EXAMPLE 2.2.7

Given:

i. No kittens are fierce; and

ii. Fluffy isn't fierce.

select the statement that is a valid conclusion, if a valid conclusion is warranted.

A. Fluffy is a kitten.

B. Fluffy has fleas.

C. Fluffy isn't a kitten.

D. None of these is warranted.

Solution

First note that the first premise is equivalent to "If one is a kitten, then one isn't fierce."

Let p be the statement "One is a kitten."

Let q be the statement "One isn't fierce."

Then the premise arrangement has this form:

p arrow q.

q.

(Note: we are treating "Fluffy" as a specific instance of something who "isn't fierce.")

This is the premise arrangement for Fallacy of the Converse, so it is not possible to form a nontrivial valid conclusion.

The correct choice is D.