Kant thought that his universalization tests would yield results that are consistent with commonsense views about the rightness and wrongness of various actions. But critics have argued that Kant's tests yield the wrong moral conclusions over a range of cases where commonsense notions about right and wrong seem fairly clear and accurate. In some cases a maxim will fail one of Kant's test (yielding a negative verdict about the corresponding action) but the action is not morally wrong (false negatives), and in other cases a maxim that featres a wrong action will pass Kant's tests, yielding a mistaken positive verdict about the act (false positives).
As an example of the first kind of case, consider the investor who intends to withdraw all of her money from the bank once the stock market index climbs another two hundred points. one cannot consistently conceive of this maxim being a universal law of nature, for reasons similar to those presented in connection with the case of false promising. If one attempts to imagine a world in which this maxim functions as a law, one ends up attempting to imagine a world in which everyone withdraws their money under the conditions specified. But since banks do not have the necessary funds on hand to support massive withdrawals, one is also attempting to imagine a world in which it is not the case that everyone in the circumstances in question withdraws their money from a bank. Thus, because the maxim cannot be universalized, the action in the maxim is morally wrong. But surely, adopting and acting on this maxim is not morally wrong, so Kant's CC test yields a false negative.
Here is an example of a false positive. Suppose that I plan to make a false promise in order to get money from someone named Igor Cycz on March 8 so that I can make a down payment on a metal detector. I thus formulate my maxim as:
"I will get money on a false promise whenever it is March 8 and I can get it from someone named Igo Cycz in order to buy a metal detector".
Now if I consider whether this maxim can be universalized, I ask whether I could consistently conceive of a world in which everyone in the circumstances in question obtains money on a false promise. Since the circumstances mentioned in my maxim are extremely rare, this maxim will pass the CC test, and so we must conclude that the actin mentioned in the maxim is morally permissible (at least in the circumstances so specified), but surely it isn't.
The problem of false negatives and false positives is related to a a more general problem for Kant's universalization tests, namely, the problem of relevant maxims. A maxim represents an agent's conception of what she is doign or proposes to do, and for every action there are innumerable possible maxims on the of which the action in question might be permformed. To make this point more clearly, suppose that I am hiding an innocent person who is being hunted by some killers. The killers come to my door and ask me whether I know where the hunted person might be hiding. Suppose I lie and deny that I know anything of the whereabouts of their intended victim. Here are a couple of the possible maxims on which I might act:
"I will tell a lie whenever I am asked a question and don't want to give the correct answer."
"I will tell a lie whenever I am asked a question whose truthful answer will likely lead to the death of an innocent person."
Both maxims fit my circumstances in the sense that they both contain correct (or what I believe to be correct) information about my circumstances. Now presumably , if I test the first maxim by Kant's tests, it will fail to be universalizable, thus implying that an act of lying in this case would be wrong. (I leave the details as an exercise for the reader.) However , if I test the other maxim by Kant's tests, it will arguably pass with the implication that the action in question is not morally wrong. Intuitively, we judge that the second maxim is, of these two, the one that should be used in testing the morality of lying in this case. What we need from kant is a principled reason for selecting one possible maxim for purposes of testing the morality of an action over the many others that might also apply to the same action. This is the problem of relevant maxims.
Critics often allege that Kant's UL version of the Categorical Imperative is useless without a solution to the problem of relevant maxims. It is useless and hence fails to satisfy the main practical aim of a moral theory, the aim of providing a useful decision procedure. Because given the multiplicity of maxims associated with any action, one can use Kant's tests to derive inconsistent moral verdicts about the same action.