How can courts resolve logical paradoxes?

Question

I was discussing OXY USA Inc. v. Schell with a friend, and he came up with this puzzle:

Supposing Company A is facing a lawsuit, has received a judgment against them in a district court, and has filed an appeal. During this time, Company A is also looking to sell the relevant business and associated liabilities to Company B, but Company B insists on an unusual term of sale: should the appeals court dismiss Company A's appeal of the district court's judgment as moot, the sale shall be void. Company B does not intervene in the case.

Now, plaintiffs, pointing to the sale of the business to Company B, move to dismiss Company A's appeal as moot. The appeals court faces the following problem:

Should the appeals court grant the appeal, Company B will have no stake in the outcome, and so the appellate decision will be purely advisory. On the other hand, should the appeals court dismiss the appeal as moot, Company B will in fact incur liability for the judgment and thus will have a stake in the outcome.

How do courts deal with self-referential situations like this that create paradoxes?

Answer 1

I'll limit my analysis to the situation you describe, and without reading the appellate opinion.

Side note: Here you portray that Company B said to Company A: "If you no longer are liable as per this ruling, I'm not interested in acquiring you". For the sake of argument, one may assume that judgement is about money (rather than certain types of act, see below), and that Company B has ulterior motives for the transaction such as money laundering. However, generally speaking it just makes no sense for Company B to require something like that.

A dismissal as moot means that the ruling appealed has no (or no longer has) legal effect, and that there is nothing that can be restored to Company A. Thus, Company A's situation is similar as if no judgment against it were in place.

In its motion to dismiss, Company A may argue that the appeal is moot, but that does not guarantee that the appellate court will reflect the alleged mootness. Instead, the appellate order is likelier to reflect that Company A withdrew its appeal. Thus, mootness is not established, and that prevents the sale from becoming void. In few words, Company A's self-referential move preempts mootness.

If the judgment consists of ordering Company A to perform an act, Company A could devise mootness by performing the act, and bringing that up to the appellate court's attention in a way that leads the appellate court to identify sua spone the occurrence of mootness. But keep in mind that the act in question must be one which can be neither reversed nor compensated for. A money judgment is no such act, as reimbursement of payments can always be ordered.

Regardless, the scenario outlined in the previous paragraph is different from the self-referential situation you describe.