EXAMPLE 2.2.6

Given:

i. All nurses are kind; and

ii. Florence isn't a nurse.

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

A. Florence is a city in Italy.

B. Florence isn't kind.

C. Florence is kind.

D. None of these is warranted.

Solution

Let p represent the statement "One is a nurse."

Let q be the statement "One is kind."

Then the premise arrangement has this form:

p arrow q.

not p.

(Note: we are treating the statement "Florence isn't a nurse" as a specific example of "not p.")

This is the premise arrangment for Fallacy of the Inverse; thus, a non-trivial valid conclusion is not warranted. The correct choice is D.

Important note: It is also possible to analyze this argument using the techniques associated with transitive reasoning.