Why is it impossible to hold both horns of a moral dilemma?

Question

Why is it not possible to hold on to both horns of a moral dilemma? Not just because a moral dilemma is defined as such, just in terms of this impossibility.

In the section covering moral dilemmas, the SEP article on deontic logic goes over the idea of waiving agglomeration to yield the proper logical image of moral dilemmas. The idea is that from OBA and OB~A, one would derive OBA&~A, i.e. a moral dilemma would require one to actualize a contradiction, "which is impossible." More saliently, it does not seem as if facing a moral dilemma is emotionally the same thing as being directly asked to actualize a contradiction. If two authority figures on a par relative to you issue contrary demands, you can't compose the demands in your mind into one hyperdemand that is not contradictory, but this is not to say that either authority figure has itself issued a contradictory demand. (Of course, some will be motivated to reject authority figures in principle, perhaps for this very kind of reason (that conflicts between authorities could translate into dilemmas), and one might think that there was "preauthorization" involved anyway, viz. besides there being authority figures, there is also a standing rule, issued by no individual authority as such, to obey authority figures; whence we can infer, from this rule and the individual demands made, a contradictory obligation.)

However, again, why is it impossible to do both things required in a moral dilemma (or all three things required in a moral trilemma, or whatever)? Suppose that we split the OB operator into "it is a yet-to-be discharged obligation that..." = YTB and "it was a sufficiently discharged obligation that..." = DOB. We would say, per a moral dilemma, that it could not be true that DOBA&DOB~A: DOB is a factive deontic operator, after all, so DOBA&DOBB → A&B. But it seems, then, that in forming the logical image of a moral dilemma, one is compelled to agglomerate the propositions on which the deontic operators are operating, i.e. to conjoin them. Otherwise, saying, "Separate obligations to do conflicting things are not equivalent to a single contradictory obligation," would be as justifiable as saying, "Separate conflicting sentences are not equivalent to a single contradictory sentence." Even though there are senses/contexts in which we simply "entertain" pairs of contradictory sentences without thinking of them as one sentence, yet if we say that two sentences are true, we do more than merely "entertain" them, and then we would add them together.

Inverted: or else might we say that DOBA&DOBB doesn't conform to agglomeration, either? This seems to open the door (beyond or around paraconsistency, maybe) to saying that one had resolved a moral dilemma not because one had violated the implied impossibility of such resolution, but because the impossibility in question had been itself defined in relation to the supposed impossibility of actualizing a contradiction, which here was not assumed, neither enacted. In other words, somehow, one had done A as well as ~A, and yet the doing of each did not amount to doing A&~A. I suspect that if we go that far in revising SDL, we will put ourselves in the unenviable position of having to explain why we are concerned about DL period, since by wiping out all the normal logical images of negation, conjunction, and so on, we turn our revised SDL into little more than a game of symbols all of whose moves involve reference to arbitrary intuitions (about the possibility of unsolvable moral dilemmas, for example).

Answer 1

Simply because in predicate logic we make the law of non-contradiction an axiom. There are other forms of logic, like the Indian tetralemma which better allows for encountering insoluble problems.

Why non-contradiction is chosen as an axiom, is a deeper question. I make the case in this answer: Why does the flow of life constantly put us in unsolvable situations? that formulating dilemma-solving as a character test, leads to a culture that is better at avoiding lose-lose situations, and can be linked to wisdom cultures from Confucianism to Solomon and biblical teachings.

In this answer: Wisdom and John Vervaeke's awakening from the meaning crises? I argue wisdom is about acting from the reconciled centre of our concerns. We tend to want to resolve contradictions between sentences, and contradictions between commitments fulfilling which would undermine each other. This is wise, just like not acting for short-term gratification at greater long-term cost is wise.

There are certainly traditions that help us sit with contradictions, rather than feel compulsively we should reconcile them. Zen koans exactly do this, and help develop our wisdom by expanding our sense of possibilities beyond our previous thinking.

The Euthyphro Dilemma is an interesting case of horns of a dilemma. Is god commanding something what defines it as good, or does god only command things that are good? If it is the former it becomes meaningless to say god is good. If the latter then goodness does not come to be known through god.

Plenty of theological strategies for this. But I bring it up to point out how trickier dilemmas work. If you accept the horns, the logical model or systemising of abstractions, you are forced into positions which may both have unlikeable consequences. Theologians might say, god is reason, and we are made in gods image in the sense of divinely imbued capacity to reason, which is to take both horns - through our godliness we come to know god's plan, which is good.

In physics it's very common to find an apparent contradiction means our models aren't good enough, we need new models. Blackhole singularities are a good example. A super clear example I like that relates to a dilemma, is the tachyonic field. Now tachyons are considered 'unphysical', the strongest indication a physicist can give that we don't expect to find them. A lot of other physics would break. This field is different, involved in tachyonic condensation, which really means that the system becomes unstable. And this is what an insoluble dilemma tells us, the horns aren't consistent, we need a new picture.

The Munchausen Trilemma shows the 'instability' of any purported justification of all knowledge by appeal to foundational thinking. None of the horns are satisfying, pointing to the framework for choosing the horns not working.

Two people can have irreconcilable models. But one person, if they are to act, must do so with a given model, or accepting ambiguities that mean not having a model. We can act with one model now, and another in a later action. But the unity of our subjectivity, means we can't split our sense of being in different models into divided experiences of the moment. Computers can happily have many routines, getting processed in parallel, and potential contradicting each other. Humans are not like that, our awareness is a 'global workspace', in which we address and reconcile things from many brain processes that cross a threshold to demand our conscious attention, and we do that in relation to our subjectivity. Our definingly human intelligence, of language and it's systemised abstractions, is specifically rooted in our expanding our subjectivity through intersubjectivity - understanding what others mean 'as if they were you' (see the Dunbar number which indicates this is why our neocortex expanded rapidly). We can relate this also to the Private Language Argument, systemising of abstractions is sharing of them, communicating them so that the systemising becomes independent of pur subjectivity. This framework reifies the self, the unity of our subjectivity, by engaging in this expansion of it, intersubjectivity.

Zen and Buddhism more generally seek to deconstruct this process, and understand what we are before this process of building up layers that reify models of the self, and being distracted from experiencing what we are in this very moment, our actual capacities separate from our picture of what we can do. Nagarjuna puts it like this:

"The victorious ones have said That emptiness is the relinquishing of all views. For whomever emptiness is a view, That one has accomplished nothing."

And Seng Ts'an put it like this:

"The Great Way is not difficult for those who have no preferences. When love and hate are both absent, everything becomes clear and undisguised. Make the smallest distinction, however, and heaven and earth are set infinitely apart. If you wish to see the truth, then hold no opinions for, or against, anything. To set up what you like against what you dislike is the disease of the mind. When the deep meaning of things is not understood, the mind's essential peace is disturbed to no avail."

You indeed do not need to be bound by the choices of a dilemma. There is a deep freedom to creatively rengage with the situation which precedes the dilemma. That is what a mind is. That is a strange loop. That is how minds are not Turing machines, and escape the halting problem of being stuck in insoluble recursions.