Imperative Logic - Ross's Paradox

Ross's Paradox

Alf Ross observed that there is a potential problem for any account of imperative inference. Classical logic validates the following inference:

P1. The room is clean.

C1. Therefore, the room is clean or grass is green.

This inference is called addition (or disjunction introduction). However, a similar inference does not seem to be valid for imperatives. Consider:

P1. Clean your room!

C1. Therefore, clean your room or burn the house down!

Ross's paradox highlights the challenge faced by anyone who wants to modify or add to the standard account of validity. The challenge is what we mean by a valid imperative inference. For valid declarative inference, the premises give you a reason to believe the conclusion. One might think that for imperative inference, the premises give you a reason to do as the conclusion says. While Ross's paradox seems to suggest otherwise, its severity has been subject of much debate.