Question

For the following syllogisms, (a) identify the figure of each mood and (b) give an interpretation that shows that the syllogism is invalid. 1. AiB, BeC, therefore AoC.

Struggling to make an interpretation that shows this to be invalid.

Answer 1

In this interpretation, the premises "AiB" (All cats are mammals, Some mammals are dogs) and "BeC" (Some mammals are dogs, All dogs are cats) are true. However, the conclusion "AoC" (All cats are dogs) is false, as not all cats are dogs.

Therefore, this interpretation demonstrates that the syllogism is invalid.

Explanation:

(a) The given syllogism "AiB, BeC, therefore AoC" belongs to the first figure of the mood AAI.

(b) To show that the syllogism is invalid, we need to provide an interpretation where the premises are true, but the conclusion is false.

Let's consider the following interpretation:

A: All cats are mammals.

B: Some mammals are dogs.

C: All cats are dogs.

In this interpretation, the premises "AiB" (All cats are mammals, Some mammals are dogs) and "BeC" (Some mammals are dogs, All dogs are cats) are true. However, the conclusion "AoC" (All cats are dogs) is false, as not all cats are dogs.

Therefore, this interpretation demonstrates that the syllogism is invalid.