"This picture inevitably recalls the description Kant gave of a thought process he called reflective judgment: a mode of thought not guided by rules for determining data, but showing itself as a possibility capable of developing such rules afterwards on the basis of results obtained reflexively."
This is a very interesting and complex statement discussed in Lyotard's essay. Earlier in the essay, Lyotard discusses theories introduced by such people as Russell, Whitehead, and McCulloch. The theories suggested human thought was based on binary decision making. In simpler terms, this means a mind based on only two spectrums. It's not necessarily important to know what the two spectrums are, rather to know that it can only think in two ways. Whether it be yes and no, or up and down, it really isn't important in the terms of Lyotard's essay and what we are trying to accomplish in studying it. In the essay, Lyotard argues that the mind absolutely does not work this way, instead, it develops it's own rules in making decisions and judgments based its surroundings.
In order to understand this argument about non-binary thinking, we must first understand the essay on a broader scale. This essay reveals and discusses that Lyotard refers to as the "inhuman". But what does such a term mean? A lot of people might suggest that it means dehumanizing in ways such as war or some other type of disaster. Lyotard suggests just the opposite. Implying that telling the story of dead humans, and the events surrounding it still suggests humanity, rather than "inhuman". I still find it very confusing as to what exactly Lyotard means by "inhuman" but it is safe to say it is definitely not the orthodox type of thinking that most people would resort to.
This unconventional thinking presents thought in comparison with a field of vision or hearing. Its perceptual experience is what makes it so unique. It allows the mind to think illogically, free from constraints and “rules”. Is this always easy to accomplish? Of course not, and Lyotard states this as clear of day to us later in the essay when he states, “Thinking and suffering overlap.” This sentence is probably the most simple and easy to understand throughout the entire essay. He wants to let us know, as straightforward as he can be, that this thought process and thinking will not come without some sort of suffering.
In making people think in such ways, Lyotard is accomplishing the goals of his arguments against binary thinking. When one thinks about something such as war or a disaster, the mind takes it upon itself to make its own set of rules to think about it. One must bend their mind away from the "yes and no" attitude to understand that Lyotard's theory of "inhuman" strays away from the normal thought process. I believe that this is why this passage is so hard to understand in its context. We must use our reflexive thought process to even begin to understand what Lyotard is trying to say.