Question

Samantha writes the following as an example of using the Law of Syllogism. Explain Samantha's error.

If an animal is a dog, then it is a mammal.
If an animal is a dog, then it has four legs.
I can conclude that if an animal has four
legs, then it is a mammal.
Choose the correct answer below.
A. The Law of Syllogism would lead to the conclusion that if an animal is a mammal, then it has four legs. Her conclusion is the converse of this, and a statement and
its converse do not necessarily have the same truth value.
B. She used the same hypothesis for both conditionals, so she cannot combine the two using the Law of Syllogism.
C. She used the same conclusion for both conditionals, so she cannot combine the two using the Law of Syllogism.
D. Her example uses the Law of Detachment, not the Law of Syllogism.

Answer 1

Samantha's example incorrectly assumes that all animals with four legs must be mammals, which is an affirmation of the consequent fallacy and not a correct use of the Law of Syllogism.

Step-by-step explanation:

The error in Samantha's use of the Law of Syllogism is that she incorrectly assumes that because all dogs have four legs and all dogs are mammals, that anything with four legs must be a mammal. This is a logical fallacy because there are animals with four legs that are not mammals (e.g., reptiles, and amphibians). The correct application of the Law of Syllogism would lead us to conclude that if an animal is a dog, then it has four legs and is a mammal; it does not allow us to conclude anything about all four-legged animals. Her conclusion is mistaken because it represents a form of the logical fallacy known as affirming the consequent, which assumes that a specific condition (having four legs) is unique to a category (mammals) when other possibilities exist (other four-legged animals).