As in his previous versions treating this material so also in the published form Parfit opens Chapter 12 considering what he terms the 'impossibility formula' of the categorical imperative. Before doing this, however, he first makes clear his generic view of what Kant takes 'maxims' to be, namely, 'policies and underlying aims'. As we will see, the two notions are far from evidently equally weighed in Parfit's account and play different roles in how he views both different formulas and different examples. As Parfit points out after having introduced the notion of "maxim" it is used by Kant to characterise some apparently divergent things since the "maxim of self-love", for example, is clearly, an "underlying aim" whilst that of making lying promises would appear rather to be a "policy". The first question one might ask, in terms of understanding Kant's account of maxims, would surely be how to relate these uses of "maxim" to each other?
However it is not obvious that this hermeneutic rule is applied by Parfit when he goes on to consider formulas and examples in Chapter 12. After describing the notion of "maxim' in the way he does Parfit next formulates something that he takes to underlie Kant's application of the test of maxims that is provided in the Formula of Universal Law as an "impossibility formula". This interpretation views FUL as stating that it is wrong to act on any maxim that "could not be a universal law". Now Parfit first expands on this view by dismissing some ways of understanding it that have been proposed before arriving at his own conception of it which is different, according to him, from how Kant himself determines it. The "stated" version of impossibility that he takes Kant to have is repeated as the same impossibility formula with which Parfit begins whilst the "actual" formula Kant uses is argued by Parfit to be different from this. The 'actual' formula is one that Parfit articulates as follows:
It is wrong to act on any maxim of which it is true that, if everyone accepted and acted on this maxim, or everyone believed that it was permissible to act upon it, that would make it impossible for anyone successfully to act upon it.
Notably the "actual" formula as Parfit states it includes a success condition that is a kind of practical restraint. It is this restraint that, it would appear, is meant to express the "underlying aim" of the impossibility formula so that the notion of impossibility becomes merely a kind of "policy" in using the success condition on Parfit's construal. In fact, however, this is to get things quite backwards as becomes apparent when Parfit applies the "actual" formula to examples.
The application to examples is meant to determine whether the formula as given will be sufficient to provide us with a wrong-making criterion. Various examples are considered to check this beginning with one that states it is alright to kill or injure others if that would benefit us. Now, taking this as a "maxim" is to view it as a form of policy which is, however, itself a specification of the more general "underlying aim" of unrestricted egoism. Parfit here follows Barbara Herman in claiming that the "actual" formula he appeals to would not prevent it from being the case that such an act could succeed. Notably, by having viewed the impossibility formula as really stating something that is measured by "success" in action Parfit has given this maxim passage in a simple way. If, however, the impossibility formula is one that is not measured in terms of "success" but in terms of coherence of universal willing in a world where it stated the law of that world it is not then seen in terms of 'success' primarily at all as 'success' is rather derivative of coherence in willing rather than the other way round as in Parfit's formula.
It is the case that Parfit is far from alone in viewing the "success" notion as the prominent element in the conception of impossibility that Kant is apparently appealing to in his consideration of universal laws. Christine Korsgaard and Barbara Herman view the question of lying in terms of it failing as a practical strategy if it were to be universally adopted as an aim, apparently without considering whether lying is itself not a policy rather than an underlying aim. Parfit himself makes this point indicating that lying usually expresses a principle of unrestricted egoism and that such a principle could not be said to be defeated by the universalisation of lying alone. Whilst that is correct it points to the need to view lying in terms of such a principle and to evaluate the sense of universalisation in terms of underlying aims rather than purely through particular policies.
Similar problems apply to the way Parfit treats other maxims in terms of the 'impossibility' notion as, when he views the maxim 'let no insult pass unavenged' he argues that this maxim, which Kant views as one that is inconsistent with itself, not to be one that must fail of universalisation since it could be universally achieved (albeit at considerable cost to all). Again it is false to view the criteria here as one of "success" since the reason why Kant speaks of it as being a notion that would be "inconsistent with itself' if universalised is not because of an implicit appeal to a simple "success" model of appraisal but rather in terms of a reference to a universal law of nature being applied to the maxim so that it applied to all. Then, given the inevitability of others feeling insulted by something or other one does and that they thus would have every right to reply to this in deadly ways if they were so inclined it would undermine the condition of agency of the one who had such inordinate pride as to state this maxim. This point is simply missed by viewing the 'success' criterion as the point of the reference to impossibility.
Parfit perhaps feels on safer ground in wielding the success criteria when he considers Kant's treatment of lying promises since here Kant indicates that the universalisation of a maxim of lying promises would fail of its intent since no one would in such a case believe promises. However the nature of Parfit's misunderstanding here is of a piece with elsewhere even if the case is one that requires subtler handling. Parfit assumes that Kant's remarks about failure of intent show that he is here using a criteria of "success" as the basis of the evaluation of the maxim and that what Kant is wishing to appeal to (in the manner of a rule consequentialist) is the need to protect certain practices that are in themselves generally valuable.
However the point here is quite different to what Parfit supposes. Promises do involve binding obligatory relations to others which is why Kant treats them as stating forms of contractual relation we have accepted. However the breaking of the promise, viewed as a universal law, is not simply the breaking of a valuable social practice. And nor is Kant's argument meant to simply show the failure in effect of the application of a certain kind of maxim. It is rather to show, as Onora O'Neill puts it, that some maxims involve themselves in a direct self-contradiction when universalised. So the aim to be achieved in the lying promise cannot be achieved when universalised and this is the point of the test, not the protection of the social practice. It is not that the failure of the aim is assessed however as a product of an application of a success condition but that the nature of "success" is shown to depend on lack of universalisation of the aim which is why the policy succeeds when it does. This is different from the case of avenging insults as there the direct aim does not get involved in a direct self-contradiction when universalised but rather is shown wanting because its universalisation would produce a world in which the adoption of the policy of avenging insults would undercut the agency whose pride was being expressed in the aim in question.
