Before I state my question: I have no formal education in philosophy but am exposed to the basics of most moral systems - (utilitarianism, altruism, etc.)

Is it possible to show that it is possible or impossible to have a moral system that is both consistent (works similarly across situations without creating paradoxes/dilemmas) and complete (applicable to all imaginable situations)?

Using something similar to Godel's Incompleteness Theorem or using axiomatic logic?

Of course, the best way to get around the question would be to assume a moral system where each and every action is acceptable i.e. put it more succinctly adhere to no moral system at all. This is not what I intend, and I would like to except such a moral system.

When I say 'moral system', I'd like it to be limited to those systems that have well - defined axioms (with the exception of the aforementioned system).

  • The first step is to found the relevant axiom systems ? Do you know some ? Jun 21, 2019 at 13:59
  • @Mauro, I do not have any one such system in mind. My question is regarding a proof that can conclusively show either that all moral systems are not - both complete and consistent or that there does exist moral systems that do satisfy those parameters.
    – hashes
    Jun 21, 2019 at 14:17
  • But you can ask for consistency only if you have a "formalized" theory available : underlying logic (rules of inference) and specific "moral theory" axioms. Jun 21, 2019 at 14:26
  • Thanks @Mauro, I'll go into this.
    – hashes
    Jun 21, 2019 at 14:29
  • To add to the point: While there may be complete and consistent formalisations of ethical systems, you either end up with something purely formal or you'd need a formalisation of all morally relevant situations, which amounts to a complete and consistent formalisation of natural language. This has proven to be futile in the first decades of the nineteenth century. Practical relations to the world are not formal.
    – Philip Klöcking
    Jun 21, 2019 at 14:33

4 Answers 4


Well, as far as utilitarianism and other gradated moral systems (aka consequentialist moral systems) are concerned they are quite complex. In order to formalize them we will have to utilize a sort of many-valued logic (more on that later).

As for deontological systems, then they are boolean and, therefore, any simple two-valued system of modal logic will work. That is, deontic morality can, and has been, formalized in the language of modal logic. Furthermore, if the system has been formalized, then we can just check that corresponding system for C&C (consistency and completeness). The system mirroring deontological ethics is generally referred to as Deontic Logic. Furthermore, we can tune deontic logic to mirror any particular deontological system by either a) restricting accessibility relations or b) introducing new axioms.

As for gradated modal systems like utilitarianism, then, as I said earlier, that is complicated:

Suppose we have an action A such that it maximizes happiness for x amount of people in scenario , and maximizes happiness for y amount of people in scenario (xy). The action A, then, becomes a function that takes in scenario(s) Sⁿ, and amount(s) xₙ, and spits out an obligation, or permission value. Therefore as you can see, this value does not have to be T or F; it can be any real number [I can explain this further if needed]. Consequently, the only logical system fit for this task would be fuzzy logic. There could be other systems. In fact, any multivalued logical system might work. The problem, however, is of formalizing nondeontic ethics. This has been quite a challenge especially since consequentialist ethics are essentially(debatable) subjective.

As you can see, C&C is not a point of concern for consequentialist ethics. What is of import is much more fundamental -- formalization.

I hope that answered your question, feel free to ask for any clarification. Regards.


(This answer is essentially a follow-up on the answer of @BertrandWittgenstein'sGhost)

First of all, we should not confuse moral systems and their properties with model-theoretical formalisations of them. I consider the question to be about the latter and I think the possibility of consistent, complete, and useful/practically applicable formalisations can be denied on the basis of Chisholm's Paradox. There are other applicable arguments to be found in this article, but I will focus on that one.

Chisholm's paradox highlights a main problem of formal ethics: The consistency of natural language propositions and their formalisations can differ in the case of normative (more easily and obvious than in the case of descriptive) propositions. In other words: While normative sentences may be perfectly independent and consistent (intuitively), it is possible that there is no appropriate formalisation that is consistent.

This is consistent with what modern philosophers like Sellars or Putnam have to say on normative sentences: other than descriptive sentences, they are, in a sense, both fact-creating (I ought to do because I say so) and fact-sustaining (I say so because it adheres to intersubjectively valid norms and people agree on that, i.e. I 'correctly' play the moral language game). The point is that normative facts are even more plastic than descriptive facts (the latter are also plastic due to the normative nature of language itself). ((neither normative nor descriptive 'facts' are to be understood in the sense of objective facts favoured by external realism here))


The best method I can think of is to propose a simple system and then test it with your parameters.

