How would you express catch-22 in Latin?

Question

Catch-22 was termed by author Joseph Heller in the book of the same name, and represents a "paradoxical situation from which an individual cannot escape because of contradictory rules or limitations."

The term is introduced by the character Doc Daneeka, an army psychiatrist who invokes "Catch-22" to explain why any pilot requesting mental evaluation for insanity—hoping to be found not sane enough to fly and thereby escape dangerous missions—demonstrates his own sanity in creating the request and thus cannot be declared insane. This phrase also means a dilemma or difficult circumstance from which there is no escape because of mutually conflicting or dependent conditions.

Are there any examples of authors from any era of Latin expressing this idea? The closest thing I can think of that would have been expressed by Latin authors is a Pyrrhic Victory, but that isn't quite the same thing.

Edit: Perhaps something related to circular reasoning?

The problem of circular reasoning has been noted in Western philosophy at least as far back as the Pyrrhonist philosopher Agrippa who includes the problem of circular reasoning among his Five Tropes of Agrippa. The Pyrrhonist philosopher Sextus Empiricus described the problem of circular reasoning as "the reciprocal trope":

The reciprocal trope occurs when what ought to be confirmatory of the object under investigation needs to be made convincing by the object under investigation; then, being unable to take either in order to establish the other, we suspend judgement about both.[5]

Answer 1

If the core idea is being in a predicament where you have several (typically two) options, but whichever you choose, the outcome will be undesirable – then we have a “dilemma.” Unfortunately, dilemma is not a classical word.

A classical (and Latin) term for a dilemma would be complexio, which Cicero defines in De Inventione (1, 45) as a way of demonstrating something irrefutably:

Necessarie demonstrantur ea, quae aliter ac dicuntur nec fieri nec probari possunt, hoc modo: «si peperit, cum viro concubuit.» Hoc genus argumentandi, quod in necessaria demonstratione versatur, maxime tractatur in dicendo aut per complexionem aut per enumerationem aut per simplicem conclusionem. Conplexio est, in qua, utrum concesseris, reprehenditur, ad hunc modum: «Si inprobus est, cur uteris? Si probus, cur accusas?»

Irrefutably proven are those things that cannot happen or be shown differently from the way they are stated, in this manner: “If she gave birth, she slept with a man.” When speaking, this type of argument, which deals with irrefutable demonstration, is mostly practiced by way of complexio, enumeratio, or conclusio. Complexio is when, whichever of two choices you take, it will be condemned, like so: “If he is a bad man, then why do you associate with him? If a good man, why do you accuse him?”

It is worth mentioning that complexio can have other meanings as well (not “skin colour,” though ;-)).

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If, on the other hand, the core idea is that the powers that be seem to give you a choice, or a way out, but on closer inspection they will have their way nevertheless, then I think this does not quite capture it.