# Would the cofinitude relation be a more realistic parameter than the exclusivity one, in the formulation of the CI?

Since I read Gödel, Escher, Bach eleven years ago, in 2011, I figured that 2022 would be a poetic time for me to reread it. (If you’ve read the book, you should know what I mean, haha!) While I was going through the section on the discovery of non-Euclidean geometry, I thought about how the author framed the issue, that various analysts had taken the parallel postulate and negated it, to see if a contradiction emerged as a result: thought about this framing modulo Kant’s claim that the categorical imperative is synthetic, then. What I came up with was:

1. You ought to act on maxims that only can not be willed as universal laws.
2. You ought to act not only on maxims that can be willed as universal laws.
3. It’s not that you ought to act only on maxims that can be willed as universal laws.

From what Kant says about agents who only use pure reason and have no empirical incentives, about how an I-ought is an I-will for those agents, I get that he must’ve traced the synthetic character of the CI to something like (2) or most likely (3) (once you flip the syntax around a little, you can get (3) from (2), sort of, anyway). But this seems to leave a conditional inverse of (1) as analytic: 4. If you ought to do anything, you ought to act only on maxims that can be willed as universal laws.

Is this realistic, though? Because then I thought about the following alternatives:

1. You ought not to include only maxims in your maxim-set that can’t be universalized, but you have to include some that can be—yet not all, then, though.
2. Your maxim-set ought to include at least n-many universalizable maxims (for some philosophically justifiable exact value, or ramifying formula maybe, for n).
3. Your maxim-set ought to include only cofinitely many maxims that can’t be universalized (so if there’s a finite upper limit n on the number of possible maxims in the set, or even if the set can be indefinitely infinite, all but m<(n/2)-many of its elements ought to be universalizable).

For reasons I don’t have time to go into, (7) looks the most justifiable, to me. (5) technically covers (7), but it’s also consistent with just m<n rather than the sharper restriction. E.g., if you have a set of 10 maxims, (5) is consistent with 9 out of 10 failing the universalization test but (7) sets the upper barrier at 4 of those test-failures.

Objection: maybe so, but maybe the sense behind (7) can be accommodated by Kant’s distinction between narrow and wide duty. Or, that is, the cofinitude relation plays into the latter horn of that distinction: a duty is wide if and only if its range (not its domain?) is cofinitely qualified in some relevant manner.

Still, people love to object to the CI by making up counterexamples in the form of maxims that seem at least permissible, if not obligatory, despite that these maxims can’t be universalized “correctly.” Sometimes the problem is that the “maxims” are too particular to be what Kant used the word “maxims” for, viz. imperatives at or above a certain threshold of generality. But sometimes it really just seems like we have innocuous principles in play that nevertheless would collapse if “everyone did that.” So besides his rigorism, what could be said in defense of Kant’s exclusivity criterion in the formulation of the CI, instead of a cofinitary or similar criterion?

Some comments, as I am not certain there is an answer proper to the question as asked.

1. The proper Kantian formulation of the CI would always be if you want to act morally, you ought to ...
2. Thus, a negation would always ask what to do if one does not want to act morally. This means following maxims that cannot be universalised, not not only following those that can. In other words, it would basically be Act only according to maxims that cannot be thought as an universal law.
3. One can always have as many non-moral maxims as one likes, you just have to live with the fact that you have an abysmal character and will be going to hell ;)

If one reads deeper into his practical philosophy and especially his later works like the Religion or the Anthropology, I think it becomes clear that there is not much difference in terms of judging the character between one who consciously is immoral with some maxims vs. someone who aspires to be immoral with all of them. Notwithstanding the fact that Kant probably thought the latter case to be a psychological impossibility.

The issue you describe seems to be aiming at morally indifferent maxims, really, which is basically the Kantian version of morally permissable acts. And the question whether this can exist for Kant is hard to answer. I'd say no. And I'd like to see a maxim proper that works like you allude to in your last paragraph.

• Since I wrote this question and offered my answer, I have significantly reconceived both my support for, and partial critique of, Kantian ethics. You remind me that I have much work to do! Dec 24, 2023 at 22:47

Let’s try out the above scheme modulo the second CI formulation:

• A. You ought to treat people never as ends in themselves but always as means only.

B. You ought to treat people never as ends or means.

C. You ought not to treat people as ends-in-themselves-and-never-as-means-only.

D. It’s not that you ought to treat people as ends in themselves and never as means only.

(A) seems more than dubious. (B) seems to omit the point of practical reasoning as such (or, then, to require, if anything, that we treat with people under some other description than “ends or means,” which description is arguably unidentifiable). And then again (C) and (D) end up relatively interchangeable (and even (B) can be folded under them if interpreted precisely enough along such lines). So the synthetic character of the CI again has to do with an existence claim for the faculty-of-ought itself, viz. it would not be that we ought to treat people like so even if our will were decided purely by reason, but we just would treat them so if that was how our will were decided. “Sic volo, sic jubeo,” indeed.

Another way, then, though, to go back and check what we are talking about is to note that the CI, even as to its content, can be framed as the synthesis or conjunction of a positive and a negative imperative: “Act on maxims that can be willed as universal laws,” and, “Don’t act on maxims that can’t be as such willed.” This is why even the CI’s content might not seem analytically given: the positive conjunct is, to be sure, “merely” a recapitulation of general law schematics, but that this also enjoins the negative conjunct of us would not immediately follow, not even by the law of negation (practical noncontradiction). Wherefore again, the question is yet posed of whether a less demanding—although potentially still taxing—limit on maxims that are not universalizable can be apropos, here. And so again we will argue from the premise that a lesser stricture is admissible even before we get to the issue of narrow-or-wide duty.

