Evaluation of Example 5: What Cannot Be Done

Passage:

“Ordinary common sense tells us ‘You cannot do what you cannot do‘ (i.e., you cannot do what, in fact, you are not capable of doing) … ”

Donna Ford, Reversing Underachievement Among Gifted Black Students 2nd. ed. (Naperville, Illinois: Sourcebooks, 2010), 130.

Analsyis:

On one hand, the quoted statement and the author's proposed meaning (provided in parenthesis) is, in all likelihood, offered as an explanation. With no argument present, no petitio principii occurs. The explanation is not necssarily circular either since “what you cannot do” can also mean in different conversational contexts either “what you are not permitted to do” or “what is physically impossible for you to do.”

On the other hand, the passage is occasionally interpreted by readers to be an (invalid) successive immediate inference as follows:
All actions you cannot do are activities you are not capable of.
[Therefore, all actions you can do are activities you are capable of.]
On this second interpretation, no petitio principii occurs either since the argument represents the contraposition and invalid conversion of a universal affirmative statement:

Statement Reason Truth Value
1. All actions you cannot do are activities you are not capable of. given true
2. All activities you are capable of are actions you can do. contraposition true
3. All actions you can do are activities you are capable of. conversion unknown