Question

P1. If one is a cat, then one is an animal P2. If one is a dog, then one is an animal C. Cats are dogs

This argument is:

Invalid


Valid, but not sound


Sound


Sound, but not valid

Answer 1

The argument is invalid as the conclusion that 'cats are dogs' does not logically follow from the premises that state only that both cats and dogs are animals.

Step-by-step explanation:

The argument presented is invalid because it contains a logical fallacy. The premises given are:

1. If one is a cat, then one is an animal.
2. If one is a dog, then one is an animal.

However, the conclusion drawn, that cats are dogs, does not logically follow from the premises. The premises simply establish that both cats and dogs are animals, but they do not support the idea that all cats are dogs. To demonstrate this, one could consider an example: if Charlie is a cat, the premises would be true, as Charlie is an animal. However, this does not mean Charlie is a dog, rendering the conclusion false.

In the context of a logical form, we might express this invalid argument pattern as:

1. P > Q
2. R > Q
3. Therefore, P = R

which is a clear misapplication of logical reasoning.