Unfortunately Parfit only responds to the problems he espies arising from application of the "success" criteria by refinements upon it, none of which, unsurprisingly, produce an improvement when applied to examples. Given this he concludes with the view that there is no useful sense "in which we could claim it to be wrong to act on maxims that could not even be universal laws", a conclusion which only follows from always viewing the impossibility criterion by connection to a success conception.
In the second part of his discussion Parfit moves away from the impossibility conception to one founded in viewing FUL in terms of the ability to will universal laws. The reference to willing is viewed in terms of consistency and contradiction so aligns with the usual way of understanding the Kantian tests. Parfit also views this discussion as part of a claim concerning the rationality of willing. This more promising direction of analysis leads Parfit next away from FUL towards the actual formula Kant uses in testing maxims in the second part of the Groundwork and in the Critique of Practical Reason, namely the law of nature formula. However Parfit views the Law of Nature formula through the prism of another one of his own devising concerning moral belief. The "moral belief formula" states:
It is wrong for us to act on some maxim unless we could rationally will it to be true that everyone believes that such acts are morally permitted.
As Parfit viewed the application of FUL to cases by means of the "success" criterion so the application of the Law of Nature formula is now seen through the prism of this claim about moral belief. The reason why this move is made is because Parfit wishes to introduce a test that is not equivalent to Kant's. Kant formulated the Law of Nature notion so that we could see what would take place if the specific aim underlying the policy formulated in our maxim were universally enacted and this is quite different from what Parfit goes on to look at. Parfit rules out consideration of "deontic beliefs" on the grounds that admission of them would lead to a "bootstrapping" account of moral reasons.
In considering the application of the moral belief formula Parfit refers again to how maxims may involve "policies" or aims but having done so fails to apply this distinction in consideration of cases. So the first problem he poses to his own criteria of moral belief concerns a "rarity objection" in terms of how maxims could be so weirdly formulated that they would have no chance of being universally stated. Here it appears that the reasons why anyone would adopt a policy of action, i.e., what their aim would be in doing so, gets completely lost as it often does when people formulate strange cases of maxims. The reason why the rarity objection is thought to hold is that Parfit assumes that it is at least logically possible someone could hold highly specific or particular maxims but in making this point he completely neglects to question what possible aims could be forwarded by doing so.
Having presented but thus failed to adequately justify this "rarity objection" Parfit turns next to a different case which does reach for an understanding of an agent's aim. However having done so Parfit now reveals an inverse problem in his account of maxims to that which has underlaid his discussion up to this point. Up until now the problem has been that in cases where the fundamental question concerned the aim of acting in certain ways he fixated only on the policies that get adopted, now, by contrast, he views policies that are worthy of endorsement as problematic for Kant because they are part of an overall aim that he would not. The case to which Parfit turns here is that of the egoist whose aim is expressed in a general thesis of doing what is best for themselves and Parfit says that it should follow from the application of the moral belief formula that whenever this person acts in accordance with this maxim they are doing something wrong. This is far from following. Kant's generic point about such a person would rather be that some of their actions were morally fine and others not but that none of them possessed true "moral worth", something quite different from saying that they were all "wrong".
To take one of the cases that Parfit formulates in relation to the egoist, it may well be the case that the egoist only pays their taxes because it would be too much trouble to their self-interest to avoid them. This means that their paying of their taxes is not an act expressive of moral worth but it does not mean that the acts involved in paying the taxes are wrong because they conform to the egoistic maxim which is, as a maxim, wrong.
A different case arises with regard to people with false moral beliefs. It may be that someone sincerely believes that it is better to deny girls education than to provide them with it but that, as one of the consequences of this belief, they expensively fund education for some boys who would otherwise never have had the opportunities in question. Whilst the general belief is a wrong one the acts they are led to perform due to it are not in themselves wrong and nor is it part of a Kantian conception of maxims to relate to them in this way.
Parfit's confusion with regard to these matters leads him to formulate the notion that there are "mixed maxims", a point introduced to argue against the fictitious problem that Kant's view implies that adoption of some types of aims renders all policies in accordance with these aims wrong. This point, as illustrated already, is quite false and thus there is no ground for thinking here of a problem of "mixed maxims" in Parfit's sense.
Having been misled by his own account Parfit now formulates a revision of Kant's formulas to respond to this non-problem of "mixed maxims". It is right to say, as Parfit does, that a general aim adopted, which itself is one that fails Kantian tests, does not in and of itself invalidate or show to be wrong specific policies endorsed by the agent in question. This does show that the aim alone does not point to the wrongness of what will be done. In many cases an aim does itself directly state something wrong as we noted above when considering the impossibility cases but in others it leads to a policy choice that, whilst in conformity with the wrong aim, is also itself not something "wrong" as it is harmonious with the Law of Nature formula. Parfit, by contrast, thinks that inasmuch as we view "maxims" as policies we shouldn't take them to be relevant at all, something whose falsity I have demonstrated above. Parfit's direction of travel is to consider acts without discussing maxims but doing so ensures that the reasons why acts are performed are not to the forefront and without this the point of the Kantian test (to view the basis of someone acting a certain way) drops out of the picture. Parfit attempts to reply to this by introducing a notion of "moral principle" instead though it should be pointed out that this notion faces the objection that it precisely introduces a deontic notion as was earlier ruled out.