Proof attempt: suppose, “You ought to act on maxims that can be willed as universal laws.” By the axiom of opposition,😨 this get us that a contrary ought-statement is ruled out. But what is that contrary? The modal term “can” points straight at the concept of possibility, which is opposed to impossibility, then. This does make it seem as though, “You ought to not act on maxims that can’t be willed as universal laws,” would follow on modal grounds, here. By framing the CI as a parameter for how we set up our maxim-sets, we could avoid that seeming, but then we would have to justify such a framing instead.

And since Kant doesn’t abstract from lower-order imperatives to a highest-order imperative about the set-up of maxim-sets, his reasoning does not support such an attempted justification as such. For him, when we trace the regress of practical reasoning backwards, the form of the law at which we arrive is, “Act on universal maxim x…” And this makes a lot of sense, since the regression at issue is from particularity to generality/universality, just the same as with theoretical reason’s backtracking. Accordingly, we’d have to have it that the higher-order imperative type to which we abstracted was something like, “Adopt maxims x…” or, “Incorporate maxims x into your maxim-set…” and then our justification would manifest quite clearly.

However, consider again switching out the terms of the first CI formulation with those of the second, this time modulo the CI as a conjunction:

• A. Treat others as ends in themselves.

B. Don’t treat others as means to other ends.

(B) is not what Kant has under the heading of the second CI formulation, though. He means that we have to adopt maxims that conform to (A), and that we can also adopt maxims that conform to, “Treat someone as a means to an end,” and as long as (A) is satisfied, satisfaction of the more instrumental attitude towards others is yet justifiable. In fact, then, the second formulation of the CI turns out to be more consistent with the maxim-set notion we are advocating for anyway.

Our last test case for our (re)interpretation of the CI will be in light of Kant’s third and potential fourth CI formulations. That there might be four is something we grant on account of the fact that Kant was not obviously perfectly consistent about how many formulations can be contrived, neither that all of them are perfectly unified. (C.f. Allen Wood’s crisp analysis of this very matter.) With respect to the third, at any rate, Kant does seem to be following the line he used in the first Critique when he offered that the third of his categories under each of his four headings could be construed as a merger of the preceding two, e.g. that “necessary” can be glossed as “actual-because-possible.” Likewise, here, “You ought to act on maxims that represent your will as a law in itself,” looks like it fuses the law-theoretic terms of the first CI formulation with the will-theoretic terms of the second.

Now, again, then:

• A. You ought to act on maxims of your law-in-itself.

B. You ought to not act on maxims of laws-in-other-things.

But so once again, (B) seems out of line. In Religion within the Limits of Reason Alone, Kant even goes out of his way to criticize the Stoics for demonizing inclinations (note also that the idea of ordered maxim-sets is acutely on display in that later text). What with his other qualifications about perfect and imperfect, or once more narrow and wide, duty, Kant allows that “latitude” in the ethics of the will is a legitimate parameter for applying the form of the law. “Worse,” if his solution to the third antinomy is correct, then empirically, all our actions can be identifiably explained as caused by inclinations regardless.🎼 It is not, then, that we can factor out inclination-theoretic representations from whatever maxims that we adopt: again, the problem is of attaching autonomy to those representations to some extent.

And so it is still not clear to us that the extremely strict process of ruling out every heteronomous maxim is what Kant’s logic (notwithstanding the flux of his wishes) requires.

Finally, suppose that Kant’s theory of categories is deficient, perhaps because his tabulation of the logical forms of judgment is, or then because it is impossible to legitimately collapse all possible terms into just twelve (or however many) fundamental types. Whatever the case may be, if, “You ought to act on maxims such that they are those which would be adopted in a kingdom of ends,” is somehow really a fourth CI formulation, yet again it is not absolutely obvious that the unrestricted negative filter on other maxims framed in the same kind of terms is overwhelmingly enjoined upon us, here. Suppose that everyone else on Earth but you died. To be fairly sure, I’m not going to allege that you could then frolic about like a lunatic and nothing of the moral law could gainsay you: mindless destruction is still such that it would not harmonize with the general possibility of a kingdom of others’ ends in tandem with yours. But it does seem as if you would be mindlessly wringing your hands, were you to “conscientiously” try at every juncture to take into account the abstract requirements of that kingdom. If I remember correctly (although I can't find a good citation right now), Kant argued against this kind of zeal when he said that, for example, deciding what kind of food to eat is not quite a moral problem as such. When other people are alive and you can affect their lives, you would do morally better not to choose to eat things in such a way as negatively affects those lives (by being gluttonous, say, or by eating things grown using cruel or unsustainable farming methods, or whatever), but just the same, the majesty of the imaginary kingdom must not let its light blind you to the potential for innocuous innocence, either.

😨According to Kant, good and evil are mathematically contrary:

Virtue (= +a) is opposed to negative lack of virtue (moral weakness = 0) as its logical opposite (contradictorie oppositum); but it is opposed to vice (= —a) as its real opposite (contrarie s. realiter oppositum)... [Doctrine of Virtue, "Discussion of an End That is Also a Duty," Remark]

In other words, evil as such is what “cancels out” the good.

🎼Kantian compatibilism is not between determinism and vague empirical feelings of possible moral responsibility, but between determinism and indeterminism itself.