Which formal fallacy is committed in the following argument: ‘If your pet is a…
2023
Which formal fallacy is committed in the following argument: ‘If your pet is a cat, then it has a tail. Your pet is not a cat. Therefore your pet does not have a tail’?
Answer: B. Denying the antecedent — CONCEPTA conditional statement P → Q says that P is sufficient for Q; it does not say that P is necessary for Q. A formal fallacy occurs when an inference…
- A.
Existential fallacy
- B.
Denying the antecedent
- C.
Exclusive Premises
- D.
Affirming the Consequent
Show answer & explanation
Correct answer: B
CONCEPT
A conditional statement P → Q says that P is sufficient for Q; it does not say that P is necessary for Q.
A formal fallacy occurs when an inference uses an invalid logical form, regardless of whether its individual statements happen to be true.
APPLICATION
Let P mean ‘the pet is a cat’ and Q mean ‘the pet has a tail’. The argument has the form P → Q, not P, therefore not Q.
Negating P does not justify negating Q, because a pet may have a tail for reasons other than being a cat.
CONTRAST
Existential fallacy improperly assumes that something exists from premises that do not guarantee existence.
Exclusive-premises fallacy arises in a categorical syllogism with two negative premises, which cannot connect the subject and predicate.
Affirming the consequent has the form P → Q, Q, therefore P; it reasons in the opposite direction from the given implication.
CROSS-CHECK AND RESULT
A dog supplies a counterexample: it is not a cat but can still have a tail. Therefore the conclusion does not follow, and the fallacy is denying the antecedent.