Asystatic issues interrupt discourse, but do not elicit answers from which any useful agreement can be obtained. They simply spin a vortex in which agreement is lost and prejudices are condensed because they do not generate any new information or alter the participants' perceptual frames in any way. They are thus either to be avoided or used to distract people.
There are four kinds of asystatic questions.
Monomeres are issues that do not bear debate because the evidence is all one-sided. The convicted parricide who begs the sentencing magistrate for leniency on the grounds that he is an orphan frames a monomere. There is no response to the claim "I deserve leniency" but astonishment and derision.
Isazon occurs when the evidence is perfectly balanced. An ancient example of this might be found in the lore surrounding Korax and his student Tisias. Korax guaranteed his teaching. If a student failed to win his first court case, Korax would refund his tuition. Tisias, who had gone into teaching rather than pleading, sued Korax on the grounds that he had never won a court case. Tisias argued that he could not lose because if the court ruled in favor of Korax, then he, Tisias, had lost the case and won his refund, and if the court decided in his favor, then the teacher would have to refund the tuition anyway. Korax argued the opposite. If Tisias won, then the refund would not be forthcoming because the condition of the guarantee was met, and if Tisias lost, then the refund would not be forthcoming because he had sued for the refund and lost. The court is said to have dismissed the case with a pun on Korax's name: from a bad crow, a rotten egg.
Ellipes is a disagreement predicated on inconclusive evidence. In a sense any radical induction will ultimately be reduced to ellipes. While it is simple enough to prove to yourself deductively that you are mortal, it is impossible to prove it inductively. By the time the only absolutely necessary example is in place, the question is moot.
Aporon occurs when no solution or even end to the inquiry is possible. This asystasis is a staple of deconstructive rhetoric and of elenchus. It arises when the premises of an argument have been so relentlessly questioned that no deductive thinking is possible. The iterative "why?" of an inquisitive child, and the ironic questions of Socrates, both lead to a vertiginous moment when there appear to be no foundational beliefs and one is left to choose among faith, despair, and anger.