The first example that comes to mind is the 'Do no harm' morality, where everything is permissible as long as it doesn't hurt someone else. Now, we can get into a whole other discussion on what hurts another person, but for the sake of this argument I'd propose it constitutes physical and/or emotional pain rather than the person's 'greater good'.

This system is definitely complete since it has two mutually exclusive categories. I am intrigued to hear how it can be inconsistent.

I don't think anyone has half-successfully attempted to deduce a moral system (as a whole) and I am certainly not up to the task. What is possible, in theory, is to deduce what is morally righteous on a case-by-case basis. Now, that isn't practical, but at least it is possible. It can also be quickened by reasoning on some rules that apply to a variety of cases (such as do no harm) and expand on them when necessary.

An interesting way to prove a moral system most likely correct would be by reasonably proving a source (which has made moral claims) is most likely infallible.

If I missed the point of your question I'd love to hear an example of what you had in mind.



  • 1
    If you have references to those taking a similar position this would strengthen your answer and give the reader a place to go for more information. Welcome! Jun 21, 2019 at 15:34
  • Interesting. That seems very much like a deontological moral system. It would be interesting to see how it would fare in the trolley problem - to do nothing and harm other people when there are other possible courses of action, would that be a violation of the 'Do no harm' morality? Feel free to flame me for incorrect or doltish inferences :).
    – hashes
    Jun 23, 2019 at 3:23
  • @Prosopon The most common way to deal with that is to deny that the responsibility for the consequences of inaction weighs as heavy as for the consequences of active engagement. Depending on the version of the trolley dilemma at hand, even that does not make much of a difference, though.
    – Philip Klöcking
    Jun 23, 2019 at 9:59
  • @Frank Hubeny I don't know of any prominent people with the said ethical system, most philosophers of morality probably do have some more complex theories. I was just trying to illustrate in lay terms a consistent and complete moral system. Thank you for the warm welcome :D Just trying to help here although I am no expert.
    – Glorius
    Jun 24, 2019 at 12:01
  • @Prosopon it is a deontological moral system. Since it's only principle is 'Do no harm', in a problem where (equal or unequal) harm is inevitable the best you can do is do nothing, which would be completely moral, according to this system, since there is no moral obligation to prevent harm. A bad system, but fits the criteria.
    – Glorius
    Jun 24, 2019 at 12:04

Since you are immediately talking about consistency and completeness, let's start from the computation theory, rather than the ethics or the presentational logic.

Those systems that have well-defined axioms and permit integer arithmetic are notoriously not complete via some version of Goedel's reasoning. It does not matter what the corresponding semantics would be. So if you have this aim at all, you would need to pursue a very odd sort of reasoning, one in which counting things can never affect the ethical outcome.

But then can any such system be precise enough that anyone would consider it 'complete'? Huge chunks of finance would need to be immediately excluded. Most of us think that the moral value of gain and risk really do depend rather finely upon arithmetical details.

Kantianism (as it gets naively employed, not necessarily as rigidly imagined by Kant himself) tends to rule out arithmetic or the complexity that would require it as an intuitive part of the definition of a maxim. But then, by focussing on autonomy, it often gives the answer 'that depends upon an arbitrary negotiation between those involved.' Does that count as being complete?

One basic problem here is that moral (and more concretely, legal) systems are not by nature consistent, they are generally overdetermined. So there are numerous equally good right answers, none of them perfect, but then arbitrary combinations of those multiple right answers are not subject to consistent reasoning without paradox.

This suggests that any real ethical system is not axiomatic, but algorithmic, and consists of negotiation processes that govern the acceptable exchange of power and seek a consistent balance. (The point I generally come back to, the central social process is a language-game.) But, by some version of Turing's thesis, powerful enough algorithmic systems almost always permit questions that have the halting problem and do not converge. Instead, the world is full of 'Julia sets' -- algorithms get hung up in infinite regress near fractal boundaries between basins of attraction. So those are not going to be complete, either.

The trend in something like a predictive consequentialism is to assume the best you could hope for if you want something complete is a system that involves ad-hoc compromises, so it is inconsistent by design, but trends toward consistency over time. "Rule utilitarianism" with some kind of cutoff on complexity would be an example -- it seems to be what judges would like to imagine they do.

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