Beauty as Judgement
The argument that calling a thing beautiful is a claim that invites agreement, not a report of private feeling.
The wiki follows Beauty in holding that beauty is not subjective preference but a form of judgement — a claim that this thing rewards attention, that others who attend will see it too, and that reasons can be given and disputed. The judgement can be wrong; that is precisely what makes it educable, and what distinguishes it from preference, which can only be reported.
The Stakes of the Retreat
Where judgement retreats into that is just not my taste, beauty retreats with it: the shared ground on which taste can be argued and improved disappears. On Beauty and Being Just adds that the capacity to be arrested by beauty is continuous with the capacity for justice — both are forms of attending to what stands independently of us. The concept page Judgement carries the full cross-domain treatment.