The cartoon makes a good point — and a valid criticism of Kant. It’s a fact that the Categorical Imperative doesn’t suggest action, it only vetoes action. It doesn’t tell you what you should do, rather it eliminates possible actions. So, if you have two or more maxims that pass the CI, then you don’t have any suggestions as to what to do. Kant’s answer to this is rather simple, you can use any secondary reason to choose between the two actions.
The more problematic objection comes in a situation in which you have conflicting duties. For example, you have a duty to save lives but in order to do so, you must lie. The example Kant uses is the “murderer at the door” example — and he comes out on the side of not lying. But, it doesn’t seem to be that simple.
Kant’s analysis is that when you lie, you involve yourself — if just accidentally — in the murderer succeeding at killing your friend. You lied, as your friend asked you to, and thus the murderer and your friend run into one another. In this situation, you don’t know the implications of your lie and thus you are just a bit responsible for your friend’s death — because, but for your lie, the person would still be alive.
Consider this example, a trusted friend is about to commit suicide by jumping off of a tall building. You know that the person’s spouse cheated on them, but you have not told your friend that you know this. The friend, via the police, asks you if you know the truth — you know that the friend will trust what you say and that if you tell them that you think their spouse has been faithful, your friend will come off of the ledge. You are also pretty certain that the friend will jump if told that their spouse has cheated. In this case, you have no intervening factors — if you lie, you will get your friend to safety and get them the help they need — if not, your friend will probably jump and die.
Kant has no answer for this objection – mostly, he denies that the duties falling out of the CI can conflict.