Hayot 63: "Here is what Kant says happens when someone sees something and judges it beautifu;. That judgment includes the 'necessary presupposition' [...] that there exists some universal pattern, a 'unity of all empirical principles' that allows an individual judgment to move from the feeling that 'I like this' to the feeling that 'This is beautiful.' For, Kant says, when I say a thing is beautiful or sublime, I do not mean that it is beautiful or sublime just for me; I mean that it is, or at least could be, beautiful or sublime for everyone. The potential universality of that apprehension--the idea that anyone could find this object beautiful, so long as I do--is what constitutes the specific act of reflecting judgment 'as a law'"
"The possibility of such a universality is assumed, for Kant, by the fact of judgment itself; without it, we have no laws and no universals, just something like preference ('vanilla ice cream tastes good to me')"
also, interestingly, "'all judgments of taste are singular judgments,' that is, not judgments about (say) roses in general, but about one rose in particular. [This reflecting judgment is] about a single rose and a single experience of its beauty--and therefore not about aesthetic experience or judgment at all"
63: "There is, therefore, something in the singular object as it gives itself to be aesthetically judged that emphasizes, or indeed relies on, a complex relationship between singularity and particularity, conceptualization and universality."