Lyotard's essay "Can Thought Go on Without a Body?" is difficult and full of many difficult passages. It is an intriguing essay, but hard to really engage with without understanding some of the more difficult parts. Parts of the first paragraph on page 11 are particularly hard to understand, and this is what I shall focus on.
By far, the most difficult sentences in this paragraph are in the middle of it: "Look here: you try to think of the event in its quod, in the advent of 'it so happens that' before any quiddity, don't you? Well, you'll grant the explosion of the sun is the quod itself, no subsequent assignment being possible." At first glance, this passage seems almost gibberish. 'Quod' has no definition by itself, outside of such latin phrases as 'quod erat demonstratum' (QED). Quiddity, according to thefreedictionary.com means "The real nature of a thing; the essence". A paraphrase of this passage might read then: 'Look here: you try to think of the event logically before its true essence, don't you? Well, you'll grant the explosion of the sun is the logical end itself, since nothing comes after it.'
The passages before and after naturally provide some context. Before the above passage, he says: "You'll have been seduced and deceived by what you call nature, by a congruence of mind and things. Claudel calls this a 'co-naissance', and Merleau-Ponty spoke of the chiasmus of the eye and the horizon, a fluid in which the mind floats. The solar explosion, the mere thought of that explosion, should awaken you from this euphoria." What Lyotard appears to be expressing here is that philospohers and the like glory in this sort of co-existence of the mind and the things that surround it, and shape it, but that this attitude will not serve them in the end, when everything is dead with the sun. That this positive attitude of the mind and things takes for granted the existence of the earth, and betrays the transitory and chance nature of human existence.
The passage after the first one, likewise provides context. In it, Lyotard states: "Of that death alone, Epicurus ought to have said what he says about death - that I have nothing to do with it, since if it's present, I'm not, and if I'm present, it's not. Human death is included in the life of the human mind. Solar death implies an irreparably exclusive disjunction between death and thought: if there's death, then there's no thought." What he seems to mean here is that when one person dies, there are other people to make sense of that loss, to understand it. But when all life is extinguised by the death of the sun, there is no one left to make any sense of it; it is just over.
The first passage, then, implies that logical thinking and most human endeavors are meaningless, because when the sun dies, it will all be over; not remembered, not even forgotten, because there would be no one left even to forget it. These passages, and indeed, the whole essay, need to be so difficult because without it the gravity of the situation, the death of the sun, would not be understood at all. If he were to simply say that 'After the sun is dead, nothing will matter' it would make no impression on any reader. Something stated so bluntly is easy to ignore; but by making the passages so difficult, the reader must wrestle to understand the meaning, and by doing so, also wrestle to understand the nature of the death of the sun, and thus Lyotard's point.