannot turn out false while every premise is true. Whether the premises actually hold in the real world is a second, independent question: an argument that is valid and whose premises are all factually true is called sound. Validity and factual truth are therefore two different labels, and almost every pairing of them is possible.
Application — read this argument as a categorical form
Name the three classes: M = four-legged creatures, P = winged creatures, S = spiders.
Premise 1, "All four-legged creatures have wings", has the form: All M are P.
Premise 2, "All spiders have exactly four legs", has the form: All S are M.
The conclusion, "All spiders have wings", has the form: All S are P.
All M are P; All S are M; therefore all S are P is the classic categorical pattern (traditionally named Barbara). If every S lies inside M and every M lies inside P, then every S must lie inside P, so the conclusion cannot escape the premises: the reasoning is valid.
Now test the facts, separately from the form. Dogs, cats and lizards are four-legged and wingless, so Premise 1 is factually false. Spiders are arachnids with eight legs, so Premise 2 is factually false. Spiders have no wings, so the conclusion is factually false as well.
Cross-check — what validity does and does not rule out
A valid form can carry factually false premises to a factually false conclusion, which is what happens here.
A valid form can even carry factually false premises to a factually true conclusion: "All cats are birds; all birds are animals; therefore all cats are animals."
The single pairing a valid form rules out is all-true premises with a factually false conclusion. That is why pointing at a false premise never by itself makes an argument invalid.
Result: the reasoning is valid, both premises are factually false, and the conclusion is factually false — a valid but unsound argument.